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Sample records for indefinite quadratic forms

  1. Binary Quadratic Forms: A Historical View

    ERIC Educational Resources Information Center

    Khosravani, Azar N.; Beintema, Mark B.

    2006-01-01

    We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

  2. Quadratic forms of projective spaces over rings

    NASA Astrophysics Data System (ADS)

    Levchuk, V. M.; Starikova, O. A.

    2006-06-01

    In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.

  3. Uniaxial indefinite material formed by helical-shaped wires

    NASA Astrophysics Data System (ADS)

    Morgado, Tiago A.; Maslovski, Stanislav I.; Silveirinha, Mário G.

    2012-06-01

    We demonstrate that a racemic array of helical-shaped metallic wires may be regarded as a local uniaxial epsilon-negative (ENG) material even when the metal conductivity is very large (e.g. in the microwave regime) and, as a result, enables strong negative refraction over a wide frequency range. Based on the negative refraction effect, we demonstrate partial focusing of p-polarized electromagnetic radiation using a planar lens formed by such a composite material. The results reported here are supported by full-wave simulations as well as by analytical calculations based on effective medium theory.

  4. Effects of MC-Type Carbide Forming and Graphitizing Elements on Thermal Fatigue Behavior of Indefinite Chilled Cast Iron Rolls

    NASA Astrophysics Data System (ADS)

    Ahiale, Godwin Kwame; Choi, Won-Doo; Suh, Yongchan; Lee, Young-Kook; Oh, Yong-Jun

    2015-11-01

    The thermal fatigue behavior of indefinite chilled cast iron rolls with various V+Nb contents and Si/Cr ratios was evaluated. Increasing the ratio of Si/Cr prolonged the life of the rolls by reducing brittle cementites. Higher V+Nb addition also increased the life through the formation of carbides that refined and toughened the martensite matrix and reduced the thermal expansion mismatch in the microstructure.

  5. The use of quadratic forms in the calculation of ground state electronic structures

    SciTech Connect

    Keller, Jaime; Weinberger, Peter

    2006-08-15

    There are many examples in theoretical physics where a fundamental quantity can be considered a quadratic form {rho}={sigma}{sub i}{rho}{sub i}=vertical bar {psi} vertical bar{sup 2} and the corresponding linear form {psi}={sigma}{sub i}{psi}{sub i} is highly relevant for the physical problem under study. This, in particular, is the case of the density and the wave function in quantum mechanics. In the study of N-identical-fermion systems we have the additional feature that {psi} is a function of the 3N configuration space coordinates and {rho} is defined in three-dimensional real space. For many-electron systems in the ground state the wave function and the Hamiltonian are to be expressed in terms of the configuration space (CS), a replica of real space for each electron. Here we present a geometric formulation of the CS, of the wave function, of the density, and of the Hamiltonian to compute the electronic structure of the system. Then, using the new geometric notation and the indistinguishability and equivalence of the electrons, we obtain an alternative computational method for the ground state of the system. We present the method and discuss its usefulness and relation to other approaches.

  6. General approach to functional forms for the exponential quadratic operators in coordinate-momentum space

    NASA Astrophysics Data System (ADS)

    Wang, Xiang-bin; Oh, C. H.; Kwek, L. C.

    1998-05-01

    In a recent paper (Nieto M M 1996 Quantum Semiclass. Opt. 8 1061, quant-ph/9605032), the one-dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering the multidimensional exponential quadratic operator (EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single-mode and double-mode EQO through the squeezed operator and the time-displacement operator of the harmonic oscillator.

  7. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  8. Timoshenko systems with indefinite damping

    NASA Astrophysics Data System (ADS)

    Muñoz Rivera, Jaime E.; Racke, Reinhard

    2008-05-01

    We consider the Timoshenko system in a bounded domain . The system has an indefinite damping mechanism, i.e. with a damping function a=a(x) possibly changing sign, present only in the equation for the rotation angle. We shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case, and provided and , for [epsilon] small enough. The decay rate will be described explicitly. In the arguments, we shall also give a new proof of exponential stability for the constant case . Moreover, we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth (SDG) property, i.e. the type of the induced semigroup coincides with the spectral bound for its generator.

  9. On polynomial preconditioning for indefinite Hermitian matrices

    NASA Technical Reports Server (NTRS)

    Freund, Roland W.

    1989-01-01

    The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

  10. Optimal stabilization of indefinite plate buckling problems

    NASA Astrophysics Data System (ADS)

    Chase, J. Geoffrey; Bhashyam, Srinivas

    2001-08-01

    Indefinite plate buckling problems arise when the applied load case results in buckling loads which are not all of the same sign. Examples include the important cases of shear buckling and general combinations of tensile and compressive in-plane edge loads. Optimal controllers which actively stabilize these general, indefinite plate buckling problems, by transforming them into a system of definite plate buckling problems, are presented. Important features of this approach include the ability to select the designed closed loop critical buckling load, and to pre-determine what load cases a given controller will stabilize when the exact load combination varies or is unknown. This last result enables the control designer to know exactly, by design, what load combinations will be stabilized. A numerical example is presented where the controllers developed are employed to stabilize multiple, definite and indefinite buckling modes for laminated composite plates similar to aircraft wing skins.

  11. Highly indefinite multigrid for eigenvalue problems

    SciTech Connect

    Borges, L.; Oliveira, S.

    1996-12-31

    Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

  12. 48 CFR 52.216-22 - Indefinite Quantity.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... furnish to the Government, when and if ordered, the supplies or services specified in the Schedule up to....216-22 Indefinite Quantity. As prescribed in 16.506(e), insert the following clause: Indefinite Quantity (OCT 1995) (a) This is an indefinite-quantity contract for the supplies or services specified,...

  13. The cataphoric use of the indefinite this in spoken narratives

    PubMed Central

    Gernsbacher, Morton Ann; Shroyer, Suzanne

    2015-01-01

    Are concepts that were introduced with the unstressed, indefinite article this, as opposed to the indefinite a/an, more accessible from listeners' mental representations? Subjects heard and then verbally continued each of a series of informal narratives. The last clause of each narrative introduced a new noun phrase that began with either the indefinite this or the indefinite a/an (e.g., this egg or an egg). When the concepts were introduced with the indefinite this, the subjects referred to them more frequently, often within the first clauses that they produced, and typically via pronouns. In contrast, when the concepts were introduced with a/an, the subjects referred to them less frequently and typically via full noun phrases. Thus, concepts introduced with the indefinite this were more accessible; therefore, the indefinite this appears to operate cataphorically to improve referential access. PMID:2796738

  14. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  15. Decision procedure for indefinite hypergeometric summation

    PubMed Central

    Gosper, R. William

    1978-01-01

    Given a summand an, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given an, finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text] and we can also conclude that [Formula: see text] is inexpressible as S(m) - S(0), for any S(n) satisfying Eq. 2. PMID:16592483

  16. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  17. Faraday rotation due to quadratic gravitation

    NASA Astrophysics Data System (ADS)

    Chen, Yihan; Liu, Liping; Tian, Wen-Xiu

    2011-01-01

    The linearized field equations of quadratic gravitation in stationary space-time are written in quasi-Maxwell form. The rotation of the polarization plane for an electromagnetic wave propagating in the gravito-electromagnetic field caused by a rotating gravitational lens is discussed. The influences of the Yukawa potential in quadratic gravitation on the gravitational Faraday rotation are investigated.

  18. Communication-avoiding symmetric-indefinite factorization

    SciTech Connect

    Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro

    2014-11-13

    We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.

  19. Communication-avoiding symmetric-indefinite factorization

    DOE PAGES

    Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro

    2014-11-13

    We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result,more » the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.« less

  20. On the Framing of One Kind of Indefinite Referring Expression: Learning Challenges and Pedagogical Implications.

    ERIC Educational Resources Information Center

    Tickoo, Asha

    2002-01-01

    Shows that two key principles of communication (the Shared Knowledge Principle and the Economy Principle), which monitor the framing of all well-formed referring expressions, are manifest in a specialized mode in the framing of focal specific indefinite referring expressions. Suggests that the special features associated with this type of…

  1. 48 CFR 452.216-72 - Evaluation Quantities-Indefinite-Delivery Contract.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 48 Federal Acquisition Regulations System 4 2011-10-01 2011-10-01 false Evaluation Quantities-Indefinite-Delivery Contract. 452.216-72 Section 452.216-72 Federal Acquisition Regulations System DEPARTMENT OF AGRICULTURE CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Texts of Provisions...

  2. 48 CFR 16.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 16.504 Indefinite... of the contract, including the number of options and the period for which the Government may extend the contract under each option; (ii) Specify the total minimum and maximum quantity of supplies...

  3. 48 CFR 16.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 16.504 Indefinite... of the contract, including the number of options and the period for which the Government may extend the contract under each option; (ii) Specify the total minimum and maximum quantity of supplies...

  4. 48 CFR 16.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 16.504 Indefinite... of the contract, including the number of options and the period for which the Government may extend the contract under each option; (ii) Specify the total minimum and maximum quantity of supplies...

  5. 48 CFR 16.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 16.504 Indefinite... of the contract, including the number of options and the period for which the Government may extend the contract under each option; (ii) Specify the total minimum and maximum quantity of supplies...

  6. Children's Optimal Interpretations of Indefinite Subjects and Objects

    ERIC Educational Resources Information Center

    de Hoop, Helen; Kramer, Irene

    2006-01-01

    We find a general, language-independent pattern in child language acquisition in which there is a clear difference between subject and object noun phrases. On one hand, indefinite objects tend to be interpreted nonreferentially, independently of word order and across experiments and languages. On the other hand, indefinite subjects tend to be…

  7. Quadratic eigenvalue problems.

    SciTech Connect

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  8. Self-replicating quadratics

    NASA Astrophysics Data System (ADS)

    Withers, Christopher S.; Nadarajah, Saralees

    2012-06-01

    We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that For n = 1, 2, … , these quadratic polynomials can be written as the product of N = 2 n quadratic polynomials in x 1/N , namely, ? , where w N is the Nth root of 1.

  9. The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.

    PubMed

    Ferrandino, Francis J

    2005-05-01

    ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.

  10. Incomplete block factorization preconditioning for indefinite elliptic problems

    SciTech Connect

    Guo, Chun-Hua

    1996-12-31

    The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

  11. Rescuing quadratic inflation

    SciTech Connect

    Ellis, John; Fairbairn, Malcolm; Sueiro, Maria E-mail: malcolm.fairbairn@kcl.ac.uk

    2014-02-01

    Inflationary models based on a single scalar field φ with a quadratic potential V = ½m{sup 2}φ{sup 2} are disfavoured by the recent Planck constraints on the scalar index, n{sub s}, and the tensor-to-scalar ratio for cosmological density perturbations, r{sub T}. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on n{sub s} and r{sub T}. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

  12. Consensus-ADMM for General Quadratically Constrained Quadratic Programming

    NASA Astrophysics Data System (ADS)

    Huang, Kejun; Sidiropoulos, Nicholas D.

    2016-10-01

    Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.

  13. An iterative method for indefinite systems of linear equations

    NASA Technical Reports Server (NTRS)

    Ito, K.

    1984-01-01

    An iterative method for solving nonsymmetric indefinite linear systems is proposed. The method involves the successive use of a modified version of the conjugate residual method. A numerical example is given to illustrate the method.

  14. Singular finite-gap operators and indefinite metrics

    NASA Astrophysics Data System (ADS)

    Grinevich, Petr G.; Novikov, Sergei P.

    2009-08-01

    In many problems the 'real' spectral data for periodic finite-gap operators (consisting of a Riemann surface with a distingulished 'point at infinity', a local parameter near this point, and a divisor of poles) generate operators with singular real coefficients. These operators are not self-adjoint in an ordinary Hilbert space of functions of a variable x (with a positive metric). In particular, this happens for the Lamé operators with elliptic potential n(n+1)\\wp(x), whose wavefunctions were found by Hermite in the nineteenth century. However, ideas in [1]-[4] suggest that precisely such Baker-Akhiezer functions form a correct analogue of the discrete and continuous Fourier bases on Riemann surfaces. For genus g>0 these operators turn out to be symmetric with respect to an indefinite (not positive definite) inner product described in this paper. The analogue of the continuous Fourier transformation is an isometry in this inner product. A description is also given of the image of this Fourier transformation in the space of functions of x\\in R. Bibliography: 24 titles.

  15. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  16. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  17. Uniform convergence of multigrid v-cycle iterations for indefinite and nonsymmetric problems

    SciTech Connect

    Bramble, J.H. . Dept. of Mathematics); Kwak, D.Y. . Dept. of Mathematics); Pasciak, J.E. . Dept. of Applied Science)

    1994-12-01

    In this paper, an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems is presented. In this multigrid method various types of smothers may be used. One type of smoother considered is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. Smothers based entirely on the original operator are also considered. One smoother is based on the normal form, that is, the product of the operator and its transpose. Other smothers studied include point and line, Jacobi, and Gauss-Seidel. It is shown that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not dependent on the number of multigrid levels).

  18. Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

    NASA Technical Reports Server (NTRS)

    Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

    1993-01-01

    In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

  19. Black box multigrid solver for definite and indefinite problems

    SciTech Connect

    Shapira, Yair

    1997-02-01

    A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples.

  20. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Leyk, Z.; Pasciak, J.E.

    1993-01-01

    The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

  1. Quintessence with quadratic coupling to dark matter

    SciTech Connect

    Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy

    2010-04-15

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  2. Possessives vs. Indefinites: Pragmatic Inference and Determiner Choice.

    ERIC Educational Resources Information Center

    Birner, Betty

    A discussion of pragmatic choice in the use of the possessive pronoun or indefinite article (e.g., "I broke my finger" versus "I broke a finger," and "My leg hurts" versus "A leg hurts") looks at the constructions in the light of a theory of division of pragmatic labor that suggests a binary system of implicature. The theory cannot account for…

  3. Solitons in quadratic media

    NASA Astrophysics Data System (ADS)

    Colin, M.; Di Menza, L.; Saut, J. C.

    2016-03-01

    In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.

  4. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  5. Analysis of Students' Error in Learning of Quadratic Equations

    ERIC Educational Resources Information Center

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  6. Quadratic spatial soliton interactions

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav

    Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

  7. Quadratic soliton self-reflection at a quadratically nonlinear interface

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

    2003-11-01

    The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

  8. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  9. Quadratic algebras for three-dimensional superintegrable systems

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2010-02-15

    The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

  10. Bunch-Kaufman factorization for real symmetric indefinite banded matrices

    NASA Technical Reports Server (NTRS)

    Jones, Mark T.; Patrick, Merrell L.

    1989-01-01

    The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization.

  11. A characterization for *-isomorphisms in an indefinite inner product space

    NASA Astrophysics Data System (ADS)

    Sivakumar, K. C.; Kamaraj, K.

    2007-05-01

    Let H1 and H2 be indefinite inner product spaces. Let L(H1) and L(H2) be the sets of all linear operators on H1 and H2, respectively. The following result is proved: If [Phi] is [*]-isomorphism from L(H1) onto L(H2) then there exists such that [Phi](T)=cUTU[*] for all T[set membership, variant]L(H1) with UU[*]=cI2, U[*]U=cI1 and c=+/-1. Here I1 and I2 denote the identity maps on H1 and H2, respectively.

  12. Effective potential and quadratic divergences

    SciTech Connect

    Einhorn, M.B. ); Jones, D.R.T. )

    1992-12-01

    We use the effective potential to give a simple derivation of Veltman's formula for the quadratic divergence in the Higgs self-energy. We also comment on the effect of going beyond the one-loop approximation.

  13. Indefinite Plasmonic Beam Engineering by In-plane Holography

    NASA Astrophysics Data System (ADS)

    Chen, J.; Li, L.; Li, T.; Zhu, S. N.

    2016-06-01

    Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs.

  14. Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

    SciTech Connect

    Bramble, J.H.; Pasciak, J.E.; Xu, J.

    1988-10-01

    We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

  15. Indefinite Plasmonic Beam Engineering by In-plane Holography.

    PubMed

    Chen, J; Li, L; Li, T; Zhu, S N

    2016-01-01

    Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs. PMID:27357133

  16. Indefinite Plasmonic Beam Engineering by In-plane Holography

    PubMed Central

    Chen, J.; Li, L.; Li, T.; Zhu, S. N.

    2016-01-01

    Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs. PMID:27357133

  17. Experimental investigations of weak definite and weak indefinite noun phrases

    PubMed Central

    Klein, Natalie M.; Gegg-Harrison, Whitney M.; Carlson, Greg N.; Tanenhaus, Michael K.

    2013-01-01

    Definite noun phrases typically refer to entities that are uniquely identifiable in the speaker and addressee’s common ground. Some definite noun phrases (e.g. the hospital in Mary had to go the hospital and John did too) seem to violate this uniqueness constraint. We report six experiments that were motivated by the hypothesis that these “weak definite” interpretations arise in “incorporated” constructions. Experiments 1-3 compared nouns that seem to allow for a weak definite interpretation (e.g. hospital, bank, bus, radio) with those that do not (e.g. farm, concert, car, book). Experiments 1 and 2 used an instruction-following task and picture-judgment task, respectively, to demonstrate that a weak definite need not uniquely refer. In Experiment 3 participants imagined scenarios described by sentences such as The Federal Express driver had to go to the hospital/farm. The imagined scenarios following weak definite noun phrases were more likely to include conventional activities associated with the object, whereas following regular nouns, participants were more likely to imagine scenarios that included typical activities associated with the subject; similar effects were observed with weak indefinites. Experiment 4 found that object-related activities were reduced when the same subject and object were used with a verb that does not license weak definite interpretations. In Experiment 5, a science fiction story introduced an artificial lexicon for novel concepts. Novel nouns that shared conceptual properties with English weak definite nouns were more likely to allow weak reference in a judgment task. Experiment 6 demonstrated that familiarity for definite articles and anti- familiarity for indefinite articles applies to the activity associated with the noun, consistent with predictions made by the incorporation analysis. PMID:23685208

  18. The Semantics of Russian Indefinite Pronouns: Scope, Domain Widening, Specificity, and Proportionality and Their Interaction

    ERIC Educational Resources Information Center

    Eremina, Olga

    2012-01-01

    The main goal of this dissertation is to consider the different types of indefinites in Russian as a system and provide a semantic account for each of them that would be able to naturally explain their distribution. The four sets of so-called 'indefinite pronouns' ("-to," "-nibud'," "-libo," and…

  19. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount...

  20. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991)...

  1. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991)...

  2. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount...

  3. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount...

  4. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount...

  5. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991)...

  6. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount...

  7. An iteration for indefinite and non-symmetric systems and its application to the Navier-Stokes equations

    SciTech Connect

    Wathen, A.; Golub, G.

    1996-12-31

    A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).

  8. Quadratic negative evidence discrimination

    SciTech Connect

    Anderson, D.N.; Redgate, T.; Anderson, K.K.; Rohay, A.C.; Ryan, F.M.

    1997-05-01

    This paper develops regional discrimination methods which use information inherent in phase magnitudes that are unmeasurable due to small amplitudes and/or high noise levels. The methods are enhancements to teleseismic techniques proposed by, and are extended to regional discrimination. Events observed at teleseismic distances are effectively identified with the M{sub s} vs m{sub b} discriminant because relative to the pressure wave energy (m{sub b}) of an event, an earthquake generates more shear wave energy (M{sub s}) than does an explosion. For some teleseismic events, the M{sub s} magnitude is difficult to measure and is known only to be below a threshold . With M{sub s} unmeasurable, the M{sub s} vs m{sub b} discriminant cannot be formed. However, if the M{sub s} is sufficiently small relative to a measured m{sub b}, then the event is still likely to be an explosion. The methods presented in this report are developed for a single seismic station, and make use of empirical evidence in the regional L{sub g} vs p{sub g} discriminant. The L{sub g} vs p{sub g} discriminant is analogous to the teleseismic M{sub s} vs m{sub b} discriminant.

  9. A modified direct preconditioner for indefinite symmetric Toeplitz systems

    SciTech Connect

    Concus, P.; Saylor, P.

    1994-12-31

    A modification is presented of the classical $O(n{sup 2})$ algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.

  10. Binary Inspiral in Quadratic Gravity

    NASA Astrophysics Data System (ADS)

    Yagi, Kent

    2015-01-01

    Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.

  11. Imaginary-scaling versus indefinite-metric quantization of the Pais-Uhlenbeck oscillator

    NASA Astrophysics Data System (ADS)

    Mostafazadeh, Ali

    2011-11-01

    Using the Pais-Uhlenbeck oscillator as a toy model, we outline a consistent alternative to the indefinite-metric quantization scheme that does not violate unitarity. We describe the basic mathematical structure of this method by giving an explicit construction of the Hilbert space of state vectors and the corresponding creation and annihilation operators. The latter satisfy the usual bosonic commutation relation and differ from those of the indefinite-metric theories by a sign in the definition of the creation operator. This change of sign achieves a definitization of the indefinite metric that gives life to the ghost states without changing their contribution to the energy spectrum.

  12. Quantum bouncer with quadratic dissipation

    NASA Astrophysics Data System (ADS)

    González, G.

    2008-02-01

    The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.

  13. Geometrical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Grewal, A. S.; Godloza, L.

    1999-01-01

    Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

  14. Exploration of Quadratic Expressions through Multiple Representations for Students with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Strickland, Tricia K.; Maccini, Paula

    2013-01-01

    The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…

  15. Orthogonality preserving infinite dimensional quadratic stochastic operators

    SciTech Connect

    Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  16. Primordial bubbles from quadratic gravity

    NASA Astrophysics Data System (ADS)

    Occhionero, Franco; Amendola, Luca

    1994-10-01

    A toy model of inflation with a first order phase transition built on a nonminimal generalization of quadratic gravity effectively implements a two field inflation and copiously spurs bubbles before the end of the slow roll. In particular, the phase transition may be brought to completion quickly enough to leave an observable signature at the large scales. We identify analytically and numerically the parameter space region capable of fitting the observed galaxy correlation function, while passing the microwave background constraints. Thus, astronomical observations can yield information upon the parameters of fundamental physics.

  17. Tuning a fuzzy controller using quadratic response surfaces

    NASA Technical Reports Server (NTRS)

    Schott, Brian; Whalen, Thomas

    1992-01-01

    Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

  18. Quadratic Expressions by Means of "Summing All the Matchsticks"

    ERIC Educational Resources Information Center

    Gierdien, M. Faaiz

    2012-01-01

    This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

  19. Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations

    ERIC Educational Resources Information Center

    Ellis, Amy B.; Grinstead, Paul

    2008-01-01

    This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

  20. Quadratic dynamical decoupling with nonuniform error suppression

    SciTech Connect

    Quiroz, Gregory; Lidar, Daniel A.

    2011-10-15

    We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.

  1. Single-photon quadratic optomechanics

    PubMed Central

    Liao, Jie-Qiao; Nori, Franco

    2014-01-01

    We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

  2. Large-scale sequential quadratic programming algorithms

    SciTech Connect

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  3. An Unexpected Influence on a Quadratic

    ERIC Educational Resources Information Center

    Davis, Jon D.

    2013-01-01

    Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

  4. Factorising a Quadratic Expression with Geometric Insights

    ERIC Educational Resources Information Center

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  5. Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

    NASA Technical Reports Server (NTRS)

    Padovan, J.; Lackney, J.

    1986-01-01

    The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

  6. Quadratic invariants for discrete clusters of weakly interacting waves

    NASA Astrophysics Data System (ADS)

    Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.

    2013-06-01

    We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.

  7. The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

    PubMed Central

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980

  8. The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.

    PubMed

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).

  9. The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.

    PubMed

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). PMID:24982980

  10. Preconditioned iterative methods for nonselfadjoint or indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Pasciak, J.E.

    1984-01-01

    We consider a Galerkin-Finite Element approximation to a general linear elliptic boundary value problem which may be nonselfadjoint or indefinite. We show how to precondition the equations so that the resulting systems of linear algebraic equations lead to iteration procedures whose iterative convergence rates are independent of the number of unknowns in the solution.

  11. Positive Definiteness via Off-Diagonal Scaling of a Symmetric Indefinite Matrix

    ERIC Educational Resources Information Center

    Bentler, Peter M.; Yuan, Ke-Hai

    2011-01-01

    Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

  12. Children's Interpretation of Indefinites in Sentences Containing Negation: A Reassessment of the Cross-Linguistic Picture

    ERIC Educational Resources Information Center

    Unsworth, Sharon; Gualmini, Andrea; Helder, Christina

    2008-01-01

    Previous research suggests that children's behavior with respect to the interpretation of indefinite objects in negative sentences may differ depending on the target language: whereas young English-speaking children tend to select a surface scope interpretation (e.g., Musolino (1998)), young Dutch-speaking children consistently prefer an inverse…

  13. 41 CFR 101-25.101-4 - Supply through indefinite quantity requirement contracts.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Supply through indefinite quantity requirement contracts. 101-25.101-4 Section 101-25.101-4 Public Contracts and Property Management... offices or agencies (the determining consideration being one of overall economy to the Government,...

  14. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  15. 48 CFR 1807.107-70 - Orders against Federal Supply Schedule contracts or other indefinite-delivery contracts awarded...

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... Supply Schedule contracts or other indefinite-delivery contracts awarded by another agency. 1807.107-70... Supply Schedule contracts or other indefinite-delivery contracts awarded by another agency. The FAR and... by another agency if the requirements consolidated under the order meet the definition of...

  16. Design of Linear Quadratic Regulators and Kalman Filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L.

    1986-01-01

    AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

  17. Quantum integrability of quadratic Killing tensors

    SciTech Connect

    Duval, C.; Valent, G.

    2005-05-01

    Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.

  18. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  19. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Fixed rates for services... options, the clause should be modified to reflect the information and data for the base period and...

  20. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT... 48 Federal Acquisition Regulations System 6 2012-10-01 2012-10-01 false Fixed rates for services... options, the clause should be modified to reflect the information and data for the base period and...

  1. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT... 48 Federal Acquisition Regulations System 6 2014-10-01 2014-10-01 false Fixed rates for services... options, the clause should be modified to reflect the information and data for the base period and...

  2. Optimal channels for channelized quadratic estimators.

    PubMed

    Kupinski, Meredith K; Clarkson, Eric

    2016-06-01

    We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem. PMID:27409452

  3. The Factorability of Quadratics: Motivation for More Techniques

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2005-01-01

    Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

  4. The Indefinite Extension of the Nuclear Non-Proliferation Treaty: A Hinderence or Help to Future Arms Control

    NASA Astrophysics Data System (ADS)

    Pella, Peter J.

    1996-05-01

    The indefinite and "unconditional" extension of the Nuclear Non-Proliferation Treaty (NPT) was achieved almost one year ago today. This outcome was a major foreign policy goal of the Clinton Administration. Some critics of the NPT's indefinite extension claim that nuclear weapons states parties to the NPT have now legitimized their possession of nuclear weapons for all time and that there is no incentive for future nuclear arms control and disarmament measures. A discussion of how the indefinite extension of the NPT has affected the nuclear arms control landscape and the prospects for future disarmament measures will be discussed.

  5. An ACA briefing on indefinite NPT extension and on the Moscow summit

    SciTech Connect

    Keeny, S.M. Jr; Mendelsohn, J.; Hartman, A.A.

    1995-06-01

    On May 17, the Arms Control Association (ACA) held a new conference to address important aspects of two events of fundamental importance that occurred in rapid succession. These were the decision by consensus on May 11 by member states meeting in New York to extend indefinitely the nuclear Non-Proliferation Treaty (NPT)- and the May 9-10 summit in Moscow between President Bill Clinton and Russian President Boris Yeltsin.

  6. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  7. Quadratic-Like Dynamics of Cubic Polynomials

    NASA Astrophysics Data System (ADS)

    Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen

    2016-02-01

    A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.

  8. On orthogonality preserving quadratic stochastic operators

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-01

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  9. On orthogonality preserving quadratic stochastic operators

    SciTech Connect

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  10. Guises and disguises of quadratic divergences

    SciTech Connect

    Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  11. On the Local Maxima of a Constrained Quadratic Form

    ERIC Educational Resources Information Center

    Bhowmik, Jahar L.

    2006-01-01

    This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

  12. Integration of the Quadratic Function and Generalization

    ERIC Educational Resources Information Center

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  13. On the electrodynamics of an absorbing uniaxial nonpositive determined (indefinite) medium

    SciTech Connect

    Baranov, D. G.; Vinogradov, A. P.; Simovskii, K. R.; Nefedov, I. S.; Tret'yakov, S. A.

    2012-04-15

    It is shown that a surface plasmon, whose decay length infinitely increases as it approaches the threshold frequency, can propagate over the surface of a half-space filled with a uniaxial indefinite absorbing metamaterial. At the threshold frequency itself, a new phenomenon is observed-upon incidence of a TM-polarized wave on the absorbing material, a real Brewster angle exists, and in the case of a plate made of such a metamaterial, 'reflectionless' reflection is observed when two plane waves are incident on the plate from two sides. In the latter case, complete destructive interference of reflected and transmitted waves occurs.

  14. A generalization of Baker's quadratic formulae for hyperelliptic ℘-functions

    NASA Astrophysics Data System (ADS)

    Athorne, Chris

    2011-07-01

    We present a generalization of a compact form, due to Baker, for quadratic identities satisfied by the three-index ℘-functions on curves of genus g=2, and a further generalization of a new result in genus g=3. The compact forms involve a bordered determinant containing 2(g-1)(g+1) free parameters.

  15. Geometric Approaches to Quadratic Equations from Other Times and Places.

    ERIC Educational Resources Information Center

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  16. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-12-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  17. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-01-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  18. Convex quadratic optimization on artificial neural networks

    SciTech Connect

    Adler, I.; Verma, S.

    1994-12-31

    We present continuous-valued Hopfield recurrent neural networks on which we map convex quadratic optimization problems. We consider two different convex quadratic programs, each of which is mapped to a different neural network. Activation functions are shown to play a key role in the mapping under each model. The class of activation functions which can be used in this mapping is characterized in terms of the properties needed. It is shown that the first derivatives of penalty as well as barrier functions belong to this class. The trajectories of dynamics under the first model are shown to be closely related to affine-scaling trajectories of interior-point methods. On the other hand, the trajectories of dynamics under the second model correspond to projected steepest descent pathways.

  19. Use of quadratic components for buckling calculations

    SciTech Connect

    Dohrmann, C.R.; Segalman, D.J.

    1996-12-31

    A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.

  20. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  1. Extended Decentralized Linear-Quadratic-Gaussian Control

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    2000-01-01

    A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

  2. Communications circuit including a linear quadratic estimator

    DOEpatents

    Ferguson, Dennis D.

    2015-07-07

    A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

  3. Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

    NASA Astrophysics Data System (ADS)

    Lee, T.-W.; An, Keju

    2016-06-01

    We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

  4. Half-quadratic-based iterative minimization for robust sparse representation.

    PubMed

    He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan

    2014-02-01

    Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.

  5. The use of definite and indefinite articles by children with specific language impairment.

    PubMed

    Polite, Elgustus J; Leonard, Laurence B; Roberts, Felicia D

    2011-08-01

    Among the grammatical limitations seen in English-speaking children with specific language impairment (SLI) is a prolonged period of using articles (e.g., a, the) inconsistently. Most studies documenting this difficulty have focused on article omission and have not made the distinction between definite and indefinite article contexts. In this study, there were 36 participants: 12 5-year-olds with SLI, 12 typically-developing children matched for age, and 12 younger, typically-developing children matched with participants in the SLI group according to mean length of utterance. All 36 children participated in a task requiring indefinite article use, and a task requiring use of the definite article, in which the referent of the noun had already been established in the discourse. The children with SLI showed less use of definite articles in particular, relative to both groups of typically-developing children. Substitutions as well as omissions were seen. The findings suggest that the article limitations of the children with SLI were attributable in part to an incomplete understanding of how definite articles are to be used.

  6. Submucosal Endoscopic Sampling for Indefinite Gastric Linitis Plastica Infiltrating into the Submucosal Layer.

    PubMed

    Chiyo, Taiga; Kobara, Hideki; Mori, Hirohito; Katsuki, Naomi; Haba, Reiji; Masaki, Tsutomu

    2015-09-01

    The diagnosis of diffuse-type gastric cancer, named linitis plastica (LP), is difficult because of its infiltration into the submucosa. Conventional endoscopic biopsy sampling may show false-negative results because the superficial mucosa is often normal. These macroscopic features do not often permit the distinction between benign and malignant lesions, and sampling methods have some limitations. Accordingly, a secure sampling method is required in order to increase the diagnostic yield. We have developed a submucosal tunneling technique for sampling submucosal tumors, which can visualize tumor surfaces and obtain tissue samples under direct vision. We report a rare case of indefinite gastric LP that could be diagnosed by this method. As multiple biopsies and endoscopic ultrasound (EUS)-guided fine needle aspiration (FNA) did not help us histologically diagnose the lesion, our new method of submucosal endoscopy which has advantages of visualizing tumor surfaces and obtaining tissue samples under direct vision in the submucosa was introduced. Histological examination of all acquired samples confirmed the presence of a poorly differentiated adenocarcinoma. The present case demonstrates that this method is a reasonable option for indefinite LP with features inflating into submucosa, providing an update on the contemporary concepts. PMID:26405710

  7. Quadratic Programming for Allocating Control Effort

    NASA Technical Reports Server (NTRS)

    Singh, Gurkirpal

    2005-01-01

    A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

  8. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  9. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  10. Stabilization of feedback control and stabilizability optimal solution for nonlinear quadratic problems

    NASA Astrophysics Data System (ADS)

    Popescu, Mihai; Dumitrache, Alexandru

    2011-05-01

    This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented by bilinear differential systems of the form x˙=A(x)x+B(x)u,x(0)=x0. One selects an adequate factorization of A( x) such that the analyzed system should be controllable. Employing the Hamilton-Jacobi equation it results the matrix algebraic equation of Riccati associated to the optimum problem. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, as well as the adjoint system corresponding to those functions. Thus one obtains a matrix differential equation where the solution representing the positive defined symmetric matrix P( x), verifies the Riccati algebraic equation. The stability analysis for the autonomous systems solution resulting for the determined feedback control is performed using the Liapunov function method. Finally we present certain significant cases.

  11. On Methods for the Analysis of Indefinite Stimuli Perception Characteristics: an fMRT Study of Gender-Specific Differences.

    PubMed

    Fyodorov, A A; Pervushina, O N; Bliznyuk, M V; Khoroshilov, B M; Melnikov, M E; Mazhirina, K G; Stark, M B; Savelov, A A; Petrovsky, E D; Kozlova, L I

    2016-07-01

    Comparative identification of cerebral regions activated in men and women during perception of indefinite images was carried out by fMRT and psychological testing. Nine men and nine women aged 20-26 years took part in the study. The volunteers examined simple geometric figures, slightly structurized images (tables from Rorschach's test), and images of impossible figures. Activation in the cerebellum and visual cortex (bilateral) was more pronounced in women in response to all types of images and less so in the right G. temporalis medius. The right frontal regions (G. precentralis, G. frontalis superior, G. frontalis medius) were also stronger activated in women in response to indefinite stimuli. PMID:27492400

  12. Holographic entropy increases in quadratic curvature gravity

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.

    2015-09-01

    Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.

  13. Indefinite self-renewal of ESCs through Myc/Max transcriptional complex-independent mechanisms.

    PubMed

    Hishida, Tomoaki; Nozaki, Yuriko; Nakachi, Yutaka; Mizuno, Yosuke; Okazaki, Yasushi; Ema, Masatsugu; Takahashi, Satoru; Nishimoto, Masazumi; Okuda, Akihiko

    2011-07-01

    Embryonic stem cells (ESCs) can self-renew indefinitely under the governance of ESC-specific transcriptional circuitries in which each transcriptional factor regulates distinct or overlapping sets of genes with other factors. c-Myc is a key player that is crucially involved in maintaining the undifferentiated state and the self-renewal of ESCs. However, the mechanism by which c-Myc helps preserve the ESC status is still poorly understood. Here we addressed this question by performing loss-of-function studies with the Max gene, which encodes the best-characterized partner protein for all Myc family proteins. Although Myc/Max complexes are widely regarded as crucial regulators of the ESC status, our data revealed that ESCs do not absolutely require these complexes in certain contexts and that this requirement is restricted to empirical ESC culture conditions without a MAPK inhibitor.

  14. The unconditional release of mentally ill offenders from indefinite commitment: a study of Missouri insanity acquittees.

    PubMed

    Linhorst, D M

    1999-01-01

    Using a database of all Missouri insanity acquittees committed on July 1, 1997 (N = 873) and all insanity acquittees unconditionally released from 1986 through 1997 (N = 193), this study calculated the lengths of commitment and identified variables associated with the unconditional release of insanity acquittees from indefinite commitment by the mental health and criminal justice systems. The study found that 85 percent of insanity acquittees were still under commitment 5 years after acquittal and 76 percent 10 years after acquittal. Factors that decreased the odds of being unconditionally released included never having been married; having a psychotic disorder, a mood disorder, a substance abuse disorder, or mental retardation/borderline intellectual functioning; and having committed a serious crime. These results support achievement of the intended goal of Missouri's insanity acquittee statute, which is to maximize public safety considerations, but have had the unintended effect of increasing the inpatient insanity acquittee population, resulting in fewer resources for voluntary patients.

  15. Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

    SciTech Connect

    Hintermueller, M.; Kao, C.-Y.; Laurain, A.

    2012-02-15

    This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this threshold value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.

  16. Three-dimensional nanometer-scale optical cavities of indefinite medium.

    PubMed

    Yao, Jie; Yang, Xiaodong; Yin, Xiaobo; Bartal, Guy; Zhang, Xiang

    2011-07-12

    Miniaturization of optical cavities has numerous advantages for enhancing light-matter interaction in quantum optical devices, low-threshold lasers with minimal power consumption, and efficient integration of optoelectronic devices at large scale. However, the realization of a truly nanometer-scale optical cavity is hindered by the diffraction limit of the nature materials. In addition, the scaling of the photon life time with the cavity size significantly reduces the quality factor of small cavities. Here we theoretically present an approach to achieve ultrasmall optical cavities using indefinite medium with hyperbolic dispersion, which allows propagation of electromagnetic waves with wave vectors much larger than those in vacuum enabling extremely small 3D cavity down to (λ/20)(3). These cavities exhibit size-independent resonance frequencies and anomalous scaling of quality factors in contrast to the conventional cavities, resulting in nanocavities with both high Q/V(m) ratio and broad bandwidth.

  17. User's guide for SOL/QPSOL: a Fortran package for quadratic programming

    SciTech Connect

    Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.

    1983-07-01

    This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.

  18. Classification of the quantum two-dimensional superintegrable systems with quadratic integrals and the Staeckel transforms

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2008-05-15

    The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -{h_bar}{sup 2} plus a quantum deformation of order {h_bar}{sup 4} and {h_bar}{sup 6}. The systems inside the classes are transformed using Staeckel transforms in the quantum case as in the classical case. The general form of the Staeckel transform between superintegrable systems is discussed.

  19. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  20. Contact symmetries of constrained quadratic Lagrangians

    NASA Astrophysics Data System (ADS)

    Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

    2016-01-01

    The conditions for the existence of (polynomial in the velocities) contact symmetries of constrained systems that are described by quadratic Lagrangians is presented. These Lagrangians mainly appear in mini-superspace reductions of gravitational plus matter actions. In the literature, one usually adopts a gauge condition (mostly for the lapse N) prior to searching for symmetries. This, however, is an unnecessary restriction which may lead to a loss of symmetries and consequently to the respective integrals of motion. A generalization of the usual procedure rests in the identification of the lapse function N as an equivalent degree of freedom and the according extension of the infinitesimal generator. As a result, conformal Killing tensors (with appropriate conformal factors) can define integrals of motion (instead of just Killing tensors used in the regular gauge fixed case). Additionally, rheonomic integrals of motion - whose existence is unique in this type of singular systems - of various orders in the momenta can be constructed. An example of a relativistic particle in a pp-wave space-time and under the influence of a quadratic potential is illustrated.

  1. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... President or Congress. (ii) It involves a danger to the United States' safety, security, or stability that... national program specifically intended to combat the threat to national safety, security, or stability. (2...-indefinite appointments is necessary for economy and efficiency. Except as provided by paragraphs (c) and...

  2. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 5 Administrative Personnel 1 2012-01-01 2012-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  3. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 5 Administrative Personnel 1 2014-01-01 2014-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  4. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  5. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 5 Administrative Personnel 1 2013-01-01 2013-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  6. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

    NASA Astrophysics Data System (ADS)

    Bizyaev, I. A.; Kozlov, V. V.

    2015-12-01

    We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

  7. Quadratic quantum cosmology with Schutz' perfect fluid

    NASA Astrophysics Data System (ADS)

    Vakili, Babak

    2010-01-01

    We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the f(R) gravity. Using Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wavefunction of the universe. In the case of f(R) = R2 (pure quadratic model), for some particular choices of the perfect fluid source, exact solutions to the SWD equation can be obtained and the corresponding results are compared to the usual f(R) = R model.

  8. A note on the fundamental unit in some types of the real quadratic number fields

    NASA Astrophysics Data System (ADS)

    Özer, Ö.

    2016-10-01

    Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.

  9. BOB CAT: A Large-Scale Review and Delphi Consensus for Management of Barrett’s Esophagus With No Dysplasia, Indefinite for, or Low-Grade Dysplasia

    PubMed Central

    Bennett, Cathy; Moayyedi, Paul; Corley, Douglas A.; DeCaestecker, John; Falck-Ytter, Yngve; Falk, Gary; Vakil, Nimish; Sanders, Scott; Vieth, Michael; Inadomi, John; Aldulaimi, David; Ho, Khek-Yu; Odze, Robert; Meltzer, Stephen J.; Quigley, Eamonn; Gittens, Stuart; Watson, Peter; Zaninotto, Giovanni; Iyer, Prasad G.; Alexandre, Leo; Ang, Yeng; Callaghan, James; Harrison, Rebecca; Singh, Rajvinder; Bhandari, Pradeep; Bisschops, Raf; Geramizadeh, Bita; Kaye, Philip; Krishnadath, Sheila; Fennerty, M. Brian; Manner, Hendrik; Nason, Katie S.; Pech, Oliver; Konda, Vani; Ragunath, Krish; Rahman, Imdadur; Romero, Yvonne; Sampliner, Richard; Siersema, Peter D.; Tack, Jan; Tham, Tony C.K.; Trudgill, Nigel; Weinberg, David S.; Wang, Jean; Wang, Kenneth; Wong, Jennie Y.Y.; Attwood, Stephen; Malfertheiner, Peter; MacDonald, David; Barr, Hugh; Ferguson, Mark K.; Jankowski, Janusz

    2015-01-01

    OBJECTIVES Barrett’s esophagus (BE) is a common premalignant lesion for which surveillance is recommended. This strategy is limited by considerable variations in clinical practice. We conducted an international, multidisciplinary, systematic search and evidence-based review of BE and provided consensus recommendations for clinical use in patients with nondysplastic, indefinite, and low-grade dysplasia (LGD). METHODS We defined the scope, proposed statements, and searched electronic databases, yielding 20,558 publications that were screened, selected online, and formed the evidence base. We used a Delphi consensus process, with an 80% agreement threshold, using GRADE (Grading of Recommendations Assessment, Development and Evaluation) to categorize the quality of evidence and strength of recommendations. RESULTS In total, 80% of respondents agreed with 55 of 127 statements in the final voting rounds. Population endoscopic screening is not recommended and screening should target only very high-risk cases of males aged over 60 years with chronic uncontrolled reflux. A new international definition of BE was agreed upon. For any degree of dysplasia, at least two specialist gastrointestinal (GI) pathologists are required. Risk factors for cancer include male gender, length of BE, and central obesity. Endoscopic resection should be used for visible, nodular areas. Surveillance is not recommended for <5 years of life expectancy. Management strategies for indefinite dysplasia (IND) and LGD were identified, including a de-escalation strategy for lower-risk patients and escalation to intervention with follow-up for higher-risk patients. CONCLUSIONS In this uniquely large consensus process in gastroenterology, we made key clinical recommendations for the escalation/de-escalation of BE in clinical practice. We made strong recommendations for the prioritization of future research. PMID:25869390

  10. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

    SciTech Connect

    Golubkov, A A; Makarov, Vladimir A

    2011-11-30

    We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

  11. Balloon-assisted enteroscopy for suspected Meckel’s diverticulum and indefinite diagnostic imaging workup

    PubMed Central

    Gomes, Guilherme Francisco; Bonin, Eduardo Aimore; Noda, Rafael William; Cavazzola, Leandro Totti; Bartholomei, Thiago Ferreira

    2016-01-01

    Meckel’s diverticulum (MD) is estimated to affect 1%-2% of the general population, and it represents a clinically silent finding of a congenital anomaly in up to 85% of the cases. In adults, MD may cause symptoms, such as overt occult lower gastrointestinal bleeding. The diagnostic imaging workup includes computed tomography scan, magnetic resonance imaging enterography, technetium 99m scintigraphy (99mTc) using either labeled red blood cells or pertechnetate (known as the Meckel’s scan) and angiography. The preoperative detection rate of MD in adults is low, and many patients ultimately undergo exploratory laparoscopy. More recently, however, endoscopic identification of MD has been possible with the use of balloon-assisted enteroscopy via direct luminal access, which also provides visualization of the diverticular ostium. The aim of this study was to review the diagnosis by double-balloon enteroscopy of 4 adults with symptomatic MD but who had negative diagnostic imaging workups. These cases indicate that balloon-assisted enteroscopy is a valuable diagnostic method and should be considered in adult patients who have suspected MD and indefinite findings on diagnostic imaging workup, including negative Meckel’s scan. PMID:27803776

  12. Immunotoxin Against a Donor MHC Class II Molecule Induces Indefinite Survival of Murine Kidney Allografts

    PubMed Central

    Brown, K.; Nowocin, A. K.; Meader, L.; Edwards, L. A.; Smith, R. A.

    2016-01-01

    Rejection of donor organs depends on the trafficking of donor passenger leukocytes to the secondary lymphoid organs of the recipient to elicit an immune response via the direct antigen presentation pathway. Therefore, the depletion of passenger leukocytes may be clinically applicable as a strategy to improve graft survival. Because major histocompatibility complex (MHC) class II+ cells are most efficient at inducing immune responses, selective depletion of this population from donor grafts may dampen the alloimmune response and prolong graft survival. In a fully MHC mismatched mouse kidney allograft model, we describe the synthesis of an immunotoxin, consisting of the F(ab′)2 fragment of a monoclonal antibody against the donor MHC class II molecule I‐Ak conjugated with the plant‐derived ribosomal inactivating protein gelonin. This anti–I‐Ak gelonin immunotoxin depletes I‐Ak expressing cells specifically in vitro and in vivo. When given to recipients of kidney allografts, it resulted in indefinite graft survival with normal graft function, presence of Foxp3+ cells within donor grafts, diminished donor‐specific antibody formation, and delayed rejection of subsequent donor‐type skin grafts. Strategies aimed at the donor arm of the immune system using agents such as immunotoxins may be a useful adjuvant to existing recipient‐orientated immunosuppression. PMID:26799449

  13. Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems

    NASA Astrophysics Data System (ADS)

    Ropp, David L.; Shadid, John N.

    2005-03-01

    In this paper numerical results are reviewed [D.L. Ropp, J.N. Shadid, C.C. Ober, Studies of the accuracy of time integration methods for reaction-diffusion equations, J. Comput. Phys. 194 (2) (2004) 544-574] that demonstrate that common second-order operator-splitting methods can exhibit instabilities when integrating the Brusselator equations out to moderate times of about seven periods of oscillation. These instabilities are manifested as high wave number spatial errors. In this paper, we further analyze this problem, and present a theorem for stability of operator-splitting methods applied to linear reaction-diffusion equations with indefinite reaction terms which controls both low and high wave number instabilities. A corollary shows that if L-stable methods are used for the diffusion term the high wave number instability will be controlled more easily. In the absence of L-stability, an additional time step condition that suppresses the high wave number modes appears to guarantee convergence at the asymptotic order for the operator-splitting method. Numerical results for a model problem confirm this theory, and results for the Brusselator problem agree as well.

  14. Clinical significance and management of Barrett's esophagus with epithelial changes indefinite for dysplasia.

    PubMed

    Thota, Prashanthi N; Kistangari, Gaurav; Esnakula, Ashwini K; Gonzalo, David Hernandez; Liu, Xiu-Li

    2016-08-01

    Barrett's esophagus (BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥ 1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma (EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia (IND), low grade dysplasia (LGD) or high grade dysplasia (HGD). Biopsies are diagnosed as IND when the epithelial abnormalities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND. PMID:27602241

  15. Clinical significance and management of Barrett’s esophagus with epithelial changes indefinite for dysplasia

    PubMed Central

    Thota, Prashanthi N; Kistangari, Gaurav; Esnakula, Ashwini K; Gonzalo, David Hernandez; Liu, Xiu-Li

    2016-01-01

    Barrett’s esophagus (BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥ 1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma (EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia (IND), low grade dysplasia (LGD) or high grade dysplasia (HGD). Biopsies are diagnosed as IND when the epithelial abnormalities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND. PMID:27602241

  16. The medium is NOT the message or Indefinitely long-term file storage at Leeds University

    NASA Technical Reports Server (NTRS)

    Holdsworth, David

    1996-01-01

    Approximately 3 years ago we implemented an archive file storage system which embodies experiences gained over more than 25 years of using and writing file storage systems. It is the third in-house system that we have written, and all three systems have been adopted by other institutions. This paper discusses the requirements for long-term data storage in a university environment, and describes how our present system is designed to meet these requirements indefinitely. Particular emphasis is laid on experiences from past systems, and their influence on current system design. We also look at the influence of the IEEE-MSS standard. We currently have the system operating in five UK universities. The system operates in a multi-server environment, and is currently operational with UNIX (SunOS4, Solaris2, SGI-IRIX, HP-UX), NetWare3 and NetWare4. PCs logged on to NetWare can also archive and recover files that live on their hard disks.

  17. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    ERIC Educational Resources Information Center

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  18. Visualising the Roots of Quadratic Equations with Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  19. Some Paradoxical Results for the Quadratically Weighted Kappa

    ERIC Educational Resources Information Center

    Warrens, Matthijs J.

    2012-01-01

    The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

  20. Convexity preserving C2 rational quadratic trigonometric spline

    NASA Astrophysics Data System (ADS)

    Dube, Mridula; Tiwari, Preeti

    2012-09-01

    A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.

  1. Geometric quadratic stochastic operator on countable infinite set

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  2. Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

    USGS Publications Warehouse

    Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

    1971-01-01

    Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

  3. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  4. Optimal power flow using sequential quadratic programming

    NASA Astrophysics Data System (ADS)

    Nejdawi, Imad M.

    1999-11-01

    Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.

  5. A Quadratic Closure for Compressible Turbulence

    SciTech Connect

    Futterman, J A

    2008-09-16

    We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

  6. A comparison of weight average and direct boundary fitting of sedimentation velocity data for indefinite polymerizing systems.

    PubMed

    Sontag, C A; Stafford, W F; Correia, J J

    2004-03-01

    Analysis of sedimentation velocity data for indefinite self-associating systems is often achieved by fitting of weight average sedimentation coefficients (s(20,w)) However, this method discriminates poorly between alternative models of association and is biased by the presence of inactive monomers and irreversible aggregates. Therefore, a more robust method for extracting the binding constants for indefinite self-associating systems has been developed. This approach utilizes a set of fitting routines (SedAnal) that perform global non-linear least squares fits of up to 10 sedimentation velocity experiments, corresponding to different loading concentrations, by a combination of finite element simulations and a fitting algorithm that uses a simplex convergence routine to search parameter space. Indefinite self-association is analyzed with the software program isodesfitter, which incorporates user provided functions for sedimentation coefficients as a function of the degree of polymerization for spherical, linear and helical polymer models. The computer program hydro was used to generate the sedimentation coefficient values for the linear and helical polymer assembly mechanisms. Since this curve fitting method directly fits the shape of the sedimenting boundary, it is in principle very sensitive to alternative models and the presence of species not participating in the reaction. This approach is compared with traditional fitting of weight average data and applied to the initial stages of Mg(2+)-induced tubulin self-associating into small curved polymers, and vinblastine-induced tubulin spiral formation. The appropriate use and limitations of the methods are discussed. PMID:15043931

  7. Indefinite for non‐invasive neoplasia lesions in gastric intestinal metaplasia: the immunophenotype

    PubMed Central

    Mauro Cassaro; Rugge, Massimo; Tieppo, Chiara; Giacomelli, Luciano; Velo, Daniela; Nitti, Donato

    2007-01-01

    Background In the Padova International Classification, gastric precancerous lesions are labelled as “indefinite for non‐invasive neoplasia” (Indef‐NiN) cytohistological alterations mimicking non‐invasive neoplasia (NiN), but lacking all the attributes required for a definite NiN categorisation. Aim To apply a panel of immunohistochemical (IHC) markers of cell proliferation (Mib1), intestinal differentiation (Cdx2), apoptosis (pro‐caspase 3) and cell immortalisation (hTERT) to compare the IHC profiles of a series of precancerous lesions arising in gastric intestinalised (ie, IM‐positive) glands. Materials and methods By applying the histological criteria consistently provided by both the Padova Classification and the World Health Organization International Agency, 112 consecutive cases were considered: intestinal metaplasia (IM; n = 54), Indef‐NiN in IM‐positive gastric glands (n = 28) and low‐grade (LG) NiN (n = 30). In each histological category, the expression of the marker was separately scored in superficial, proliferative and coil compartments. Results In all glandular compartments, Mib1, Cdx2, hTERT and pro‐caspase 3 were consistently more expressed in LG‐NiN than in either IM or Indef‐NiN lesions (analysis of variance: p<0.001). Significant ORs (calculated by ordinal logistic regression analysis for each glandular compartment) associated IM, Indef‐NiN and LG‐NiN with the expression of the considered markers. Conclusions A consistent overexpression (unrestricted to the proliferative zone) of IHC markers of cell proliferation, intestinal differentiation, decreased apoptosis and cell immortalisation differentiates LG‐NiN from both (simple) IM and Indef‐NiN (arising in IM). An increased proliferative activity in the proliferative zone discriminates Indef‐NiN lesions (ie, hyperproliferative IM) from IM. Such divergent IHC profiles may provide a rationale for scheduling follow‐up protocols more properly tailored on

  8. Phase recovery based on quadratic programming

    NASA Astrophysics Data System (ADS)

    Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na

    2014-11-01

    Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.

  9. Degenerate nonlinear programming with a quadratic growth condition.

    SciTech Connect

    Anitescu, M.; Mathematics and Computer Science

    2000-01-01

    We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.

  10. Classification of constraints and degrees of freedom for quadratic discrete actions

    SciTech Connect

    Höhn, Philipp A.

    2014-11-15

    We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph

  11. On the time evolution operator for time-dependent quadratic Hamiltonians

    SciTech Connect

    Fernandez, F. M.

    1989-07-01

    The Schr/umlt o/dinger equation with a time-dependent quadratic Hamiltonian isinvestigated. The time-evolution operator is written as a product of exponentialoperators determined by the Heisenberg equations of motion. This productoperator is shown to be global in the occupation number representation when theHamiltonian is Hermitian. The success of some physical applications of theproduct-form representation is explained.

  12. Finite-element analysis of earing using non-quadratic yield surfaces

    SciTech Connect

    Logan, R.W.

    1995-06-18

    During deep draw cupping, the phenomenon known as earing may occur as the cup wall is formed, resulting in a periodic variation of cup wall height around the perimeter of the finished cup. This is generally due to planar anisotropy of flow in rolled sheet product. It is generally observed that the anisotropy parameter R will vary in the plane of the sheet when ears are observed in cupping, with a parameter {Delta}R describing the variation of R in the plane of the sheet. For many common textures in face-centered and body-centered materials, the ears form relative to the sheet rolling direction at 0{degrees} and 90{degrees} around the perimeter if {Delta}R>0, and at -45{degrees} and +45{degrees} if {Delta}R<0. There is extensive experimental evidence that ear height shows a linear correlation with {Delta}R/R, but attempts to duplicate this using the finite-element method are highly dependent on both the methodology and yield surface used. It was shown previously that using a coarse mesh and the quadratic Hill yield surface tends to greatly under predict earing. In this study, we have used two different finite-element codes developed at LLNL to examine the predicted earing using both quadratic Hill and alternative non-quadratic yield surfaces. These results are compared to experimental data and conclusions drawn about the most desirable closed-form yield surfaces to duplicate the observed earing phenomena.

  13. On a 'Mysterious' Case of a Quadratic Hamiltonian

    NASA Astrophysics Data System (ADS)

    Sakovich, Sergei

    2006-07-01

    We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painlevé test for integrability.

  14. AdS waves as exact solutions to quadratic gravity

    SciTech Connect

    Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin

    2011-04-15

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

  15. Multivariable design of improved linear quadratic regulation control for MIMO industrial processes.

    PubMed

    Zhang, Ridong; Lu, Renquan; Jin, Qibing

    2015-07-01

    In this study, a multivariable linear quadratic control system using a new state space structure was developed for the chamber pressure in the industrial coke furnace. Such processes typically have complex and nonlinear dynamic behavior, which causes the performance of controllers using conventional design and tuning to be poor or to require significant effort in practice. The process model is first treated into a new state space form and the implementation of linear quadratic control is designed using this new model structure. Performance in terms of regulatory/servo, disturbance rejection and measurement noise problems were all compared with the recent model predictive control strategy. Results revealed that the control system showed more robustness and improved the closed-loop process performance under model/process mismatches.

  16. Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

    SciTech Connect

    Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.

    2012-07-15

    The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.

  17. A 3D Frictional Segment-to-Segment Contact Method for Large Deformations and Quadratic Elements

    SciTech Connect

    Puso, M; Laursen, T; Solberg, J

    2004-04-01

    Node-on-segment contact is the most common form of contact used today but has many deficiencies ranging from potential locking to non-smooth behavior with large sliding. Furthermore, node-on-segment approaches are not at all applicable to higher order discretizations (e.g. quadratic elements). In a previous work, [3, 4] we developed a segment-to-segment contact approach for eight node hexahedral elements based on the mortar method that was applicable to large deformation mechanics. The approach proved extremely robust since it eliminated the over-constraint that caused 'locking' and provided smooth force variations in large sliding. Here, we extend this previous approach to treat frictional contact problems. In addition, the method is extended to 3D quadratic tetrahedrals and hexahedrals. The proposed approach is then applied to several challenging frictional contact problems that demonstrate its effectiveness.

  18. Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

    SciTech Connect

    Budanov, V.G.

    1987-12-01

    In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function.

  19. A transient, quadratic nodal method for triangular-Z geometry

    SciTech Connect

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  20. The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

    NASA Astrophysics Data System (ADS)

    Yan, Litan; Liu, Junfeng; Chen, Chao

    2014-11-01

    In this paper, we study the generalized quadratic covariation of f(BH) and BH defined by $ [f(BH),BH](H)t:=\\lim_\\varepsilon\\downarrow 0}(1)/(\\varepsilon2H)\\int 0t{f(BHs+\\varepsilon) -f(BHs)}(BHs+\\varepsilon-BH_s)ds2H in probability, where f is a Borel function and BH is a fractional Brownian motion with Hurst index 0 < H < 1/2. We construct a Banach space {H} of measurable functions such that the generalized quadratic covariation exists in L2(Ω) and the Bouleau-Yor identity takes the form [f(BH),BH]t(H)=-\\int_ {R}}f(x){L}H(dx,t) provided f\\in {H}, where {L}^{H}(x, t) is the weighted local time of BH. These are also extended to the time-dependent case, and as an application we give the identity between the generalized quadratic covariation and the 4-covariation [g(BH), BH, BH, BH] when H = 1/4.

  1. On Volterra quadratic stochastic operators with continual state space

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  2. A Projection Neural Network for Constrained Quadratic Minimax Optimization.

    PubMed

    Liu, Qingshan; Wang, Jun

    2015-11-01

    This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

  3. New type of Weyl semimetal with quadratic double Weyl fermions

    PubMed Central

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

    2016-01-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

  4. New type of Weyl semimetal with quadratic double Weyl fermions.

    PubMed

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid

    2016-02-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

  5. New type of Weyl semimetal with quadratic double Weyl fermions.

    PubMed

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid

    2016-02-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs.

  6. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.

    2016-06-01

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.

  7. Quadratic α‧-corrections to heterotic double field theory

    NASA Astrophysics Data System (ADS)

    Lee, Kanghoon

    2015-10-01

    We investigate α‧-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim ⁡ G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α‧-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α‧.

  8. Radar Rainfall Estimation using a Quadratic Z-R equation

    NASA Astrophysics Data System (ADS)

    Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

    2016-04-01

    The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

  9. A Unified Approach to Teaching Quadratic and Cubic Equations.

    ERIC Educational Resources Information Center

    Ward, A. J. B.

    2003-01-01

    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  10. Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir

    NASA Astrophysics Data System (ADS)

    Gomis, Joaquim; Longhi, Giorgio

    2016-01-01

    We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.

  11. Finding the Best Quadratic Approximation of a Function

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2011-01-01

    This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

  12. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  13. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

    PubMed Central

    Wang, Di; Kleinberg, Robert D.

    2009-01-01

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

  14. Solving quadratic programming problems by delayed projection neural network.

    PubMed

    Yang, Yongqing; Cao, Jinde

    2006-11-01

    In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

  15. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    ERIC Educational Resources Information Center

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  16. Confidence set interference with a prior quadratic bound. [in geophysics

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  17. Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

    NASA Astrophysics Data System (ADS)

    Bai, Zheng-Jian; Datta, Biswa Nath; Wang, Jinwei

    2010-04-01

    The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant "no spill-over property" of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show

  18. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  19. Fiches pratiques: Domino gastronomique; Ticket de metro; Articles definis et indefinis; Texte en scenes (Practical Ideas: Gastronomic Dominos; Metro Ticket; Definite and Indefinite Articles; Text on Stage).

    ERIC Educational Resources Information Center

    Grigoriou, Marianthi; And Others

    1992-01-01

    Four language classroom activities are described, including a food game, a culture and language activity based on a Paris Metro ticket, an exercise in the use of definite and indefinite articles using a film poster, and a classroom adaptation of a fairy tale for dramatic oral presentation. (MSE)

  20. Tableau-based protein substructure search using quadratic programming

    PubMed Central

    Stivala, Alex; Wirth, Anthony; Stuckey, Peter J

    2009-01-01

    Background Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database. Results We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques. Conclusion We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC. PMID:19450287

  1. Gravitomagnetic effects in quadratic gravity with a scalar field

    NASA Astrophysics Data System (ADS)

    Finch, Andrew; Said, Jackson Levi

    2016-10-01

    The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

  2. Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices

    NASA Astrophysics Data System (ADS)

    Suris, Yuri B.

    1997-08-01

    A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.

  3. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  4. Discrete quadratic solitons with competing second-harmonic components

    SciTech Connect

    Setzpfandt, Frank; Pertsch, Thomas; Sukhorukov, Andrey A.

    2011-11-15

    We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.

  5. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  6. A Riccati approach for constrained linear quadratic optimal control

    NASA Astrophysics Data System (ADS)

    Sideris, Athanasios; Rodriguez, Luis A.

    2011-02-01

    An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.

  7. Measurement of quadratic electrogyration effect in castor oil

    NASA Astrophysics Data System (ADS)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  8. Revisiting the naturalness problem: Who is afraid of quadratic divergences?

    NASA Astrophysics Data System (ADS)

    Aoki, Hajime; Iso, Satoshi

    2012-07-01

    It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences—which can always be absorbed into a position of the critical surface—should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.

  9. Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum.

    PubMed

    Stone, G; Chapman, B; Lovell, D

    2009-11-01

    In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (D(T)), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a D(T)-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes.

  10. Ground states for irregular and indefinite superlinear Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Ackermann, Nils; Chagoya, Julián

    2016-11-01

    We consider the existence of a ground state for the subcritical stationary semilinear Schrödinger equation - Δu + u = a (x) | u| p - 2 u in H1, where a ∈L∞ (RN) may change sign. Our focus is on the case where loss of compactness occurs at the ground state energy. By providing a new variant of the Splitting Lemma we do not need to assume the existence of a limit problem at infinity, be it in the form of a pointwise limit for a as | x | → ∞ or of asymptotic periodicity. That is, our problem may be irregular at infinity. In addition, we allow a to change sign near infinity, a case that has never been treated before.

  11. Implementation of an Evolving non Quadratic Anisotropic Behaviour for the Closed Packed Materials

    SciTech Connect

    Revil-Baudard, Benoit; Massoni, Elisabeth

    2010-06-15

    In this paper, the mechanical behaviour of alpha-titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al.[1], to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switch between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows defining all the parameters needed to model the elasto-plastic behaviour. Simulations of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis.

  12. Formalism for the solution of quadratic Hamiltonians with large cosine terms

    NASA Astrophysics Data System (ADS)

    Ganeshan, Sriram; Levin, Michael

    2016-02-01

    We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

  13. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    SciTech Connect

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-02-28

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

  14. Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score

    PubMed Central

    Zhang, Zhongheng; Ji, Xuqing

    2016-01-01

    Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness. PMID:27734905

  15. Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

    NASA Astrophysics Data System (ADS)

    Landsman, Zinoviy

    2008-10-01

    We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

  16. Compact stellar models obeying quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj

    2016-10-01

    In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.

  17. Rigorous performance bounds for quadratic and nested dynamical decoupling

    SciTech Connect

    Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.

    2011-12-15

    We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

  18. Reaction Wheel Control Design Using Linear Quadratic Controller

    NASA Astrophysics Data System (ADS)

    Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.

    2016-01-01

    This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.

  19. Frontogenesis driven by horizontally quadratic distributions of density

    NASA Technical Reports Server (NTRS)

    Jacqmin, David

    1991-01-01

    Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

  20. Restart-Based Genetic Algorithm for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Misevicius, Alfonsas

    The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.

  1. Quantum mechanical study of a generic quadratically coupled optomechanical system

    NASA Astrophysics Data System (ADS)

    Shi, H.; Bhattacharya, M.

    2013-04-01

    Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.

  2. Neural network for solving convex quadratic bilevel programming problems.

    PubMed

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

    2014-03-01

    In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.

  3. Nios II hardware acceleration of the epsilon quadratic sieve algorithm

    NASA Astrophysics Data System (ADS)

    Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio

    2010-04-01

    The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ɛ-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.

  4. On a quadratic transformation due to Kummer and its generalizations

    NASA Astrophysics Data System (ADS)

    Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om

    2016-05-01

    The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.

  5. Quadratic integrand double-hybrid made spin-component-scaled

    NASA Astrophysics Data System (ADS)

    Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo

    2016-03-01

    We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

  6. Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

    PubMed

    Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun

    2016-06-10

    We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.

  7. Electroweak vacuum stability and finite quadratic radiative corrections

    NASA Astrophysics Data System (ADS)

    Masina, Isabella; Nardini, Germano; Quiros, Mariano

    2015-08-01

    If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales, the cutoff is not unique and each SM sector has its own UV cutoff Λi. We have performed this calculation assuming the minimal supersymmetric standard model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λi, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the focus point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.

  8. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    SciTech Connect

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-06-23

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.

  9. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

  10. Quadratic Reciprocity and the Group Orders of Particle States

    SciTech Connect

    DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

    2001-06-01

    The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

  11. Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

    NASA Technical Reports Server (NTRS)

    Choi, Benjamin B.

    2002-01-01

    Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

  12. Linear quadratic stochastic control of atomic hydrogen masers.

    PubMed

    Koppang, P; Leland, R

    1999-01-01

    Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.

  13. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    PubMed

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

  14. An Instability Index Theory for Quadratic Pencils and Applications

    NASA Astrophysics Data System (ADS)

    Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

    2014-04-01

    Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

  15. Implementation of Multivariate Quadratic Quasigroup for Wireless Sensor Network

    NASA Astrophysics Data System (ADS)

    Maia, Ricardo José Menezes; Barreto, Paulo Sérgio Licciardi Messeder; de Oliveira, Bruno Trevizan

    Wireless sensor networks (WSN) consists of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in WSN, matching public key cryptosystems (PKC) for these networks is an open research problem. Recently a new PKC based on quasigroups multivariate quadratic. Experiments performed show that MQQ performed in less time than existing major PKC, so that some articles claim that has MQQ speed of a typical symmetric block cipher. Considering features promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. This paper implements in nesC a new class of public key algorithm called Multivariate Quadratic Quasigroup. This implementation focuses on modules for encryption and decryption of 160-bit MQQ, the modules have been implemented on platforms TelosB and MICAz. We measured execution time and space occupied in the ROM and RAM of the sensors.

  16. Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

    NASA Astrophysics Data System (ADS)

    Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

    2016-08-01

    Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

  17. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1979-01-01

    Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

  18. Theory of non-collinear interactions of acoustic waves in an isotropic material with hysteretic quadratic nonlinearity.

    PubMed

    Gusev, Vitalyi

    2002-01-01

    A particular form of the energy potential (cubic in strains) is proposed, which leads to the bow-tie behavior of the nonlinear modulus in an isotropic material with hysteresis of quadratic nonlinearity. The nonlinear scattering of a weak probe wave in the field of a strong pump wave is analyzed. It is demonstrated that collinear interactions of the shear waves are allowed in materials with nonlinearity hysteresis. Both in collinear and non-collinear frequency-mixing processes the combination frequency is composed of the probe wave frequency and one of the even harmonics of the pump wave. In general, the developed theory predicts that in the presence of the hysteretic nonlinearity the number of possible resonant scattering processes increases. In particular, if frequency-mixing processes are forbidden in the material with the elastic quadratic nonlinearity (for a fixed ratio of primary frequencies), they may be allowed in the materials with hysteretic quadratic nonlinearity. Moreover, in materials with hysteresis of the nonlinearity the resonant frequency mixing for a fixed ratio of primary frequencies may be allowed for multiple mutual orientations of the primary wave vectors. PMID:11831826

  19. Repopulation Kinetics and the Linear-Quadratic Model

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

    2009-08-01

    The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

  20. Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories

    NASA Astrophysics Data System (ADS)

    Adamson, L. N. C.; Osbaldestin, A. H.

    2014-03-01

    We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.

  1. Quadratic Finite Element Method for 1D Deterministic Transport

    SciTech Connect

    Tolar, Jr., D R; Ferguson, J M

    2004-01-06

    In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

  2. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.

    PubMed

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-12

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986

  3. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-01

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.

  4. Recognition of Graphs with Convex Quadratic Stability Number

    NASA Astrophysics Data System (ADS)

    Pacheco, Maria F.; Cardoso, Domingos M.

    2009-09-01

    A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.

  5. Schwarz and multilevel methods for quadratic spline collocation

    SciTech Connect

    Christara, C.C.; Smith, B.

    1994-12-31

    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  6. Wind turbine power tracking using an improved multimodel quadratic approach.

    PubMed

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables.

  7. Cosmology for quadratic gravity in generalized Weyl geometry

    NASA Astrophysics Data System (ADS)

    Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.

    2016-04-01

    A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.

  8. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

  9. Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling

    SciTech Connect

    Fowler, Jack F.

    2009-04-01

    Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.

  10. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    SciTech Connect

    Ita, B. I.

    2014-11-12

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

  11. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  12. Pseudo-continuous-time quadratic regulators with pole placement in a specific region

    NASA Technical Reports Server (NTRS)

    Shieh, L. S.; Zhang, J. L.; Ganesan, S.

    1990-01-01

    The paper comments on the pseudo-continuous-time quadratic regulator developed in an earlier paper. It also presents a new digital redesign technique, based on matching all the states at all the sampling instants, for finding the pseudo-continuous-time quadratic regulator.

  13. Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

    ERIC Educational Resources Information Center

    Pathak, H. K.; Grewal, A. S.

    2002-01-01

    This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

  14. The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system

    NASA Astrophysics Data System (ADS)

    Li, Chengzhi; Llibre, Jaume

    2009-12-01

    We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.

  15. Unified dark energy and dust dark matter dual to quadratic purely kinetic K-essence

    NASA Astrophysics Data System (ADS)

    Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana

    2016-02-01

    We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar-field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a "dust" fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of f(R) = R - α R^2 generalized gravity. Upon deriving the corresponding "Einstein-frame" effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic "k-essence" gravity-matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler-DeWitt quantization of the dual purely kinetic "k-essence" gravity-matter model is also briefly discussed.

  16. Quadratic Fermi node in a 3D strongly correlated semimetal.

    PubMed

    Kondo, Takeshi; Nakayama, M; Chen, R; Ishikawa, J J; Moon, E-G; Yamamoto, T; Ota, Y; Malaeb, W; Kanai, H; Nakashima, Y; Ishida, Y; Yoshida, R; Yamamoto, H; Matsunami, M; Kimura, S; Inami, N; Ono, K; Kumigashira, H; Nakatsuji, S; Balents, L; Shin, S

    2015-12-07

    Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  17. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  18. Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?

    PubMed

    Schönberg, C H L

    2015-04-01

    Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.

  19. Inverse problem of quadratic time-dependent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing

    2015-08-01

    Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

  20. Dynamics and linear quadratic optimal control of flexible multibody systems

    NASA Astrophysics Data System (ADS)

    Tung, Chin-Wei

    1994-12-01

    An efficient algorithm for the modeling, dynamic analysis, and optimal control of flexible multibody systems (FMBS) is presented. The cantilevered Bernoulli-Euler beam model and the assumed mode method are used to represent flexibility of elastic bodies in 3D vibration problems. Centrifugal stiffening effects are introduced to correctly represent the dynamic response. The governing equations of motion are based on Kane's equations, adopting a recursive formulation and strategic positioning of the generalized coordinates. The linear quadratic optimization scheme is employed to formulate the vibration control problem. The solutions to the Riccati equation and the use of Kalman gain as optimal control feedbacks to the control of flexibility are also introduced. Based on the optimal control theory and the property of the built-in redundancy for flexible multibody systems, the performance index measure in the optimization control of such systems can be classified into two manifolds: (1) using the extra degrees of freedom resulting from redundancy as control inputs and choosing an integral-type performance index which results in a global optimization scheme and (2) using the joint forces and torques as control inputs and allowing the system output state to keep close track to a reference state while the performance index is kept minimum. Several numerical examples are presented to demonstrate the effectiveness of the methodologies developed.

  1. Junction conditions in quadratic gravity: thin shells and double layers

    NASA Astrophysics Data System (ADS)

    Reina, Borja; Senovilla, José M. M.; Vera, Raül

    2016-05-01

    The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

  2. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  3. Quadratic isothermal amplification for the detection of microRNA.

    PubMed

    Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan

    2014-03-01

    This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ∼2 h.

  4. Quadratic stabilisability of multi-agent systems under switching topologies

    NASA Astrophysics Data System (ADS)

    Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long

    2014-12-01

    This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

  5. Quadratic Fermi node in a 3D strongly correlated semimetal

    DOE PAGES

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; et al

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

  6. Linear versus quadratic portfolio optimization model with transaction cost

    NASA Astrophysics Data System (ADS)

    Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

    2014-06-01

    Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

  7. GR angular momentum in the quadratic spinor Lagrangian formulation

    NASA Astrophysics Data System (ADS)

    Li, Siao-Jing

    2016-08-01

    We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.

  8. Quadratic Fermi node in a 3D strongly correlated semimetal

    SciTech Connect

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  9. Quadratic Fermi node in a 3D strongly correlated semimetal

    PubMed Central

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-01-01

    Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

  10. A decentralized linear quadratic control design method for flexible structures

    NASA Technical Reports Server (NTRS)

    Su, Tzu-Jeng; Craig, Roy R., Jr.

    1990-01-01

    A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

  11. Gravity waves from non-minimal quadratic inflation

    SciTech Connect

    Pallis, Constantinos; Shafi, Qaisar

    2015-03-12

    We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.

  12. Quadratic adaptive algorithm for solving cardiac action potential models.

    PubMed

    Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

    2016-10-01

    An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. PMID:27639239

  13. On the two-dimensional classical motion of a charged particle in an electromagnetic field with an additional quadratic integral of motion

    NASA Astrophysics Data System (ADS)

    Marikhin, V. G.

    2013-06-01

    The problem of quadratic Hamiltonians with an electromagnetic field commuting in the sense of the standard Poisson brackets has been considered. It has been shown that, as in the quantum case, any such pair can be reduced to the canonical form, which makes it possible to construct the complete classification of the solutions in the class of meromorphic solutions for the main function of one variable. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables, which is similar to that in the theory of integrable tops. This transformation has been considered for the two-dimensional Hamiltonian of a charged particle with an additional quadratic integral of motion.

  14. Choice of functional form and the demand for air quality

    SciTech Connect

    Bender, B.; Gronberg, T.J.; Hwang, H.S.

    1980-11-01

    The quadratic Box-Cox approach is examined to determine its usefulness in demand research. In the absence of information about hedonic price and household demand structures, the flexible form is invaluable in both stages of the Rosen demand estimation procedure. The quadratic Box-Cox form permits a statistical investigation of a wide variety of specific hypotheses concerning specifications. Commonly-used functional forms in both the hedonic and demand stages are shown in the samples to be founded upon unacceptably restrictive hypotheses. The impact of changes in functional form upon demand-elasticity estimates and benefit estimates justify concern over the functional form-selection process. 8 references, 4 tables.

  15. Convergence properties of a quadratic approach to the inverse-scattering problem

    NASA Astrophysics Data System (ADS)

    Persico, Raffaele; Soldovieri, Francesco; Pierri, Rocco

    2002-12-01

    The local-minima question that arises in the framework of a quadratic approach to inverse-scattering problems is investigated. In particular, a sufficient condition for the absence of local minima is given, and some guidelines to ensure the reliability of the algorithm are outlined for the case of data not belonging to the range of the relevant quadratic operator. This is relevant also when an iterated solution procedure based on a quadratic approximation of the electromagnetic scattering at each step is considered.

  16. Stability of the equilibrium positions of an engine with nonlinear quadratic springs

    NASA Astrophysics Data System (ADS)

    Stănescu, Nicolae-Doru; Popa, Dinel

    2014-06-01

    Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.

  17. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  18. On ideal structure in quadratic DDS in R{sup 2}

    SciTech Connect

    Kutnjak, Milan

    2008-11-13

    We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.

  19. Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

    ERIC Educational Resources Information Center

    Brilleslyper, Michael A.

    2004-01-01

    Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

  20. Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game

    NASA Astrophysics Data System (ADS)

    Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed

    This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

  1. Models of quadratic quantum algebras and their relation to classical superintegrable systems

    SciTech Connect

    Kalnins, E. G.; Miller, W.; Post, S.

    2009-05-15

    We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.

  2. Optimal two-point static calibration of measurement systems with quadratic response

    SciTech Connect

    Pallas-Areny, Ramon; Jordana, Josep; Casas, Oscar

    2004-12-01

    Measurement devices and instruments must be calibrated after manufacture to correct for component and assembly tolerances, and periodically to correct for drift and aging effects. The number of reference inputs needed for calibration depends on the actual transfer characteristic and the desired accuracy. Often, a linear characteristic is assumed for simplicity, either for the overall input range (global linearization) or for successive input subranges (piecewise linearization). Thus, only two reference inputs are needed for each straight line. This two-point static calibration can be easily implemented in any system having some basic computation capability and allows for the correction of zero and gain errors, and of their drifts if the system is periodically calibrated. Often, the reference inputs for that calibration are the end values of the measurement range (or subrange). However, this is not always the optimal selection because the calibration error is minimal for those reference inputs only, which are not necessarily the most relevant inputs for the system being considered. This article proposes three optimization criteria for the selection of calibration points: limiting the maximal error (LME), minimizing the integral square error (ISE), and minimizing the integral absolute error (IAE). Each of these criteria needs reference inputs whose values are symmetrical with respect to the midrange input (x{sub c}), have the form x{sub c}{+-}{delta}x/(2{radical}n) when the measurand has a uniform probability distribution function, {delta}x being the measurement span, and do not depend on the nonlinearity of the actual response, provided this is quadratic. The factor n depends on the particular criterion selected: n=2 for LME, n=3 for ISE, and n=4 for IAE. These three criteria give parallel calibration lines and can also be applied to other nonlinear responses by dividing the measurement span into convenient intervals. The application of those criteria to the

  3. Optimal two-point static calibration of measurement systems with quadratic response

    NASA Astrophysics Data System (ADS)

    Pallàs-Areny, Ramon; Jordana, Josep; Casas, Óscar

    2004-12-01

    Measurement devices and instruments must be calibrated after manufacture to correct for component and assembly tolerances, and periodically to correct for drift and aging effects. The number of reference inputs needed for calibration depends on the actual transfer characteristic and the desired accuracy. Often, a linear characteristic is assumed for simplicity, either for the overall input range (global linearization) or for successive input subranges (piecewise linearization). Thus, only two reference inputs are needed for each straight line. This two-point static calibration can be easily implemented in any system having some basic computation capability and allows for the correction of zero and gain errors, and of their drifts if the system is periodically calibrated. Often, the reference inputs for that calibration are the end values of the measurement range (or subrange). However, this is not always the optimal selection because the calibration error is minimal for those reference inputs only, which are not necessarily the most relevant inputs for the system being considered. This article proposes three optimization criteria for the selection of calibration points: limiting the maximal error (LME), minimizing the integral square error (ISE), and minimizing the integral absolute error (IAE). Each of these criteria needs reference inputs whose values are symmetrical with respect to the midrange input (xc), have the form xc±Δx/(2√n) when the measurand has a uniform probability distribution function, Δx being the measurement span, and do not depend on the nonlinearity of the actual response, provided this is quadratic. The factor n depends on the particular criterion selected: n=2 for LME, n=3 for ISE, and n=4 for IAE. These three criteria give parallel calibration lines and can also be applied to other nonlinear responses by dividing the measurement span into convenient intervals. The application of those criteria to the linearization of a type

  4. Total decoupling of general quadratic pencils, Part II: Structure preserving isospectral flows

    NASA Astrophysics Data System (ADS)

    Chu, Moody T.; Del Buono, Nicoletta

    2008-01-01

    Quadratic pencils, λ2M+λC+K, where M, C, and K are n×n real matrices with or without some additional properties such as symmetry, connectivity, bandedness, or positive definiteness, arise in many important applications. Recently an existence theory has been established, showing that almost all n-degree-of-freedom second-order systems can be reduced to n totally independent single-degree-of-freedom second-order subsystems by real-valued isospectral transformations. In contrast to the common knowledge that generally no three matrices can be diagonalized simultaneously by equivalence transformations, these isospectral transformations endeavor to maintain a special linearization form called the Lancaster structure and do break down M, C and K into diagonal matrices simultaneously. However, these transformations depend on the matrices in a rather complicated way and, hence, are difficult to construct directly. In this paper, a second part of a continuing study, a closed-loop control system that preserves both the Lancaster structure and the isospectrality is proposed as a means to achieve the diagonal reduction. Consequently, these transformations are acquired.

  5. Degradation reliability modeling based on an independent increment process with quadratic variance

    NASA Astrophysics Data System (ADS)

    Wang, Zhihua; Zhang, Yongbo; Wu, Qiong; Fu, Huimin; Liu, Chengrui; Krishnaswamy, Sridhar

    2016-03-01

    Degradation testing is an important technique for assessing life time information of complex systems and highly reliable products. Motivated by fatigue crack growth (FCG) data and our previous study, this paper develops a novel degradation modeling approach, in which degradation is represented by an independent increment process with linear mean and general quadratic variance functions of test time or transformed test time if necessary. Based on the constructed degradation model, closed-form expressions of failure time distribution (FTD) and its percentiles can be straightforwardly derived and calculated. A one-stage method is developed to estimate model parameters and FTD. Simulation studies are conducted to validate the proposed approach, and the results illustrate that the approach can provide reasonable estimates even for small sample size situations. Finally, the method is verified by the FCG data set given as the motivating example, and the results show that it can be considered as an effective degradation modeling approach compared with the multivariate normal model and graphic approach.

  6. Complex complete quadratic combination method for damped system with repeated eigenvalues

    NASA Astrophysics Data System (ADS)

    Yu, Ruifang; Zhou, Xiyuan; Abduwaris, Abduwahit

    2016-09-01

    A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.

  7. Geometry and quadratic nonlinearity of charge transfer complexes in solution: a theoretical study.

    PubMed

    Mukhopadhyay, S; Pandey, Ravindra; Das, Puspendu K; Ramasesha, S

    2011-01-28

    In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO∕S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, β(HRS) and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

  8. ORACLS: A system for linear-quadratic-Gaussian control law design

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  9. Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

    SciTech Connect

    Mukhopadhyay, S.; Ramasesha, S.; Pandey, Ravindra; Das, Puspendu K.

    2011-01-28

    In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, {beta}{sub HRS} and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

  10. Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach.

    PubMed

    Zhang, Xian-Ming; Han, Qing-Long

    2014-06-01

    This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.

  11. A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

    PubMed Central

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-01

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

  12. Quadratic electro-optic effect in the nonconjugated conductive polymer iodine-doped trans-polyisoprene, an organic nanometallic system

    NASA Astrophysics Data System (ADS)

    Shrivastava, S.; Thakur, M.

    2011-05-01

    Thin films of 1,4-trans-polyisoprene have been prepared on various substrates from toluene solution and characterized using Fourier transform infrared (FTIR) spectroscopy, optical absorption spectroscopy and X-ray diffraction before and after doping with iodine. The optical absorption spectrum at low doping shows two peaks: one at 4.2 eV and the other at 3.2 eV. X-ray diffraction indicates an increase of (111) and (122) peak intensities upon doping. Quadratic electro-optic measurements have been made using field-induced birefringence. The Kerr coefficients as measured (3.5×10 -10 m/V 2 at 633 nm and 2.5×10 -10 m/V 2 at 1.55 μm) are exceptionally large, and they have been attributed to the subnanometer-size metallic domains formed upon doping and charge transfer.

  13. SERS assay of telomerase activity at single-cell level and colon cancer tissues via quadratic signal amplification.

    PubMed

    Shi, Muling; Zheng, Jing; Liu, Changhui; Tan, Guixiang; Qing, Zhihe; Yang, Sheng; Yang, Jinfeng; Tan, Yongjun; Yang, Ronghua

    2016-03-15

    As an important biomarker and therapeutic target, telomerase has attracted extensive attention concerning its detection and monitoring. Recently, enzyme-assisted amplification approaches have provided useful platforms for the telomerase activity detection, however, further improvement in sensitivity is still hindered by the single-step signal amplification. Herein, we develop a quadratic signal amplification strategy for ultrasensitive surface-enhanced Raman scattering (SERS) detection of telomerase activity. The central idea of our design is using telomerase-induced silver nanoparticles (AgNPs) assembly and silver ions (Ag(+))-mediated cascade amplification. In our approach, each telomerase-aided DNA sequence extension could trigger the formation of a long double-stranded DNA (dsDNA), making numerous AgNPs assembling along with this long strand through specific Ag-S bond, to form a primary amplification element. For secondary amplification, each conjugated AgNP was dissolved into Ag(+), which can effectively induce the 4-aminobenzenethiol (4-ABT) modified gold nanoparticles (AuNPs@4-ABT) to undergo aggregation to form numerous "hot-spots". Through quadratic amplifications, a limit of detection down to single HeLa cell was achieved. More importantly, this method demonstrated good performance when applied to tissues from colon cancer patients, which exhibits great potential in the practical application of telomerase-based cancer diagnosis in early stages. To demonstrate the potential in screening the telomerase inhibitors and telomerase-targeted drugs, the proposed design is successfully employed to measure the inhibition of telomerase activity by 3'-azido-3'-deoxythymidine.

  14. Maass Forms and Quantum Modular Forms

    NASA Astrophysics Data System (ADS)

    Rolen, Larry

    This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his

  15. An inner-outer nonlinear programming approach for constrained quadratic matrix model updating

    NASA Astrophysics Data System (ADS)

    Andretta, M.; Birgin, E. G.; Raydan, M.

    2016-01-01

    The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil.

  16. Detection of code spread OFDM based on 0-1 integer quadratic programming

    NASA Astrophysics Data System (ADS)

    Elghariani, Ali; Zoltowski, Michael D.

    2012-05-01

    In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.

  17. Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2

    SciTech Connect

    Ellis, John; García, Marcos A.G.; Olive, Keith A.; Nanopoulos, Dimitri V. E-mail: garciagarcia@physics.umn.edu E-mail: olive@physics.umn.edu

    2014-05-01

    The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ∝ φ{sup n} : n ≅ 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

  18. Optimal Linear Quadratic Regulators for Control of Nonlinear Mechanical Systems with Redundant Degrees-of-Freedom

    NASA Astrophysics Data System (ADS)

    Arimoto, Suguru

    An optimal regulator problem for endpoint position control of a robot arm with (or without) redundancy in its total degrees-of-freedom (DOF) is solved by combining Riemannian geometry with nonlinear control theory. Given a target point, within the task-space, that the arm endpoint should reach, a task-space position feedback with joint damping is shown to asymptotically stabilize reaching movements even if the number of DOF of the arm is greater than the dimension of the task space and thereby the inverse kinematics is ill-posed. Usually the speed of convergence of the endpoint trajectory is unsatisfactory, depending on the choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing a performance index composed of an integral of joint dissipation energy plus a linear quadratic form of the task-space control input and output is introduced. It is then shown that the Hamilton-Jacobi-Bellman equation derived from the principle of optimality is solvable in control variables and the Hamilton-Jacobi equation itself has an explicit solution. Although the state of the original dynamics (the Euler-Lagrange equation) with DOF-redundancy contains uncontrollable and unobservable manifolds, the dynamics satisfies a nonlinear version of the Kalman-Yakubovich-Popov lemma and the task-space input-output passivity. An inverse problem of optimal regulator design for robotic arms under the effect of gravity is also tackled by combining Riemannian geometry with passivity-based control theory.

  19. Calculation of eigenfunctions of bounded waveguide with quadratic refractive index

    NASA Astrophysics Data System (ADS)

    Kirilenko, M. S.; Zubtsov, R. O.; Khonina, S. N.

    2016-08-01

    In this work, the one-dimensional finite fractional Fourier transform has been considered in application to gradient optical waveguides. The eigenfunctions of it has been discussed. The relation between obtained functions, Hermite-Gaussian modes and spheroidal functions has been shown. The dependence of input domain width and number of nonzero eigenfunctions of transformation has been demonstrated. The functions which recover its form at given distance from the front plane have been calculated.

  20. Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

    PubMed

    Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

    2016-03-21

    Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics.

  1. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

    PubMed Central

    Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  2. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

    PubMed

    McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

    2013-12-13

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model. PMID:24483652

  3. Convex half-quadratic criteria and interacting auxiliary variables for image restoration.

    PubMed

    Idier, J

    2001-01-01

    This paper deals with convex half-quadratic criteria and associated minimization algorithms for the purpose of image restoration. It brings a number of original elements within a unified mathematical presentation based on convex duality. Firstly, the Geman and Yang's and Geman and Reynolds's constructions are revisited, with a view to establishing the convexity properties of the resulting half-quadratic augmented criteria, when the original nonquadratic criterion is already convex. Secondly, a family of convex Gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the Geman and Reynolds's construction.

  4. Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

    NASA Astrophysics Data System (ADS)

    Sandoval-Santana, J. C.; Ibarra-Sierra, V. G.; Cardoso, J. L.; Kunold, A.

    2016-04-01

    We develop a Lie algebraic approach to systematically calculate the evolution operator of a system described by a generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.

  5. A new one-layer neural network for linear and quadratic programming.

    PubMed

    Gao, Xingbao; Liao, Li-Zhi

    2010-06-01

    In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.

  6. Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential

    NASA Astrophysics Data System (ADS)

    Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei

    2016-07-01

    In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.

  7. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

    PubMed

    McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

    2013-12-13

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

  8. OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE

    PubMed Central

    Xie, Xianchao; Kou, S. C.; Brown, Lawrence

    2015-01-01

    This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778

  9. Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space

    SciTech Connect

    Daszkiewicz, Marcin; Walczyk, Cezary J.

    2008-05-15

    The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.

  10. Genetic analysis of indefinite division in human cells: Evidence for a cell senescence-related gene(s) on human chromosome 4

    SciTech Connect

    Yi Ning; Ledbetter, D.H.; Smith, J.R.; Pereira-Smith, O.M. ); Weber, J.L. ); Killary, A.M. )

    1991-07-01

    Earlier studies had demonstrated that fusion of normal with immortal human cells yielded hybrids having limited division potential. This indicated that the phenotype of limited proliferation (cellular senescence) is dominant and that immortal cells result from recessive changes in normal growth-regulatory genes. In additional studies, the authors exploited the fact that the immortal phenotype is recessive and, by fusing various immortal human cell lines with each other, identified four complementation groups for indefinite division. Assignment of cell lines to specific groups allowed us to take a focused approach to identify the chromosomes and genes involved in growth regulation that have been modified in immortal cells. They report here that introduction of a normal human chromosome 4 into three immortal cell lines (HeLa, J82, T98G) assigned to complementation group B resulted in loss of proliferation and reversal of the immortal phenotype. No effect on the proliferation potential of cell lines representative of the other complementation groups was observed. This result suggests that a gene(s) involved in cellular senescence and normal growth regulation resides on chromosome 4.

  11. Closed-loop structural stability for linear-quadratic optimal systems

    NASA Technical Reports Server (NTRS)

    Wong, P. K.; Athans, M.

    1975-01-01

    This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.

  12. Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.

    PubMed

    Kiselev, Aleksei P; Plachenov, Alexandr B

    2016-04-01

    The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.

  13. Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

    ERIC Educational Resources Information Center

    Schafer, William D.; Wang, Yuh-Yin

    A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

  14. Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.

    PubMed

    Rivera, Mariano; Dalmau, Oscar

    2012-03-01

    We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.

  15. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  16. A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

    ERIC Educational Resources Information Center

    Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

    2012-01-01

    Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

  17. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1980-01-01

    Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

  18. Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

    ERIC Educational Resources Information Center

    Didis, Makbule Gozde; Erbas, Ayhan Kursat

    2015-01-01

    This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…

  19. Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry

    ERIC Educational Resources Information Center

    Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo

    2014-01-01

    The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…

  20. Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

    ERIC Educational Resources Information Center

    Han, Kyung T.; Rudner, Lawrence M.

    2014-01-01

    This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

  1. Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets

    ERIC Educational Resources Information Center

    Benacka, Jan

    2010-01-01

    This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…

  2. Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane

    ERIC Educational Resources Information Center

    McDonald, Todd

    2006-01-01

    This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

  3. Horizontal Distance Travelled by a Mobile Experiencing a Quadratic Drag Force: Normalized Distance and Parametrization

    ERIC Educational Resources Information Center

    Vial, Alexandre

    2007-01-01

    We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…

  4. Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

    ERIC Educational Resources Information Center

    Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

    2011-01-01

    Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

  5. Optical synthetic-aperture radar processor archietecture with quadratic phase-error correction

    SciTech Connect

    Dickey, F.M.; Mason, J.J. )

    1990-10-15

    Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.

  6. Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

    ERIC Educational Resources Information Center

    Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

    2015-01-01

    The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

  7. Optical synthetic-aperture radar processor architecture with quadratic phase-error correction.

    PubMed

    Dickey, F M; Mason, J J

    1990-10-15

    Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.

  8. A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery

    NASA Technical Reports Server (NTRS)

    Athans, M.

    1986-01-01

    In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.

  9. Failures and Inabilities of High School Students about Quadratic Equations and Functions

    ERIC Educational Resources Information Center

    Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma

    2015-01-01

    In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

  10. Calibration of Gurson-type models for porous sheet metals with anisotropic non-quadratic plasticity

    NASA Astrophysics Data System (ADS)

    Gologanu, M.; Kami, A.; Comsa, D. S.; Banabic, D.

    2016-08-01

    The growth and coalescence of voids in sheet metals are not only the main active mechanisms in the final stages of fracture in a necking band, but they also contribute to the forming limits via changes in the normal directions to the yield surface. A widely accepted method to include void effects is the development of a Gurson-type model for the appropriate yield criterion, based on an approximate limit analysis of a unit cell containing a single spherical, spheroidal or ellipsoidal void. We have recently [2] obtained dissipation functions and Gurson-type models for porous sheet metals with ellipsoidal voids and anisotropic non-quadratic plasticity, including yield criteria based on linear transformations (Yld91 and Yld2004-18p) and a pure plane stress yield criteria (BBC2005). These Gurson-type models contain several parameters that depend on the void and cell geometries and on the selected yield criterion. Best results are obtained when these key parameters are calibrated via numerical simulations using the same unit cell and a few representative loading conditions. The single most important such loading condition corresponds to a pure hydrostatic macroscopic stress (pure pressure) and the corresponding velocity field found during the solution of the limit analysis problem describes the expansion of the cavity. However, for the case of sheet metals, the condition of plane stress precludes macroscopic stresses with large triaxiality or ratio of mean stress to equivalent stress, including the pure hydrostatic case. Also, pure plane stress yield criteria like BBC2005 must first be extended to 3D stresses before attempting to develop a Gurson-type model and such extensions are purely phenomenological with no due account for the out- of-plane anisotropic properties of the sheet. Therefore, we propose a new calibration method for Gurson- type models that uses only boundary conditions compatible with the plane stress requirement. For each such boundary condition we use

  11. Mapped quadrats in sagebrush steppe: long-term data for analyzing demographic rates and plant-plant interactions.

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This historical dataset consists of a series of permanent 1-m2 quadrats located on the sagebrush steppe in eastern Idaho, USA. The key aspect of the data is that during each growing season, all individual plants in each quadrat were identified and mapped. The combination of a long time-series with f...

  12. A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

    PubMed Central

    Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

    2012-01-01

    Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data. PMID:22429193

  13. An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

    NASA Technical Reports Server (NTRS)

    Canavos, G. C.

    1974-01-01

    A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

  14. Learning control for minimizing a quadratic cost during repetitions of a task

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang

    1990-01-01

    In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

  15. Error analysis of the quadratic nodal expansion method in slab geometry

    SciTech Connect

    Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.

    1994-10-01

    As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.

  16. Quadratic Herman-Wallis factors in the fundamental bands of linear molecules

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1987-10-01

    General theoretical formulas are derived for the coefficients in the terms M˜12 and M˜13 of the effective molecular dipole moment operator, and applied to the parallel and perpendicular fundamentals of linear molecules. The Herman-Wallis factors for P- and R-branch lines are F PR = [1 + A 1m + A 2PRm 2] 2, m = δ J( J' + J″ + 1)/2 and for Q-branch lines F Q = [1 + A 2QJ ( J + 1)] 2 The quadratic coefficients A2PR and A2Q depend on up to cubic potential derivatives and quadratic dipole derivatives. Calculated A2PR and A2Q values for the fundamentals of CO 2 do not agree well with recent measurements of Johns, and possible reasons for the discrepancies are discussed.

  17. The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

    NASA Technical Reports Server (NTRS)

    Townsend, Barbara K.

    1986-01-01

    A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

  18. Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

    NASA Technical Reports Server (NTRS)

    Koppang, Paul; Leland, Robert

    1996-01-01

    Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

  19. Quadratic spline collocation and parareal deferred correction method for parabolic PDEs

    NASA Astrophysics Data System (ADS)

    Liu, Jun; Wang, Yan; Li, Rongjian

    2016-06-01

    In this paper, we consider a linear parabolic PDE, and use optimal quadratic spline collocation (QSC) methods for the space discretization, proceed the parareal technique on the time domain. Meanwhile, deferred correction technique is used to improve the accuracy during the iterations. The error estimation is presented and the stability is analyzed. Numerical experiments, which is carried out on a parallel computer with 40 CPUs, are attached to exhibit the effectiveness of the hybrid algorithm.

  20. Inter-annual precipitation changes as quadratic signals in the GRACE time-variable gravity

    NASA Astrophysics Data System (ADS)

    Ogawa, R.; Chao, B. F.; Heki, K.

    2009-04-01

    The Gravity Recovery and Climate Experiment (GRACE) satellite mission has been producing scientific results on mass variations on inter-annual timescales, e.g. melting of ice sheet in Greenland and mountain glaciers in Alaska, Eastern Africa drought, water level increase in Caspian Sea, etc. In these discussions only linear trends and the seasonal components have been analyzed in the monthly GRACE time series, whereas little attention has been paid so far to the existence of the quadratic changes which signify the temporal accelerations. With over 6 years of GRACE data and revisiting the time-variable gravity field of various regions, we find that such acceleration/deceleration terms are quite often significantly different from zero. They include East Africa, near Obi River, Caspian Sea, Black Sea, Central Asia, and southern South America, whereof discussions of linear trends without specifying the epochs are inadequate. Here we investigate geophysical implication of these quadratic terms; in particular gravity changes in land areas reflect, to a large extent, soil moisture variations. Soil moisture is the time integration of water fluxes, i.e. precipitation, evapotranspiration and runoff. Here we consider that the linear trend in precipitation is responsible for the quadratic change in gravity, and examine trends of observed precipitation in various regions from CMAP (Climate Prediction Center Merged Analysis of Precipitation). Thus, in order to compare linear trend in CMAP and acceleration in GRACE, we calculate month-to-month difference of equivalent water depth at GRACE grid points, and modeled them with seasonal variations and linear trends. We found good agreement between their geographical distributions although amplitudes are smaller in GRACE, meaning the quadratic gravity changes in the GRACE data do reflect inter-annual changes of precipitation fairly faithfully.

  1. Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  2. Random vibrations of quadratic damping systems. [optimum damping analysis for automobile suspension system

    NASA Technical Reports Server (NTRS)

    Sireteanu, T.

    1974-01-01

    An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.

  3. Quadratically convergent algorithm for fractional occupation numbers in density functional theory

    NASA Astrophysics Data System (ADS)

    Cancès, Eric; Kudin, Konstantin N.; Scuseria, Gustavo E.; Turinici, Gabriel

    2003-03-01

    The numerical solution of the electronic structure problem in Kohn-Sham density functional theory may in certain cases yield fractional occupancy of the single-particle orbitals. In this paper, we propose a quadratically convergent approach for simultaneous optimization of orbitals and occupancies in systems with fractional occupation numbers (FONs). The starting guess for orbitals and FONs is obtained via the relaxed constraint algorithm. Numerical results are presented for benchmark cases.

  4. A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

    NASA Technical Reports Server (NTRS)

    Hanson, R. J.; Krogh, Fred T.

    1992-01-01

    A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

  5. A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

    NASA Astrophysics Data System (ADS)

    Mestel, B. D.; Osbaldestin, A. H.

    2004-10-01

    We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

  6. Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

    NASA Astrophysics Data System (ADS)

    Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

    Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

  7. Interpretation of the power response of a fuel cell with a quadratic logistic differential equation

    SciTech Connect

    Gonzalez, E.R.

    1996-06-01

    The interpretation of the behavior of a fuel cell may be done on the basis of models that require specific assumptions on both the description of the system and the mathematical treatment. This work shows that the power response of a fuel cell can be described by a quadratic logistic differential equation. In this way the interpretation of the dynamical behavior of the system can be done with the general concepts of dissipation, nonlinearity, and feedback.

  8. Tilt measurement and compensation algorithm for holographic data storage with optimized quadratic windows

    NASA Astrophysics Data System (ADS)

    Son, Kyungchan; Lim, Sung-Yong; Lee, Jae-seong; Jeong, Wooyoung; Yang, Hyunseok

    2016-09-01

    In holographic data storage, tilt is one of the critical disturbances. There are two types of tilt: tangential and radial. In real systems, tangential and radial tilt occur simultaneously. Thus, it is difficult to measure and compensate for tilt. In this study, using a quadratic window, which compares the intensity of a certain area, a tilt error signal was generated and compensated for with the proposed algorithm. The compensated image obtained satisfied a 0.3 dB tolerance.

  9. A path-following interior-point algorithm for linear and quadratic problems

    SciTech Connect

    Wright, S.J.

    1993-12-01

    We describe an algorithm for the monotone linear complementarity problem that converges for many positive, not necessarily feasible, starting point and exhibits polynomial complexity if some additional assumptions are made on the starting point. If the problem has a strictly complementary solution, the method converges subquadratically. We show that the algorithm and its convergence extend readily to the mixed monotone linear complementarity problem and, hence, to all the usual formulations of the linear programming and convex quadratic programming problems.

  10. Bifurcation Diagrams and Quotient Topological Spaces Under the Action of the Affine Group of a Family of Planar Quadratic Vector Fields

    NASA Astrophysics Data System (ADS)

    Cerba Diaconescu, Oxana; Schlomiuk, Dana; Vulpe, Nicolae

    In this article, we consider the class QSL4{u +vc+w^c, ∞ } of all real quadratic differential systems (dx)/(dt) = p(x, y), (dy)/(dt) = q(x, y) with gcd(p, q) = 1, having invariant lines of total multiplicity four and two complex and one real infinite singularities. We first construct compactified canonical forms for the class QSL4{u +vc+w^c, ∞ } so as to include limit points in the 12-dimensional parameter space of this class. We next construct the bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits and we show that these are due to many symmetries under the group action. To retain the essence of the dynamics we finally construct the quotient spaces under the action of the group G = Aff(2, ℝ) × ℝ* of affine transformations and time homotheties and we place the phase portraits in these quotient spaces. The final diagrams retain only the necessary information to capture the dynamics under the motion in the parameter space as well as under this group action. We also present here necessary and sufficient conditions for an affine line to be invariant of multiplicity k for a quadratic system.

  11. Emotion suppression moderates the quadratic association between RSA and executive function

    PubMed Central

    Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

    2016-01-01

    There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

  12. Fast-rolling shutter compensation based on piecewise quadratic approximation of a camera trajectory

    NASA Astrophysics Data System (ADS)

    Lee, Yun Gu; Kai, Guo

    2014-09-01

    Rolling shutter effect commonly exists in a video camera or a mobile phone equipped with a complementary metal-oxide semiconductor sensor, caused by a row-by-row exposure mechanism. As video resolution in both spatial and temporal domains increases dramatically, removing rolling shutter effect fast and effectively becomes a challenging problem, especially for devices with limited hardware resources. We propose a fast method to compensate rolling shutter effect, which uses a piecewise quadratic function to approximate a camera trajectory. The duration of a quadratic function in each segment is equal to one frame (or half-frame), and each quadratic function is described by an initial velocity and a constant acceleration. The velocity and acceleration of each segment are estimated using only a few global (or semiglobal) motion vectors, which can be simply predicted from fast motion estimation algorithms. Then geometric image distortion at each scanline is inferred from the predicted camera trajectory for compensation. Experimental results on mobile phones with full-HD video demonstrate that our method can not only be implemented in real time, but also achieve satisfactory visual quality.

  13. A new gradient-based neural network for solving linear and quadratic programming problems.

    PubMed

    Leung, Y; Chen, K Z; Jiao, Y C; Gao, X B; Leung, K S

    2001-01-01

    A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality constraints are properly handled. The simulation results show that the proposed neural network is feasible and efficient.

  14. Frequency-independent approach to calculate physical optics radiations with the quadratic concave phase variations

    NASA Astrophysics Data System (ADS)

    Wu, Yu Mao; Teng, Si Jia

    2016-11-01

    In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this work makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.

  15. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  16. Quadratic nonlinear models for optimizing electrostatic separation of crushed waste printed circuit boards using response surface methodology.

    PubMed

    Qin, Yufei; Wu, Jiang; Zhou, Quan; Xu, Zhenming

    2009-08-15

    The electrostatic separation has proved to be an effective and environment-friendly treatment for the recovery of crushed waste printed circuit boards (PCBs). In this paper a more sophisticated response surface methodology was applied to build quadratic models and optimize the three main factors on a roll-type electrostatic separator. The sample of granular mixture got from crushed PCB wastes (size 0.3-0.45 mm, containing 25% metal and 75% nonmetal). According to the analysis of the experiment data, some quadratic effects were found, and two quadratic models for conductor production (C) and middling production (M) were established. The results indicated that the high voltage level and roll speed are the most important factors for the process. Because of the existence of the quadratic effect, the highest efficiency can also be achieved at a lower voltage level (27-29 kV) compared with a maximum voltage level.

  17. Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling.

    PubMed

    Rodríguez, K; Argüelles, A; Colomé-Tatché, M; Vekua, T; Santos, L

    2010-07-30

    We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.

  18. Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling

    SciTech Connect

    Rodriguez, K.; Argueelles, A.; Colome-Tatche, M.; Vekua, T.; Santos, L.

    2010-07-30

    We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2) x SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Neel order in spin-1/2 gases.

  19. On a two-dimensional Schrödinger equation with a magnetic field with an additional quadratic integral of motion

    NASA Astrophysics Data System (ADS)

    Marikhin, V. G.

    2011-10-01

    The problem of commuting quadratic quantum operators with a magnetic field has been considered. It has been shown that any such pair can be reduced to the canonical form, which makes it possible to construct an almost complete classification of the solutions of equations that are necessary and sufficient for a pair of operators to commute with each other. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables; this change is similar to that in the theory of integrable tops. As an example, this procedure has been considered for the two-dimensional Schrödinger equation with the magnetic field; this equation has an additional quantum integral of motion.

  20. A versatile immobilization-free photoelectrochemical biosensor for ultrasensitive detection of cancer biomarker based on enzyme-free cascaded quadratic amplification strategy.

    PubMed

    Ge, Lei; Wang, Wenxiao; Hou, Ting; Li, Feng

    2016-03-15

    In this work, an ultrasensitive immobilization-free photoelectrochemical (PEC) biosensor was successfully developed for the first time based on a novel enzyme-free cascaded quadratic signal amplification strategy. This rationally designed homogeneous dual amplification strategy consists of a target-analog recycling circuit based on catalytic hairpin assembly (CHA) and a hybridization chain reaction (HCR) mediated amplification circuit. In the presence of carcinoembryonic antigen (CEA), a proof-of-concept target, target-analog is released to trigger the upstream CHA recycling circuit. The generated dsDNA complexes from CHA recycling could further induce the downstream HCR amplification, leading to the formation of numerous hemin/G-quadruplex DNAzymes. This would accordingly stimulate the biocatalytic precipitation of 4-chloro-1-naphthol, inducing a distinct decrease in the photocurrent signal due to the formed insoluble/insulating products on electrode surface. Under the optimal conditions, this PEC biosensor achieved ultrasensitive detection of CEA down to the atto-gram level. The introduction of this aptamer-based cascaded quadratic amplification strategy not only remarkably improves the selectivity and sensitivity of CEA assay, but also allows the ultrasensitive detection of other proteins by designing specific aptamers, providing a universal, isothermal and label-free PEC biosensing platform for ultrasensitive detection of different kinds of cancer biomarkers and holding a great potential for early-diagnosis of cancer.

  1. On the Impact of a Quadratic Acceleration Term in the Analysis of Position Time Series

    NASA Astrophysics Data System (ADS)

    Bogusz, Janusz; Klos, Anna; Bos, Machiel Simon; Hunegnaw, Addisu; Teferle, Felix Norman

    2016-04-01

    The analysis of Global Navigation Satellite System (GNSS) position time series generally assumes that each of the coordinate component series is described by the sum of a linear rate (velocity) and various periodic terms. The residuals, the deviations between the fitted model and the observations, are then a measure of the epoch-to-epoch scatter and have been used for the analysis of the stochastic character (noise) of the time series. Often the parameters of interest in GNSS position time series are the velocities and their associated uncertainties, which have to be determined with the highest reliability. It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. This non-linear motion could be a response to purely geophysical processes, for example, elastic rebound of the Earth's crust due to ice mass loss in Greenland, artefacts due to deficiencies in bias mitigation models, for example, of the GNSS satellite and receiver antenna phase centres, or any combination thereof. In this study we have simulated 20 time series with different stochastic characteristics such as white, flicker or random walk noise of length of 23 years. The noise amplitude was assumed at 1 mm/y-/4. Then, we added the deterministic part consisting of a linear trend of 20 mm/y (that represents the averaged horizontal velocity) and accelerations ranging from minus 0.6 to plus 0.6 mm/y2. For all these data we estimated the noise parameters with Maximum Likelihood Estimation (MLE) using the Hector software package without taken into account the non-linear term. In this way we set the benchmark to then investigate how the noise properties and velocity uncertainty may be affected by any un-modelled, non-linear term. The velocities and their uncertainties versus the accelerations for

  2. A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

    NASA Astrophysics Data System (ADS)

    Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.

    2009-12-01

    A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

  3. Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions

    PubMed Central

    Li, Chunhua; Hayashi, Nakao

    2014-01-01

    The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2-dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in n-dimensional space, where n ≥ 2. The existence of scattering operators and finite time blow-up of the solutions for the systems in higher space dimensions is also shown. PMID:25143965

  4. Thermodynamical first laws of black holes in quadratically-extended gravities

    NASA Astrophysics Data System (ADS)

    Fan, Zhong-Ying; Lü, H.

    2015-03-01

    Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical, toric, or hyperbolic isometries in these theories. This allows us to derive or rederive the first laws for a wide range of black holes in the literature. Furthermore, we construct many new exact solutions and obtain their first laws.

  5. Quadratic algebra for superintegrable monopole system in a Taub-NUT space

    NASA Astrophysics Data System (ADS)

    Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

    2016-09-01

    We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrödinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.

  6. The propagator of the Calogero-Moser system in an external quadratic potential

    NASA Astrophysics Data System (ADS)

    Fleury, M.

    1998-12-01

    We obtain the Hamilton operator of the Calogero-Moser quantum system in an external quadratic potential by conjugating the radial part for the action of SO( n) by conjugacy of the Hamilton operator of the quantum harmonic oscillator on the Euclidean vector space of real symmetric matrices. Then, with Mehler's formula, we derive the propagator of the problem. We also investigate some schemes to change the interaction constant. For two-particle systems, we obtain explicit formulae, whereas for many-particle systems, we reduce the computation of the propagator to finding a definite integral. We give also the short time approximation, the energy levels and the trace of the propagation operator.

  7. Applications of a quadratic extended interior penalty function for structural optimization

    NASA Technical Reports Server (NTRS)

    Haftka, R. T.; Starnes, J. H., Jr.

    1975-01-01

    A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.

  8. Thin-shell wormholes with a double layer in quadratic F (R ) gravity

    NASA Astrophysics Data System (ADS)

    Eiroa, Ernesto F.; Figueroa Aguirre, Griselda

    2016-08-01

    We present a family of spherically symmetric Lorentzian wormholes in quadratic F (R ) gravity, with a thin shell of matter corresponding to the throat. At each side of the shell, the geometry has a different constant value of the curvature scalar R . The junction conditions determine the equation of state between the pressure and energy density at the throat, where a double layer is also located. We analyze the stability of the configurations under perturbations preserving the spherical symmetry. In particular, we study thin-shell wormholes with mass and charge. We find that there exist values of the parameters for which stable static solutions are possible.

  9. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

    1989-01-01

    A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

  10. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  11. Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

  12. The quarter-point quadratic isoparametric element as a singular element for crack problems

    NASA Technical Reports Server (NTRS)

    Hussain, M. A.; Lorensen, W. E.; Pflegel, G.

    1976-01-01

    The quadratic isoparametric elements which embody the inverse square root singularity are used for calculating the stress intensity factors at tips of cracks. The strain singularity at a point or an edge is obtained in a simple manner by placing the mid-side nodes at quarter points in the vicinity of the crack tip or an edge. These elements are implemented in NASTRAN as dummy elements. The method eliminates the use of special crack tip elements and in addition, these elements satisfy the constant strain and rigid body modes required for convergence.

  13. Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence

    NASA Astrophysics Data System (ADS)

    Fortunati, Alessandro; Wiggins, Stephen

    2014-09-01

    The aim of this paper is to prove a Kolmogorov type result for a nearly integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists in the possibility to choose an arbitrarily small decaying coefficient consistently with the perturbation size. The proof, based on the Lie series formalism, is a generalization of a work by A. Giorgilli.

  14. Patent Network Analysis and Quadratic Assignment Procedures to Identify the Convergence of Robot Technologies

    PubMed Central

    Lee, Woo Jin; Lee, Won Kyung

    2016-01-01

    Because of the remarkable developments in robotics in recent years, technological convergence has been active in this area. We focused on finding patterns of convergence within robot technology using network analysis of patents in both the USPTO and KIPO. To identify the variables that affect convergence, we used quadratic assignment procedures (QAP). From our analysis, we observed the patent network ecology related to convergence and found technologies that have great potential to converge with other robotics technologies. The results of our study are expected to contribute to setting up convergence based R&D policies for robotics, which can lead new innovation. PMID:27764196

  15. A simplified dual neural network for quadratic programming with its KWTA application.

    PubMed

    Liu, Shubao; Wang, Jun

    2006-11-01

    The design, analysis, and application of a new recurrent neural network for quadratic programming, called simplified dual neural network, are discussed. The analysis mainly concentrates on the convergence property and the computational complexity of the neural network. The simplified dual neural network is shown to be globally convergent to the exact optimal solution. The complexity of the neural network architecture is reduced with the number of neurons equal to the number of inequality constraints. Its application to k-winners-take-all (KWTA) operation is discussed to demonstrate how to solve problems with this neural network.

  16. Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras

    NASA Technical Reports Server (NTRS)

    Byrnes, C. I.

    1980-01-01

    It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

  17. Quadratic and rate-independent limits for a large-deviations functional

    NASA Astrophysics Data System (ADS)

    Bonaschi, Giovanni A.; Peletier, Mark A.

    2016-07-01

    We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers' law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ` L log L' gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.

  18. Finding common quadratic Lyapunov functions for switched linear systems using particle swarm optimisation

    NASA Astrophysics Data System (ADS)

    Ordóñez-Hurtado, R. H.; Duarte-Mermoud, M. A.

    2012-01-01

    It is undoubtedly important to be able to ensure the existence of a common quadratic Lyapunov function (CQLF) for a given switched system because this is proof of its asymptotic stability, but equally important is the ability to calculate it in order to obtain more specific information about the behaviour of the switched system under analysis. This article describes the development of a new methodology for calculating a CQLF based on particle swarm optimisation (PSO) once the existence of a CQLF has been assured. Several comparative analyses are presented to show the strengths and advantages of the proposed methodology.

  19. A Bi-Projection Neural Network for Solving Constrained Quadratic Optimization Problems.

    PubMed

    Xia, Youshen; Wang, Jun

    2016-02-01

    In this paper, a bi-projection neural network for solving a class of constrained quadratic optimization problems is proposed. It is proved that the proposed neural network is globally stable in the sense of Lyapunov, and the output trajectory of the proposed neural network will converge globally to an optimal solution. Compared with existing projection neural networks (PNNs), the proposed neural network has a very small model size owing to its bi-projection structure. Furthermore, an application to data fusion shows that the proposed neural network is very effective. Numerical results demonstrate that the proposed neural network is much faster than the existing PNNs.

  20. A new linear quadratic optimal controller for the 34-meter high efficiency antenna position loop

    NASA Technical Reports Server (NTRS)

    Nickerson, J. A.

    1987-01-01

    The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.

  1. Mechanistic model of radiation-induced cancer after fractionated radiotherapy using the linear-quadratic formula

    SciTech Connect

    Schneider, Uwe

    2009-04-15

    A simple mechanistic model for predicting cancer induction after fractionated radiotherapy is developed. The model is based upon the linear-quadratic model. The inductions of carcinomas and sarcomas are modeled separately. The linear-quadratic model of cell kill is applied to normal tissues which are unintentionally irradiated during a cancer treatment with radiotherapy. Tumor induction is modeled such that each transformation process results in a tumor cell. The microscopic transformation parameter was chosen such that in the limit of low dose and acute exposure, the parameters of the linear-no-threshold model for tumor induction were approached. The differential equations describing carcinoma and sarcoma inductions can be solved analytically. Cancer induction in this model is a function of treatment dose, the cell kill parameters ({alpha},{beta}), the tumor induction variable ({mu}), and the repopulation parameter ({xi}). Carcinoma induction shows a bell shaped behavior as long as cell repopulation is small. Assuming large cell repopulation rates, a plateaulike function is approached. In contrast, sarcoma induction is negligible for low doses and increases with increasing dose up to a constant value. The proposed model describes carcinoma and sarcoma inductions after fractionated radiotherapy as an analytical function of four parameters. In the limit of low dose and for an instant irradiation it reproduces the results of the linear-no-threshold model. The obtained dose-response curves for cancer induction can be implemented with other models such as the organ-equivalent dose model to predict second cancers after radiotherapy.

  2. A reduced successive quadratic programming strategy for errors-in-variables estimation.

    SciTech Connect

    Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

    1992-01-01

    Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases at least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.

  3. Airborne gravimetry data sparse reconstruction via L1-norm convex quadratic programming

    NASA Astrophysics Data System (ADS)

    Yang, Ya-Peng; Wu, Mei-Ping; Tang, Gang

    2015-06-01

    In practice, airborne gravimetry is a sub-Nyquist sampling method because of the restrictions imposed by national boundaries, financial cost, and database size. In this study, we analyze the sparsity of airborne gravimetry data by using the discrete Fourier transform and propose a reconstruction method based on the theory of compressed sensing for large-scale gravity anomaly data. Consequently, the reconstruction of the gravity anomaly data is transformed to a L1-norm convex quadratic programming problem. We combine the preconditioned conjugate gradient algorithm (PCG) and the improved interior-point method (IPM) to solve the convex quadratic programming problem. Furthermore, a flight test was carried out with the homegrown strapdown airborne gravimeter SGA-WZ. Subsequently, we reconstructed the gravity anomaly data of the flight test, and then, we compared the proposed method with the linear interpolation method, which is commonly used in airborne gravimetry. The test results show that the PCG-IPM algorithm can be used to reconstruct large-scale gravity anomaly data with higher accuracy and more effectiveness than the linear interpolation method.

  4. Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings

    NASA Astrophysics Data System (ADS)

    Zhang, Lin; Kong, Hong-Yan

    2014-02-01

    Many works are based on the steady-state analysis of mean-value dynamics in electro- or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x0 but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.

  5. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  6. The design of dual-mode complex signal processors based on quadratic modular number codes

    NASA Astrophysics Data System (ADS)

    Jenkins, W. K.; Krogmeier, J. V.

    1987-04-01

    It has been known for a long time that quadratic modular number codes admit an unusual representation of complex numbers which leads to complete decoupling of the real and imaginary channels, thereby simplifying complex multiplication and providing error isolation between the real and imaginary channels. This paper first presents a tutorial review of the theory behind the different types of complex modular rings (fields) that result from particular parameter selections, and then presents a theory for a 'dual-mode' complex signal processor based on the choice of augmented power-of-2 moduli. It is shown how a diminished-1 binary code, used by previous designers for the realization of Fermat number transforms, also leads to efficient realizations for dual-mode complex arithmetic for certain augmented power-of-2 moduli. Then a design is presented for a recursive complex filter based on a ROM/ACCUMULATOR architecture and realized in an augmented power-of-2 quadratic code, and a computer-generated example of a complex recursive filter is shown to illustrate the principles of the theory.

  7. Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

    PubMed

    Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

    2016-02-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition.

  8. Quadratic Herman-Wallis contributions associated with vibration-rotation resonances

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1988-12-01

    The quadratic terms A2PRm2 and A2QJ( J + 1) in the Herman-Wallis correction factors for infrared line intensities in linear molecules are normally small for transitions between nonresonant states, but significant values are obtained for transitions involving states perturbed by Fermi or l-type resonance. Detailed equations are given for these quadratic Herman-Wallis terms in transitions from a nonresonant state to the Fermi dyad [(1, 0 0, V' 3), (0, 2 0, V' 3)] together with its l-resonance partner (0, 2 2 e, V' 3). Applications to the parallel bands [(1, 0 0, 1), (0, 2 0, 1)] ← (0, 0 0, 0) and the perpendicular bands [(1, 0 0, 0), (0, 2 0, 0), (0, 2 2, 0)] ← (0, 1 1, 0) of CO 2 and to the parallel bands [(1, 0 0, 0), (0, 2 0, 0)] ← (0, 0 0, 0) of N 2O give good agreement with recent measurements. In particular, the pattern of A2 coefficients in the three perpendicular bands of CO 2, in which the A2 coefficients have been found by Johns to be small for all three pairs of P and R branches and for the Q branch to the l = 2 component, but not for the Q branches to the l = 0 components, is shown to be due to cancellations between contributions in all branches except these two Q branches.

  9. Modelling Ocean Dissipation in Icy Satellites: A Comparison of Linear and Quadratic Friction

    NASA Astrophysics Data System (ADS)

    Hay, H.; Matsuyama, I.

    2015-12-01

    Although subsurface oceans are confirmed in Europa, Ganymede, Callisto, and strongly suspected in Enceladus and Titan, the exact mechanism required to heat and maintain these liquid reservoirs over Solar System history remains a mystery. Radiogenic heating can supply enough energy for large satellites whereas tidal dissipation provides the best explanation for the presence of oceans in small icy satellites. The amount of thermal energy actually contributed to the interiors of these icy satellites through oceanic tidal dissipation is largely unquantified. Presented here is a numerical model that builds upon previous work for quantifying tidally dissipated energy in the subsurface oceans of the icy satellites. Recent semi-analytical models (Tyler, 2008 and Matsuyama, 2014) have solved the Laplace Tidal Equations to estimate the time averaged energy flux over an orbital period in icy satellite oceans, neglecting the presence of a solid icy shell. These models are only able to consider linear Rayleigh friction. The numerical model presented here is compared to one of these semi-analytical models, finding excellent agreement between velocity and displacement solutions for all three terms to the tidal potential. Time averaged energy flux is within 2-6% of the analytical values. Quadratic (bottom) friction is then incorporated into the model, replacing linear friction. This approach is commonly applied to terrestrial ocean dissipation studies where dissipation scales nonlinearly with velocity. A suite of simulations are also run for the quadratic friction case which are then compared to and analysed against recent scaling laws developed by Chen and Nimmo (2013).

  10. Human detection by quadratic classification on subspace of extended histogram of gradients.

    PubMed

    Satpathy, Amit; Jiang, Xudong; Eng, How-Lung

    2014-01-01

    This paper proposes a quadratic classification approach on the subspace of Extended Histogram of Gradients (ExHoG) for human detection. By investigating the limitations of Histogram of Gradients (HG) and Histogram of Oriented Gradients (HOG), ExHoG is proposed as a new feature for human detection. ExHoG alleviates the problem of discrimination between a dark object against a bright background and vice versa inherent in HG. It also resolves an issue of HOG whereby gradients of opposite directions in the same cell are mapped into the same histogram bin. We reduce the dimensionality of ExHoG using Asymmetric Principal Component Analysis (APCA) for improved quadratic classification. APCA also addresses the asymmetry issue in training sets of human detection where there are much fewer human samples than non-human samples. Our proposed approach is tested on three established benchmarking data sets--INRIA, Caltech, and Daimler--using a modified Minimum Mahalanobis distance classifier. Results indicate that the proposed approach outperforms current state-of-the-art human detection methods. PMID:23708804

  11. Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin

    NASA Astrophysics Data System (ADS)

    Vines, Justin; Kunst, Daniela; Steinhoff, Jan; Hinderer, Tanja

    2016-05-01

    We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamiltonian for the test-body limit of the spinning two-body problem in general relativity, valid for generic orbits and spin orientations, to quadratic order in the test spin. This fully relativistic Hamiltonian is then expanded in post-Newtonian orders and in powers of the Kerr spin parameter, allowing comparisons with the test-mass limits of available post-Newtonian results. Both the fully relativistic Hamiltonian and the results of its expansion can inform the construction of waveform models, especially effective-one-body models, for the analysis of gravitational waves from compact binaries.

  12. Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin

    NASA Astrophysics Data System (ADS)

    Vines, Justin; Kunst, Daniela; Steinhoff, Jan; Hinderer, Tanja

    2016-03-01

    We derive a Hamiltonian for an extended spinning test-body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamiltonian for the test-body limit of the spinning two-body problem in general relativity, valid for generic orbits and spin orientations, to quadratic order in the test spin. This fully relativistic Hamiltonian is then expanded in post-Newtonian orders and in powers of the Kerr spin parameter, allowing comparisons with and extensions of the test-mass limits of available post-Newtonian results. Both the fully relativistic Hamiltonian and the results of its expansion can inform the construction of waveform models, especially effective-one-body models, for the analysis of gravitational waves from compact binaries.

  13. Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

    NASA Technical Reports Server (NTRS)

    Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

    2009-01-01

    The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

  14. Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

    PubMed Central

    Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

    2016-01-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

  15. On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

    NASA Technical Reports Server (NTRS)

    Younis, Bassam A.; Gatski, Thomas B.; Speziale, Charles G.

    1994-01-01

    Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

  16. An analysis of spectral envelope-reduction via quadratic assignment problems

    NASA Technical Reports Server (NTRS)

    George, Alan; Pothen, Alex

    1994-01-01

    A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

  17. Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy's law

    NASA Astrophysics Data System (ADS)

    Liu, Wenchao; Yao, Jun; Chen, Zhangxin; Liu, Yuewu

    2016-02-01

    A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy's flow problem, the exact analytical solution for the case of Darcy's flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.

  18. A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming.

    PubMed

    Liu, Q; Wang, J

    2008-04-01

    In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.

  19. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

    PubMed Central

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

  20. Typical Orbits of Quadratic Polynomials with a Neutral Fixed Point: Brjuno Type

    NASA Astrophysics Data System (ADS)

    Cheraghi, Davoud

    2013-09-01

    We describe the topological behavior of typical orbits of complex quadratic polynomials {P_{α}(z) = e^{2 π α {i}} z + z2}, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.

  1. An efficient ensemble of radial basis functions method based on quadratic programming

    NASA Astrophysics Data System (ADS)

    Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian

    2016-07-01

    Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.

  2. Dynamics of an optomechanical system with quadratic coupling: Effect of first order correction to adiabatic elimination

    PubMed Central

    Jiang, Cheng; Cui, Yuanshun; Chen, Guibin

    2016-01-01

    We explore theoretically the dynamics of an optomechanical system in which a resonantly driven cavity mode is quadratically coupled to the displacement of a mechanical resonator. Considering the first order correction to adiabatic elimination, we obtain the analytical expression of optomechanical damping rate which is negative and depends on the position of the mechanical resonator. After comparing the numerical results between the full simulation of Langevin equations, adiabatic elimination, and first order correction to adiabatic elimination, we explain the dynamics of the system in terms of overall mechanical potential and optomechanical damping rate. The antidamping induced by radiation pressure can result in self-sustained oscillation of the mechanical resonator. Finally, we discuss the time evolution of the intracavity photon number, which also shows that the effect of first order correction cannot be neglected when the ratio of the cavity decay rate to the mechanical resonance frequency becomes smaller than a critical value. PMID:27752125

  3. Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Lorenz, C. F.

    1979-01-01

    Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

  4. Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

    NASA Technical Reports Server (NTRS)

    Badavi, F. F.; Everhart, Joel L.

    1987-01-01

    This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

  5. Thermodynamics of charged rotating black branes in Brans-Dicke theory with quadratic scalar field potential

    SciTech Connect

    Dehghani, M. H.; Pakravan, J.; Hendi, S. H.

    2006-11-15

    We construct a class of charged rotating solutions in (n+1)-dimensional Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic potential and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can present black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute the finite Euclidean action through the use of counterterm method, and obtain the conserved and thermodynamic quantities by using the relation between the action and free energy in grand-canonical ensemble. We find that these quantities satisfy the first law of thermodynamics, and the entropy does not follow the area law.

  6. Regularized quadratic cost-function for integrating wave-front gradient fields.

    PubMed

    Villa, Jesús; Rodríguez, Gustavo; Ivanov, Rumen; González, Efrén

    2016-05-15

    From the Bayesian regularization theory we derive a quadratic cost-function for integrating wave-front gradient fields. In the proposed cost-function, the term of conditional distribution uses a central-differences model to make the estimated function well consistent with the observed gradient field. As will be shown, the results obtained with the central-differences model are superior to the results obtained with the backward-differences model, commonly used in other integration techniques. As a regularization term we use an isotropic first-order differences Markov Random-Field model, which acts as a low-pass filter reducing the errors caused by the noise. We present simulated and real experiments of the proposal applied in the Foucault test, obtaining good results.

  7. Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds

    SciTech Connect

    Devecioglu, Deniz Olgu; Sarioglu, Oezguer

    2011-01-15

    We extend the Abbott-Deser-Tekin procedure of defining conserved quantities of asymptotically constant-curvature spacetimes, and give an analogous expression for the conserved charges of geometries that are solutions of quadratic curvature gravity models in generic D dimensions and that have arbitrary asymptotes possessing at least one Killing isometry. We show that the resulting charge expression correctly reduces to its counterpart when the background is taken to be a space of constant curvature and, moreover, is background gauge invariant. As applications, we compute and comment on the energies of two specific examples: the three-dimensional Lifshitz black hole and a five-dimensional companion of the first, whose energy has never been calculated before.

  8. Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

    NASA Technical Reports Server (NTRS)

    Natarajan, R.; Brown, R. A.

    1986-01-01

    The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

  9. Singular linear-quadratic control problem for systems with linear delay

    SciTech Connect

    Sesekin, A. N.

    2013-12-18

    A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.

  10. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1987-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  11. Observer based output feedback tuning for underwater remotely operated vehicle based on linear quadratic performance

    NASA Astrophysics Data System (ADS)

    Aras, Mohd Shahrieel Mohd; Abdullah, Shahrum Shah; Kamarudin, Muhammad Nizam; Rahman, Ahmad Fadzli Nizam Abdul; Azis, Fadilah Abd; Jaafar, Hazriq Izzuan

    2015-05-01

    This paper describes the effectiveness of observer-based output feedback for Unmanned Underwater Vehicle (UUV) with Linear Quadratic Regulation (LQR) performance. Tuning of observer parameters is crucial for tracking purpose. Prior to tuning facility, the ranges of observer and LQR parameters are obtained via system output cum error. The validation of this technique using unmanned underwater vehicles called Remotely Operated Vehicle (ROV) modelling helps to improve steady state performance of system response. The ROV modeling is focused for depth control using ROV 1 developed by the Underwater Technology Research Group (UTeRG). The results are showing that this technique improves steady state performances in term of overshoot and settling time of the system response.

  12. Decoupled control analysis of a large flexible space antenna with linear quadratic regulator comparisons

    NASA Technical Reports Server (NTRS)

    Young, J. W.; Hamer, H. A.; Johnson, K. G.

    1984-01-01

    A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.

  13. Robust reinforcement learning control using integral quadratic constraints for recurrent neural networks.

    PubMed

    Anderson, Charles W; Young, Peter Michael; Buehner, Michael R; Knight, James N; Bush, Keith A; Hittle, Douglas C

    2007-07-01

    The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning.

  14. Asymptotic performance of the quadratic discriminant function to skewed training samples.

    PubMed

    Adebanji, Atinuke; Asamoah-Boaheng, Michael; Osei-Tutu, Olivia

    2016-01-01

    This study investigates the asymptotic performance of the quadratic discriminant function (QDF) under skewed training samples. The main objective of this study is to evaluate the performance of the QDF under skewed distribution considering different sample size ratios, varying the group centroid separators and the number of variables. Three populations [Formula: see text] with increasing group centroid separator function were considered. A multivariate normal distributed data was simulated with MatLab R2009a. There was an increase in the average error rates of the sample size ratios 1:2:2 and 1:2:3 as the total sample size increased asymptotically in the skewed distribution when the centroid separator increased from 1 to 3. The QDF under the skewed distribution performed better for the sample size ratio 1:1:1 as compared to the other sampling ratios and under centroid separator [Formula: see text]. PMID:27652103

  15. Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

    NASA Technical Reports Server (NTRS)

    Turso, James A.; Litt, Jonathan S.

    2004-01-01

    A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

  16. Study on MAX-MIN Ant System with Random Selection in Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Iimura, Ichiro; Yoshida, Kenji; Ishibashi, Ken; Nakayama, Shigeru

    Ant Colony Optimization (ACO), which is a type of swarm intelligence inspired by ants' foraging behavior, has been studied extensively and its effectiveness has been shown by many researchers. The previous studies have reported that MAX-MIN Ant System (MMAS) is one of effective ACO algorithms. The MMAS maintains the balance of intensification and diversification concerning pheromone by limiting the quantity of pheromone to the range of minimum and maximum values. In this paper, we propose MAX-MIN Ant System with Random Selection (MMASRS) for improving the search performance even further. The MMASRS is a new ACO algorithm that is MMAS into which random selection was newly introduced. The random selection is one of the edgechoosing methods by agents (ants). In our experimental evaluation using ten quadratic assignment problems, we have proved that the proposed MMASRS with the random selection is superior to the conventional MMAS without the random selection in the viewpoint of the search performance.

  17. A quadratic energy minimization framework for signal loss estimation from arbitrarily sampled ultrasound data.

    PubMed

    Hennersperger, Christoph; Mateus, Diana; Baust, Maximilian; Navab, Nassir

    2014-01-01

    We present a flexible and general framework to iteratively solve quadratic energy problems on a non uniform grid, targeted at ultrasound imaging. Therefore, we model input samples as the nodes of an irregular directed graph, and define energies according to the application by setting weights to the edges. To solve the energy, we derive an effective optimization scheme, which avoids both the explicit computation of a linear system, as well as the compounding of the input data on a regular grid. The framework is validated in the context of 3D ultrasound signal loss estimation with the goal of providing an uncertainty estimate for each 3D data sample. Qualitative and quantitative results for 5 subjects and two target regions, namely US of the bone and the carotid artery, show the benefits of our approach, yielding continuous loss estimates. PMID:25485401

  18. Non-Gaussianity and gravitational waves from a quadratic and self-interacting curvaton

    SciTech Connect

    Fonseca, Jose; Wands, David

    2011-03-15

    In this paper we consider how non-Gaussianity of the primordial density perturbation and the amplitude of gravitational waves from inflation can be used to determine parameters of the curvaton scenario for the origin of structure. We show that in the simplest quadratic model, where the curvaton evolves as a free scalar field, measurement of the bispectrum relative to the power spectrum, f{sub NL}, and the tensor-to-scalar ratio can determine both the expectation value of the curvaton field during inflation and its dimensionless decay rate relative to the curvaton mass. We show how these predictions are altered by the introduction of self-interactions, in models where higher-order corrections are determined by a characteristic mass scale and discuss how additional information about primordial non-Gaussianity and scale dependence may constrain curvaton interactions.

  19. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    NASA Astrophysics Data System (ADS)

    Das, S.; Goswami, K.; Datta, B. N.

    2016-05-01

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of a loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Finally the most robust set of feedback matrices is selected from the set of probabilistically characterized optimal closed-loop system to implement the new methodology for design of active controlled structures. Numerical examples are presented to illustrate the proposed methodology.

  20. Numerical Simulation of Three-dimensional Flow Field in Quadrate Stirred Tanks

    NASA Astrophysics Data System (ADS)

    Wu, Y. B.; Feng, W.

    In the paper based on the Computational Fluid Dynamics (CFD) method three-dimensional flow fields are studied using FLUENT software. Sliding mesh method, RNG к - ɛ turbulent model and second-order upwind difference scheme are used to perform the numerical simulation. Firstly, the prediction capabilities of the turbulence models used in the simulation are assessed in detail. Secondly, numerical study is focused on the velocity field of an actual quadrate stirred tank with a dual 45 degrees pitched four-blade turbine in given conditions of design and operation parameters. Finally, the influences of design and operation parameters on mixing effects are analyzed by the simulation of the turbulence intensity. The study provides reference aids for optimization of design and operation parameters.

  1. A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

    NASA Technical Reports Server (NTRS)

    Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.

    1978-01-01

    A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

  2. Skyrmions with quadratic band touching fermions: A way to achieve charge 4e superconductivity

    NASA Astrophysics Data System (ADS)

    Moon, Eun-Gook

    2012-06-01

    We study Skyrmion quantum numbers, charge, and statistics, in (2+1) dimension induced by quadratic band touching (QBT) fermions. It is shown that induced charge of Skyrmions is twice bigger than corresponding Dirac particles’ and their statistics are always bosonic. Applying to the Bernal stacking bilayer graphene, we show that Skyrmions of quantum spin Hall are charge 4e bosons, so their condensation realizes charge 4e superconductivity. The phase transition could be of second order, and one candidate theory of the transition is an O(5) nonlinear sigma model with a nonzero Wess-Zumino-Witten term. We calculate the renormalization group beta function of the model perturbatively and propose a possible phase diagram. We also discuss how QBT fermions are different from two copies of Dirac particles.

  3. Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

    USGS Publications Warehouse

    Lefkoff, L.J.; Gorelick, S.M.

    1986-01-01

    Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

  4. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    SciTech Connect

    Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.

    2014-12-10

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

  5. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    NASA Astrophysics Data System (ADS)

    Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.

    2014-12-01

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

  6. Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

    SciTech Connect

    Di Nunno, Giulia; Khedher, Asma; Vanmaele, Michèle

    2015-12-15

    We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure with infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.

  7. Dispersion of quadratic nonlinearity of polarized films of chromophore-containing polyimides in the range of resonance absorption

    NASA Astrophysics Data System (ADS)

    Yakimansky, A. V.; Nosova, G. I.; Solovskaya, N. A.; Smirnov, N. N.; Plekhanov, A. I.; Simanchuk, A. E.; Gorkovenko, A. I.

    2011-07-01

    Detailed investigations of the second harmonic generation of a series of new chromophore-containing polyimides in the range of their absorption bands are performed. Polymer films with thickness of 100-400 nm were spin-cast on glass substrates and corona poled. For the samples, the quadratic nonlinearity coefficients are determined from the intensity of the second harmonic generation signal. Fundamental wavelength was varied from 800 to 1400 nm. The quadratic nonlinear coefficient d33 of these materials with respect to the reference sample of quartz crystal are estimated. Maximum values of the second harmonic generation coefficient, d33, are 25-50 pm/V.

  8. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  9. Biologically effective dose distribution based on the linear quadratic model and its clinical relevance

    SciTech Connect

    Lee, S.P.; Smathers, J.B.; Withers, H.R.

    1995-09-30

    Radiotherapy plans based on physical dose distributions do not necessarily entirely reflect the biological effects under various fractionation schemes. Over the past decade, the linear-quadratic (LQ) model has emerged as a convenient tool to quantify biological effects for radiotherapy. In this work, we set out to construct a mechanism to display biologically oriented dose distribution based on the LQ model. A computer program that converts a physical dose distribution calculated by a commercially available treatment planning system to a biologically effective dose (BED) distribution has been developed and verified against theoretical calculations. This software accepts a user`s input of biological parameters for each structure of interest (linear and quadratic dose-response and repopulation kinetic parameters), as well as treatment scheme factors (number of fractions, fractional dose, and treatment time). It then presents a two-dimensional BED display in conjunction with anatomical structures. Furthermore, to facilitate clinicians` intuitive comparison with conventional fractionation regimen, a conversion of BED to normalized isoeffective dose (NID) is also allowed. We have demonstrated the feasibility of constructing a biologically oriented dose distribution for clinical practice of radiotherapy. The discordance between physical dose distributions and the biological counterparts based on the given treatment schemes was quantified. The computerized display of BED at nonprescription points greatly enhanced the versatility of this tool. Although the routine use of this implementation in clinical radiotherapy should be cautiously done, depending largely on the accuracy of the published biological parameters, it may, nevertheless, help the clinicians derive an optimal treatment plan with a particular fractionation scheme or use it as a quantitative tool for outcome analysis in clinical research. 45 refs., 3 figs., 5 tabs.

  10. Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

    NASA Astrophysics Data System (ADS)

    Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

    2016-03-01

    To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

  11. Nonhydrostatic correction for shallow water equations with quadratic vertical pressure distribution: A Boussinesq-type equation

    NASA Astrophysics Data System (ADS)

    Jeschke, Anja; Behrens, Jörn

    2015-04-01

    In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.

  12. Quadratic coupling between a classical nanomechanical oscillator and a single spin

    NASA Astrophysics Data System (ADS)

    Dhingra, Shonali

    Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellen theta2 sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NVcontaining diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.

  13. Permission Forms

    ERIC Educational Resources Information Center

    Zirkel, Perry A.

    2005-01-01

    The prevailing practice in public schools is to routinely require permission or release forms for field trips and other activities that pose potential for liability. The legal status of such forms varies, but they are generally considered to be neither rock-solid protection nor legally valueless in terms of immunity. The following case and the…

  14. The method of minimal normal forms

    SciTech Connect

    Mane, S.R.; Weng, W.T.

    1992-01-01

    Normal form methods for solving nonlinear differential equations are reviewed and the comparative merits of three methods are evaluated. The concept of the minimal normal form is explained and is shown to be superior to other choices. The method is then extended to apply to the evaluation of discrete maps of an accelerator or storage ring. Such an extension, as suggested in this paper, is more suited for accelerator-based applications than a formulation utilizing continuous differential equations. A computer code has been generated to systematically implement various normal form formulations for maps in two-dimensional phase space. Specific examples of quadratic and cubic nonlinear fields were used and solved by the method developed. The minimal normal form method shown here gives good results using relatively low order expansions.

  15. The method of minimal normal forms

    SciTech Connect

    Mane, S.R.; Weng, W.T.

    1992-12-31

    Normal form methods for solving nonlinear differential equations are reviewed and the comparative merits of three methods are evaluated. The concept of the minimal normal form is explained and is shown to be superior to other choices. The method is then extended to apply to the evaluation of discrete maps of an accelerator or storage ring. Such an extension, as suggested in this paper, is more suited for accelerator-based applications than a formulation utilizing continuous differential equations. A computer code has been generated to systematically implement various normal form formulations for maps in two-dimensional phase space. Specific examples of quadratic and cubic nonlinear fields were used and solved by the method developed. The minimal normal form method shown here gives good results using relatively low order expansions.

  16. On the convergence of inexact Uzawa algorithms

    SciTech Connect

    Welfert, B.D.

    1994-12-31

    The author considers the solution of symmetric indefinite systems which can be cast in matrix block form, where diagonal blocks A and C are symmetric positive definite and semi-definite, respectively. Systems of this type arise frequently in quadratic minimization problems, as well as mixed finite element discretizations of fluid flow equation. The author uses the Uzawa algorithm to precondition the matrix equations.

  17. Calculation of SHG in periodically poled crystals by specifying a spatially periodic dependence of the quadratic nonlinearity in a single-domain crystal

    SciTech Connect

    Dmitriev, Valentin G; Singh, Ranjit

    2004-10-31

    A method is developed for calculating SHG in linearly homogeneous periodically poled nonlinear crystals (PPNC) by specifying a spatially inhomogeneous periodic distribution of the quadratic-nonlinearity parameter in the form of a 'small-scale' elliptic sine, whose half-period forms one domain with the characteristic 'microplateau' of the nonlinearity parameter and interdomain walls. It is found that, because the domain length should be equal to the coherence length when the quasi-phase-matching condition is fulfilled, and if the coherence length is calculated in the fixed-field approximation, the dependence of the harmonic amplitude on the longitudinal coordinate has the form of a 'large-scale' elliptic sine with a broad 'macroplateau' corresponding to a certain (in the case of quasi-phase matching, to virtually 100%) transformation; however, the mismatch in a domain is never completely compensated by the reciprocal lattice vector. In this case, the phase trajectories inside one domain have the form of a sequence: an unstable focus, a limit cycle ('macroplateau'), a stable focus. This picture repeats in the next domain. It is shown that the width of the SHG phase-matching curve in a PPNC in the regime of strong energy exchange, taking secondary maxima into account, can be considerably (by several times) larger than the width calculated in the fixed-field approximation. (nonlinear optical phenomena)

  18. Good form.

    PubMed

    Sorrel, Amy Lynn

    2015-03-01

    New standardized prior authorization forms for health care services and prescription drugs released by the Texas Department of Insurance promise to alleviate administrative busy work and its related costs.

  19. Some Comments on the Use of de Moivre's Theorem to Solve Quadratic Equations with Real or Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

  20. Target-aptamer binding triggered quadratic recycling amplification for highly specific and ultrasensitive detection of antibiotics at the attomole level.

    PubMed

    Wang, Hongzhi; Wang, Yu; Liu, Su; Yu, Jinghua; Xu, Wei; Guo, Yuna; Huang, Jiadong

    2015-05-14

    A novel electrochemical aptasensor for ultrasensitive detection of antibiotics by combining polymerase-assisted target recycling amplification with strand displacement amplification with the help of polymerase and nicking endonuclease has been reported. This work is the first time that target-aptamer binding triggered quadratic recycling amplification has been utilized for electrochemical detection of antibiotics.

  1. Solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential

    NASA Astrophysics Data System (ADS)

    Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

    2014-11-01

    The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.

  2. A comparison of nested quadrat and point-line intercept sampling methods for fire effects monitoring in shortgrass prairie

    USGS Publications Warehouse

    Benjamin, Pamela K.; Stumpf, Julie A.; Pavlovic, Noel B.

    2003-01-01

    Within the National Park Service (NPS) and other federal land-managing agencies, there has been widespread application of the use of standardized fire-effects monitoring protocols. While standardization is often desirable, researchers and managers have come to recognize that 1 method does not work in all habitats with regard to application and efficiency. In 1999, in response to a wildfire that burned over 2428 ha of prairie habitat within Alibates Flint Quarries National Monument (ALFL) and Lake Meredith National Recreation Area (LAMR), Texas, long-term monitoring using a newer nested quadrat frequency/importance score method was implemented. In 2001, a 2-y study was initiated to compare the time and information-gathering efficacy of the nested quadrat method with the current NPS protocol used for monitoring fire effects within grassland systems. Both sampling methods were performed within burned and unburned mesa-top prairie habitats. No statistically significant differences were detected for total species richness between the 2 methods. However, the point-line intercept transects required significantly more time to sample compared to the nested quadrats. Within shortgrass prairie habitats the nested quadrat method appears to be a more efficient and effective sampling strategy than traditional point-line intercept methods.

  3. Using the method of dual quadratic solutions to solve systems of polynomial equations in the complex domain

    SciTech Connect

    Shor, N.Z.; Berezovskii, O.A.

    1995-05-01

    In general, the dual solutions are applied in the branch and bound scheme to solve the optimization problem. Of special interest, however, are problems that can be reduced to a quadratic problem with {Omega}-property. In this paper, we consider one such problem, namely the problem of solving a system of polynomial equations in complex variables.

  4. A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

    ERIC Educational Resources Information Center

    Kelava, Augustin; Nagengast, Benjamin

    2012-01-01

    Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

  5. Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences

    SciTech Connect

    Keller, Jaime

    2008-09-17

    The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalar forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)

  6. Students' Understanding of the Concept of Vertex of Quadratic Functions in Relation to Their Personal Meaning of the Concept of Vertex

    ERIC Educational Resources Information Center

    Childers, Annie Burns; Vidakovic, Draga

    2014-01-01

    This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or…

  7. Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

    NASA Technical Reports Server (NTRS)

    Kottapalli, Sesi; Leyland, Jane

    2014-01-01

    In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

  8. A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

    PubMed Central

    Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

    2016-01-01

    The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585

  9. AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L. C.

    1984-01-01

    AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

  10. Quadratic nonlinear optical parameters of 7% MgO-doped LiNbO3 crystal

    NASA Astrophysics Data System (ADS)

    Kulyk, B.; Kapustianyk, V.; Figà, V.; Sahraoui, B.

    2016-06-01

    Pure and 7% MgO-doped lithium niobate (LiNbO3) single crystals were grown by the Czochralski technique. The shift of optical absorption edge in 7% MgO-doped crystal in direction of shorter wavelength compared to undoped crystal was observed. The second harmonic generation measurements of 7% MgO-doped LiNbO3 crystal were performed at room temperature by means of the rotational Maker fringe technique using Nd:YAG laser generating at 1064 nm in picoseconds regime. Experimentally obtained value of nonlinear optical coefficient d33 for 7% MgO-doped LiNbO3 was found to be less than for undoped crystal but higher than for 5% MgO-doped. I-type phase-matched second harmonic generation was achieved and the value of phase-matched angle was calculated. High quadratic nonlinearity together with tolerance to intensive laser irradiation makes 7% MgO-doped LiNbO3 crystal interesting for application in optoelectronics.

  11. Linear-quadratic-regulator pointing control system design for a high-altitude balloon payload

    SciTech Connect

    White, J.E.; Etter, J.R.

    1987-11-01

    A pointing control system design for the science package of a NASA high-altitude research balloon is described. The balloon assembly consists of a single helium balloon connected to a payload recovery parachute, payload gondola, and ballast hopper. Pointing of the scientific payload is accomplished via an arrangement of drive motors and a flywheel. Linear quadratic regulator (LQR) synthesis techniques are employed to produce the azimuth and elevation controller designs. The use of LQR synthesis is motivated by the azimuthal dynamic coupling encountered between the balloon and gondola. Two control devices are employed in azimuth, one of which is a decoupler motor and the other a flywheel. The decoupler motor is intended to isolate the gondola from the balloon such that the flywheel can be accelerated or decelerated about a steady-state angular velocity to provide precise azimuthal pointing. The multiple-input/multiple-output nature of the azimuth pointing problem is best handled in a matrix synthesis procedure such as LQR. The controller design methodology is explained, and a combination of time responses and singular value analyses are used to analytically evaluate the performance of the control system. 11 refs., 17 figs.

  12. Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints

    NASA Technical Reports Server (NTRS)

    Burken, John J.; Frost, Susan A.; Taylor, Brian R.

    2011-01-01

    When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.

  13. Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene.

    PubMed

    Pujari, Sumiran; Lang, Thomas C; Murthy, Ganpathy; Kaul, Ribhu K

    2016-08-19

    We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state. PMID:27588872

  14. Changes in Obesity Odds Ratio among Iranian Adults, since 2000: Quadratic Inference Functions Method

    PubMed Central

    Etemad, Koorosh; Seifi, Behjat; Mohammad, Kazem; Biglarian, Akbar; Koohpayehzadeh, Jalil

    2016-01-01

    Background. Monitoring changes in obesity prevalence by risk factors is relevant to public health programs that focus on reducing or preventing obesity. The purpose of this paper was to study trends in obesity odds ratios (ORs) for individuals aged 20 years and older in Iran by using a new statistical methodology. Methods. Data collected by the National Surveys in Iran, from 2000 through 2011. Since responses of the member of each cluster are correlated, the quadratic inference functions (QIF) method was used to model the relationship between the odds of obesity and risk factors. Results. During the study period, the prevalence rate of obesity increased from 12% to 22%. By using QIF method and a model selection criterion for performing stepwise regression analysis, we found that while obesity prevalence generally increased in both sexes, all ages, all employment, residence, and smoking levels, it seems to have changes in obesity ORs since 2000. Conclusions. Because obesity is one of the main risk factors for many diseases, awareness of the differences by factors allows development of targets for prevention and early intervention. PMID:27803729

  15. Wave operators to a quadratic nonlinear Klein-Gordon equation in two space dimensions revisited

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.; Tonegawa, Satoshi

    2012-08-01

    We continue to study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions {(partialt2-Δ+m2) u=λ u2,( t,x) in{R}×{R}2}. We prove that if u1+in{H}^{3/2+3γ,1}( {R}2),{ }u2+in{H}^{1/2+3γ,1}( {R} 2), where {γin( 0,1/4)} and the norm {Vert u1+Vert_{{H}1^{3/2+γ}}+Vert u2+Vert_{{H}1^{1/2+γ}}≤ρ,} then there exist ρ > 0 and T > 1 such that the nonlinear Klein-Gordon equation has a unique global solution {uin{C}( [ T,infty) ;{H}^{1/2}( {R}2) ) } satisfying the asymptotics Vert u( t) -u0 ( t) Vert _{{H}^{1/2}} ≤ Ct^{-1/2-γ} for all t > T, where u 0 denotes the solution of the free Klein-Gordon equation.

  16. Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate

    NASA Astrophysics Data System (ADS)

    Aklouche, Omar; Pelat, Adrien; Maugeais, Sylvain; Gautier, François

    2016-08-01

    An acoustic black hole (ABH) is a pit of power law profile inserted in a plate with internal damping. Such a pit with varying thickness leads to local variations of wave propagation properties and has been found to be an efficient vibration damper. In this paper, the ABH is seen as a penetrable obstacle and is studied through its scattering properties. A wave based model is developed within the framework of the Kirchhoff theory for a thin plate of locally varying thickness. It is shown that analytical solutions can be found in the case of a pit of quadratic profile and for uniform damping properties (without added layer). A major outcome of the model is the derivation of the dispersion relations giving a detailed analysis of the behavior of the waves within the ABH. Particularly, cut-on frequencies below which no wave propagates within the ABH are derived and thus give interpretation of the well known typical ABH efficiency threshold frequency for damping vibrations. The analysis is led from numerical computations of the dispersion curves, the scattering diagrams and the scattering cross-section, which are compared to the case of a simple hole. The results show that the ABH behaves as a resonant scatterer, which is a key outcome of this study. The so-called trapped modes, which describe free damped oscillations of the ABH, are responsible for variations of the scattering cross-section with frequency. These variations are investigated thanks to a parametric study on the geometrical properties of the ABH.

  17. Excited state properties and quadratic optical nonlinearities in charged organic chromophores: Theoretical analysis

    NASA Astrophysics Data System (ADS)

    Inerbaev, Talgat M.; Saito, Shigeki; Belosludov, Rodion V.; Mizuseki, Hiroshi; Takahashi, Masae; Kawazoe, Yoshiyuki

    2006-12-01

    As it has been found experimentally [K. Clays and B. Coe, Chem. Mater. 15, 642 (2003); B. J. Coe et al., 126, 10418 (2004)], elongation of the conjugation path length and N-arylation in stilbazolium chromophores both lead to substantial enhancement of the molecular optical nonlinearities. In the present contribution the authors perform a quantum chemical analysis of the excited state properties and quadratic nonlinear optical responses of a series of this type of dyes. Nonlinear optical responses are estimated by both finite-field and two-state model approaches that demonstrate an excellent qualitative mutual agreement. Time-dependent density functional theory calculations on the isolated cations predict redshift in the energy of the intramolecular charge transfer transition that is overestimated for cations with the longer conjugation path length. At the same time, in comparison with the Stark spectroscopy measurements the differences between the excited and ground state dipole moments are grossly underestimated for all compounds. The inclusion of solvent effect by polarizable continuum model affords a better agreement with experiment for these quantities. The authors' calculations demonstrate the crucial dependence of the electronic excitation properties on the way of the investigated compound geometry optimization. The origin of such dependence is discussed.

  18. Excited state properties and quadratic optical nonlinearities in charged organic chromophores: theoretical analysis.

    PubMed

    Inerbaev, Talgat M; Saito, Shigeki; Belosludov, Rodion V; Mizuseki, Hiroshi; Takahashi, Masae; Kawazoe, Yoshiyuki

    2006-12-21

    As it has been found experimentally [K. Clays and B. Coe, Chem. Mater. 15, 642 (2003); B. J. Coe et al., 126, 10418 (2004)], elongation of the conjugation path length and N-arylation in stilbazolium chromophores both lead to substantial enhancement of the molecular optical nonlinearities. In the present contribution the authors perform a quantum chemical analysis of the excited state properties and quadratic nonlinear optical responses of a series of this type of dyes. Nonlinear optical responses are estimated by both finite-field and two-state model approaches that demonstrate an excellent qualitative mutual agreement. Time-dependent density functional theory calculations on the isolated cations predict redshift in the energy of the intramolecular charge transfer transition that is overestimated for cations with the longer conjugation path length. At the same time, in comparison with the Stark spectroscopy measurements the differences between the excited and ground state dipole moments are grossly underestimated for all compounds. The inclusion of solvent effect by polarizable continuum model affords a better agreement with experiment for these quantities. The authors' calculations demonstrate the crucial dependence of the electronic excitation properties on the way of the investigated compound geometry optimization. The origin of such dependence is discussed. PMID:17190565

  19. Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

    USGS Publications Warehouse

    Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

    1997-01-01

    One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

  20. Multiple target detection in video using quadratic multi-frame correlation filtering

    SciTech Connect

    Kerekes, Ryan A; Kumar, B. V. K. Vijaya

    2008-01-01

    Most integrated target detection and tracking systems employ state-space models to keep track of an explicit number o findividual targets. Recently, a non-state-space framework was developed for enhancing target detection in video by applying probabilistic motion models to the soft information in correlation outputs before thresholding. This framework has been referred to as multi-frame correlation ltering (MFCF), and because it avoids the use of state-space models and the formation of explicit tracks, the framework is well-suited for handling scenes with unknown numbers of targets at unknown positions. In this paper, we propose to use quadratic correlation lters(QCFs)in the MFCF framework for robust target detection. We test our detection algorithm on real and synthe sized single-target and multi-target video sequences. Simulation results show that MFCF can signi cantly reduce (to zero in the best case) the false alarm rates of QCFs at detection rates above 95%in the presence of large amounts of uncorrelated noise. We also show that MFCF is more adept at rejecting those false peaks due to uncorrelated noise rather than those due to clutter and compression noise; consequently, we show that lters used in the framework should be made to favor clutter rejection over noise tolerance.

  1. Irrigation Control in the Presence of Salinity: Extended Linear Quadratic Approach

    NASA Astrophysics Data System (ADS)

    Bras, Rafael L.; Seo, Dong-Jun

    1987-07-01

    An intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic (ELQ) control. The ELQ control is well-suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon. A conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration. For the intraseasonal model to be effective against perennial salt accumulation in the root zone, it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season, thus avoiding any significant leaching prior to the next growing season. This long-term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level. The ELQ control is employed in a case study of expected net benefit maximization over an irrigation season of corn in Fort Morgan, Colorado. The results, in general, correspond well with expected irrigation schedules under different conditions and provide valuable information on both short- and long-term aspects of irrigation control under saline conditions. The ELQ control, being an analytic iterative solution scheme with theoretically guaranteed fast convergence, has a distinct computational advantage over state-of-the-art procedures.

  2. Finite-size effects on the quasistatic displacement pulse in a solid specimen with quadratic nonlinearity.

    PubMed

    Nagy, Peter B; Qu, Jianmin; Jacobs, Laurence J

    2013-09-01

    There is an unresolved debate in the scientific community about the shape of the quasistatic displacement pulse produced by nonlinear acoustic wave propagation in an elastic solid with quadratic nonlinearity. Early analytical and experimental studies suggested that the quasistatic pulse exhibits a right-triangular shape with the peak displacement of the leading edge being proportional to the length of the tone burst. In contrast, more recent theoretical, analytical, numerical, and experimental studies suggested that the quasistatic displacement pulse has a flat-top shape where the peak displacement is proportional to the propagation distance. This study presents rigorous mathematical analyses and numerical simulations of the quasistatic displacement pulse. In the case of semi-infinite solids, it is confirmed that the time-domain shape of the quasistatic pulse generated by a longitudinal plane wave is not a right-angle triangle. In the case of finite-size solids, the finite axial dimension of the specimen cannot simply be modeled with a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. More profoundly, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second order harmonic pulses generated by the same transducer. PMID:23967911

  3. Stability and monotone convergence of generalised policy iteration for discrete-time linear quadratic regulations

    NASA Astrophysics Data System (ADS)

    Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

    2016-03-01

    In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.

  4. Giant quadratic electro-optical effect during polarization switching in ultrathin ferroelectric polymer films

    NASA Astrophysics Data System (ADS)

    Blinov, L. M.; Lazarev, V. V.; Palto, S. P.; Yudin, S. G.

    2012-04-01

    The low-frequency quadratic electro-optical effect with a maximum electro-optical coefficient of g = 8 × 10-19 m2/V2 (i.e., four orders of magnitude greater than the standard high-frequency value) has been studied in thin films of ferroelectric polymer PVDF(70%)-TrFE(30%). The observed effect is related to the process of spontaneous polarization switching, during which the electron oscillators of C-F and C-H dipole groups rotate to become parallel to the applied field. As a result, the ellipsoid of the refractive index exhibits narrowing in the direction perpendicular to the field. The field dependence of the electro-optical coefficient g correlates with that of the apparent dielectric permittivity, which can be introduced under the condition of ferroelectric polarization switching. The observed electro-optical effect strongly decreases when the frequency increases up to several hundred hertz. The temperature dependence of the effect exhibits clearly pronounced hysteresis in the region of the ferroelectric phase transition.

  5. Antenna Linear-Quadratic-Gaussian (LQG) Controllers: Properties, Limits of Performance, and Tuning Procedure

    NASA Technical Reports Server (NTRS)

    Gawronski, W.

    2004-01-01

    Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.

  6. Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

  7. Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

    NASA Astrophysics Data System (ADS)

    Pujari, Sumiran; Lang, Thomas C.; Murthy, Ganpathy; Kaul, Ribhu K.

    2016-08-01

    We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U /t despite the U =0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2 +1 )D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

  8. Giant quadratic electro-optical effect during polarization switching in ultrathin ferroelectric polymer films

    SciTech Connect

    Blinov, L. M. Lazarev, V. V.; Palto, S. P.; Yudin, S. G.

    2012-04-15

    The low-frequency quadratic electro-optical effect with a maximum electro-optical coefficient of g = 8 Multiplication-Sign 10{sup -19} m{sup 2}/V{sup 2} (i.e., four orders of magnitude greater than the standard high-frequency value) has been studied in thin films of ferroelectric polymer PVDF(70%)-TrFE(30%). The observed effect is related to the process of spontaneous polarization switching, during which the electron oscillators of C-F and C-H dipole groups rotate to become parallel to the applied field. As a result, the ellipsoid of the refractive index exhibits narrowing in the direction perpendicular to the field. The field dependence of the electro-optical coefficient g correlates with that of the apparent dielectric permittivity, which can be introduced under the condition of ferroelectric polarization switching. The observed electro-optical effect strongly decreases when the frequency increases up to several hundred hertz. The temperature dependence of the effect exhibits clearly pronounced hysteresis in the region of the ferroelectric phase transition.

  9. Imitating winner or sympathizing loser? Quadratic effects on cooperative behavior in prisoners' dilemma games

    NASA Astrophysics Data System (ADS)

    Lu, Peng

    2015-10-01

    Cooperation is vital in human societies and therefore is widely investigated in the evolutionary game theory. Varieties of mechanisms have been proposed to overcome temptation and promote cooperation. Existing studies usually believe that agents are rational, but irrationalism such as emotions and feelings matters as well. Winner and loser are defined by their payoffs. In addition to admiring and imitating winners, the mechanism of sympathizing and imitating losers is introduced into the model as an alternative action rule, and each one plays the prisoners' dilemma game with eight neighbors under the influence of both irrationalism and rationalism. Rationalism refers to imitating winner to get highest payoff, and irrationalism means that people sympathize and adopt the actions of losers. As it is widely recognized that temptation reduces cooperation, this study focuses on the effect of sympathy on cooperation within a certain group or society. If it overcomes temptation that leads to defection, sympathy will be a powerful mechanism to promote cooperative behavior. Simulation results indicate that sympathy and temptation shares similar quadratic relationships with cooperation. Both sympathy and temptation undermine cooperation below their thresholds, and they both promote cooperation above their thresholds. Temptation not only reduces cooperation but also promote it as temptation goes beyond the threshold. Although sympathy is a good merit or human nature that is beneficial to society, a crisis or collapse of cooperation is inevitable when the sympathy propensity is relatively smaller. After cooperation reaches a minimal bottom, it then rises increasingly and dramatically, which brings a much brighter future of the society.

  10. Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

    NASA Astrophysics Data System (ADS)

    Norman, Patrick; Jensen, Hans Jørgen Aa.

    2004-10-01

    The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process β(-2ω;ω,ω). It is shown that relativistic corrections to property values are substantial in these cases—the orientationally averaged hyperpolarizabilities in the static limit β¯(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown.

  11. Quadratic response functions in the time-dependent four-component Hartree-Fock approximation.

    PubMed

    Norman, Patrick; Jensen, Hans Jørgen Aa

    2004-10-01

    The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process beta(-2omega;omega,omega). It is shown that relativistic corrections to property values are substantial in these cases--the orientationally averaged hyperpolarizabilities in the static limit beta(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown. PMID:15446908

  12. Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna

    NASA Technical Reports Server (NTRS)

    Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.

    1994-01-01

    The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.

  13. Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.

  14. The isomerization barrier in cyanocyclobutadienes: an ab initio multireference average quadratic coupled cluster study.

    PubMed

    Eckert-Maksić, Mirjana; Lischka, Hans; Maksić, Zvonimir B; Vazdar, Mario

    2009-07-23

    The energy profiles of the isomerization of mono, di-, and tetracyano-substituted cyclobutadienes (CBDs) are computed at the multireference average quadratic coupled cluster/complete active space self-consistent field level of theory. It was found that the energy barrier heights for the automerization reaction are 2.6 (tetracyano-CBD), 5.1 (1,3-dicyano-CBD), and 6.4 (cyano-CBD) kcal mol(-1), implying that they are lowered relative to that in the parent CBD (6.4 kcal mol(-1)), the monosubstituted derivative being an exception. Since the free CBD shuttles between two equivalent structures even at low temperature of 10 K, it follows that bond-stretch isomerism does not take place in cyanocyclobutadienes. Instead, these compounds exhibit rapid fluxional interconversion at room temperature between two bond-stretch isomers by the double bond flipping mechanism. The reason behind the decrease in the barrier heights is identified as a slightly enhanced resonance effect at the saddle points separating two (equivalent) bond-stretch isomers, compared to that in the equilibrium structures, predominantly due to the diradical character of the former. It is also shown that the energy gap between the singlet ground state saddle point structure and the first triplet equilibrium geometry decreases upon multiple substitution by the cyano groups. The splitting of the S and T energy is small being within the range of 6.5-8.2 kcal mol(-1).

  15. Topological mott insulator in three-dimensional systems with quadratic band touching.

    PubMed

    Herbut, Igor F; Janssen, Lukas

    2014-09-01

    We argue that a three-dimensional electronic system with the Fermi level at the quadratic band touching point such as HgTe could be unstable with respect to the spontaneous formation of the (topological) Mott insulator at arbitrary weak long-range Coulomb interaction. The mechanism of the instability can be understood as the collision of Abrikosov's non-Fermi liquid fixed point with another, quantum critical, fixed point, which approaches it in the coupling space as the system's dimensionality d→dlow+, with the "lower critical dimension" 2

  16. Plebański-Demiański solution of general relativity and its expressions quadratic and cubic in curvature: Analogies to electromagnetism

    NASA Astrophysics Data System (ADS)

    Boos, Jens

    2015-07-01

    Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution — the exact seven parameter solution of Plebański-Demiański (PD) — to demonstrate these analogies for a physically meaningful spacetime. The two quadratic curvature invariants B2 - E2 and EṡB are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel-Robinson tensor reads (B2 + E2)2 for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy-momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel-Robinson 3-form, from which the Bel-Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: In the original polynomial PD coordinates and in a modified Boyer-Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.

  17. Lie algebraic approach of a charged particle in presence of a constant magnetic field via the quadratic invariant

    SciTech Connect

    Abdalla, M. Sebawe; Elkasapy, A.I.

    2010-08-15

    In this paper we consider the problem of a charged harmonic oscillator under the influence of a constant magnetic field. The system is assumed to be isotropic and the magnetic field is applied along the z-axis. The canonical transformation is invoked to remove the interaction term and the system is reduced to a model containing the second harmonic generation. Two classes of the real and complex quadratic invariants (constants of motion) are obtained. We have employed the Lie algebraic technique to find the most general solution for the wave function for both real and complex invariants. Some discussions related to the advantage of using the quadratic invariants to solve the Cauchy problem instead of the direct use of the Hamiltonian itself are also given.

  18. Temperature dependence of Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal

    NASA Astrophysics Data System (ADS)

    Lu, Qieni; Han, Jinxin; Dai, Haitao; Ge, Baozhen; Zhao, Shuang

    2015-08-01

    We measure temperature dependence on Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal simultaneously in this work, based on digital holographic interferometry (DHI). And the spatial distribution of the field-induced refractive index change can also be visualized and estimated by numerically retrieving sequential phase maps of Mn:Fe:KTN crystal from recording digital holograms in different states. The refractive indices decrease with increasing temperature and quadratic polarized optical coefficient is insensitive to temperature. The experimental results suggest that the DHI method presented here is highly applicable in both visualizing the temporal and spatial behavior of the internal electric field and accurately measuring electro-optic coefficient for electrooptical media.

  19. Modeling and performance analysis of the fractional order quadratic Boost converter in discontinuous conduction mode-discontinuous conduction mode

    NASA Astrophysics Data System (ADS)

    Tan, Cheng; Liang, Zhi-Shan

    2016-03-01

    In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM-DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM-DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.

  20. Transforming spreadsheet-based numerical and graphical quadratic sequences into pencil-paper algebraic expressions, and prospective teachers

    NASA Astrophysics Data System (ADS)

    Faaiz Gierdien, M.

    2011-01-01

    This note demonstrates multiple representations (numerical and graphical) of spreadsheet-based quadratic sequences together with prospective teachers' pencil-paper transformations of these numerical sequences into a corresponding symbolization as algebraic expressions. With the majority of prospective teachers, the experience of school mathematics is one of disaffection. They are in a teacher education programme that offers them certification to teach up to grade nine in the public schools. Their work illustrates processes, such as recognizing and extending patterns, by specializing and generalizing particular functional relationships. Insights gained from various methods used by them, together with the instructional affordances, i.e. the instructional benefits of spreadsheets, represent a curricular continuity between quadratic, numerical sequences and related algebraic expressions and suggest a possible change to the order in which the two are introduced.

  1. On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap

    NASA Astrophysics Data System (ADS)

    Chen, Xuwen

    2013-11-01

    We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.

  2. Energy management of a power-split plug-in hybrid electric vehicle based on genetic algorithm and quadratic programming

    NASA Astrophysics Data System (ADS)

    Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen

    2014-02-01

    This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.

  3. Evaluation of a photovoltaic energy mechatronics system with a built-in quadratic maximum power point tracking algorithm

    SciTech Connect

    Chao, R.M.; Ko, S.H.; Lin, I.H.; Pai, F.S.; Chang, C.C.

    2009-12-15

    The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)

  4. A cross-linguistic investigation of the acquisition of the pragmatics of indefinite and definite reference in two-year-olds.

    PubMed

    Rozendaal, Margot Isabella; Baker, Anne Edith

    2008-11-01

    The acquisition of reference involves both morphosyntax and pragmatics. This study investigates whether Dutch, English and French two- to three-year-old children differentiate in their use of determiners between non-specific/specific reference, newness/givenness in discourse and mutual/no mutual knowledge between interlocutors. A brief analysis of the input shows a clear association between form and function, although there are some language differences in this respect. As soon as determiner use can be statistically analyzed, the children show a relatively adult-like pattern of association for the distinctions of non-specific/specific and newness/givenness. The distinction between mutual/no mutual knowledge appears later. Reference involving no mutual knowledge is scarcely evidenced in the input and barely used by the children at this age. The development of associations is clearly related to the rate of determiner development, the French being quickest, then the English, then the Dutch.

  5. A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

    NASA Technical Reports Server (NTRS)

    Shyu, H. C.; Reed, I. S.; Truong, T. K.; Hsu, I. S.; Chang, J. J.

    1987-01-01

    A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.

  6. Identify five kinds of simple super-secondary structures with quadratic discriminant algorithm based on the chemical shifts.

    PubMed

    Kou, Gaoshan; Feng, Yonge

    2015-09-01

    The biological function of protein is largely determined by its spatial structure. The research on the relationship between structure and function is the basis of protein structure prediction. However, the prediction of super secondary structure is an important step in the prediction of protein spatial structure. Many algorithms have been proposed for the prediction of protein super secondary structure. However, the parameters used by these methods were primarily based on amino acid sequences. In this paper, we proposed a novel model for predicting five kinds of protein super secondary structures based on the chemical shifts (CSs). Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in five kinds of protein super secondary structures by using the analysis of variance (ANOVA). Secondly, we used chemical shifts of six nuclei as features, and combined with quadratic discriminant analysis (QDA) to predict five kinds of protein super secondary structures. Finally, we achieved the averaged sensitivity, specificity and the overall accuracy of 81.8%, 95.19%, 82.91%, respectively in seven-fold cross-validation. Moreover, we have performed the prediction by combining the five different chemical shifts as features, the maximum overall accuracy up to 89.87% by using the C,Cα,Cβ,N,Hα of Hα chemical shifts, which are clearly superior to that of the quadratic discriminant analysis (QDA) algorithm by using 20 amino acid compositions (AAC) as feature in the seven-fold cross-validation. These results demonstrated that chemical shifts (CSs) are indeed an outstanding parameter for the prediction of five kinds of super secondary structures. In addition, we compared the prediction of the quadratic discriminant analysis (QDA) with that of support vector machine (SVM) by using the same six CSs as features. The result suggested that the quadratic discriminant analysis method by using chemical shifts as features is a good predictor for protein super

  7. Revealing a quantum feature of dimensionless uncertainty in linear and quadratic potentials by changing potential intervals

    NASA Astrophysics Data System (ADS)

    Kheiri, R.

    2016-09-01

    As an undergraduate exercise, in an article (2012 Am. J. Phys. 80 780–14), quantum and classical uncertainties for dimensionless variables of position and momentum were evaluated in three potentials: infinite well, bouncing ball, and harmonic oscillator. While original quantum uncertainty products depend on {{\\hslash }} and the number of states (n), a dimensionless approach makes the comparison between quantum uncertainty and classical dispersion possible by excluding {{\\hslash }}. But the question is whether the uncertainty still remains dependent on quantum number n. In the above-mentioned article, there lies this contrast; on the one hand, the dimensionless quantum uncertainty of the potential box approaches classical dispersion only in the limit of large quantum numbers (n\\to ∞ )—consistent with the correspondence principle. On the other hand, similar evaluations for bouncing ball and harmonic oscillator potentials are equal to their classical counterparts independent of n. This equality may hide the quantum feature of low energy levels. In the current study, we change the potential intervals in order to make them symmetric for the linear potential and non-symmetric for the quadratic potential. As a result, it is shown in this paper that the dimensionless quantum uncertainty of these potentials in the new potential intervals is expressed in terms of quantum number n. In other words, the uncertainty requires the correspondence principle in order to approach the classical limit. Therefore, it can be concluded that the dimensionless analysis, as a useful pedagogical method, does not take away the quantum feature of the n-dependence of quantum uncertainty in general. Moreover, our numerical calculations include the higher powers of the position for the potentials.

  8. Linear and quadratic models of point process systems: contributions of patterned input to output.

    PubMed

    Lindsay, K A; Rosenberg, J R

    2012-08-01

    In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike.

  9. Quadratic Time-Frequency Analysis of Hydroacoustic Signals as Applied to Acoustic Emissions of Large Whales

    NASA Astrophysics Data System (ADS)

    Le Bras, Ronan; Victor, Sucic; Damir, Malnar; Götz, Bokelmann

    2014-05-01

    In order to enrich the set of attributes in setting up a large database of whale signals, as envisioned in the Baleakanta project, we investigate methods of time-frequency analysis. The purpose of establishing the database is to increase and refine knowledge of the emitted signal and of its propagation characteristics, leading to a better understanding of the animal migrations in a non-invasive manner and to characterize acoustic propagation in oceanic media. The higher resolution for signal extraction and a better separation from other signals and noise will be used for various purposes, including improved signal detection and individual animal identification. The quadratic class of time-frequency distributions (TFDs) is the most popular set of time-frequency tools for analysis and processing of non-stationary signals. Two best known and most studied members of this class are the spectrogram and the Wigner-Ville distribution. However, to be used efficiently, i.e. to have highly concentrated signal components while significantly suppressing interference and noise simultaneously, TFDs need to be optimized first. The optimization method used in this paper is based on the Cross-Wigner-Ville distribution, and unlike similar approaches it does not require prior information on the analysed signal. The method is applied to whale signals, which, just like the majority of other real-life signals, can generally be classified as multicomponent non-stationary signals, and hence time-frequency techniques are a natural choice for their representation, analysis, and processing. We present processed data from a set containing hundreds of individual calls. The TFD optimization method results into a high resolution time-frequency representation of the signals. It allows for a simple extraction of signal components from the TFD's dominant ridges. The local peaks of those ridges can then be used for the signal components instantaneous frequency estimation, which in turn can be used as

  10. Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation

    NASA Astrophysics Data System (ADS)

    Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.

    2015-11-01

    We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.

  11. Revealing a quantum feature of dimensionless uncertainty in linear and quadratic potentials by changing potential intervals

    NASA Astrophysics Data System (ADS)

    Kheiri, R.

    2016-09-01

    As an undergraduate exercise, in an article (2012 Am. J. Phys. 80 780-14), quantum and classical uncertainties for dimensionless variables of position and momentum were evaluated in three potentials: infinite well, bouncing ball, and harmonic oscillator. While original quantum uncertainty products depend on {{\\hslash }} and the number of states (n), a dimensionless approach makes the comparison between quantum uncertainty and classical dispersion possible by excluding {{\\hslash }}. But the question is whether the uncertainty still remains dependent on quantum number n. In the above-mentioned article, there lies this contrast; on the one hand, the dimensionless quantum uncertainty of the potential box approaches classical dispersion only in the limit of large quantum numbers (n\\to ∞ )—consistent with the correspondence principle. On the other hand, similar evaluations for bouncing ball and harmonic oscillator potentials are equal to their classical counterparts independent of n. This equality may hide the quantum feature of low energy levels. In the current study, we change the potential intervals in order to make them symmetric for the linear potential and non-symmetric for the quadratic potential. As a result, it is shown in this paper that the dimensionless quantum uncertainty of these potentials in the new potential intervals is expressed in terms of quantum number n. In other words, the uncertainty requires the correspondence principle in order to approach the classical limit. Therefore, it can be concluded that the dimensionless analysis, as a useful pedagogical method, does not take away the quantum feature of the n-dependence of quantum uncertainty in general. Moreover, our numerical calculations include the higher powers of the position for the potentials.

  12. SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics

    PubMed Central

    Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

    2015-01-01

    Motivation: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of O(n6). Subsequently, numerous faster ‘Sankoff-style’ approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity (≥ quartic time). Results: Breaking this barrier, we introduce the novel Sankoff-style algorithm ‘sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)’, which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff’s original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25838465

  13. Firing rate of the noisy quadratic integrate-and-fire neuron.

    PubMed

    Brunel, Nicolas; Latham, Peter E

    2003-10-01

    We calculate the firing rate of the quadratic integrate-and-fire neuron in response to a colored noise input current. Such an input current is a good approximation to the noise due to the random bombardment of spikes, with the correlation time of the noise corresponding to the decay time of the synapses. The key parameter that determines the firing rate is the ratio of the correlation time of the colored noise, tau(s), to the neuronal time constant, tau(m). We calculate the firing rate exactly in two limits: when the ratio, tau(s)/tau(m), goes to zero (white noise) and when it goes to infinity. The correction to the short correlation time limit is O(tau(s)/tau(m)), which is qualita tively different from that of the leaky integrate-and-fire neuron, where the correction is O( radical tau(s)/tau(m)). The difference is due to the different boundary conditions of the probability density function of the membrane potential of the neuron at firing threshold. The correction to the long correlation time limit is O(tau(m)/tau(s)). By combining the short and long correlation time limits, we derive an expression that provides a good approximation to the firing rate over the whole range of tau(s)/tau(m) in the suprathreshold regime-that is, in a regime in which the average current is sufficient to make the cell fire. In the subthreshold regime, the expression breaks down somewhat when tau(s) becomes large compared to tau(m).

  14. Cocrystal dissociation in the presence of water: a general approach for identifying stable cocrystal forms.

    PubMed

    Eddleston, Mark D; Madusanka, Nadeesh; Jones, William

    2014-09-01

    In previous studies, cocrystals have been shown to be susceptible to dissociation at high humidity because of differences in the solubilities of the two coformer molecules, especially when these molecules can form hydrates. Contrastingly, however, the propensity of the pharmaceutically active compound caffeine to hydrate formation is reduced by cocrystallization with oxalic acid. Here, the stability of the oxalic acid cocrystal of caffeine is investigated from a thermodynamic perspective through the use of aqueous slurries of caffeine hydrate and oxalic acid dihydrate. Conversion to the anhydrous caffeine-oxalic acid cocrystal occurred under these conditions confirming that this form is thermodynamically stable in an aqueous environment. The slurry methodology was further developed as a general approach to screening for cocrystals that are not susceptible to dissociation at high humidity. In this manner, cocrystals of the hydrate-forming molecules theophylline, carbamazepine, and piroxicam that are stable at high humidity, indefinitely avoiding hydrate formation, were identified.

  15. Label-free molecular beacon-based quadratic isothermal exponential amplification: a simple and sensitive one-pot method to detect DNA methyltransferase activity.

    PubMed

    Xue, Qingwang; Wang, Lei; Jiang, Wei

    2015-09-11

    We developed a one-pot label-free molecular beacon-mediated quadratic isothermal exponential amplification strategy (LFMB-QIEA) for simple, rapid and sensitive DNA methyltransferase (MTase) activity detection.

  16. Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering.

    PubMed

    Pandey, Ravindra; Ghosh, Sampa; Mukhopadhyay, S; Ramasesha, S; Das, Puspendu K

    2011-01-28

    We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, β(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D=I(2ω,X,X)/I(2ω,Z,X) and D(')=I(2ω,X,C)/I(2ω,Z,C) in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, β(HRS), and the value of macroscopic depolarization ratios, D and D('), are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical β(HRS), D and D(') values as a function of the geometry of the complex. The calculated β(HRS), D, and D(') values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30° is observed. Thus, we have demonstrated in

  17. Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

    PubMed

    Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

    2015-04-01

    Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy.

  18. Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

    SciTech Connect

    Chithiika Ruby, V.; Senthilvelan, M.; Lakshmanan, M.; Chandrasekar, V. K.

    2015-01-15

    We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered forms of the Hamiltonian. We implement point canonical transformation method to map one-dimensional time-independent position dependent mass Schrödinger equation endowed with potentials onto constant mass counterparts which are considered to be exactly solvable. We observe that a class of mass functions and the corresponding potentials give rise to solutions that do not depend on any particular ordering, leading to the removal of ambiguity in it. In this case, it is imperative that the ordering is Hermitian. For non-Hermitian ordering, we show that the class of systems can also be exactly solvable and is also shown to be iso-spectral using suitable similarity transformations. We also discuss the normalization of the eigenfunctions obtained from both Hermitian and non-Hermitian orderings. We illustrate the technique with the quadratic Liénard type nonlinear oscillators, which admit position dependent mass Hamiltonians.

  19. Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

    PubMed

    Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

    2015-04-01

    Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. PMID:25746821

  20. Quadratic Electro-Optic Effect in the Nonconjugated Conductive Co-polymer Iodine-doped Styrene-Butadiene-Rubber Measured at 633 nm and 1550 nm

    NASA Astrophysics Data System (ADS)

    Telang, Gurudutt; Thakur, Mrinal

    2012-02-01

    The quadratic electro-optic effect in the nonconjugated conductive co-polymer film of styrene-butadiene-rubber (SBR) has been measured using field-induced birefringence method. Thin films of styrene-butadiene-rubber have been prepared on various substrates from a chloroform solution and characterized using optical absorption spectroscopy, FTIR and DSC before and after doping with iodine. The optical absorption spectrum at low doping shows two peaks: one at 4.27 eV and the other at 3.2 eV corresponding to the radical cation and charge-transfer transition. FTIR data indicate =C-H vibration bands (964 cm-1 and 910 cm-1) of polybutadiene decrease upon doping due to transformation of the double bonds into radical cations. The Kerr coefficients as measured at 633 nm and at 1550 nm are 3.1x10-10 m/V^2 and 1.3x10-10 m/V^2 respectively. These exceptionally large values have been attributed to the subnanometer metallic domains formed upon doping and charge-transfer involving isolated double-bonds.