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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. Weight of quadratic forms and graph states

    NASA Astrophysics Data System (ADS)

    Cosentino, Alessandro; Severini, Simone

    2009-11-01

    We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

  3. 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.

  4. Quadratic minima and modular forms II

    NASA Astrophysics Data System (ADS)

    Brent, Barry

    We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two even positive-definite quadratic form. These bounds extend partial results in part I.

  5. Quadratic Forms for the Fermionic Unitary Gas Model

    NASA Astrophysics Data System (ADS)

    Finco, Domenico; Teta, Alessandro

    2012-04-01

    We consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zero-range interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the so-called Skornyakov-Ter-Martirosyan extension Hα, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then Hα is not a self-adjoint and bounded from below operator, and this in particular suggests that the so-called Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied.

  6. Maximization of Sums of Quotients of Quadratic Forms and Some Generalizations.

    ERIC Educational Resources Information Center

    Kiers, Henk A. L.

    1995-01-01

    Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

  7. 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.

  8. Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

    NASA Technical Reports Server (NTRS)

    Juang, J.-N.; Turner, J. D.; Chun, H. M.

    1984-01-01

    Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

  9. Anisotropic models with two fluids in linear and quadratic forms of f( T) gravitational theories

    NASA Astrophysics Data System (ADS)

    Nashed, Gamal G. L.

    2015-06-01

    Recent astronomical observations show that the universe may be anisotropic on large scales. The Union2 SnIa data hint that the universe has a preferred direction. If such a cosmological privileged axis indeed exists, one has to consider an anisotropic expanding universe, instead of the isotropic cosmological model. In this study, we apply the field equations of quadratic form of the modified teleparallel gravitational theories, f( T)= T+ ɛT 2, to anisotropic model. We assume two fluid components, the matter components have two equation of states (EoS). We study different equation of states for the linear case and show that there is no recombination era between the two fluids. For the quadratic one, we assume two equations of state corresponding to dark matter. In this model we obtain an inflation model and show that the values of the parameter, in the early universe, ɛ are depend on the sign of the cosmological constant.

  10. 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.

  11. Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

    NASA Astrophysics Data System (ADS)

    Hong, Xiaochun; Xie, Shaolong; Chen, Longwei

    In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b],, we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree n, depend linearly on n.

  12. 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…

  13. 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.

  14. 48 CFR 652.216-70 - Ordering-Indefinite-Delivery Contract.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...-Delivery Contract. 652.216-70 Section 652.216-70 Federal Acquisition Regulations System DEPARTMENT OF STATE... Ordering—Indefinite-Delivery Contract. As prescribed in 616.506-70, insert the following clause: Ordering—Indefinite-Delivery Contracts (APR 2004) The Government shall use one of the following forms to issue...

  15. Conditions for the non-negativity of integral quadratic forms with constant coefficients on a half-axis

    SciTech Connect

    Milyutin, A A

    2002-04-30

    An integral quadratic functional with constant coefficients on a half-axis is considered. A necessary and sufficient condition for its non-negativity at all square integrable pairs of functions related by a linear ODE is proposed, which is based on the Hamilton-Jacobi inequality. A connection between this condition and the well-known frequency criterion is established.

  16. 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.

  17. 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.

  18. The Class of Indefinites in Vietnamese.

    ERIC Educational Resources Information Center

    Michaelis, Laura A.

    Vietnamese has a group of semantically amorphous indefinite words and phrases whose meanings appear to be refined according to the particular syntactic or pragmatic context in which they are embedded. In appropriate environments, they are the functional equivalents of the English "who, someone, anyone, whoever, everyone." Analysis of the…

  19. Efficient second-harmonic generation in micrometer-thick slabs with indefinite permittivity

    NASA Astrophysics Data System (ADS)

    Ciattoni, A.; Spinozzi, E.

    2012-04-01

    We theoretically predict efficient optical second-harmonic generation (SHG) from a micrometer-thick slab consisting of a quadratic nonlinear anisotropic medium whose linear principal permittivities have, at the fundamental wavelength, real parts of different signs (indefinite permittivity) and magnitude smaller than 1. We show that, by illuminating the slab with a p-polarized fundamental wave (with intensity of a few MW/cm2), highly efficient scattering of the second-harmonic field occurs in conditions at which the slab is linearly fully transparent for the fundamental wave. The high efficiency of the SHG process stems from the enhancement of the longitudinal field, perpendicular to the slab surface, produced by the very small value of the slab dielectric permittivities. We investigate the role played by medium losses, showing that, even in the strong-absorption regime, the described process yields a second-harmonic field which is much stronger than that produced by a standard (not indefinite) nonlinear slab.

  20. 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

  1. 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…

  2. 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.

  3. Communication-avoiding symmetric-indefinite factorization

    DOE PAGESBeta

    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

  4. 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.

  5. 48 CFR 19.804-6 - Indefinite delivery contracts.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Indefinite delivery contracts. 19.804-6 Section 19.804-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION...) Program) 19.804-6 Indefinite delivery contracts. (a) Separate offers and acceptances must not be made...

  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. 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.

  9. 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.

  10. 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.

  11. L -functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field

    NASA Astrophysics Data System (ADS)

    Louboutin, Stephane

    1992-07-01

    Starting from the analytic class number formula involving its L-function, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class number tables. Then, using class field theory, we will construct a periodic character &chi , defined on the ring of integers of a field K that is a quadratic extension of a principal imaginary quadratic field k, such that the zeta function of K is the product of the zeta function of k and of the L-function L(s,χ) . We will then determine an integral representation of this L-function that enables us to calculate the class number of K numerically, as soon as its regulator is known. It will also provide us with an upper bound for these class numbers, showing that Hua's bound for the class numbers of imaginary and real quadratic fields is not the best that one could expect. We give statistical results concerning the class numbers of the first 50000 quadratic extensions of {Q}(i) with prime relative discriminant (and with K/Q a non-Galois quartic extension). Our analytic calculation improves the algebraic calculation used by Lakein in the same way as the analytic calculation of the class numbers of real quadratic fields made by Williams and Broere improved the algebraic calculation consisting in counting the number of cycles of reduced ideals. Finally, we give upper bounds for class numbers of K that is a quadratic extension of an imaginary quadratic field k which is no longer assumed to be of class number one.

  12. 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).

  13. 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).

  14. 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)

  15. 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]…

  16. 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.

  17. 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.

  18. 48 CFR 216.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... contracts. 216.504 Section 216.504 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM, DEPARTMENT OF DEFENSE CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite... accordance with FAR 16.504(c)(1)(ii)(D) shall be submitted to the Director, Defense Procurement...

  19. 48 CFR 216.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... contracts. 216.504 Section 216.504 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM, DEPARTMENT OF DEFENSE CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite... contracts. (2) The head of the agency must notify the congressional defense committees within 30 days...

  20. 48 CFR 216.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... contracts. 216.504 Section 216.504 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM, DEPARTMENT OF DEFENSE CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite... accordance with FAR 16.504(c)(1)(ii)(D) shall be submitted to the Director, Defense Procurement...

  1. 48 CFR 216.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... contracts. 216.504 Section 216.504 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM, DEPARTMENT OF DEFENSE CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite... accordance with FAR 16.504(c)(1)(ii)(D) shall be submitted to the Director, Defense Procurement...

  2. 48 CFR 16.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... contract file. The contracting officer may determine that a class of acquisitions is not appropriate for... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Indefinite-quantity contracts. 16.504 Section 16.504 Federal Acquisition Regulations System FEDERAL ACQUISITION...

  3. Licensers and Meanings: Structural Properties of Dependent Indefinites

    ERIC Educational Resources Information Center

    Fitzgibbons, Natalia Viktorovna

    2010-01-01

    This dissertation investigates licensing conditions of dependent indefinite pronouns, such as negative concord items and pronouns that depend on the presence of a c-commanding quantifier. In Chapter 2, I examine freestanding negative concord items in Russian. I provide a novel empirical generalization that freestanding negative concord items…

  4. Understanding English Non-Count Nouns and Indefinite Articles

    ERIC Educational Resources Information Center

    Tsuchida, Takehiro

    2010-01-01

    The fact that English non-count abstract nouns such as knowledge are compatible with the indefinite article a/an is not only perplexing for second language (L2) learners of English but also troublesome for both native and non-native English teachers. This paper does research on this curious phenomenon of English grammar to clarify its mechanism…

  5. 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.

  6. 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.

  7. 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.

  8. 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…

  9. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  10. 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

  11. 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.

  12. 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…

  13. 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.

  14. 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.

  15. Focusing and negative refraction in anisotropic indefinite permittivity media

    NASA Astrophysics Data System (ADS)

    Marshall, Sara; Amirkhizi, Alireza V.; Nemat-Nasser, Sia

    2009-03-01

    Materials that exhibit negative refraction demonstrate physical phenomena that may be used for novel applications. This work serves to evaluate the possibility of hyperbolic focusing due to an indefinite anisotropic permittivity tensor. Two single-loop antennas were used to approximately achieve a transverse magnetic (TM) point source and detector. Using an Agilent 8510C Vector Network Analyzer (VNA), the frequency spectrum was scanned between 7 and 9 GHz. Relative gain or loss measurements were taken at equal spatial steps around the center of the sample. A scanning robot allowed for the automatic scanning of the space behind the sample in the x, y, and z directions, to establish the focusing patterns, and to compare the signal amplitudes in the presence and absence of the sample. The robot was controlled using LabVIEW, which also collected the data from the VNA and passed it to Matlab for processing. A soft focusing spot was observed when the antennas were placed in a symmetric configuration with respect to the sample. These results suggest a method of focusing electromagnetic waves using negative refraction in indefinite materials.

  16. An alternative method on quadratic programming problems

    NASA Astrophysics Data System (ADS)

    Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.

    2015-05-01

    In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.

  17. 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

  18. 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.

  19. 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.

  20. 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

  1. 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

  2. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... FOR INTERNATIONAL DEVELOPMENT CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 716.505-70 Vetting orders under indefinite delivery contracts. (a) The task order contracting officer will specify in the request for task or delivery order proposals whether the order...

  3. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... FOR INTERNATIONAL DEVELOPMENT CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 716.505-70 Vetting orders under indefinite delivery contracts. (a) The task order contracting officer will specify in the request for task or delivery order proposals whether the order...

  4. 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…

  5. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 5 2014-10-01 2014-10-01 false Vetting orders under indefinite delivery contracts. 716.505-70 Section 716.505-70 Federal Acquisition Regulations System AGENCY FOR INTERNATIONAL DEVELOPMENT CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 716.505-70 Vetting...

  6. 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).

  7. 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.

  8. Tubular optical microcavities of indefinite medium for sensitive liquid refractometers.

    PubMed

    Tang, Shiwei; Fang, Yangfu; Liu, Zhaowei; Zhou, Lei; Mei, Yongfeng

    2016-01-01

    Optical microcavities enable circulated light to intensively interact with a detecting liquid, thus promising high sensitivity in fluidic refractometers. Based on Mie scattering theory, we propose a tubular metamaterial device for liquid sensing, which utilizes anisotropic metamaterials with hyperbolic dispersion called indefinite media (IM). Besides traditional whispering gallery modes (WGMs), such tubular cavities can support surface plasmon polariton (SPP) WGMs, enabling high sensitivity liquid detection. Three configurations of such metamaterial tubes for sensing are discussed: tube-in-liquid, hollow-tube-in-liquid and liquid-in-tube; these are analyzed using numerical formulas and compared with dielectric and metal materials. Compared with traditional dielectric media (DM), the IM tubular cavity exhibits a higher sensitivity (S), which is close to that of a metal tubular cavity. However, compared with metal media, such an IM cavity can achieve higher quality (Q) factors similar to the DM tubular cavity. Therefore, the IM tubular cavity can offer the highest figures of merit (QS) for the sensing performance among the three types of materials. Our results suggest a novel tubular optofluidic device based on metamaterials, which could be useful for liquid refractometers. PMID:26605851

  9. 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.

  10. 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.

  11. On the connection of the quadratic Lienard equation with an equation for the elliptic functions

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.

    2015-07-01

    The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.

  12. Coherent states for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Contreras-Astorga, Alonso; Fernández C, David J.; Velázquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  13. 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.

  14. A Version of Quadratic Regression with Interpretable Parameters.

    ERIC Educational Resources Information Center

    Cudeck, Robert; du Toit, Stephen H. C.

    2002-01-01

    Suggests an alternative form of the quadratic model that has the same expectation function of the original model but has the useful feature that its parameters are interpretable. Provides examples of a simple regression problem and a nonlinear mixed-effects model. (SLD)

  15. 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…

  16. Quadratic expressions by means of `summing all the matchsticks'

    NASA Astrophysics Data System (ADS)

    Faaiz Gierdien, M.

    2012-09-01

    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 linear and not quadratic. It will be shown that a pedagogy of 'summing all the matchsticks' is central to the emergence of quadratic expressions. This pedagogy involves generational and transformational activities which are considered as some of the main activities of algebra. Key elements to these activities are processes such as recognizing and extending patterns, and specializing and generalizing particular functional relationships. Implications of these processes in terms of algebraic thinking are considered.

  17. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  18. 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}.

  19. Geometrical and Graphical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  20. 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

  1. 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.

  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. The generalized logistic equation with indefinite weight driven by the square root of the Laplacian

    NASA Astrophysics Data System (ADS)

    Marinelli, Alessio; Mugnai, Dimitri

    2014-09-01

    We consider an elliptic problem driven by the square root of the negative Laplacian in the presence of a general logistic function having an indefinite weight. We prove a bifurcation result for the associated Dirichlet problem via regularity estimates of independent interest for when the weight belongs only to certain Lebesgue spaces.

  6. 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…

  7. 41 CFR 101-25.101-4 - Supply through indefinite quantity requirement contracts.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 41 Public Contracts and Property Management 2 2011-07-01 2007-07-01 true Supply through indefinite quantity requirement contracts. 101-25.101-4 Section 101-25.101-4 Public Contracts and Property Management Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS SUPPLY...

  8. 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 Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS SUPPLY...

  9. 41 CFR 101-25.101-4 - Supply through indefinite quantity requirement contracts.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 41 Public Contracts and Property Management 2 2014-07-01 2012-07-01 true Supply through indefinite quantity requirement contracts. 101-25.101-4 Section 101-25.101-4 Public Contracts and Property Management Federal Property Management Regulations System FEDERAL PROPERTY MANAGEMENT REGULATIONS SUPPLY...

  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. 18 CFR 1304.409 - Indefinite or temporary moorage of recreational vessels.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 18 Conservation of Power and Water Resources 2 2011-04-01 2011-04-01 false Indefinite or temporary moorage of recreational vessels. 1304.409 Section 1304.409 Conservation of Power and Water Resources TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION...

  12. 18 CFR 1304.409 - Indefinite or temporary moorage of recreational vessels.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 18 Conservation of Power and Water Resources 2 2012-04-01 2012-04-01 false Indefinite or temporary moorage of recreational vessels. 1304.409 Section 1304.409 Conservation of Power and Water Resources TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION...

  13. A new Krylov-subspace method for symmetric indefinite linear systems

    SciTech Connect

    Freund, R.W.; Nachtigal, N.M.

    1994-10-01

    Many important applications involve the solution of large linear systems with symmetric, but indefinite coefficient matrices. For example, such systems arise in incompressible flow computations and as subproblems in optimization algorithms for linear and nonlinear programs. Existing Krylov-subspace iterations for symmetric indefinite systems, such as SYMMLQ and MINRES, require the use of symmetric positive definite preconditioners, which is a rather unnatural restriction when the matrix itself is highly indefinite with both many positive and many negative eigenvalues. In this note, the authors describe a new Krylov-subspace iteration for solving symmetric indefinite linear systems that can be combined with arbitrary symmetric preconditioners. The algorithm can be interpreted as a special case of the quasi-minimal residual method for general non-Hermitian linear systems, and like the latter, it produces iterates defined by a quasi-minimal residual property. The proposed method has the same work and storage requirements per iteration as SYMMLQ or MINRES, however, it usually converges in considerably fewer iterations. Results of numerical experiments are reported.

  14. 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…

  15. 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.

  16. 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

  17. 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

  18. Quadratic boundedness of uncertain nonlinear dynamic systems

    NASA Astrophysics Data System (ADS)

    Brockman, Mark Lawrence

    Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.

  19. Quadratic nonlinear Klein-Gordon equation in one dimension

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.

    2012-10-01

    We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = λv2, t ∈ R, x ∈ R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ∈ R, where v0 and v1 are real-valued functions, λ ∈ R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

  20. Exploring {{W}}_{∞ } in the quadratic basis

    NASA Astrophysics Data System (ADS)

    Procházka, Tomáš

    2015-09-01

    We study the operator product expansions in the chiral algebra {W}_{∞ } , first using the associativity conditions in the basis of primary generating fields and then using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form expression for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using properties of these bilocal fields. In the last part we verify the consistency with results derived previously by studying minimal models of {W}_{∞ } and comparing them to known reductions of {W}_{∞ } to {W}_N . The results we obtain illustrate nicely the role of triality symmetry in the representation theory of {W}_{∞ }.

  1. 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)

  2. 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.

  3. Quadratic Stochastic Operators with Countable State Space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir

    2016-03-01

    In this paper, we provide the classes of Poisson and Geometric quadratic stochastic operators with countable state space, study the dynamics of these operators and discuss their application to economics.

  4. 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.)

  5. 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.

  6. Polychromatic solitons in a quadratic medium.

    PubMed

    Towers, I N; Malomed, B A

    2002-10-01

    We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate. PMID:12443362

  7. Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators

    NASA Astrophysics Data System (ADS)

    Marquette, Ian

    2011-06-01

    We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in terms of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.

  8. 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

  9. 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,…

  10. Cyclicity of a fake saddle inside the quadratic vector fields

    NASA Astrophysics Data System (ADS)

    De Maesschalck, P.; Rebollo-Perdomo, S.; Torregrosa, J.

    2015-01-01

    This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic.

  11. Fast approximate quadratic programming for graph matching.

    PubMed

    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

  12. 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

  13. Limit cycles near hyperbolas in quadratic systems

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume

    In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.

  14. Heredity in one-dimensional quadratic maps

    NASA Astrophysics Data System (ADS)

    Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.

    1998-12-01

    In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.

  15. 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.

  16. 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.

  17. 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.

  18. 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.)

  19. 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…

  20. Fourier analysis of quadratic phase interferograms

    NASA Astrophysics Data System (ADS)

    Muñoz-Maciel, Jesús; Mora-González, Miguel; Casillas-Rodríguez, Francisco J.; Peña-Lecona, Francisco G.

    2015-06-01

    A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

  1. 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.

  2. Slow light, open-cavity formation, and large longitudinal electric field on a slab waveguide made of indefinite permittivity metamaterials

    NASA Astrophysics Data System (ADS)

    Lu, W. T.; Sridhar, S.

    2010-07-01

    The optical properties of slab waveguides made of indefinite permittivity (ɛ) materials (IEMs) are considered. In this medium, the real part of the transverse permittivity is negative while that of the longitudinal permittivity is positive. At any given frequency, the IEM waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward wave. The remainder are backward waves which can have a very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity if loss is absent. Above the critical thickness, the waveguide supports complex-conjugate decay modes instead of propagating modes. The presence of loss in IEMs will lift the TM mode degeneracy, resulting in modes with finite group velocity. A feasible realization is proposed. The performance of the IEM waveguide is analyzed and possible applications are discussed, which are supported by numerical calculations. These slab waveguides can be used to make optical delay lines in optical buffers to slow down and trap light, to form open cavities, to generate strong longitudinal electric fields, and as phase shifters in optical integrated circuits. Although the presence of loss will hinder these applications, gain can be introduced to compensate the loss and enhance the performance.

  3. Clifford group, stabilizer states, and linear and quadratic operations over GF(2)

    SciTech Connect

    Dehaene, Jeroen; Moor, Bart de

    2003-10-01

    We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.

  4. A variant of the Kochen-Specker theorem localising value indefiniteness

    NASA Astrophysics Data System (ADS)

    Abbott, Alastair A.; Calude, Cristian S.; Svozil, Karl

    2015-10-01

    The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave noncontextually, one can nonetheless only conclude that some observables (in this set) are value indefinite. In this paper, we prove a variant of the Kochen-Specker theorem showing that, under the same assumption of noncontextuality, if a single one-dimensional projection observable is assigned the definite value 1, then no one-dimensional projection observable that is incompatible (i.e., non-commuting) with this one can be assigned consistently a definite value. Unlike standard proofs of the Kochen-Specker theorem, in order to localise and show the extent of value indefiniteness, this result requires a constructive method of reduction between Kochen-Specker sets. If a system is prepared in a pure state |ψ>, then it is reasonable to assume that any value assignment (i.e., hidden variable model) for this system assigns the value 1 to the observable projecting onto the one-dimensional linear subspace spanned by |ψ>, and the value 0 to those projecting onto linear subspaces orthogonal to it. Our result can be interpreted, under this assumption, as showing that the outcome of a measurement of any other incompatible one-dimensional projection observable cannot be determined in advance, thus formalising a notion of quantum randomness.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Optimal Approximation of Quadratic Interval Functions

    NASA Technical Reports Server (NTRS)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  14. 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...

  15. 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…

  16. The effects of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation

    NASA Astrophysics Data System (ADS)

    Ramos Quoirin, Humberto; Umezu, Kenichiro

    2014-12-01

    We investigate a semilinear elliptic equation with a logistic nonlinearity and an indefinite nonlinear boundary condition, both depending on a parameter λ. Overall, we analyze the effect of the indefinite nonlinear boundary condition on the structure of the positive solutions set. Based on variational and bifurcation techniques, our main results establish the existence of three nontrivial non-negative solutions for some values of λ, as well as their asymptotic behavior. These results suggest that the positive solutions set contains an S-shaped component in some case, as well as a combination of a C-shaped and an S-shaped components in another case.

  17. 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

  18. On least squares approximations to indefinite problems of the mixed type

    NASA Technical Reports Server (NTRS)

    Fix, G. J.; Gunzburger, M. D.

    1978-01-01

    A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

  19. Sequential quadratic programming method for determining the minimum energy path.

    PubMed

    Burger, Steven K; Yang, Weitao

    2007-10-28

    A new method, referred to as the sequential quadratic programming method, is presented for determining minimum energy paths. The method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method can efficiently determine the reaction mechanism, from which transition state can be easily identified and refined with other methods. To improve the resolution of the path close to the transition state, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller-Brown potential, amide hydrolysis, and an 89 atom cluster taken from the active site of 4-oxalocrotonate tautomerase for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate. PMID:17979319

  20. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  1. 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.

  2. 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.

  3. 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.

  4. 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...

  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. 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...

  7. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 5 Administrative Personnel 1 2011-01-01 2011-01-01 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...

  8. 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...

  9. 48 CFR 1807.107-70 - Orders against Federal Supply Schedule contracts or other indefinite-delivery contracts awarded...

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Orders against Federal Supply Schedule contracts or other indefinite-delivery contracts awarded by another agency. 1807.107-70 Section 1807.107-70 Federal Acquisition Regulations System NATIONAL AERONAUTICS AND SPACE ADMINISTRATION COMPETITION AND ACQUISITION...

  10. 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.

  11. Developed Adomian method for quadratic Kaluza-Klein relativity

    NASA Astrophysics Data System (ADS)

    Azreg-Aïnou, Mustapha

    2010-01-01

    We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4 × 4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic five-dimensional GR, derive some of their properties using ADecM and construct the most general unique power series solutions. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.

  12. 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.

  13. Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models

    NASA Technical Reports Server (NTRS)

    Clayton, D. D.

    1985-01-01

    Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.

  14. 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

  15. Quadratic relations in continuous and discrete Painlevé equations

    NASA Astrophysics Data System (ADS)

    Ramani, A.; Grammaticos, B.; Tamizhmani, T.

    2000-04-01

    The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.

  16. 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

  17. Tailored loss discrimination in indefinite metamaterial-clad hollow-core fibers.

    PubMed

    Tuniz, Alessandro; Zeisberger, Matthias; Schmidt, Markus A

    2016-07-11

    We analyze the modal attenuation properties of silica hollow-core fibers with a gold-wire based indefinite metamaterial cladding at 10.6 µm. We find that by varying the metamaterial feature sizes and core diameter, the loss discrimination can be tailored such that either the HE11, TE01 or TM01 mode has the lowest loss, which is particularly difficult to achieve for the radially polarized mode in commonly used hollow-core fibers. Furthermore, it is possible to tailor the HE11 and TM01 modes in the metamaterial-clad waveguide so that they possess attenuations lower than in hollow tubes composed of the individual constituent materials. We show that S-parameter retrieval techniques in combination with an anisotropic dispersion equation can be used to predict the loss discrimination properties of such fibers. These results pave the way for the design of metamaterial hollow-core fibers with novel guidance properties, in particular for applications demanding cylindrically polarized modes. PMID:27410842

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

    PubMed

    Brown, K; Nowocin, A K; Meader, L; Edwards, L A; Smith, R A; Wong, W

    2016-04-01

    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-A(k) conjugated with the plant-derived ribosomal inactivating protein gelonin. This anti-I-A(k) gelonin immunotoxin depletes I-A(k) 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

  19. 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.

  20. 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

  1. 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

  2. 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.

  3. 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.

  4. 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.)

  5. 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…

  6. 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.

  7. Hydroxyl functionalized thermosensitive microgels with quadratic crosslinking density distribution.

    PubMed

    Elmas, Begum; Tuncel, Murvet; Senel, Serap; Patir, S; Tuncel, Ali

    2007-09-01

    N-isopropylacrylamide (NIPA) based uniform thermosensitive microgels were synthesized by dispersion polymerization by using relatively hydrophilic crosslinking agents with hydroxyl functionality. Glycerol dimethacrylate (GDMA), pentaerythritol triacrylate (PETA) and pentaerythritol propoxylate triacrylate (PEPTA) were used as crosslinking agents with different hydrophilicities. A protocol was first proposed to determine the crosslinking density distribution in the thermosensitive microgel particles by confocal laser scanning microscopy (CLSM). The microgels were fluorescently labeled by using hydroxyl group of the crosslinking agent. The CLSM observations performed with the microgels synthesized by three different crosslinking agents showed that the crosslinking density exhibited a quadratic decrease with the increasing radial distance in the spherical microgel particles. This structure led to the formation of more loose gel structure on the particle surface with respect to the center. Then the use of hydrophilic crosslinking agents in the dispersion polymerization of NIPA made possible the synthesis of thermosensitive microgels carrying long, flexible and chemically derivatizable (i.e., hydroxyl functionalized) fringes on the surface by a single-stage dispersion polymerization. The microgels with all crosslinking agents exhibited volume phase transition with the increasing temperature. The microgel obtained by the most hydrophilic crosslinking agent, GDMA exhibited higher hydrodynamic diameters in the fully swollen form at low temperatures than those obtained by PETA and PEPTA. Higher hydrodynamic size decrease from fully swollen form to the fully shrunken form was also observed with the same microgel. PMID:17532327

  8. 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

  9. Quadratic divergences and quantum gravitational contributions to gauge coupling constants

    NASA Astrophysics Data System (ADS)

    Toms, David J.

    2011-10-01

    The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

  10. Potential harms outweigh benefits of indefinite monitoring of stable adnexal masses.

    PubMed

    Suh-Burgmann, Elizabeth; Kinney, Walter

    2015-12-01

    The management of women with asymptomatic adnexal masses should aim to balance potential benefit with potential harm. While masses with highly worrisome features or other signs of malignancy should be referred for surgery, the vast majority of masses have an indeterminate or benign appearance and are candidates for observation. Evidence supports the use of initial short-term serial ultrasound in distinguishing between benign and malignant masses. However, benefit from prolonged, potentially life-long monitoring of stable masses has not been demonstrated. Since the goal of monitoring an adnexal mass is to observe for worrisome growth or increasing complexity as an indicator of malignancy, if the mass remains stable, the likelihood of malignancy and therefore, the potential benefit of observation wanes with time. The recognition that Type 2 high grade serous cancers, which are responsible for the majority of deaths from ovarian cancer, arise from fallopian tube rather than ovarian precursors, further diminishes the likelihood that monitoring a stable ovarian mass will lead to early diagnosis of high grade disease. While some Type 1 cancers may develop from ovarian precursors, the available data suggest that any measurable benefit of monitoring known lesions for detection of these cancers is realized within the first year of observation. The argument in favor of indefinite, potentially life-long monitoring of stable masses also fails to adequately account for the risks of perpetual imaging, which include the risk of incidental findings, an increased likelihood of unnecessary surgery, patient anxiety and cost. It is not always better to order a test than not order a test. Given the absence of evidence of benefit, observation of stable small adnexal masses should be limited in duration in order to minimize potential harms. PMID:26363476

  11. 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.

  12. 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.

  13. 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.

  14. A linear-quadratic-Gaussian control problem with innovations-feedthrough solution

    NASA Technical Reports Server (NTRS)

    Platzman, L. K.; Johnson, T. L.

    1976-01-01

    The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. Direct Orthogonal Distance to Quadratic Surfaces in 3D.

    PubMed

    Lott, Gus K

    2014-09-01

    Discovering the orthogonal distance to a quadratic surface is a classic geometric task in vision, modeling, and robotics. I describe a simple, efficient, and stable direct solution for the orthogonal distance (foot-point) to an arbitrary quadratic surface from a general finite 3D point. The problem is expressed as the intersection of three quadratic surfaces, two of which are derived from the requirement of orthogonality of two non-coincident planes with the tangent plane to the quadric. A sixth order single-variable polynomial is directly generated in one coordinate of the surface point. The method detects intersection points at infinity and operates smoothly across all real quadratic surface classes. The method also geometrically detects continuums of orthogonal points (i.e., from the exact center of a sphere). I discuss algorithm performance, compare it to a state-of-the-art estimator, demonstrate the algorithm on synthetic data, and describe extension to arbitrary dimension. PMID:26352239

  20. 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.

  1. Quadratic function approaching method for magnetotelluric soundingdata inversion

    SciTech Connect

    Liangjun, Yan; Wenbao, Hu; Zhang, Keni

    2004-04-05

    The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.

  2. AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.

    1994-01-01

    AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user

  3. Gap solitons in a nonlinear quadratic negative-index cavity.

    PubMed

    Scalora, Michael; de Ceglia, Domenico; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Centini, Marco; Bloemer, Mark J

    2007-06-01

    We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton. PMID:17677375

  4. Numerical solution of quadratic matrix equations for free vibration analysis of structures

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1975-01-01

    This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

  5. 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.

  6. 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.

  7. Moments for general quadratic densities in n dimensions

    SciTech Connect

    Furman, Miguel A.

    2002-03-20

    We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

  8. 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.

  9. Use of non-quadratic yield surfaces in design of optimal deep-draw blank geometry

    SciTech Connect

    Logan, R.W.

    1995-12-01

    Planar anisotropy in the deep-drawing of sheet can lead to the formation of ears in cylindrical cups and to undesirable metal flow in the blankholder in the general case. For design analysis purposes in non-linear finite-element codes, this anisotropy is characterized by the use of an appropriate yield surface which is then implemented into codes such as DYNA3D . The quadratic Hill yield surface offers a relatively straightforward implementation and can be formulated to be invariant to the coordinate system. Non-quadratic yield surfaces can provide more realistic strength or strain increment ratios, but they may not provide invariance and thus demand certain approximations. Forms due to Hosford and Badat et al. have been shown to more accurately address the earning phenomenon. in this work, use is made of these non-quadratic yield surfaces in order to determine the optimal blank shape for cups and other shapes using ferrous and other metal blank materials with planar anisotropy. The analyses are compared to previous experimental studies on non-uniform blank motion due to anisotropy and asymmetric geometry.

  10. 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.

  11. 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.

  12. On Volterra quadratic stochastic operators with continual state space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-01

    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 (V λ )(A ) = ∫X ∫X P (x ,y ,A )d λ (x )d λ (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 n →∞ Vn(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.

  13. 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

  14. 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

  15. 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.

  16. Analysis of integral controls in linear quadratic regulator design

    NASA Technical Reports Server (NTRS)

    Slater, G. L.

    1979-01-01

    The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

  17. A Note on the Linearly and Quadratically Weighted Kappa Coefficients.

    PubMed

    Li, Pingke

    2016-09-01

    The linearly and quadratically weighted kappa coefficients are popular statistics in measuring inter-rater agreement on an ordinal scale. It has been recently demonstrated that the linearly weighted kappa is a weighted average of the kappa coefficients of the embedded 2 by 2 agreement matrices, while the quadratically weighted kappa is insensitive to the agreement matrices that are row or column reflection symmetric. A rank-one matrix decomposition approach to the weighting schemes is presented in this note such that these phenomena can be demonstrated in a concise manner. PMID:27246436

  18. A quadratic weight selection algorithm. [for optimal flight control

    NASA Technical Reports Server (NTRS)

    Broussard, J. R.

    1981-01-01

    A new numerical algorithm is presented which determines a positive semi-definite state weighting matrix in the linear-quadratic optimal control design problem. The algorithm chooses the weighting matrix by placing closed-loop eigenvalues and eigenvectors near desired locations using optimal feedback gains. A simplified flight control design example is used to illustrate the algorithms capabilities.

  19. Solving the Quadratic Capacitated Facilities Location Problem by Computer.

    ERIC Educational Resources Information Center

    Cote, Leon C.; Smith, Wayland P.

    Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

  20. 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.

  1. Finding Optimal Gains In Linear-Quadratic Control Problems

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.; Scheid, Robert E., Jr.

    1990-01-01

    Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

  2. 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.

  3. 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.

  4. Selfsimilarity in a Class of Quadratic-Quasiperiodic Chains

    NASA Astrophysics Data System (ADS)

    Kaneko, Masanobu; Odagaki, Takashi

    1993-04-01

    We prove that quasiperiodic chains associated with a class of quadratic irrational numbers have an inflation symmetry and can be generated from a regular chain by a hyperinflation. We devise the explicit method to find the hyperinflation symmetry and discuss the properties of such a class of quasiperiodic sequences.

  5. Unravelling Student Challenges with Quadratics: A Cognitive Approach

    ERIC Educational Resources Information Center

    Kotsopoulos, Donna

    2007-01-01

    The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

  6. 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…

  7. 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)

  8. ORACLS - A linear-quadratic-Gaussian computer-aided design package

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1982-01-01

    ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

  9. 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.

  10. Persistence, Turing Instability and Hopf Bifurcation in a Diffusive Plankton System with Delay and Quadratic Closure

    NASA Astrophysics Data System (ADS)

    Zhao, Jiantao; Wei, Junjie

    A reaction-diffusion plankton system with delay and quadratic closure term is investigated to study the interactions between phytoplankton and zooplankton. Sufficient conditions independent of diffusion and delay are obtained for the persistence of the system. Our conclusions show that diffusion can induce Turing instability, delay can influence the stability of the positive equilibrium and induce Hopf bifurcations to occur. The computational formulas which determine the properties of bifurcating periodic solutions are given by calculating the normal form on the center manifold, and some numerical simulations are carried out for illustrating the theoretical results.

  11. Coherent anti-Stokes Raman spectroscopy utilizing phase mismatched cascaded quadratic optical interactions in nonlinear crystals

    PubMed Central

    Petrov, Georgi I.; Zhi, Miaochan; Yakovlev, Vladislav V.

    2013-01-01

    We experimentally investigated the nonlinear optical interaction between the instantaneous four-wave mixing and the cascaded quadratic frequency conversion in commonly used nonlinear optical KTP and LiNbO3 with the aim of a possible background suppression of the non-resonant background in coherent anti-Stokes Raman scattering. The possibility of background-free heterodyne coherent anti-Stokes Raman scattering microspectroscopy is investigated at the interface formed by a liquid (isopropyl alcohol) and a nonlinear crystal (LiNbO3). PMID:24514791

  12. 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)

  13. Tandem time-of-flight mass spectrometer (TOF-TOF) with a quadratic-field ion mirror

    NASA Astrophysics Data System (ADS)

    Giannakopulos, Anastassios E.; Thomas, Benjamin; Colburn, Alex W.; Reynolds, David J.; Raptakis, Emmanuel N.; Makarov, Alexander A.; Derrick, Peter J.

    2002-05-01

    A tandem time-of-flight (TOF-TOF) mass spectrometer comprised of two ion mirrors is described. The first ion mirror, which is a linear-field, single-stage mirror (MS1) with an intermediate collision cell, has been designed to provide the temporal focus necessary for the second, quadratic-field ion mirror (MS2) to function effectively. Due to the wide energy-range focusing capabilities of the quadratic field employed in the second ion mirror all the fragment ions can be collected in one spectrum without the need to step the reflecting working voltage of the MS2. The size of the active area of the microchannel plate detector used in the preliminary experiments was the limiting factor governing the collection efficiently of fragment ions. The use of the first ion mirror to provide temporal focusing of the precursor ion packet at the first focal point of the quadratic mirror used as the MS2 requires no alteration of the focusing conditions for different masses, in contrast to delayed extraction or postsource pulsed focusing. Precursor ions formed by matrix-assisted laser desorption/ionization were mass-selected with an ion gate located before the collision cell and the fragment ions were mass analyzed using the quadratic-field ion mirror. Experimental results demonstrating effective high-energy collision-induced dissociation of polymer and fullerene molecule-ions are presented.

  14. Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms

    NASA Astrophysics Data System (ADS)

    Benayadi, Saïd; Makhlouf, Abdenacer

    2014-02-01

    The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras equipped with symmetric invariant nondegenerate bilinear forms. We provide several constructions leading to examples and extend the Double Extension Theory to this class of nonassociative algebras. Elements of Representation Theory for Hom-Lie algebras, including adjoint and coadjoint representations, are supplied with application to quadratic Hom-Lie algebras. Centerless involutive quadratic Hom-Lie algebras are characterized. We reduce the case where the twist map is invertible to the study of involutive quadratic Lie algebras. Also, we establish a correspondence between the class of involutive quadratic Hom-Lie algebras and quadratic simple Lie algebras with symmetric involution.

  15. FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING

    EPA Science Inventory

    An automated, fiber optic point quadrat system for vegetation sampling is described. Because the effective point diameter of the system never exceeds 25um it minimizes the substantial errors which can arise with conventional point quadrats. Automatic contact detection eliminates ...

  16. 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.

  17. 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.

  18. Construction of Lagrangian Local Symmetries for General Quadratic Theory

    NASA Astrophysics Data System (ADS)

    Deriglazov, A. A.

    We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of the so-called structure matrices of the Dirac formalism are obtained. The procedure fulfill in terms of initial variables of the theory, and does not imply either separation of constraints on first and second class subsets or any other choice of basis for constraints.

  19. 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.

  20. 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.

  1. Quadratic mutual information for dimensionality reduction and classification

    NASA Astrophysics Data System (ADS)

    Gray, David M.; Principe, José C.

    2010-04-01

    A research area based on the application of information theory to machine learning has attracted considerable interest in the last few years. This research area has been coined information-theoretic learning within the community. In this paper we apply elements of information-theoretic learning to the problem of automatic target recognition (ATR). A number of researchers have previously shown the benefits of designing classifiers based on maximizing the mutual information between the class data and the class labels. Following prior research in information-theoretic learning, in the current results we show that quadratic mutual information, derived using a special case of the more general Renyi's entropy, can be used for classifier design. In this implementation, a simple subspace projection classifier is formulated to find the optimal projection weights such that the quadratic mutual information between the class data and the class labels is maximized. This subspace projection accomplishes a dimensionality reduction of the raw data set wherein information about the class membership is retained while irrelevant information is discarded. A subspace projection based on this criterion preserves as much class discriminability as possible within the subspace. For this paper, laser radar images are used to demonstrate the results. Classification performance against this data set is compared for a gradient descent MLP classifier and a quadratic mutual information MLP classifier.

  2. Macroscopic assembly of indefinitely long and parallel nanowires into large area photodetection circuitry.

    PubMed

    Ozgur, Erol; Aktas, Ozan; Kanik, Mehmet; Yaman, Mecit; Bayindir, Mehmet

    2012-05-01

    Integration of nanowires into functional devices with high yields and good reliability turned out to be a lot more challenging and proved to be a critical issue obstructing the wide application of nanowire-based devices and exploitation of their technical promises. Here we demonstrate a relatively easy macrofabrication of a nanowire-based imaging circuitry using a recently developed nanofabrication technique. Extremely long and polymer encapsulated semiconducting nanowire arrays, mass-produced using the iterative thermal drawing, facilitate the integration process; we manually aligned the fibers containing selenium nanowires over a lithographically defined circuitry. Controlled etching of the encapsulating polymer revealed a monolayer of nanowires aligned over an area of 1 cm(2) containing a 10 × 10 pixel array. Each light-sensitive pixel is formed by the contacting hundreds of parallel photoconductive nanowires between two electrodes. Using the pixel array, alphabetic characters were identified by the circuitry to demonstrate its imaging capacity. This new approach makes it possible to devise extremely large nanowire devices on planar, flexible, or curved substrates with diverse functionalities such as thermal sensors, phase change memory, and artificial skin. PMID:22494446

  3. 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.

  4. 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.

  5. Quadratic programming-based approach for autonomous vehicle path planning in space

    NASA Astrophysics Data System (ADS)

    Chen, Yang; Han, Jianda; Wu, Huaiyu

    2012-07-01

    Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.

  6. N = 2 SUGRA BPS multi-center solutions, quadratic prepotentials and Freudenthal transformations

    NASA Astrophysics Data System (ADS)

    Fernández-Melgarejo, J. J.; Torrente-Lujan, E.

    2014-05-01

    We present a detailed description of N = 2 stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a systematic use of the algebraic properties of the matrix of second derivatives of the prepotential, , which in this case is a scalar-independent matrix. In particular we obtain bounds on the physical parameters of the multicenter solution such as horizon areas and ADM mass. We discuss the possibility and convenience of setting up a basis of the symplectic vector space built from charge eigenvectors of the , the set of vectors (P± q a) with P± -eigenspace projectors. The anti-involution matrix can be understood as a Freudenthal duality . We show that this duality can be generalized to "Freudenthal transformations" under which the horizon area, ADM mass and intercenter distances scale up leaving constant the scalars at the fixed points. In the special case λ = 1, "-rotations", the transformations leave invariant the solution. The standard Freudenthal duality can be written as . We argue that these generalized transformations leave invariant not only the quadratic prepotential theories but also the general stringy extremal quartic form Δ4, Δ4( x) = Δ4(cos θx + sin θ ) and therefore its entropy at lowest order.

  7. 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.

  8. Multivariable quadratic synthesis of an advanced turbofan engine controller

    NASA Technical Reports Server (NTRS)

    Dehoff, R. L.; Hall, W. E., Jr.

    1978-01-01

    A digital controller for an advanced turbofan engine utilizing multivariate feedback is described. The theoretical background of locally linearized control synthesis is reviewed briefly. The application of linear quadratic regulator techniques to the practical control problem is presented. The design procedure has been applied to the F100 turbofan engine, and details of the structure of this system are explained. Selected results from simulations of the engine and controller are utilized to illustrate the operation of the system. It is shown that the general multivariable design procedure will produce practical and implementable controllers for modern, high-performance turbine engines.

  9. 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.

  10. 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.

  11. 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.

  12. Analysis of electroperforated materials using the quadrat counts method

    NASA Astrophysics Data System (ADS)

    Miranda, E.; Garzón, C.; Martínez-Cisneros, C.; Alonso, J.; García-García, J.

    2011-06-01

    The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.

  13. Quadratic Interaction Functional for General Systems of Conservation Laws

    NASA Astrophysics Data System (ADS)

    Bianchini, Stefano; Modena, Stefano

    2015-09-01

    For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

  14. 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.

  15. 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.

  16. 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.

  17. 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. PMID:27409038

  18. Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

    NASA Astrophysics Data System (ADS)

    Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández

    Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.

  19. 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.

  20. 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

  1. 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.

  2. 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.

  3. 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.

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

    PubMed Central

    RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

    2013-01-01

    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

  5. 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.

  6. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

    NASA Astrophysics Data System (ADS)

    Xu, Jiuping; Li, Jun

    2002-09-01

    In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

  7. 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.

  8. Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations

    NASA Astrophysics Data System (ADS)

    Mishra, Sudhakara

    1991-02-01

    We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of

  9. Dark state in a nonlinear optomechanical system with quadratic coupling

    NASA Astrophysics Data System (ADS)

    Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng

    We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).

  10. 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.