Fixed point theorems for generalized contractions in ordered metric spaces
NASA Astrophysics Data System (ADS)
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
Some fixed point theorems in generating space of b-quasi-metric family.
Kumari, P Sumati; Sarwar, Muhammad
2016-01-01
The purpose of this work is to study some properties of "Generating space of b-quasi-metric family"(simply [Formula: see text]-family) and derive some fixed point theorems using some standard contractions. Presented theorems extend and generalize many well-known results in the literature of fixed point theory .
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings
NASA Astrophysics Data System (ADS)
Feng, Yuqiang; Liu, Sanyang
2006-05-01
In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc.
Searching for fixed point combinators by using automated theorem proving: A preliminary report
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, THETA must satisfy the equation THETAx = x(THETAx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs.
On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem
NASA Astrophysics Data System (ADS)
Eldred, A. Anthony; Anuradha, J.; Veeramani, P.
2007-12-01
We consider two generalizations of Nadler's theorem, one proved by Mizoguchi and Takahashi in response to the Reich conjecture and another theorem proved by Kaneko. We show that due to the additional conditions of these theorems the given multi-valued map reduces to a multi-valued contraction mapE We prove this result by showing that the orbit of the multi-valued map is bounded under the contractive conditions of the two generalizations.
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. PMID:24757423
Fixed points for weakly inward mappings in Banach spaces
NASA Astrophysics Data System (ADS)
Xu, Shaoyuan; Jia, Baoguo; Li, Guo-Zhen
2006-07-01
S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,[Omega],P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=[mu]x, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works.
Characterizations of fixed points of quantum operations
Li Yuan
2011-05-15
Let {phi}{sub A} be a general quantum operation. An operator B is said to be a fixed point of {phi}{sub A}, if {phi}{sub A}(B)=B. In this note, we shall show conditions under which B, a fixed point {phi}{sub A}, implies that B is compatible with the operation element of {phi}{sub A}. In particular, we offer an extension of the generalized Lueders theorem.
The Euler Line and Nine-Point-Circle Theorems.
ERIC Educational Resources Information Center
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Fixed points of quantum gravity.
Litim, Daniel F
2004-05-21
Euclidean quantum gravity is studied with renormalization group methods. Analytical results for a nontrivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameters in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.
Image integrity authentication scheme based on fixed point theory.
Li, Xu; Sun, Xingming; Liu, Quansheng
2015-02-01
Based on the fixed point theory, this paper proposes a new scheme for image integrity authentication, which is very different from digital signature and fragile watermarking. By the new scheme, the sender transforms an original image into a fixed point image (very close to the original one) of a well-chosen transform and sends the fixed point image (instead of the original one) to the receiver; using the same transform, the receiver checks the integrity of the received image by testing whether it is a fixed point image and locates the tampered areas if the image has been modified during the transmission. A realization of the new scheme is based on Gaussian convolution and deconvolution (GCD) transform, for which an existence theorem of fixed points is proved. The semifragility is analyzed via commutativity of transforms, and three commutativity theorems are found for the GCD transform. Three iterative algorithms are presented for finding a fixed point image with a few numbers of iterations, and for the whole procedure of image integrity authentication; a fragile authentication system and a semifragile one are separately built. Experiments show that both the systems have good performance in transparence, fragility, security, and tampering localization. In particular, the semifragile system can perfectly resist the rotation by a multiple of 90° flipping and brightness attacks.
Contractive multifunctions, fixed point inclusions and iterated multifunction systems
NASA Astrophysics Data System (ADS)
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2007-06-01
We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x[set membership, variant]Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x0[set membership, variant]X to a point x[set membership, variant]XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT as well as a "generalized collage theorem" for contractive multifunctions. These results can then be used to solve inverse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems.
Renormalization Group Trajectories Between Two Fixed Points
NASA Astrophysics Data System (ADS)
Abdesselam, Abdelmalek
2010-03-01
We report on our recent rigorous construction of complete renormalization group trajectories between two fixed points for the three-dimensional phi-four model with modified propagator considered by Brydges, Mitter and Scoppola (BMS). These are discrete critical trajectories which connect the ultraviolet Gaussian fixed point to the nontrivial BMS infrared fixed point which is an analogue of the Wilson-Fisher fixed point. The renormalization group map is defined rigorously and nonperturbatively, without using the hierarchical approximation. The trajectories are constructed by a fixed point argument in a suitable Banach space of sequences, where one perturbs a nonlinear one-dimensional iteration.
Anderson Acceleration for Fixed-Point Iterations
Walker, Homer F.
2015-08-31
The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.
Gravitational Fixed Points from Perturbation Theory
Niedermaier, Max R.
2009-09-04
The fixed point structure of the renormalization flow in higher derivative gravity is investigated in terms of the background covariant effective action using an operator cutoff that keeps track of powerlike divergences. Spectral positivity of the gauge fixed Hessian can be satisfied upon expansion in the asymptotically free higher derivative coupling. At one-loop order in this coupling strictly positive fixed points are found for the dimensionless Newton constant g{sub N} and the cosmological constant lambda, which are determined solely by the coefficients of the powerlike divergences. The renormalization flow is asymptotically safe with respect to this fixed point and settles on a lambda(g{sub N}) trajectory after O(10) units of the renormalization mass scale to accuracy 10{sup -7}.
Gravitational fixed points from perturbation theory.
Niedermaier, Max R
2009-09-01
The fixed point structure of the renormalization flow in higher derivative gravity is investigated in terms of the background covariant effective action using an operator cutoff that keeps track of powerlike divergences. Spectral positivity of the gauge fixed Hessian can be satisfied upon expansion in the asymptotically free higher derivative coupling. At one-loop order in this coupling strictly positive fixed points are found for the dimensionless Newton constant g(N) and the cosmological constant lambda, which are determined solely by the coefficients of the powerlike divergences. The renormalization flow is asymptotically safe with respect to this fixed point and settles on a lambda(g(N)) trajectory after O(10) units of the renormalization mass scale to accuracy 10(-7).
NASA Astrophysics Data System (ADS)
Young, Frederic; Siegel, Edward
Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!
Quantum entanglement and fixed-point bifurcations
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-04-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.
Precise Point Positioning with Partial Ambiguity Fixing
Li, Pan; Zhang, Xiaohong
2015-01-01
Reliable and rapid ambiguity resolution (AR) is the key to fast precise point positioning (PPP). We propose a modified partial ambiguity resolution (PAR) method, in which an elevation and standard deviation criterion are first used to remove the low-precision ambiguity estimates for AR. Subsequently the success rate and ratio-test are simultaneously used in an iterative process to increase the possibility of finding a subset of decorrelated ambiguities which can be fixed with high confidence. One can apply the proposed PAR method to try to achieve an ambiguity-fixed solution when full ambiguity resolution (FAR) fails. We validate this method using data from 450 stations during DOY 021 to 027, 2012. Results demonstrate the proposed PAR method can significantly shorten the time to first fix (TTFF) and increase the fixing rate. Compared with FAR, the average TTFF for PAR is reduced by 14.9% for static PPP and 15.1% for kinematic PPP. Besides, using the PAR method, the average fixing rate can be increased from 83.5% to 98.2% for static PPP, from 80.1% to 95.2% for kinematic PPP respectively. Kinematic PPP accuracy with PAR can also be significantly improved, compared to that with FAR, due to a higher fixing rate. PMID:26067196
Existence and data dependence of fixed points for multivalued operators on gauge spaces
NASA Astrophysics Data System (ADS)
Espínola, Rafael; Petrusel, Adrian
2005-09-01
The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued a[alpha]-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petrusel, and Sîntamarian [I.A. Rus, A. Petrusel, A. Sîntamarian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].
Secure Computation with Fixed-Point Numbers
NASA Astrophysics Data System (ADS)
Catrina, Octavian; Saxena, Amitabh
Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.
Fixed point results for G-α-contractive maps with application to boundary value problems.
Hussain, Nawab; Parvaneh, Vahid; Roshan, Jamal Rezaei
2014-01-01
We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α -admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.
Strongly coupled fixed point in φ 4 theory
NASA Astrophysics Data System (ADS)
Hegg, Anthony; Phillips, Philip W.
2016-07-01
We show explicitly how a fixed point can be constructed in scalar g\\varphi4 theory from the solutions to a nonlinear eigenvalue problem. The fixed point is unstable and characterized by ν=2/d (correlation length exponent), η=1/2-d/8 (anomalous dimension). For d = 2, these exponents reproduce to those of the Ising model which can be understood from the codimension of the critical point. The testable prediction of this fixed point is that the specific heat exponent vanishes. 2d critical Mott systems are well described by this new fixed point.
Huang, Na; Ma, Changfeng
2014-01-01
We present a fixed-point iterative method for solving systems of nonlinear equations. The convergence theorem of the proposed method is proved under suitable conditions. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach.
Solving a system of Volterra-Fredholm integral equations of the second kind via fixed point method
NASA Astrophysics Data System (ADS)
Hasan, Talaat I.; Salleh, Shaharuddin; Sulaiman, Nejmaddin A.
2015-12-01
In this paper, we consider the system of Volterra-Fredholm integral equations of the second kind (SVFI-2). We propose fixed point method (FPM) to solve SVFI-2. In addition, a few theorems and new algorithm is introduced. They are supported by numerical examples and simulations using Matlab. The results are reasonably good when compared with the exact solutions.
Floating-to-Fixed-Point Conversion for Digital Signal Processors
NASA Astrophysics Data System (ADS)
Menard, Daniel; Chillet, Daniel; Sentieys, Olivier
2006-12-01
Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.
Krasnoselski Mann iteration for hierarchical fixed-point problems
NASA Astrophysics Data System (ADS)
Moudafi, Abdellatif
2007-08-01
This paper deals with a method for approximating a solution of the following fixed-point problem: find \\tilde{x} \\in {\\cal H}; \\tilde{x} = (proj_{Fix(T)} \\circ P) \\tilde{x} , where {\\cal H} is a Hilbert space, P and T are two nonexpansive mappings on a closed convex subset D and projFix(T) denotes the metric projection on the set of fixed points of T. This amounts to saying that \\tilde{x} is the fixed point of T which satisfies a variational inequality depending on a given criterion P, namely: find \\tilde{x} \\in {\\cal H}; 0\\in (I-P)\\tilde{x}+N_{ Fix(T)}\\tilde{x} , where NFix(T) denotes the normal cone to the set of fixed points of T. Convergence results for the proposed method are proved. It should be noted that the proposed method can be regarded as a generalized version of Krasnoselski-Mann's iteration for solving a broader class of problems than the original KM algorithm, namely hierarchical fixed-point problems. This class is very interesting because it covers monotone variational inequality on fixed-point sets, minimization problems over equilibrium constraints, hierarchical minimization problems,.... The special aspect of the algorithm together with convergence results makes it an original and theoretically interesting scheme. On the other hand, the framework is general enough and permits us to treat in a unified way several iterative schemes, recovering, developing and improving some known related convergence results in this field.
Fixed-point bifurcation analysis in biological models using interval polynomials theory.
Rigatos, Gerasimos G
2014-06-01
The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the evaluation of the type of stability for each fixed point through the computation of the eigenvalues of the Jacobian matrix that is associated with the system's nonlinear dynamics model. Stage (ii) requires the computation of the roots of the characteristic polynomial of the Jacobian matrix. This problem is nontrivial since the coefficients of the characteristic polynomial are functions of the bifurcation parameter and the latter varies within intervals. To obtain a clear view about the values of the roots of the characteristic polynomial and about the stability features they provide to the system, the use of interval polynomials theory and particularly of Kharitonov's stability theorem is proposed. In this approach, the study of the stability of a characteristic polynomial with coefficients that vary in intervals is equivalent to the study of the stability of four polynomials with crisp coefficients computed from the boundaries of the aforementioned intervals. The efficiency of the proposed approach for the analysis of fixed-point bifurcations in nonlinear models of biological neurons is tested through numerical and simulation experiments.
A new compact fixed-point blackbody furnace
Hiraka, K.; Oikawa, H.; Shimizu, T.; Kadoya, S.; Kobayashi, T.; Yamada, Y.; Ishii, J.
2013-09-11
More and more NMIs are realizing their primary scale themselves with fixed-point blackbodies as their reference standard. However, commercially available fixed-point blackbody furnaces of sufficient quality are not always easy to obtain. CHINO Corp. and NMIJ, AIST jointly developed a new compact fixed-point blackbody furnace. The new furnace has such features as 1) improved temperature uniformity when compared to previous products, enabling better plateau quality, 2) adoption of the hybrid fixed-point cell structure with internal insulation to improve robustness and thereby to extend lifetime, 3) easily ejectable and replaceable heater unit and fixed-point cell design, leading to reduced maintenance cost, 4) interchangeability among multiple fixed points from In to Cu points. The replaceable cell feature facilitates long term maintenance of the scale through management of a group of fixed-point cells of the same type. The compact furnace is easily transportable and therefore can also function as a traveling standard for disseminating the radiation temperature scale, and for maintaining the scale at the secondary level and industrial calibration laboratories. It is expected that the furnace will play a key role of the traveling standard in the anticipated APMP supplementary comparison of the radiation thermometry scale.
Local completeness, drop theorem and Ekeland's variational principle
NASA Astrophysics Data System (ADS)
Qiu, Jing-Hui
2005-11-01
By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Danes' drop theorem, Ekeland's variational principle, Caristi's fixed points theorem and Phelps lemma are equivalent to each other.
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2012 CFR
2012-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2014 CFR
2014-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2013 CFR
2013-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2011 CFR
2011-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Interconnection of private operational fixed point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS....137 Interconnection of private operational fixed point-to-point microwave stations....
Towards a complete renormalization group trajectory between two fixed points
NASA Astrophysics Data System (ADS)
Abdesselam, Abdelmalek
2007-12-01
We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.
Stray thermal influences in zinc fixed-point cells
Rudtsch, S.; Aulich, A.; Monte, C.
2013-09-11
The influence of thermal effects is a major uncertainty contribution to the calibration of Standard Platinum Resistance Thermometers (SPRTs) in fixed-point cells. Axial heat losses strongly depend on the fixed-point temperature, constructional details of cells and SPRTs and the resulting heat transfer between cell, thermometer, furnace and environment. At the zinc point contributions by heat conduction and thermal radiation must be considered. Although the measurement of temperature gradients in the re-entrant well of a fixed-point cell provides very important information about the influence of axial heat losses, further investigations are required for a reliable estimate of the resulting uncertainty contribution. It is shown that specific modifications of a zinc fixed-point cell, following generally accepted principles, may result in systematic deviations of the measured fixed-point temperatures larger than typically stated in the uncertainty budget of National Metrology Institutes (NMIs). The underlying heat transport processes are investigated and the consequences for the construction of zinc cells are discussed.
Implicit function theorem as a realization of the Lagrange principle. Abnormal points
Arutyunov, A V
2000-02-28
A smooth non-linear map is studied in a neighbourhood of an abnormal (degenerate) point. Inverse function and implicit function theorems are proved. The proof is based on the examination of a family of constrained extremal problems; second-order necessary conditions, which make sense also in the abnormal case, are used in the process. If the point under consideration is normal, then these conditions turn into the classical ones.
Border collisions inside the stability domain of a fixed point
NASA Astrophysics Data System (ADS)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2016-05-01
Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.
Fixed-Rate Compressed Floating-Point Arrays.
Lindstrom, Peter
2014-12-01
Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation.
Fixed-Rate Compressed Floating-Point Arrays.
Lindstrom, Peter
2014-12-01
Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation. PMID:26356981
Measurement of thermodynamic temperature of high temperature fixed points
Gavrilov, V. R.; Khlevnoy, B. B.; Otryaskin, D. A.; Grigorieva, I. A.; Samoylov, M. L.; Sapritsky, V. I.
2013-09-11
The paper is devoted to VNIIOFI's measurements of thermodynamic temperature of the high temperature fixed points Co-C, Pt-C and Re-C within the scope of the international project coordinated by the Consultative Committee for Thermometry working group 5 'Radiation Thermometry'. The melting temperatures of the fixed points were measured by a radiance mode radiation thermometer calibrated against a filter radiometer with known irradiance spectral responsivity via a high temperature black body. This paper describes the facility used for the measurements, the results and estimated uncertainties.
Fixed Point Problems for Linear Transformations on Pythagorean Triples
ERIC Educational Resources Information Center
Zhan, M.-Q.; Tong, J.-C.; Braza, P.
2006-01-01
In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…
Non-thermal fixed point in a holographic superfluid
NASA Astrophysics Data System (ADS)
Ewerz, Carlo; Gasenzer, Thomas; Karl, Markus; Samberg, Andreas
2015-05-01
We study the far-from-equilibrium dynamics of a (2 + 1)-dimensional super-fluid at finite temperature and chemical potential using its holographic description in terms of a gravitational system in 3 + 1 dimensions. Starting from various initial conditions corresponding to ensembles of vortex defects we numerically evolve the system to long times. At intermediate times the system exhibits Kolmogorov scaling the emergence of which depends on the choice of initial conditions. We further observe a universal late- time regime in which the occupation spectrum and different length scales of the superfluid exhibit scaling behaviour. We study these scaling laws in view of superfluid turbulence and interpret the universal late-time regime as a non-thermal fixed point of the dynamical evolution. In the holographic superfluid the non-thermal fixed point can be understood as a stationary point of the classical equations of motion of the dual gravitational description.
Fixed-rate compressed floating-point arrays
Lindstrom, P.
2014-03-30
ZFP is a library for lossy compression of single- and double-precision floating-point data. One of the unique features of ZFP is its support for fixed-rate compression, which enables random read and write access at the granularity of small blocks of values. Using a C++ interface, this allows declaring compressed arrays (1D, 2D, and 3D arrays are supported) that through operator overloading can be treated just like conventional, uncompressed arrays, but which allow the user to specify the exact number of bits to allocate to the array. ZFP also has variable-rate fixed-precision and fixed-accuracy modes, which allow the user to specify a tolerance on the relative or absolute error.
Fixed-rate compressed floating-point arrays
2014-03-30
ZFP is a library for lossy compression of single- and double-precision floating-point data. One of the unique features of ZFP is its support for fixed-rate compression, which enables random read and write access at the granularity of small blocks of values. Using a C++ interface, this allows declaring compressed arrays (1D, 2D, and 3D arrays are supported) that through operator overloading can be treated just like conventional, uncompressed arrays, but which allow the user tomore » specify the exact number of bits to allocate to the array. ZFP also has variable-rate fixed-precision and fixed-accuracy modes, which allow the user to specify a tolerance on the relative or absolute error.« less
Gravity Duals of Lifshitz-Like Fixed Points
Kachru, Shamit; Liu, Xiao; Mulligan, Michael; /Stanford U., Phys. Dept. /SLAC
2008-11-05
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
Gravity duals of Lifshitz-like fixed points
NASA Astrophysics Data System (ADS)
Kachru, Shamit; Liu, Xiao; Mulligan, Michael
2008-11-01
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t→λzt, x→λx; we focus on the case with z=2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemble forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.
Thermal analysis on the realization of the tin fixed point
NASA Astrophysics Data System (ADS)
Tsai, S. F.
2013-09-01
A study on the thermal analysis of a new tin fixed-point open cell within a new three-zone furnace was carried out. The stability at the setting temperatures of liquid-solid coexisting together with some degree Celsius lower and higher than the tin fixed point; and the axial uniformity of furnace while tin is still in solid phase were investigated and analyzed. The impurities effect on the depression in temperature was investigated in terms of ΔT (Tobserved-T1/F=0) and the inverse of the melted fraction (1/F) relationship during the melting and the following freezing realizations at various temperature settings of furnace. These thermal analysis results were also compared with those estimated by the CCT-WG1 recommended SIE (sum of individual estimates) method, which leads to a temperature correction along with a corresponding uncertainty through the individual impurity content detected by GDMS (glow discharge mass spectrometry).
Fixed points, stable manifolds, weather regimes, and their predictability.
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-12-01
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model's fixed points in phase space. The model dynamics is characterized by the coexistence of multiple "weather regimes." To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, "bred vectors" and singular vectors. These results are then verified in the framework of ensemble forecasts issued from "clouds" (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemblemore » forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.« less
The computational core and fixed point organization in Boolean networks
NASA Astrophysics Data System (ADS)
Correale, L.; Leone, M.; Pagnani, A.; Weigt, M.; Zecchina, R.
2006-03-01
In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows us to prune simple logical cascades and underdetermined variables, returning thereby the computational core of the network. Second, we apply the cavity method to analyse the number and organization of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter being characterized by the existence of an exponential number of macroscopically separated fixed point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied in the analysis of and in silico experiments on the gene regulatory networks of baker's yeast (Saccharomyces cerevisiae) and the segment-polarity genes of the fruitfly Drosophila melanogaster.
Fixed point structure of quenched, planar quantum electrodynamics
Love, S.T.
1986-07-01
Gauge theories exhibiting a hierarchy of fermion mass scales may contain a pseudo-Nambu-Boldstone boson of spontaneously broken scale invariance. The relation between scale and chiral symmetry breaking is studied analytically in quenched, planar quantum electrodynamics in four dimensions. The model possesses a novel nonperturbative ultraviolet fixed point governing its strong coupling phase which requires the mixing of four fermion operators. 12 refs.
Assigning thermodynamic temperatures to high-temperature fixed-points
NASA Astrophysics Data System (ADS)
Woolliams, E. R.; Bloembergen, P.; Machin, G.
2013-09-01
Workpackage five of the High Temperature Fixed-Point research programme will determine the thermodynamic temperature for the equilibrium melting transition of the pure eutectic systems of Re-C, Pt-C and Co-C and, in addition, the freezing point of Cu. Measurements of four different cells of each type will be made by nine participating laboratories. This paper describes how the melt sensitivity to the rate of the previous freeze, furnace effects and cell impurities will be accounted for and how the results will be combined allowing for all existing correlations.
A drop theorem without vector topology
NASA Astrophysics Data System (ADS)
Wong, Chi-Wing
2007-05-01
Danes' drop theorem is extended to bornological vector spaces. An immediate application is to establish Ekeland-type variational principle and its equivalence, Caristi fixed point theorem, in bornological vector spaces. Meanwhile, since every locally convex space becomes a convex bornological vector space when equipped with the canonical von Neumann bornology, Qiu's generalization of Danes' work to locally convex spaces is recovered.
Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer
Golubev, D.; Utsumi, Y.; Marthaler, M.; Schön, G.
2013-12-04
Motivated by recent experiments on the real-time single-electron counting through a semiconductor GaAs double quantum dot (DQD) by a nearby quantum point contact (QPC), we develop the full-counting statistics of coupled DQD and QPC system. By utilizing the time-scale separation between the dynamics of DQD and QPC, we derive the modified master equation with tunneling rates depending on the counting fields, which fulfill the detailed fluctuation theorem. Furthermore, we derive universal relations between the non-linear corrections to the current and noise, which can be verified in experiments.
Fate of CPN-1 fixed points with q monopoles.
Block, Matthew S; Melko, Roger G; Kaul, Ribhu K
2013-09-27
We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles. PMID:24116811
Fixed-point error analysis of Winograd Fourier transform algorithms
NASA Technical Reports Server (NTRS)
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Fixed Point Transformations Based Iterative Control of a Polymerization Reaction
NASA Astrophysics Data System (ADS)
Tar, József K.; Rudas, Imre J.
As a paradigm of strongly coupled non-linear multi-variable dynamic systems the mathematical model of the free-radical polymerization of methyl-metachrylate with azobis (isobutyro-nitrile) as an initiator and toluene as a solvent taking place in a jacketed Continuous Stirred Tank Reactor (CSTR) is considered. In the adaptive control of this system only a single input variable is used as the control signal (the process input, i.e. dimensionless volumetric flow rate of the initiator), and a single output variable is observed (the process output, i.e. the number-average molecular weight of the polymer). Simulation examples illustrate that on the basis of a very rough and primitive model consisting of two scalar variables various fixed-point transformations based convergent iterations result in a novel, sophisticated adaptive control.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors. PMID:27563948
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Ryttov, Thomas A.
2016-08-01
We suggest how to consistently calculate the anomalous dimension γ* of the ψ ¯ ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n +1 loop beta function and n loop anomalous dimension are known, then γ* can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O (Δfn) , where Δf=N¯ f-Nf , Nf is the number of flavors, and N¯f is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δf. We then compute γ* through O (Δf2) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ* is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ* through O (Δf3) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ* are observed for a large range of flavors.
Comparison of three Co-C fixed points constructed using different crucible lining materials
NASA Astrophysics Data System (ADS)
Todd, A. D. W.; Woods, D. J.
2013-09-01
The melting plateaus of three Co-C fixed points for radiation thermometry with different constructions were measured and compared. Two of the fixed points were of the hybrid type and contained either carbon composite cloth or pyrolytic graphite sheet between the graphite sleeve and the crucible wall. The third fixed point contained only the graphite sleeve. Little difference was found in the shapes of the melting curves between the fixed points. Given a comparison uncertainty of 37 mK (k = 1), there were, however, significant differences in the melting temperatures determined for each of the fixed points. Over three days of measurement, the melting temperature of the fixed point filled using the pyrolytic sheet drifted up by nearly 140 mK.
NASA Astrophysics Data System (ADS)
Heikkila, S.
2007-08-01
In this paper we apply generalized iteration methods to prove comparison results which show how fixed points of a multifunction can be bounded by least and greatest fixed points of single-valued functions. As an application we prove existence and comparison results for fixed points of multifunctions. These results are applied to normal-form games, by proving existence and comparison results for pure and mixed Nash equilibria and their utilities.
Copper Fixed-Point Measurements for Radiation Thermometry at National Research Council
NASA Astrophysics Data System (ADS)
Todd, A. D. W.; Woods, D. J.
2014-07-01
Due to its high transition temperature relative to other fixed points defined in the International Temperature Scale of 1990 (ITS-90) and its relatively low cost compared to silver and gold, copper is often chosen as the fixed point used to define the ITS-90 above 1235 K at national measurement institutes. Measurement of the copper freezing point can be done in a variety of furnaces. Although there are a large number of copper fixed-point designs, we expect the freezing temperatures to be the same. The difference between realizing different sized fixed points and the use of different furnaces in which to realize them is explored here. A traditional, large aperture fixed-point containing over 600 g of copper is compared to a hybrid-type fixed point containing only 15 g of copper and a commercial fixed point. Three types of furnaces including a heat-pipe furnace, a compact furnace, and a high-temperature blackbody were used to realize the copper freezing point. Between the fixed-point types, only the length of the plateau differed. However, a significant difference was found between the freezing temperatures determined in the different furnaces, and this difference was independent of cell type.
Triple point of e-deuterium as an accurate thermometric fixed point
Pavese, F.; McConville, G.T.
1986-01-01
The triple point of deuterium (18.7/sup 0/K) is the only possibility for excluding vapor pressure measurements in the definition of a temperature scale based on fixed points between 13.81 and 24.562/sup 0/K. This paper reports an investigation made at the Istituto di Metrologia and Mound Laboratory, using extremely pure deuterium directly sealed at the production plant into small metal cells. The large contamination by HD of commercially available gas, that cannot be accounted and corrected for due to its increase in handling, was found to be very stable with time after sealing in IMGC cells. HD contamination can be limited to less than 100 ppM in Monsanto cells, both with n-D/sub 2/ and e-D/sub 2/, when filled directly from the thermal diffusion column and sealed at the factory. e-D/sub 2/ requires a special deuterated catalyst. The triple point temperature of e-D/sub 2/ has been determined to be: T(NPL-IPTS-68) = 18.7011 +- 0.002/sup 0/K. 20 refs., 3 figs., 2 tabs.
Area law for fixed points of rapidly mixing dissipative quantum systems
Brandão, Fernando G. S. L.; Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David
2015-10-15
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure or the system is frustration free.
A New Co-C Eutectic Fixed-Point Cell for Thermocouple Calibration at
NASA Astrophysics Data System (ADS)
Failleau, G.; Deuzé, T.; Jouin, D.; Mokdad, S.; Briaudeau, S.; Sadli, M.
2014-07-01
The eutectic Co-C is a promising system to serve as a thermometric fixed point beyond the freezing point of copper (). Some national metrology institutes have developed, characterized, and compared their Co-C fixed-point cells based on conventional designs. Indeed, the fixed-point cells constructed are directly inspired by the technologies applied to the fixed points of the ITS-90 to the lower levels of temperature. By studying the eutectic metal-carbon systems, is appears that the high temperatures of implementation give a set of difficulties, such as the strong mechanical stresses on the graphite crucibles, due to the important thermal expansion of the eutectic alloys during their phase transitions. If these devices are suitable with research activities to serve like primary standards, it is not envisaged to propose them for a direct application to the calibration activities for the industry. As regards the limited robustness of the conventional fixed-point cells constructed, an intensive use of these device would not be reasonable, in term of cost for example. In this paper, a new Co-C fixed-point design is introduced. This low cost device has been developed specifically for intensive use in thermocouple calibration activities, with the aim of achieving the lowest level of uncertainties as is practicable. Thus, in this paper, the metrological characterization of this device is also presented, and a direct comparison to a primary Co-C fixed-point cell previously constructed is discussed.
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
NASA Astrophysics Data System (ADS)
Nikolić, Zoran; Nguyen, Ha Thai; Frantz, Gene
2007-12-01
Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs) to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.
NASA Astrophysics Data System (ADS)
Dittmore, Andrew; Trail, Collin; Olsen, Thomas; Wiener, Richard J.
2003-11-01
We have previously demonstrated the experimental control of chaos in a Modified Taylor-Couette system with hourglass geometry( Richard J. Wiener et al), Phys. Rev. Lett. 83, 2340 (1999).. Identifying fixed points susceptible to algorithms for the control of chaos is key. We seek to learn about this process in the accessible numerical model of the damped, driven pendulum. Following Baker(Gregory L. Baker, Am. J. Phys. 63), 832 (1995)., we seek points susceptible to the OGY(E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64), 1196 (1990). algorithm. We automate the search for fixed points that are candidates for control. We present comparisons of the space of candidate fixed points with the bifurcation diagrams and Poincare sections of the system. We demonstrate control at fixed points which do not appear on the attractor. We also show that the control algorithm may be employed to shift the system between non-communicating branches of the attractor.
Implementation Considerations for Automotive Vision Systems on a Fixed-Point DSP
NASA Astrophysics Data System (ADS)
Nikolić, Zoran
In this chapter we evaluate numerical requirements for implementation of camera-based lateral position detection algorithms, such as lane keep assistant (LKA) and lane departure warning (LDW) on a fixed-point DSP. We first present methods that address the challenges and requirements of fixed-point design process. The flow proposed is targeted at converting C/C++ code with floating-point operations into C code with integer operations that can then be fed through the native C compiler for a fixed-point DSP. Advanced code optimization and an implementation by DSP-specific, fixed-point C code generation are introduced. We then demonstrate the conversion flow on tracking example (extended Kalman filter) using synthetically generated data, and we analyze trade-offs for algorithm implementation in fixed-point arithmetic. By using the techniques described in this chapter speed can be increased by a factor of up to 10 compared to floating-point emulation on fixed-point hardware.
Error tolerance in an NMR implementation of Grover's fixed-point quantum search algorithm
Xiao Li; Jones, Jonathan A.
2005-09-15
We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance quantum computer, searching for either one or two matching items in an unsorted database of four items. In this algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, so that the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored.
Conducting fixed points for inhomogeneous quantum wires: A conformally invariant boundary theory
NASA Astrophysics Data System (ADS)
Sedlmayr, N.; Morath, D.; Sirker, J.; Eggert, S.; Affleck, I.
2014-01-01
Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is "healing," which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.
Analysis of fixed point FFT for Fourier domain optical coherence tomography systems.
Ali, Murtaza; Parlapalli, Renuka; Magee, David P; Dasgupta, Udayan
2009-01-01
Optical coherence tomography (OCT) is a new imaging modality gaining popularity in the medical community. Its application includes ophthalmology, gastroenterology, dermatology etc. As the use of OCT increases, the need for portable, low power devices also increases. Digital signal processors (DSP) are well suited to meet the signal processing requirements of such a system. These processors usually operate on fixed precision. This paper analyzes the issues that a system implementer faces implementing signal processing algorithms on fixed point processor. Specifically, we show the effect of different fixed point precisions in the implementation of FFT on the sensitivity of Fourier domain OCT systems. PMID:19965018
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom). PMID:26196806
NASA Astrophysics Data System (ADS)
Viesca, R. C.
2014-12-01
A fault's transition from slow creep to the propagation of an earthquake-generating dynamic rupture is thought to start as a quasi-static slip instability. Here we examine how such an instability develops on a sliding interface whose strength is governed by a slip rate- and state-dependent friction, where the state variable evolves according to the aging law. We find that the development occurs as the attraction of a dynamical system to a fixed point. The fixed points are such that the state of slip and the rate at which velocity diverges (and its spatial distribution) are known. The fixed points are independent of the manner of external forcing and the values of slip rate and state before the onset of instability. For a fault under uniform normal stress and frictional properties, the sole parameter that determines the fixed point (to within a translational invariance) is the ratio of the frictional parameters, a/b (where, for steady-state rate weakening, 0fixed points are asymptotically stable; however, stability is lost for a/b above that value. Increasing a/b above this critical value leads to a series of Hopf bifurcations. This cascade of bifurcations signals a quasi-periodic route to chaos, implying the existence of a second, larger, critical value of a/b (corresponding to the value at which the third Hopf bifurcation occurs), above which the slip instability may develop in a chaotic fashion. The fixed-point solutions, as well as the critical thresholds concerning their stability, depend on the configuration of slip (e.g., in/anti-plane or mixed-mode slip) and the elastic environment in which the interface is embedded (e.g., a slip surface between elastic half-spaces or one lying below and parallel to a free surface); solving for a fixed point reduces to the solution of an equivalent problem of an equilibrium slip-weakening fracture; and fixed-point stability is determined by linear stability analysis. Solutions of
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
2015-10-01
We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
Side Effects in Time Discounting Procedures: Fixed Alternatives Become the Reference Point
2016-01-01
Typical research on intertemporal choice utilizes a two-alternative forced choice (2AFC) paradigm requiring participants to choose between a smaller sooner and larger later payoff. In the adjusting-amount procedure (AAP) one of the alternatives is fixed and the other is adjusted according to particular choices made by the participant. Such a method makes the alternatives unequal in status and is speculated to make the fixed alternative a reference point for choices, thereby affecting the decision made. The current study shows that fixing different alternatives in the AAP influences discount rates in intertemporal choices. Specifically, individuals’ (N = 283) choices were affected to just the same extent by merely fixing an alternative as when choices were preceded by scenarios explicitly imposing reference points. PMID:27768759
Large- and Small-Aperture Fixed-Point Cells of Cu, Pt C, and Re C
NASA Astrophysics Data System (ADS)
Anhalt, Klaus; Wang, Yunfen; Yamada, Yoshiro; Hartmann, Jürgen
2008-06-01
Extending the application of metal (carbide) carbon eutectic fixed-point cells to radiometry, e.g., for measurements in irradiance mode, requires fixed-point cells with large apertures. In order to make large-aperture cells more readily usable in furnace systems with smaller furnace tubes commonly used for small-aperture fixed-point cells, a novel cell design was developed. For each of Cu, Pt C, and Re C fixed points, two types of fixed-point cells were manufactured, the small- and large-aperture cell. For Pt C and Re C, the large-aperture cells were filled with a hyper-eutectic metal carbon mixture; for the small cells, a hypo-eutectic mixture was used for filling. For each material, the small and large cells were compared with respect to radiometric differences. Whereas plateau shape and melting temperature are in good agreement for the small- and large-aperture Cu cells, a larger difference was observed between small- and large-aperture cells of Pt C and Re C, respectively. The origin of these observations, attributed to the temperature distribution inside the furnace, ingot contamination during manufacture, and non-uniform ingot formation for the larger cells, is discussed. The comparison of measurements by a radiation thermometer and filter radiometer of the Re C and Pt C large-aperture cells showed large differences that could be explained only by a strong radiance distribution across the cavity bottom. Further investigations are envisaged to clarify the cause.
One-parameter semigroups of analytic functions, fixed points and the Koenigs function
Goryainov, Victor V; Kudryavtseva, Olga S
2011-07-31
Analogues of the Berkson-Porta formula for the infinitesimal generator of a one-parameter semigroup of holomorphic maps of the unit disc into itself are obtained in the case when, along with a Denjoy-Wolff point, there also exist other fixed points. With each one-parameter semigroup a so-called Koenigs function is associated, which is a solution, common for all elements of the one-parameter semigroup, of a certain functional equation (Schroeder's equation in the case of an interior Denjoy-Wolff point and Abel's equation in the case of a boundary Denjoy-Wolff point). A parametric representation for classes of Koenigs functions that takes account of the Denjoy-Wolff point and other fixed points of the maps in the one-parameter semigroup is presented. Bibliography: 19 titles.
Fixed-point drift and hysteresis in frequency-scaled unimanual coordination.
James, Eric G
2012-01-01
Research on human rhythmic coordination has shown that the in-phase and antiphase coordination modes are typically stable and that the coordination of asymmetric effectors frequently exhibits fixed-point drift. The author extended research on symmetry breaking in coordination dynamics by examining a frequency-scaled unimanual pronation-supination task. The results showed symmetry breaking and fixed-point drift, with the radioulnar joint increasingly more phase advanced than the shoulder with increments in movement frequency. Hysteresis was also observed, as the relative phase patterns produced at 3 of the 4 movement frequencies were lower in the upward frequency scaling direction than in the downward direction. These results showed that the dynamic properties of symmetry breaking and fixed-point drift in unimanual pronation-supination movements were consistent with prior research and modeling. The hysteresis effect was explained as potentially being due to the control structures that organize this redundant coordination task.
Fe-C eutectic fixed-point cells for contact thermometry: an investigation and comparison
NASA Astrophysics Data System (ADS)
Elliott, C. J.; Pearce, J. V.; Failleau, G.; Deuzé, T.; Briaudeau, S.; Sadli, M.; Machin, G.
2012-02-01
Five iron-carbon (Fe-C) eutectic fixed-point cells have been constructed between NPL and LNE-Cnam to investigate the robustness and to measure the agreement of their melting temperatures. Each cell was constructed with a different selection of materials sourced by NPL and LNE-Cnam. The measured emfs at the Fe-C fixed-point temperature (~1153 °C), compared between cells, agree within around 1.98 µV (~90 mK), where the most important contribution to the uncertainty of each measurement is the inhomogeneity associated with the measuring Pt/Pd thermocouple. This demonstrates that these cells are suitable for use as secondary fixed-point cells in contact thermometry but the robustness of the presented cells is not found to be sufficient for maintaining their integrity during repeated cycling procedures.
Normal form solutions of dynamical systems in the basin of attraction of their fixed points
NASA Astrophysics Data System (ADS)
Bountis, Tassos; Tsarouhas, George; Herman, Russell
1998-10-01
The normal form theory of Poincaré, Siegel and Arnol'd is applied to an analytically solvable Lotka-Volterra system in the plane, and a periodically forced, dissipative Duffing's equation with chaotic orbits in its 3-dimensional phase space. For the planar model, we determine exactly how the convergence region of normal forms about a nodal fixed point is limited by the presence of singularities of the solutions in the complex t-plane. Despite such limitations, however, we show, in the case of a periodically driven system, that normal forms can be used to obtain useful estimates of the basin of attraction of a stable fixed point of the Poincaré map, whose ``boundary'' is formed by the intersecting invariant manifolds of a second hyperbolic fixed point nearby.
Miniature Fixed-Point Cell Approaches for Monitoring of Thermocouple Stability
NASA Astrophysics Data System (ADS)
Failleau, G.; Elliott, C. J.; Deuzé, T.; Pearce, J. V.; Machin, G.; Sadli, M.
2014-07-01
In the framework of the European Metrology Research Project ENG08 "MetroFission," LNE-Cnam and NPL have undertaken cooperative research into the development of temperature measurement solutions for the next generation of nuclear fission power plants. Currently, in-pile temperature monitoring is usually performed with nickel-based (Type K or N) thermocouples. When these thermocouples are exposed to a neutron flux, the thermoelements transmute, leading to large and unknown drifts in output. In addition, it is impossible to routinely recalibrate the thermocouples after irradiation for obvious reasons of safety. To alleviate this problem, both LNE-Cnam and NPL have developed, via differing approaches, in situ calibration methods for the thermocouples. The self-validating thermocouple methodologies are based on the principle of a miniature fixed-point cell to be co-located with the thermocouple measurement junction in use. The drift of the thermocouple can be monitored and corrected for by regular determination of the output at the phase transition of the fixed-point material: in effect performing regular in situ calibration checks. The two institutes have constructed miniature fixed-point cells for use at three different temperatures; the freezing point of silver ; LNE-Cnam), the freezing point of copper ; LNE-Cnam and NPL), and the melting point of Fe-C (; NPL). This paper introduces the construction and validation of the miniature fixed-point cells prior to use, to ensure traceability to the ITS-90. A comparison of the performance of the two cell designs is discussed, where typical industrial Type N thermocouples have been used for measurement of the fixed-point cells. Such initial measurements demonstrate the feasibility of each of these two approaches.
Parallel fixed point implementation of a radial basis function network in an FPGA.
de Souza, Alisson C D; Fernandes, Marcelo A C
2014-01-01
This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA.
Stability of the fixed points of the complex Swift-Hohenberg equation
NASA Astrophysics Data System (ADS)
Khairudin, N. I.; Abdullah, F. A.; Hassan, Y. A.
2016-02-01
We performed an investigation of the stability of fixed points in the complex Swift- Hohenberg equation using a variational formulation. The analysis is based on fixed points Euler-Lagrange equations and analytically showed that the Jacobian eigenvalues touched the imaginary axis and in general, Hopf bifurcation arises. The eigenvalues undergo a stability criterion in order to have Hopf's stability. Trial functions and linear loss dispersion parameter ε are responsible for the existence of stable pulse solutions in this system. We study behavior of the stable soliton-like solutions as we vary a bifurcation ε.
High-Density Fixed Point for Radially Compressed Single-Component Plasmas
Danielson, J. R.; Surko, C. M.; O'Neil, T. M.
2007-09-28
Rotating electric fields are used to compress electron plasmas confined in a Penning-Malmberg trap. Bifurcation and hysteresis are observed between low-density and high-density steady states as a function of the applied electric field amplitude and frequency. These observations are explained in terms of torque-balanced fixed points using a simple model of the torques on the plasma. Perturbation experiments near the high-density fixed point are used to determine the magnitude, frequency, and voltage dependence of the drive torque. The broader implications of these results are discussed.
Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
NASA Astrophysics Data System (ADS)
Herbut, Igor F.
2016-07-01
Spontaneous chiral symmetry breaking in three-dimensional (d =3 ) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a critical number of fermions N =Nc. We discuss the root of universality of Nc in this picture, together with some features of the phase boundary in the (d ,N ) plane. In particular, it is shown that as d →4 , Nc→0 with a constant slope, our best estimate of which suggests that Nc=2.89 in d =3 .
Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA
de Souza, Alisson C. D.; Fernandes, Marcelo A. C.
2014-01-01
This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA. PMID:25268918
Combined GPS/GLONASS precise point positioning with fixed GPS ambiguities.
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-09-18
Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF.
Combined GPS/GLONASS Precise Point Positioning with Fixed GPS Ambiguities
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-01-01
Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF. PMID:25237901
Fixed-point arithmetic for mobile devices: a fingerprinting verification case study
NASA Astrophysics Data System (ADS)
Moon, Yiu S.; Luk, Franklin T.; Ho, Ho C.; Tang, T. Y.; Chan, Kit C.; Leung, C. W.
2002-12-01
Mobile devices use embedded processors with low computing capabilities to reduce power consumption. Since floating-point arithmetic units are power hungry, computationally intensive jobs must be accomplished with either digital signal processors or hardware co-processors. In this paper, we propose to perform fixed-point arithmetic on an integer hardware unit. We illustrate the advantages of our approach by implementing fingerprint verification on mobile devices.
Fixed Points of Contractive Mappings in b-Metric-Like Spaces
Hussain, Nawab; Roshan, Jamal Rezaei
2014-01-01
We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results. PMID:25143980
Long-Term Stability of WC-C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Khlevnoy, B. B.; Grigoryeva, I. A.
2015-03-01
The tungsten carbide-carbon peritectic (WC-C) melting transition is an attractive high-temperature fixed point with a temperature of . Earlier investigations showed high repeatability, small melting range, low sensitivity to impurities, and robustness of WC-C that makes it a prospective candidate for the highest fixed point of the temperature scale. This paper presents further study of the fixed point, namely the investigation of the long-term stability of the WC-C melting temperature. For this purpose, a new WC-C cell of the blackbody type was built using tungsten powder of 99.999 % purity. The stability of the cell was investigated during the cell aging for 50 h at the cell working temperature that tooks 140 melting/freezing cycles. The method of investigation was based on the comparison of the WC-C tested cell with a reference Re-C fixed-point cell that reduces an influence of the probable instability of a radiation thermometer. It was shown that after the aging period, the deviation of the WC-C cell melting temperature was with an uncertainty of.
Intermediate fixed point in a Luttinger liquid with elastic and dissipative backscattering
NASA Astrophysics Data System (ADS)
Altland, Alexander; Gefen, Yuval; Rosenow, Bernd
2015-08-01
In a recent work [A. Altland, Y. Gefen, and B. Rosenow, Phys. Rev. Lett. 108, 136401 (2012), 10.1103/PhysRevLett.108.136401], we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed point landscape, and scaling near those fixed points. Our analysis is nonperturbative in the elastic tunneling amplitudes, employing an instanton calculation in one or two of the available elastic tunneling channels. Our analysis accounts for nontrivial Klein factors, which represent anyonic or fermionic statistics. These Klein factors need to be taken into account due to the fact that higher-order tunneling processes take place. In particular, we find a stable fixed point, where an incoming current is split 1/2 -1/2 between a forward and a backward scattered beams. This intermediate fixed point, between complete backscattering and full forward scattering, is stable for the Luttinger parameter g <1 .
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Operation of internal transmitter control... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be...
Comparison of the copper blackbody fixed-point cavities between NIS and LNE-Cnam
NASA Astrophysics Data System (ADS)
Ahmed, M. G.; Ali, K.; Bourson, F.; Sadli, M.
2013-09-01
This paper describes the results of a bilateral comparison at the copper blackbody fixed point (1084.62 °C), one of the defining fixed points of the International Temperature Scale of 1990 in the high-temperature range. The ‘National Institute of Standards—Egypt (NIS)’ and the ‘Laboratoire Commun de Métrologie--France (LNE-Cnam)’ undertook such a comparison using an NIS linear pyrometer ‘LP4’ as a circulating radiation thermometer between the two laboratories. The main objective of this work was to compare the realizations of the copper blackbody fixed point for radiation thermometers and establish the level of agreement between the two laboratories in the high-temperature range. The comparison measurements revealed a slightly lower temperature of the NIS copper point than that of the LNE-Cnam copper point by about 0.08 °C. This difference is not significant with regard to the uncertainty and the stability of the pyrometer estimated as 0.15 °C. A second comparison was made a few months later by comparing simultaneously the two copper points at the LNE-Cnam premises. This comparison allowed determining a temperature difference of 0.045 ± 0.030 °C between the two cells, with the temperature of the LNE-Cnam cell being higher than that of NIS.
NASA Astrophysics Data System (ADS)
Pearce, Jonathan V.; Gisby, John A.; Steur, Peter P. M.
2016-08-01
A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.
NASA Astrophysics Data System (ADS)
Bojkovski, J.; Veliki, T.; Zvizdić, D.; Drnovšek, J.
2011-08-01
The objective of project EURAMET 1127 (Bilateral comparison of triple point of mercury and melting point of gallium) in the field of thermometry is to compare realization of a triple point of mercury (-38.8344 °C) and melting point of gallium (29.7646 °C) between the Slovenian national laboratory MIRS/UL-FE/LMK and the Croatian national laboratory HMI/FSB-LPM using a long-stem 25 Ω standard platinum resistance thermometer (SPRT). MIRS/UL/FE-LMK participated in a number of intercomparisons on the level of EURAMET. On the other hand, the HMI/LPM-FSB laboratory recently acquired new fixed-point cells which had to be evaluated in the process of intercomparisons. A quartz-sheathed SPRT has been selected and calibrated at HMI/LPM-FSB at the triple point of mercury, the melting point of gallium, and the water triple point. A second set of measurements was made at MIRS/UL/FE-LMK. After its return, the SPRT was again recalibrated at HMI/LPM-FSB. In the comparison, the W value of the SPRT has been used. Results of the bilateral intercomparison confirmed that the new gallium cell of the HMI/LPM-FSB has a value that is within uncertainty limits of both laboratories that participated in the exercise, while the mercury cell experienced problems. After further research, a small leakage in the mercury fixed-point cell has been found.
Device-independent test of causal order and relations to fixed-points
NASA Astrophysics Data System (ADS)
Baumeler, Ämin; Wolf, Stefan
2016-03-01
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities—just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature. PMID:27386356
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
The virial theorem for the Polarizable Continuum Model.
Cammi, R
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
NASA Astrophysics Data System (ADS)
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d =2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d =3 or Kraichnan-Batchelor in d =2 ) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d=2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d=3 or Kraichnan-Batchelor in d=2) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work. PMID:27415353
Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point
NASA Astrophysics Data System (ADS)
Vosk, Ronen; Altman, Ehud
2013-02-01
We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as loglogt found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.
Indirect Determination of the Thermodynamic Temperature of a Gold Fixed-Point Cell
NASA Astrophysics Data System (ADS)
Battuello, M.; Girard, F.; Florio, M.
2010-09-01
Since the value T 90(Au) was fixed on the ITS-90, some determinations of the thermodynamic temperature of the gold point have been performed which form, with other renormalized results of previous measurements by radiation thermometry, the basis for the current best estimates of ( T - T 90)Au = 39.9 mK as elaborated by the CCT-WG4. Such a value, even if consistent with the behavior of T - T 90 differences at lower temperatures, is quite influenced by the low values of T Au as determined with few radiometric measurements. At INRIM, an independent indirect determination of the thermodynamic temperature of gold was performed by means of a radiation thermometry approach. A fixed-point technique was used to realize approximated thermodynamic scales from the Zn point up to the Cu point. A Si-based standard radiation thermometer working at 900 nm and 950 nm was used. The low uncertainty presently associated to the thermodynamic temperature of fixed points and the accuracy of INRIM realizations, allowed scales with an uncertainty lower than 0.03 K in terms of the thermodynamic temperature to be realized. A fixed-point cell filled with gold, 99.999 % in purity, was measured, and its freezing temperature was determined by both interpolation and extrapolation. An average T Au = 1337.395 K was found with a combined standard uncertainty of 23 mK. Such a value is 25 mK higher than the presently available value as derived by the CCT-WG4 value of ( T - T 90)Au = 39.9 mK.
NASA Astrophysics Data System (ADS)
Machin, G.; Teixeira, R.; Lu, X.; Lowe, D.
2015-03-01
There is an on-going requirement to perform scale comparisons above the silver point with reduced uncertainties. Previous comparisons have been performed with high stability lamps or radiation thermometers, neither of which were able to achieve the required uncertainty. Ideally a set of driftless unknown temperature fixed points would be used to compare scales, but up to now such artifacts did not exist. This study develops blind high-temperature comparison artifacts based on doped versions of the high-temperature fixed point (HTFP) Ni-C (nominal temperature ). At INMETRO three HTFP blackbodies were constructed, one of pure Ni-C and two doped with different levels of Cu. To ascertain the effect of doping on the transition temperature, the cells were compared to the reference pure Ni-C cell. The doped cells were then transported to NPL and their temperatures measured. NPL was not informed of the INMETRO result ensuring that the measurements remained blind. The cells were then returned to INMETRO and re-measured to establish their stability. The temperatures measured at INMETRO and NPL were then compared and showed very good equivalence of the scale at the fixed-point temperatures. The results of the comparison of the NPL and INMETRO temperature scale, at nominally , are reported, along with evidence of the stability of the artifacts determined from repeat measurements. These promising results indicate that it may be possible to make HTFPs with altered temperatures which are stable enough to serve as comparison artifacts.
UV fixed-point structure of the three-dimensional Thirring model
Gies, Holger; Janssen, Lukas
2010-10-15
We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group. We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic renormalization group flow using a full basis of fermionic four-point functions in the pointlike limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-N{sub f} limit. In addition to the Thirring universality class, which is characterized by one relevant direction (also at finite N{sub f}), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The N{sub f} dependence of the Thirring fixed point sheds further light on the existence of an N{sub f}-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.
Tympanic thermometer performance validation by use of a body-temperature fixed point blackbody
NASA Astrophysics Data System (ADS)
Machin, Graham; Simpson, Robert
2003-04-01
The use of infrared tympanic thermometers within the medical community (and more generically in the public domain) has recently grown rapidly, displacing more traditional forms of thermometry such as mercury-in-glass. Besides the obvious health concerns over mercury the increase in the use of tympanic thermometers is related to a number of factors such as their speed and relatively non-invasive method of operation. The calibration and testing of such devices is covered by a number of international standards (ASTM1, prEN2, JIS3) which specify the design of calibration blackbodies. However these calibration sources are impractical for day-to-day in-situ validation purposes. In addition several studies (e.g. Modell et al4, Craig et al5) have thrown doubt on the accuracy of tympanic thermometers in clinical use. With this in mind the NPL is developing a practical, portable and robust primary reference fixed point source for tympanic thermometer validation. The aim of this simple device is to give the clinician a rapid way of validating the performance of their tympanic thermometer, enabling the detection of mal-functioning thermometers and giving confidence in the measurement to the clinician (and patient!) at point of use. The reference fixed point operates at a temperature of 36.3 °C (97.3 °F) with a repeatability of approximately +/- 20 mK. The fixed-point design has taken into consideration the optical characteristics of tympanic thermometers enabling wide-angled field of view devices to be successfully tested. The overall uncertainty of the device is estimated to be is less than 0.1°C. The paper gives a description of the fixed point, its design and construction as well as the results to date of validation tests.
Experimental Investigation of the Cr3C2 C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Zheng, W.; Yamada, Y.; Wang, Y.
2008-06-01
The Cr3C2 C (1,826°C) peritectic point was investigated for its performance as a high-temperature fixed point. Dependence on the impurity content was observed, although it was less severe for the higher of the two equilibrium temperatures obtained with the same cell, the Cr3C2 C peritectic point, than for the lower, the Cr7C3 Cr3C2 eutectic point. Thermal history had an effect on the melting plateau duration, but not on the point-of-inflection temperature nor on the melting range. The melting rate had no apparent effect. The repeatability evaluated as the standard deviation of the repeated melting plateaux within a day was 20 mK for the Cr3C2 C peritectic point, while for the Cr7C3 Cr3C2 eutectic point, this was 210 mK. For both the Cr3C2 C peritectic and the Cr7C3 Cr3C2 eutectic, the freezing plateaux often showed deep supercools, which made them unsuitable for use. The observed good repeatability shows the peritectic-point performance to be comparable to the best MC-eutectic high-temperature fixed points investigated so far. The insensitivity to thermal history constitutes an important and practical advantage. The low price of chromium is a clear benefit as compared to Pt C (1,738°C) or Ru C (1,953°C) eutectic points, the M C eutectic points in this temperature range.
Comparisons between transect and fixed point in a oceanic turbulent flow: statistical analyses
NASA Astrophysics Data System (ADS)
Koziol, Lucie; Schmitt, Francois G.; Artigas, Felipe; Lizon, Fabrice
2016-04-01
Oceanological processes possess important fluctuations over large ranges of spatial and temporal scales. These fluctuations are related with the turbulence of the ocean. Usually, in turbulence, one considers fixed point Eulerian measurements, or Lagrangian measurements following an elements of fluid. On the other hand, in oceanography, measurements are often done from a boat operating over a transect, where the boat is moving in the medium at a fixed speed (relative to the flow). Here the aim of our study is to consider if such moving reference frame is modifying the statistics of the measurements. For this we compare two type of measurements at high frequency: fixed point measurements, and transect measurements, where the boat is moving at a fixed speed relative to the flow. 1 Hz fluorometer measurements are considered in both cases. Measurements have been done the same day, under similar conditions. Power spectra of time series are considered, as well as local mean and variance measurements along each transect. It is found that the spectral scaling slope of the measurement is not modified, but the variance is very different, being much larger for the moving frame. Such result needs theoretical understanding and has potential important consequence regarding the measurement that are done at high frequency on moving frames in oceanography.
2+1 flavor QCD with the fixed point action in the epsilon-regime
NASA Astrophysics Data System (ADS)
Hasenfratz, P.; Hierl, D.; Maillart, V.; Niedermayer, F.; Schafer, A.; Weiermann, C.; Weingart, M.
We generated configurations with the approximate fixed-point Dirac operator $D_\\mathrm{FP}$ on a $12^4$ lattice with $a \\approx 0.13 $fm where the scale was set by $r_0$. The distributions of the low lying eigenvalues in different topological sectors were compared with those of the Random Matrix Theory which leads to a prediction of the chiral condensate.
Long-Term Monitoring of Thermocouple Stability with Miniature Fixed-Point Cells
NASA Astrophysics Data System (ADS)
Elliott, C. J.; Failleau, G.; Deuzé, T.; Sadli, M.; Pearce, J. V.; Machin, G.
2014-04-01
In the framework of the European Metrology Research Programme ENG08 "MetroFission" project, two National Measurement Institutes, LNE-Cnam (France) and NPL (UK), have cooperatively developed methods of in situ validation of thermocouple output for application in next-generation nuclear fission power plants. Miniature fixed-point cells for use at three temperatures were constructed in the first step of this project: at the freezing point of silver (), the freezing point of copper (), and the melting point of the iron-carbon eutectic (). This paper reports the results of a second step in the study, where the robustness of the self-validation method has been investigated. Typical industrial Type N thermocouples have been employed with each of the miniature fixed-point devices installed, and repeatedly thermally cycled through the melting and freezing transitions of the fixed-point ingots. The devices have been exposed to a total of up to 90 h in the molten state. Furthermore, the LNE-Cnam devices were also subjected to fast cool-down rates, on five occasions, where the rate is estimated to have been between and . The devices are shown to be repeatable, reliable, and robust over the course of these tests. The drift of the Type N thermocouple has been identified separately to the behavior of the device. A reliable method for improving thermocouple performance and process control is therefore demonstrated. Requirements for implementation and the advantages of each approach for monitoring and correcting thermocouple drift are discussed, and an uncertainty budget for self-validation is presented.
Fixed points of the SRG evolution and the on-shell limit of the nuclear force
NASA Astrophysics Data System (ADS)
Arriola, E. Ruiz; Szpigel, S.; Timóteo, V. S.
2016-08-01
We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff λ → 0 may be obtained from the eigenvalues of the Hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit λ → 0 on a finite momentum grid. Another issue we investigate is the location on the diagonal of the Hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A = 2 , 3 , 4 systems are investigated and related to the occurrence of a Tjon-line which emerges as the minimum of an avoided crossing between Eα = 4Et - 3Ed and Eα = 2Et. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S-waves.
Mazor, Ofer; Laurent, Gilles
2005-11-23
Projection neurons (PNs) in the locust antennal lobe exhibit odor-specific dynamic responses. We studied a PN population, stimulated with five odorants and pulse durations between 0.3 and 10 s. Odor representations were characterized as time series of vectors of PN activity, constructed from the firing rates of all PNs in successive 50 ms time bins. Odor representations by the PN population can be described as trajectories in PN state space with three main phases: an on transient, lasting 1-2 s; a fixed point, stable for at least 8 s; and an off transient, lasting a few seconds as activity returns to baseline. Whereas all three phases are odor specific, optimal stimulus separation occurred during the transients rather than the fixed points. In addition, the PNs' own target neurons respond least when their PN-population input stabilized at a fixed point. Steady-state measures of activity thus seem inappropriate to understand the neural code in this system.
Study on the Impurity Effect in the Realization of Silver Fixed Point
NASA Astrophysics Data System (ADS)
Tsai, S. F.
2016-03-01
The application of a thermal analysis model to estimate the temperature depression from the ideal fixed-point temperature is important, especially when the chemical analysis of the sample in a cell is insufficient or the cell might have been contaminated during fabrication. This study extends previous work, on thermal analysis with the tin point, to an investigation of the impurity dependence of the silver-point temperature. Close agreement was found between the temperature depression (-0.36 mK) inferred from the thermal analysis of the measured fixed-point plateau and the temperature depression (-0.32 mK) inferred using the sum of individual estimates (SIE) method with an impurity analysis based on glow discharge mass spectrometry. Additionally, the results of the thermal analysis manifest no significant dependence on the rate of solidification, and the scatter of observed gradients was within 0.36 mK among five plateaux with different temperature settings of the furnace. Although the results support the application of both the SIE method and thermal analysis for the silver point, further experiments with cell-to-cell comparisons linked to thermal analysis, a study of the thermometer-furnace systematic effects, the oxygen effect, and the locus of the freezing plateau should be investigated to reach a firm conclusion.
Robust Optimization of Fixed Points of Nonlinear Discrete Time Systems with Uncertain Parameters
NASA Astrophysics Data System (ADS)
Kastsian, Darya; Monnigmann, Martin
2010-01-01
This contribution extends the normal vector method for the optimization of parametrically uncertain dynamical systems to a general class of nonlinear discrete time systems. Essentially, normal vectors are used to state constraints on dynamical properties of fixed points in the optimization of discrete time dynamical systems. In a typical application of the method, a technical dynamical system is optimized with respect to an economic profit function, while the normal vector constraints are used to guarantee the stability of the optimal fixed point. We derive normal vector systems for flip, fold, and Neimark-Sacker bifurcation points, because these bifurcation points constitute the stability boundary of a large class of discrete time systems. In addition, we derive normal vector systems for a related type of critical point that can be used to ensure a user-specified disturbance rejection rate in the optimization of parametrically uncertain systems. We illustrate the method by applying it to the optimization of a discrete time supply chain model and a discretized fermentation process model.
NASA Astrophysics Data System (ADS)
Yamada, Y.; Wang, Y.; Sasajima, N.
2006-10-01
WC-C, Cr3C2-C and Mn7C3-C peritectic systems were investigated for their potential of serving as high-temperature reference points in thermometry. Mixtures of high-purity graphite powder with W, Cr and Mn powder of 99.99%, 99.9% and 99.95% purity by mass, respectively, were placed in graphite blackbody crucibles and melting/freezing plateaus were observed by means of a radiation thermometer. The observed melting temperatures were 2749 °C (WC-C), 1826 °C (Cr3C2-C) and 1331 °C (Mn7C3-C), with a repeatability—in each case—of 0.02 K. The melting range for WC-C and Cr3C2-C peritectics was roughly 0.1 K. WC-C showed a flat freezing plateau that agreed with the melting plateau within the repeatability. The three fixed points are possible candidates, like the metal (carbide)-carbon eutectic fixed points, in the realization of an improved high-temperature scale above the copper point.
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
Estimating the Contribution of Impurities to the Uncertainty of Metal Fixed-Point Temperatures
NASA Astrophysics Data System (ADS)
Hill, K. D.
2014-04-01
The estimation of the uncertainty component attributable to impurities remains a central and important topic of fixed-point research. Various methods are available for this estimation, depending on the extent of the available information. The sum of individual estimates method has considerable appeal where there is adequate knowledge of the sensitivity coefficients for each of the impurity elements and sufficiently low uncertainty regarding their concentrations. The overall maximum estimate (OME) forsakes the behavior of the individual elements by assuming that the cryoscopic constant adequately represents (or is an upper bound for) the sensitivity coefficients of the individual impurities. Validation of these methods using melting and/or freezing curves is recommended to provide confidence. Recent investigations of indium, tin, and zinc fixed points are reported. Glow discharge mass spectrometry was used to determine the impurity concentrations of the metals used to fill the cells. Melting curves were analyzed to derive an experimental overall impurity concentration (assuming that all impurities have a sensitivity coefficient equivalent to that of the cryoscopic constant). The two values (chemical and experimental) for the overall impurity concentrations were then compared. Based on the data obtained, the pragmatic approach of choosing the larger of the chemical and experimentally derived quantities as the best estimate of the influence of impurities on the temperature of the freezing point is suggested rather than relying solely on the chemical analysis and the OME method to derive the uncertainty component attributable to impurities.
Uncertainty due to non-linearity in radiation thermometers calibrated by multiple fixed points
Yamaguchi, Y.; Yamada, Y.
2013-09-11
A new method to estimate the uncertainty due to non-linearity is described on the n= 3 scheme basis. The expression of uncertainty is mathematically derived applying the random walk method. The expression is simple and requires only the temperatures of the fixed points and a relative uncertainty value for each flux-doubling derived from the non-linearity measurement. We also present an example of the method, in which the uncertainty of temperature measurement by a radiation thermometer is calculated on the basis of non-linearity measurement.
Standard map in magnetized relativistic systems: fixed points and regular acceleration.
de Sousa, M C; Steffens, F M; Pakter, R; Rizzato, F B
2010-08-01
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.
Unitarity violation at the Wilson-Fisher fixed point in 4 -ɛ dimensions
NASA Astrophysics Data System (ADS)
Hogervorst, Matthijs; Rychkov, Slava; van Rees, Balt C.
2016-06-01
We consider the continuation of free and interacting scalar field theory to noninteger spacetime dimension d . We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection positivity in Euclidean signature). In particular, the theories contain negative-norm states unless d is a positive integer. These negative-norm states can be obtained via the operator product expansion from simple positive-norm operators, and are therefore an integral part of the theory. At the Wilson-Fisher fixed point the nonunitarity leads to the existence of complex anomalous dimensions. We demonstrate that they appear already at leading order in the epsilon expansion.
New Sealed Cells for Realization of Cryogenic Fixed Points at NMIJ/AIST
NASA Astrophysics Data System (ADS)
Nakano, Tohru; Tamura, Osamu; Sakurai, Hirohisa
2003-09-01
New sealed cells have been developed at the National Metrology Institute of Japan (NMIJ), which are used for realization of the cryogenic fixed points of the International Temperature Scale of 1990. A metal O-ring made of stainless steel is introduced as a sealing device for the sealed cells. The triple point of equilibrium hydrogen (e-H2) is realized using the new sealed cells containing hydrogen and ferric oxy-hydroxide as a catalyst for the ortho-para equilibration. Double anomalous peaks on the heat capacity curves are observed at temperatures just below the triple point, but they are suppressed by reducing the amount of the catalyst. The reduction of the amount of catalyst allows one to obtain more reliable melting curves for e-H2. The triple-point temperature of e-H2 obtained by the new sealed cells is in good agreement with those reported previously in measurements of open cells by assuming that the dependence of the triple-point temperature on the deuterium content is 5.4 μK per ppm of deuterium in hydrogen.
Development of a new radiometer for the thermodynamic measurement of high temperature fixed points
Dury, M. R.; Goodman, T. M.; Lowe, D. H.; Machin, G.; Woolliams, E. R.
2013-09-11
The National Physical Laboratory (NPL) has developed a new radiometer to measure the thermodynamic melting point temperatures of high temperature fixed points with ultra-low uncertainties. In comparison with the NPL's Absolute Radiation Thermometer (ART), the 'THermodynamic Optical Radiometer' (THOR) is more portable and compact, with a much lower size-of-source effect and improved performance in other parameters such as temperature sensitivity. It has been designed for calibration as a whole instrument via the radiance method, removing the need to calibrate the individual subcomponents, as required by ART, and thereby reducing uncertainties. In addition, the calibration approach has been improved through a new integrating sphere that has been designed to have greater uniformity.
Influence of Impurities and Filling Protocol on the Aluminum Fixed Point
NASA Astrophysics Data System (ADS)
Renaot, E.; Valin, M. H.; Elgourdou, M.
2008-06-01
To improve the uncertainty of the aluminum fixed point, a study was launched by LNE-INM/CNAM in the framework of the EUROMET Project 732 “Toward more accurate temperature fixed points” (Coordinating laboratory: LNE-INM/CNAM, 17 partner countries). A new open cell was filled with aluminum of 99.99995% purity. A French laboratory carried out elemental analysis of the sample using glow discharge-mass spectrometry (GD-MS). The values of the equilibrium distribution coefficient k and of the derivative {δ T_{{l}}/δ ci_{{l}}} of the temperature of the liquidus line with respect to the concentration of impurity i will be obtained through collaboration with a French physical and chemical laboratory. In the past, some aluminum cells were opened after several melts and freezes. The aluminum ingot was sticking to the graphite crucible, indicating that physicochemical reactions had likely occurred between Al and C. To avoid this reaction, an effort was made to draw benefit from the Al2O3 film that appears immediately on the surface of the aluminum ingot when it is exposed to oxygen. The open aluminum cell was tested in different furnaces and with different thermal insulator arrangements inside the fixed-point assembly. The observed drifts of the plateaux were always larger than the expected values. The cell was opened to inspect the aluminum ingot. The ingot was extracted easily, since no sticking to the crucible had occurred. The aluminum showed a very bright surface, but the presence of many “craters” throughout the thickness of the ingot was surprising. In some cases, the thermometer well was even apparent.
Investigation of TiC C Eutectic and WC C Peritectic High-Temperature Fixed Points
NASA Astrophysics Data System (ADS)
Sasajima, Naohiko; Yamada, Yoshiro
2008-06-01
TiC C eutectic (2,761°C) and WC C peritectic (2,749°C) fixed points were investigated to compare their potential as high-temperature thermometric reference points. Two TiC C and three WC C fixed-point cells were constructed, and the melting and freezing plateaux were evaluated by means of radiation thermometry. The repeatability of the TiC C eutectic within a day was 60 mK with a melting range roughly 200 mK. The repeatability of the melting temperature of the WC C peritectic within 1 day was 17 mK with a melting range of ˜70 mK. The repeatability of the freezing temperature of the WC C peritectic was 21 mK with a freezing range less than 20 mK. One of the TiC C cells was constructed from a TiC and graphite powder mixture. The filling showed the reaction with the graphite crucible was suppressed and the ingot contained less voids, although the lack of high-purity TiC powder poses a problem. The WC C cells were easily constructed, like metal carbon eutectic cells, without any evident reaction with the crucible. From these results, it is concluded that the WC C peritectic has more potential than the TiC C eutectic as a high-temperature reference point. The investigation of the purification of the TiC C cell during filling and the plateau observation are also reported.
Optimization of the thermogauge furnace for realizing high temperature fixed points
Wang, T.; Dong, W.; Liu, F.
2013-09-11
The thermogauge furnace was commonly used in many NMIs as a blackbody source for calibration of the radiation thermometer. It can also be used for realizing the high temperature fixed point(HTFP). According to our experience, when realizing HTFP we need the furnace provide relative good temperature uniformity to avoid the possible damage to the HTFP. To improve temperature uniformity in the furnace, the furnace tube was machined near the tube ends with a help of a simulation analysis by 'ansys workbench'. Temperature distributions before and after optimization were measured and compared at 1300 °C, 1700°C, 2500 °C, which roughly correspond to Co-C(1324 °C), Pt-C(1738 °C) and Re-C(2474 °C), respectively. The results clearly indicate that through machining the tube the temperature uniformity of the Thermogage furnace can be remarkably improved. A Pt-C high temperature fixed point was realized in the modified Thermogauge furnace subsequently, the plateaus were compared with what obtained using old heater, and the results were presented in this paper.
Stability of cobalt-carbon high temperature fixed points doped with iron and platinum
NASA Astrophysics Data System (ADS)
Kňazovická, L.; Lowe, D.; Machin, G.; Davies, H.; Rani, A.
2015-04-01
High temperature fixed points (HTFPs) are stable and repeatable and make comparison of temperature scales possible at a level of uncertainty not previously possible. However, they potentially lack objectivity if the fixed-point temperature is known. Five HTFPs were constructed, one pure Co-C, two Co-C doped with Fe and two Co-C doped with Pt of differing concentrations. The candidate dopants were identified through thermochemical modelling as likely to give maximum temperature shift with minimum increase in melting range. The temperature differences of the doped systems from the pure system were determined and it was found that the addition of Fe depressed the melting temperature and the addition of Pt elevated the melting temperature, qualitatively in line with the thermochemical modelling. The higher concentration doped HTFPs were then aged for approximately 100 h with continuous melting-freezing cycles and the difference to the undoped Co-C HTFP remeasured. These differences were found to agree with those of the unaged results within the measurement uncertainties, confirming artefact stability. It is clear that the doping of HTFPs is a powerful way of constructing stable and reliable high temperature scale comparison artefacts of unknown temperature.
Use of Eutectic Fixed Points to Characterize a Spectrometer for Earth Observations
NASA Astrophysics Data System (ADS)
Salim, Saber G. R.; Fox, Nigel P.; Woolliams, Emma R.; Winkler, Rainer; Pegrum, Heather M.; Sun, Tong; Grattan, Ken T. V.
2007-12-01
A small palm-sized, reference spectrometer, mounted on a remote-controlled model helicopter is being developed and tested by the National Physical Laboratory (NPL) in conjunction with City University, London. The developed system will be used as a key element for field vicarious calibration of optical earth observation systems in the visible-near infrared (VNIR) region. The spectrometer is hand held, low weight, and uses a photodiode array. It has good stray light rejection and wide spectral coverage, allowing simultaneous measurements from 400 to 900 nm. The spectrometer is traceable to NPL’s primary standard cryogenic radiometer via a high-temperature metal-carbon eutectic fixed-point blackbody. Once the fixed-point temperature has been determined (using filter radiometry), the eutectic provides a high emissivity and high stability source of known spectral radiance over the emitted spectral range. All wavelength channels of the spectrometer can be calibrated simultaneously using the eutectic transition without the need for additional instrumentation. The spectrometer itself has been characterized for stray light performance and wavelength accuracy. Its long-term and transportation stability has been proven in an experiment that determined the “World’s Bluest Sky”—a process that involved 56 flights, covering 100,000 km in 72 days. This vicarious calibration methodology using a eutectic standard is presented alongside the preliminary results of an evaluation study of the spectrometer characteristics.
Investigation of Furnace Uniformity and its Effect on High-Temperature Fixed-Point Performance
NASA Astrophysics Data System (ADS)
Khlevnoy, B.; Sakharov, M.; Ogarev, S.; Sapritsky, V.; Yamada, Y.; Anhalt, K.
2008-02-01
A large-area furnace BB3500YY was designed and built at the VNIIOFI as a furnace for high-temperature metal (carbide)-carbon (M(C)-C) eutectic fixed points and was then investigated at the NMIJ. The dependence of the temperature uniformity of the furnace on various heater and cell holder arrangements was investigated. After making some improvements, the temperature of the central part of the furnace was uniform to within 2K over a length of 40 mm—the length of the fixed-point cell—at a temperature of 2,500°C. With this furnace, the melting plateaux of Re-C and TiC-C were shown to be better than those observed in other furnaces. For instance, a Re-C cell showed melting plateaux with a 0.1K melting range and a duration of about 40 min. Furthermore, to verify the capability of the furnace to fill cells, one Re-C and one TiC-C cell were made using the BB3500YY. The cells were then compared to a Re-C cell made in a Nagano furnace and a TiC-C cell filled in a BB3200pg furnace. The agreement in plateau shapes demonstrates the capability of the BB3500YY furnace to also function as a filling furnace.
Acoustic resonator providing fixed points of temperature between 0.1 and 2 K
NASA Astrophysics Data System (ADS)
Salmela, Anssi; Tuoriniemi, Juha; Pentti, Elias; Sebedash, Alexander; Rysti, Juho
2009-02-01
Below 2 K the speed of second sound in mixtures of liquid 3He and 4He first increases to a maximum of 30-40 m/s at about 1 K and then decreases again at lower temperatures to values below 15 m/s. The exact values depend on the concentration and pressure of the mixture. This can be exploited to provide fixed points in temperature by utilizing a resonator with appropriate dimensions and frequency to excite standing waves in the resonator cavity filled with helium mixture. We demonstrate that commercially mass produced quartz tuning forks can be used for this purpose. They are meant for frequency standards operating at 32 kHz. Their dimensions are typically of order 1 mm matching the wavelength of the second sound in helium mixtures at certain values of temperature. Due to the complicated geometry, we observe some 20 sharp acoustic resonances in the range 0.1ell 2 K having temperature resolution of order 1 μK. The quartz resonators are cheap, compact, simple to implement, easy to measure with great accuracy, and, above all, they are not sensitive to magnetic field, which is a great advantage compared to fixed point devices based on superconductivity transitions. The reproducibility of the resonance pattern upon thermal cycling remains to be verified.
Dipeptide Aggregation in Aqueous Solution from Fixed Point-Charge Force Fields.
Götz, Andreas W; Bucher, Denis; Lindert, Steffen; McCammon, J Andrew
2014-04-01
The description of aggregation processes with molecular dynamics simulations is a playground for testing biomolecular force fields, including a new generation of force fields that explicitly describe electronic polarization. In this work, we study a system consisting of 50 glycyl-l-alanine (Gly-Ala) dipeptides in solution with 1001 water molecules. Neutron diffraction experiments have shown that at this concentration, Gly-Ala aggregates into large clusters. However, general-purpose force fields in combination with established water models can fail to correctly describe this aggregation process, highlighting important deficiencies in how solute-solute and solute-solvent interactions are parametrized in these force fields. We found that even for the fully polarizable AMOEBA force field, the degree of association is considerably underestimated. Instead, a fixed point-charge approach based on the newly developed IPolQ scheme [Cerutti et al. J. Phys. Chem.2013, 117, 2328] allows for the correct modeling of the dipeptide aggregation in aqueous solution. This result should stimulate interest in novel fitting schemes that aim to improve the description of the solvent polarization effect within both explicitly polarizable and fixed point-charge frameworks.
NASA Astrophysics Data System (ADS)
Goldberg, Daniel N.; Krishna Narayanan, Sri Hari; Hascoet, Laurent; Utke, Jean
2016-05-01
We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.
Temperature determination of the Si-SiC eutectic fixed point using thermocouples
NASA Astrophysics Data System (ADS)
Suherlan; Kim, Yong-Gyoo; Joung, Wukchul; Yang, Inseok
2015-04-01
The temperature of the Si-SiC eutectic fixed point for use in thermocouple thermometry has been determined. Three Si-SiC cells were fabricated from pure silicon powder within separate graphite crucibles. Each of the three cells was cycled through 17 melt-freeze cycles and subjected to temperatures above 1400 °C for a period of approximately 73 h, and none showed any sign of mechanical failure. The melting transition was measured using three types of thermocouple: one type S, one type B, and two Pt/Pd thermocouples calibrated at the fixed points of Ag, Cu, Fe-C, Co-C, and Pd (only for type B). The transition temperature, measured using the type S and two Pt/Pd thermocouples, was (1410.0 ± 0.8) °C with k = 2. However, the measurement uncertainty using the type B thermocouple was as large as 1.5 °C (k = 2) due to the inhomogeneity of the thermocouple. The repeatability of the three Si-SiC cells was calculated to be 0.3 °C, and the extremes of the temperature measurement differed by 0.8 °C.
Stability of a cubic fixed point in three dimensions: Critical exponents for generic N
NASA Astrophysics Data System (ADS)
Varnashev, K. B.
2000-06-01
The detailed analysis of the global structure of the renormalization-group (RG) flow diagram for a model with isotropic and cubic interactions is carried out in the framework of the massive field theory directly in three dimensions (3D) within an assumption of isotropic exchange. Perturbative expansions for RG functions are calculated for arbitrary N up to four-loop order and resummed by means of the generalized Padé-Borel-Leroy technique. Coordinates and stability matrix eigenvalues for the cubic fixed point are found under the optimal value of the transformation parameter. Critical dimensionality of the model is proved to be equal to Nc=2.89+/-0.02 that agrees well with the estimate obtained on the basis of the five-loop ɛ expansion [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)] resummed by the above method. As a consequence, the cubic fixed point should be stable in 3D for N>=3, and the critical exponents controlling phase transitions in three-dimensional magnets should belong to the cubic universality class. The critical behavior of the random Ising model being the nontrivial particular case of the cubic model when N=0 is also investigated. For all physical quantities of interest the most accurate numerical estimates with their error bounds are obtained. The results achieved in the work are discussed along with the predictions given by other theoretical approaches and experimental data.
Woolliams, E R; Anhalt, K; Ballico, M; Bloembergen, P; Bourson, F; Briaudeau, S; Campos, J; Cox, M G; del Campo, D; Dong, W; Dury, M R; Gavrilov, V; Grigoryeva, I; Hernanz, M L; Jahan, F; Khlevnoy, B; Khromchenko, V; Lowe, D H; Lu, X; Machin, G; Mantilla, J M; Martin, M J; McEvoy, H C; Rougié, B; Sadli, M; Salim, S G R; Sasajima, N; Taubert, D R; Todd, A D W; Van den Bossche, R; van der Ham, E; Wang, T; Whittam, A; Wilthan, B; Woods, D J; Woodward, J T; Yamada, Y; Yamaguchi, Y; Yoon, H W; Yuan, Z
2016-03-28
The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represents 95% coverage. These results are the best consensus estimates obtained from measurements made using various spectroradiometric primary thermometry techniques by nine different national metrology institutes. The good agreement between the institutes suggests that spectroradiometric thermometry techniques are sufficiently mature (at least in those institutes) to allow the direct realization of thermodynamic temperature above 1234 K (rather than the use of a temperature scale) and that metal-carbon eutectics can be used as high-temperature fixed points for thermodynamic temperature dissemination. The results directly support the developing mise en pratique for the definition of the kelvin to include direct measurement of thermodynamic temperature.
Woolliams, E R; Anhalt, K; Ballico, M; Bloembergen, P; Bourson, F; Briaudeau, S; Campos, J; Cox, M G; del Campo, D; Dong, W; Dury, M R; Gavrilov, V; Grigoryeva, I; Hernanz, M L; Jahan, F; Khlevnoy, B; Khromchenko, V; Lowe, D H; Lu, X; Machin, G; Mantilla, J M; Martin, M J; McEvoy, H C; Rougié, B; Sadli, M; Salim, S G R; Sasajima, N; Taubert, D R; Todd, A D W; Van den Bossche, R; van der Ham, E; Wang, T; Whittam, A; Wilthan, B; Woods, D J; Woodward, J T; Yamada, Y; Yamaguchi, Y; Yoon, H W; Yuan, Z
2016-03-28
The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represents 95% coverage. These results are the best consensus estimates obtained from measurements made using various spectroradiometric primary thermometry techniques by nine different national metrology institutes. The good agreement between the institutes suggests that spectroradiometric thermometry techniques are sufficiently mature (at least in those institutes) to allow the direct realization of thermodynamic temperature above 1234 K (rather than the use of a temperature scale) and that metal-carbon eutectics can be used as high-temperature fixed points for thermodynamic temperature dissemination. The results directly support the developing mise en pratique for the definition of the kelvin to include direct measurement of thermodynamic temperature. PMID:26903099
A Comparison of Visual Fields with Fixed and Moving Fixation Points. Volume I
NASA Astrophysics Data System (ADS)
McLean, William E.
2002-09-01
Four procedures were used to measure the extent of the detection fields of four primary meridians of the binocular visual fields of four subjects. Procedure I (Moving Target) used a horizontally moving target and a stationary fixation point. Procedure II (Fixed Target) used a stationary target and a horizontally moving fixation point. Procedure III (Saccadic Move) used a saccadic eye movement between two stationary horizontal fixation points and a stationary target. Procedure IV (Flashed Target) used a stationary fixation point and a .6 second flashed target. The results from the dynamic procedures (I and II) and the two static procedures (III and IV) were very similar for each subject. In the dynamic procedures, the relationship between a change in contrast and an equivalent change in velocity tends to support Bloch's Law (IxT=C) between 2 deg/s and 20 deg/s for a given retinal location. The relationship between the reciprocal of relative single glimpse probability of four subjects measured in this study and the mean detection times for comparable stimuli taken from Krendel and Wodinsky's study (1960) appear to be linear and highly correlated (.92 to .99). Volume I of this report details the technical report and volume II contains the appendices.
NASA Astrophysics Data System (ADS)
Lampitt, Richard; Cristini, Luisa; Alexiou, Sofia
2015-04-01
The Fixed point Open Ocean Observatory network (FixO3, http://www.fixo3.eu/ ) integrates 23 European open ocean fixed point observatories and improves access to these infrastructures for the broader community. These provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Started in September 2013 with a budget of 7 Million Euros over 4 years, the project has 29 partners drawn from academia, research institutions and SME's coordinated by the National Oceanography Centre, UK. Here we present the programme's achievements in the 18 months and the activities of the 12 Work Packages which have the objectives to: • integrate and harmonise the current procedures and processes • offer free access to observatory infrastructures to those who do not have such access, and free and open data services and products • innovate and enhance the current capability for multidisciplinary in situ ocean observation Open ocean observation is a high priority for European marine and maritime activities. FixO3 provides important data and services to address the Marine Strategy Framework Directive and in support of the European Integrated Maritime Policy. FixO3 provides a strong integrated framework of open ocean facilities in the Atlantic from the Arctic to the Antarctic and throughout the Mediterranean, enabling an integrated, regional and multidisciplinary approach to understand natural and anthropogenic change in the ocean.
New Filling Technique and Performance Evaluations of the Cr3C2-C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Sasajima, N.; Lowe, D.; Bai, C.; Yamada, Y.; Ara, C.
2011-12-01
The Cr3C2-C peritectic fixed point was investigated to test its capability to serve as a practical high-temperature fixed point. An improved filling technique where C/C sheet works as a wick and graphite paper as a hopper was applied successfully, and the long-term stability of the peritectic cell was evaluated by means of radiation thermometry. The repeatability of the melting point in one day was 7 mK with a melting range of approximately 100 mK. The cell was aged for 7 days, and the evaluated 56 melting temperatures during this period all fall within 90 mK, with a standard deviation of 19 mK. X-ray transmission photos showed that the ingot was filled uniformly in the crucible. After the evaluation of long-term stability, no clear degradation of the ingot shape and no leakage of molten metal were observed. From these results, it can be concluded that the Cr3C2-C peritectic cell has good stability and robustness, and the new filling technique was established. The impurity effect on the Cr3C2-C peritectic cell was also investigated by adding tungsten powder to another cell as the impurity component. After the observation of melting and freezing plateaux, the cell was cut in half to analyze the microstructure by means of electron probe microanalysis (EPMA) and laser ablation inductively coupled plasma mass spectrometer (LA-ICP-MS). The high concentration of impurity was observed in the area of the chromium-rich domain (eutectic mixture of Cr7C3 and Cr3C2), which suggests that impurities were rejected from the Cr3C2 peritectic phase during the peritectic freezing and were accumulated in the Cr7C3-Cr3C2 eutectic phase. This explains why the impurity effect is more severe for the Cr7C3-Cr3C2 eutectic point than for the Cr3C2-C peritectic point.
Zhang, Jingling; Jiang, Nan
2016-01-01
The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities.
NASA Technical Reports Server (NTRS)
Shimada, Seiichi; Bock, Yehuda
1992-01-01
Results are presented from temporally dense measurements of crustal deformation associated with the convergence of the Eurasian (EUR), Pacific, North American, and Philippine Sea (PHS) plates, carried out in April 1988 by a 10-station GPS fixed-point network established in central Japan. Using regional orbit relaxation methods, the analysis of the first 17-month data revealed significant horizontal deformation across the Suruga trough. Namely, it was found that a site in the northern tip of PHS plate moved nearly westward with a velocity of 28 +/-5 mm per year, and a site at the southeastern tip of EUR plate moved south-southwestward with a velocity of 18 +/-5 mm per year. A significant vertical uplift with a velocity of 20 mm/yr was detected at a site inland of the Tokai district located in the Akaishi uplift zone and at a site on the Hatsushima Island in Sagami Bay.
Investigation of Fixed Points Exceeding 2500 °C Using Metal Carbide-Carbon Eutectics
NASA Astrophysics Data System (ADS)
Sasajima, N.; Yamada, Y.; Sakuma, F.
2003-09-01
The melting and freezing plateaus of four metal carbide-carbon (MC-C) eutectics, B4C-C, δ(Mo carbide)-C, TiC-C and ZrC-C eutectics were investigated by radiation thermometry for the first time. The observed melting temperatures were 2386 °C, 2583 °C, 2761 °C and 2883 °C, respectively. The plateau shapes of δ(Mo carbide)-C, TiC-C and ZrC-C eutectics are relatively flat compared to the quite rounded plateau shape of the B4C-C eutectic. The results indicate that MC-C eutectics can establish a new series of high-temperature fixed points above 2500 °C.
Point and Fixed Plot Sampling Inventory Estimates at the Savannah River Site, South Carolina.
Parresol, Bernard, R.
2004-02-01
This report provides calculation of systematic point sampling volume estimates for trees greater than or equal to 5 inches diameter breast height (dbh) and fixed radius plot volume estimates for trees < 5 inches dbh at the Savannah River Site (SRS), Aiken County, South Carolina. The inventory of 622 plots was started in March 1999 and completed in January 2002 (Figure 1). Estimates are given in cubic foot volume. The analyses are presented in a series of Tables and Figures. In addition, a preliminary analysis of fuel levels on the SRS is given, based on depth measurements of the duff and litter layers on the 622 inventory plots plus line transect samples of down coarse woody material. Potential standing live fuels are also included. The fuels analyses are presented in a series of tables.
Density equalized map projections: a method for analysing clustering around a fixed point.
Schulman, J; Selvin, S; Merrill, D W
1988-04-01
Cases plotted on a geopolitical map entail difficulties in interpretation and analysis because of variable population density in the study area. Density equalized map projections (DEMPs) eliminate the distribution of the resident population as an interfering influence by transforming map area to be proportional to population. This paper discusses a transformation algorithm, its properties, and develops statistical methods to detect clustering of cases around a fixed point for data plotted on DEMPs. We suggest two numeric methods where exact solutions are too complicated or do not exist. Finally, we illustrate these methods using data from Denver and Jefferson counties in Colorado to investigate whether lung cancer and leukaemia incidence patterns are associated with plutonium exposure from the Rocky Flats plant site. PMID:3368676
Progress report for the CCT-WG5 high temperature fixed point research plan
Machin, G.; Woolliams, E. R.; Anhalt, K.; Bloembergen, P.; Sadli, M.; Yamada, Y.
2013-09-11
An overview of the progress in High Temperature Fixed Point (HTFP) research conducted under the auspices of the CCT-WG5 research plan is reported. In brief highlights are: Provisional long term stability of HTFPs has been demonstrated. Optimum construction methods for HTFPs have been established and high quality HTFPs of Co-C, Pt-C and Re-C have been constructed for thermodynamic temperature assignment. The major sources of uncertainty in the assignment of thermodynamic temperature have been identified and quantified. The status of absolute radiometric temperature measurement has been quantified through the circulation of a set of HTFPs. The measurement campaign to assign low uncertainty thermodynamic temperatures to a selected set of HTFPs will begin in mid-2012. It is envisaged that this will be complete by 2015 leading to HTFPs becoming routine reference standards for radiometry and high temperature metrology.
On the fixed points of monotonic operators in the critical case
NASA Astrophysics Data System (ADS)
Engibaryan, N. B.
2006-10-01
We consider the problem of constructing positive fixed points x of monotonic operators \\varphi acting on a cone K in a Banach space E. We assume that \\Vert\\varphi x\\Vert\\le\\Vert x\\Vert+\\gamma, \\gamma>0, for all x\\in K. In the case when \\varphi has a so-called non-trivial dissipation functional we construct a solution in an extension of E, which is a Banach space or a Fréchet space. We consider examples in which we prove the solubility of a conservative integral equation on the half-line with a sum-difference kernel, and of a non-linear integral equation of Urysohn type in the critical case.
Infrared cameras are potential traceable "fixed points" for future thermometry studies.
Yap Kannan, R; Keresztes, K; Hussain, S; Coats, T J; Bown, M J
2015-01-01
The National physical laboratory (NPL) requires "fixed points" whose temperatures have been established by the International Temperature Scale of 1990 (ITS 90) be used for device calibration. In practice, "near" blackbody radiators together with the standard platinum resistance thermometer is accepted as a standard. The aim of this study was to report the correlation and limits of agreement (LOA) of the thermal infrared camera and non-contact infrared temporal thermometer against each other and the "near" blackbody radiator. Temperature readings from an infrared thermography camera (FLIR T650sc) and a non-contact infrared temporal thermometer (Hubdic FS-700) were compared to a near blackbody (Hyperion R blackbody model 982) at 0.5 °C increments between 20-40 °C. At each increment, blackbody cavity temperature was confirmed with the platinum resistance thermometer. Measurements were taken initially with the thermal infrared camera followed by the infrared thermometer, with each device mounted in turn on a stand at a fixed distance of 20 cm and 5 cm from the blackbody aperture, respectively. The platinum thermometer under-estimated the blackbody temperature by 0.015 °C (95% LOA: -0.08 °C to 0.05 °C), in contrast to the thermal infrared camera and infrared thermometer which over-estimated the blackbody temperature by 0.16 °C (95% LOA: 0.03 °C to 0.28 °C) and 0.75 °C (95% LOA: -0.30 °C to 1.79 °C), respectively. Infrared thermometer over-estimates thermal infrared camera measurements by 0.6 °C (95% LOA: -0.46 °C to 1.65 °C). In conclusion, the thermal infrared camera is a potential temperature reference "fixed point" that could substitute mercury thermometers. However, further repeatability and reproducibility studies will be required with different models of thermal infrared cameras.
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
Correlation Between Immersion Profile and Measured Value of Fixed-Point Temperature
NASA Astrophysics Data System (ADS)
Shulgat, O. S.; Fuksov, V. M.; Ivanova, A. G.; Gerasimov, S. F.; Pokhodun, A. I.
2014-04-01
Assessment of thermal immersion effects in the melting and freezing points defined by the International Temperature Scale of 1990 is one of the vital issues of modern thermometry. In documents of the Consultative Committee for Thermometry, the deviation of the experimental immersion profile from the theoretical value of the hydrostatic effect at a height of about 3 cm to 5 cm from the thermometer well bottom is used for the estimation of the uncertainty due to unwanted thermal effects. This estimation assumes the occurrence of solely the hydrostatic effect all along the height of the well inner wall. Real distortions of the temperature gradient at the bottom and at the top part of the well caused by the change of heat-exchange conditions are not taken into account. To define more precisely the temperature gradient along the height of the well, a miniature PRT with a 30 mm sensitive element and a sheath length and diameter of about 60 mm and 6 mm, respectively, were used. Also, the measurements of fixed-points temperature at noticeably different slopes of immersion profiles due to variations of the thermometer heat exchange and phase transition realization conditions were produced by means of a standard platinum resistance thermometer (SPRT). The measurements were carried out at the tin and zinc freezing points. The immersion curves measured with a miniature thermometer demonstrated an increase of the temperature during its lifting in the first 1 cm to 3 cm above the bottom of the well. The measurement results at the zinc freezing point by means of the SPRT have not confirmed the correlation between the immersion curves, the received value of the Zn freezing temperature, and the estimation of its uncertainty.
NASA Astrophysics Data System (ADS)
Teratani, Yoshimichi; Sakano, Rui; Fujiwara, Ryo; Hata, Tokuro; Arakawa, Tomonori; Ferrier, Meydi; Kobayashi, Kensuke; Oguri, Akira
2016-09-01
Carbon nanotube quantum dot has four-fold degenerate one-particle levels, which bring a variety to the Kondo effects taking place in a wide tunable-parameter space. We theoretically study an emergent SU(2) symmetry that is suggested by recent magneto-transport measurements, carried out near two electrons filling. It does not couple with the magnetic field, and emerges in the case where the spin and orbital Zeeman splittings cancel each other out in two of the one-particle levels among four. This situation seems to be realized in the recent experiment. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs as magnetic field increases at two impurity-electrons filling. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. Furthermore, we consider how the singlet ground state evolves during such a crossover. Specifically, we reexamine the SU(N) Kondo singlet for M impurity-electrons filling in the limit of strong exchange interactions. We find that the nondegenerate Fermi-liquid fixed point of Nozières and Blandin can be described as abosonic Perron-Frobenius vector for M composite pairs, each of which consists of one impurity-electron and one conduction-hole. This interpretation in terms of the Perron-Frobenius theorem can also be extended to the Fermi-liquid fixed-point without the SU(N) symmetry.
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-11
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
NASA Astrophysics Data System (ADS)
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-01
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
Thermodynamic temperature determinations of Co C, Pd C, Pt C and Ru C eutectic fixed-point cells
NASA Astrophysics Data System (ADS)
Anhalt, K.; Hartmann, J.; Lowe, D.; Machin, G.; Sadli, M.; Yamada, Y.
2006-04-01
Thermodynamic temperatures during the melt and the freeze of Co-C, Pd-C, Pt-C and Ru-C metal-carbon fixed-point cells manufactured by LNE-INM/CNAM, NMIJ and NPL were determined by absolutely calibrated filter radiometers traceable to the PTB cryogenic radiometer and a radiance comparison method using an IKE LP3 radiation thermometer. The measurement uncertainties were below 400 mK at temperatures up to 2250 K. The results are in agreement within the combined uncertainties with a study on relative temperature differences of the same set of fixed-point cells. For the fixed-point cells manufactured by NPL the results are compared with a previous thermodynamic temperature measurement.
Assessment of tungsten/rhenium thermocouples with metal-carbon eutectic fixed points up to 1500°C
Gotoh, M.
2013-09-11
Four Type A thermocouples and two Type C thermocouples were calibrated at the Au fixed point and Co-C and Pd-C eutectic fixed points. The thermocouples were exposed to 1330 °C for a total of 100 hours. The maximum drift due to the exposure was found to be 4.8 °C. The fixed-point calibration EMF of these thermocouples deviated by less than 0.86% from the temperature specified by the standards ASTM E230-2003 for Type C and GOSTR 8.585-2001 for Type A. The length of one of Type A thermocouples A52 is longer than the others by 150mm. Making use of this provision it was possible to place annealed part of A52 to the temperature gradient part of calibration arrangement every time. Therefore observed aging effect was as low as 0.5 °C compared to the other thermocouples.
NASA Astrophysics Data System (ADS)
Mishra, Puneet; Singla, Sunil Kumar
2013-01-01
In the modern world of automation, biological signals, especially Electroencephalogram (EEG) and Electrocardiogram (ECG), are gaining wide attention as a source of biometric information. Earlier studies have shown that EEG and ECG show versatility with individuals and every individual has distinct EEG and ECG spectrum. EEG (which can be recorded from the scalp due to the effect of millions of neurons) may contain noise signals such as eye blink, eye movement, muscular movement, line noise, etc. Similarly, ECG may contain artifact like line noise, tremor artifacts, baseline wandering, etc. These noise signals are required to be separated from the EEG and ECG signals to obtain the accurate results. This paper proposes a technique for the removal of eye blink artifact from EEG and ECG signal using fixed point or FastICA algorithm of Independent Component Analysis (ICA). For validation, FastICA algorithm has been applied to synthetic signal prepared by adding random noise to the Electrocardiogram (ECG) signal. FastICA algorithm separates the signal into two independent components, i.e. ECG pure and artifact signal. Similarly, the same algorithm has been applied to remove the artifacts (Electrooculogram or eye blink) from the EEG signal.
NASA Astrophysics Data System (ADS)
Yokoyama, Yoshiaki; Kim, Minseok; Arai, Hiroyuki
At present, when using space-time processing techniques with multiple antennas for mobile radio communication, real-time weight adaptation is necessary. Due to the progress of integrated circuit technology, dedicated processor implementation with ASIC or FPGA can be employed to implement various wireless applications. This paper presents a resource and performance evaluation of the QRD-RLS systolic array processor based on fixed-point CORDIC algorithm with FPGA. In this paper, to save hardware resources, we propose the shared architecture of a complex CORDIC processor. The required precision of internal calculation, the circuit area for the number of antenna elements and wordlength, and the processing speed will be evaluated. The resource estimation provides a possible processor configuration with a current FPGA on the market. Computer simulations assuming a fading channel will show a fast convergence property with a finite number of training symbols. The proposed architecture has also been implemented and its operation was verified by beamforming evaluation through a radio propagation experiment.
Holographic duals of a family of Script N = 1* fixed points
NASA Astrophysics Data System (ADS)
Halmagyi, Nick; Pilch, Krzysztof; Römelsberger, Christian; Warner, Nicholas P.
2006-08-01
We construct a family of warped AdS5 compactifications of IIB supergravity that are the holographic duals of the complete set of Script N = 1* fixed points of a Bbb Z2 quiver gauge theory. This family interpolates between the T1,1 compactification with no three-form flux and the Bbb Z2 orbifold of the Pilch-Warner geometry which contains three-form flux. This family of solutions is constructed by making the most general Ansatz allowed by the symmetries of the field theory. We use Killing spinor methods because the symmetries impose two simple projection conditions on the Killing spinors, and these greatly reduce the problem. We see that generic interpolating solution has a nontrivial dilaton in the internal five-manifold. We calculate the central charge of the gauge theories from the supergravity backgrounds and find that it is (27/32) of the parent Script N = 2, quiver gauge theory. We believe that the projection conditions that we derived here will be useful for a much larger class of Script N = 1 holographic RG-flows.
Realization of the WC-C peritectic fixed point at NIM and NMIJ
Wang, T.; Bai, C.; Yuan, Z.; Dong, W.; Lu, X.; Sasajima, N.; Yamada, Y.; Ara, C.
2013-09-11
Three WC-C peritectic fixed point cells, constructed from different sources of tungsten with different nominal purities, were measured at NIM and NMIJ. The three cells were constructed at NMIJ by NIM and NMIJ staffs, and T{sub 90} values of the three cells were measured at NMIJ during the period 31 Aug. to 25 Dec. 2009. Thereafter, the three cells were then transported to NIM, and T{sub 90} values of these cells were measured from 7 Dec. 2011 to 9 Jan. 2012. The results showed that T{sub 90} values of the three cells measured at the two institutes agreed within 0.4 °C with the combined scale comparison uncertainty of 1.7 °C (k= 2). The main component of the uncertainty is not the uncertainty due to impurities of the cells but the scale uncertainty and the stability of the measurement system. From these results it can be concluded that the WC-C cell is stable enough to provide new means of international high-temperature scale comparison above 3000 K.
SU(4) Kondo effect in coupled quantum dots in parallel: Evidence of marginal fixed point
NASA Astrophysics Data System (ADS)
Eto, Mikio
2008-03-01
We theoretically study the Kondo effect in coupled quantum dots in parallel, using the scaling and NRG methods. The double quantum dots are capacitively coupled to each other, whereas they are attached to separate leads.ootnotetextA. Huebel, J. Weis and K.von Klitzing, 17th International Conference on the Electronic Properties of Two-Dimensional Systems (EP2DS, 2007). The SU(4) Kondo effect is realized when the energy levels are matched between the quantum dots. We show that (i) the Kondo temperature TK decreases with increasing |δ|, where δ is the level separation between the dots, obeying a power law [crossover from SU(4) to SU(2) Kondo effect]. (ii) The exponent of the power law is not a universal value in general.ootnotetextM. Eto, J. Phys. Soc. Jpn.74, 95 (2005). This is an evidence of the marginal fixed point of SU(4) Kondo effect.ootnotetextL. Borda et al., Phys. Rev. Lett. 90, 026602 (2003) (iii) The conductance through one of the quantum dots may show a non-monotonic behavior as a function of temperature T although the total conductance is a universal function of T/TK.
NASA Technical Reports Server (NTRS)
Alefeld, Goetz; Koshelev, Misha; Mayer, Guenter
1997-01-01
At first glance. it may seem that reconstructing the past is, in general, easier than predicting the future, because the past has already occurred and it has already left its traces, while the future is still yet to come, and so no traces of the future are available. However, in many real life situations, including problems from geophysics and celestial mechanics, reconstructing the past is much more computationally difficult than predicting the future. In this paper, we give an explanation of this difficulty. This explanation is given both on a formal level (as a theorem) and on the informal level (as a more intuitive explanation).
Vibrational eigen-modes of the 7.5-m thin meniscus mirror with axial and lateral fixed points.
NASA Astrophysics Data System (ADS)
Yamashita, Y.; Nishino, Y.
Eigen-frequencies and modes are calculated for a thin meniscus mirror of diameter 7.5 m and thickness 20 cm, whose six degrees of freedom are confined by three axial and three lateral fixed points. The patterns calculated up to mode 25 are presented.
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional strategies…
2012-01-01
A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859
Formalin Fixed Paraffin Embedded Tissue as a Starting Point for PrPSc Detection by ELISA
Technology Transfer Automated Retrieval System (TEKTRAN)
Introduction: Formalin fixed paraffin embedded tissue are regularly employed in TSE diagnosis by IHC, the standard by which all other diagnostic protocols are currently judged. While IHC affords advantages over diagnostic approaches that typically utilize fresh or frozen tissue, such as Western blot...
Competition Between Transients in the Rate of Approach to a Fixed Point.
Day, Judy; Rubin, Jonathan E; Chow, Carson C
2009-11-20
The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
Competition Between Transients in the Rate of Approach to a Fixed Point
NASA Astrophysics Data System (ADS)
Day, Judy; Rubin, Jonathan E.; Chow, Carson C.
2009-01-01
The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
NASA Astrophysics Data System (ADS)
Sadli, Mohamed; Bourson, Frédéric; Diril, Ahmet; Journeau, Christophe; Lowe, Dave; Parga, Clemente
2014-08-01
Among the activities of the European Metrology Research Programme (EMRP) project HiTeMS one work package is devoted to the development and testing of industrial solutions for long-standing temperature measurement problems at the highest temperatures. LNE-Cnam, NPL, TUBITAK-UME have worked on the design of high temperature fixed points (HTFP) suitable for in-situ temperature monitoring to be implemented in the facilities of CEA (Commissariat à l'énergie atomique et aux énergies alternatives). Several high temperature fixed point cells were constructed in these three national metrology institutes (NMIs) using a rugged version of cells based on the hybrid design of the laboratory HTFP developed and continuously improved at LNE-Cnam during the last years. The fixed points of interest were Co-C, Ru-C and Re-C corresponding to melting temperatures of 1324 °C, 1953 °C and 2474 °C respectively. The cells were characterised at the NMIs after their construction. Having proved robust enough, they were transported to CEA and tested in an induction furnace and cycled from room temperature to temperatures much above the melting temperatures (> +400 °C) with extremely high heating and cooling rates (up to 10 000 K/h). All the cells withstood the tests and the melting plateaus could be observed in all cases.
The EuroSITES network: Integrating and enhancing fixed-point open ocean observatories around Europe
NASA Astrophysics Data System (ADS)
Lampitt, Richard S.; Larkin, Kate E.; EuroSITES Consortium
2010-05-01
EuroSITES is a 3 year (2008-2011) EU collaborative project (3.5MEuro) with the objective to integrate and enhance the nine existing open ocean fixed point observatories around Europe (www.eurosites.info). These observatories are primarily composed of full depth moorings and make multidisciplinary in situ observations within the water column as the European contribution to the global array OceanSITES (www.oceansites.org). In the first 18 months, all 9 observatories have been active and integration has been significant through the maintenance and enhancement of observatory hardware. Highlights include the enhancement of observatories with sensors to measure O2, pCO2, chlorophyll, and nitrate in near real-time from the upper 1000 m. In addition, some seafloor missions are also actively supported. These include seafloor platforms currently deployed in the Mediterranean, one for tsunami detection and one to monitor fluid flow related to seismic activity and slope stability. Upcoming seafloor science missions in 2010 include monitoring benthic biological communities and associated biogeochemistry as indicators of climate change in both the Northeast Atlantic and Mediterranean. EuroSITES also promotes the development of innovative sensors and samplers in order to progress capability to measure climate-relevant properties of the ocean. These include further developing current technologies for autonomous long-term monitoring of oxygen consumption in the mesopelagic, pH and mesozooplankton abundance. Many of these science missions are directly related to complementary activities in other European projects such as EPOCA, HYPOX and ESONET. In 2010 a direct collaboration including in situ field work will take place between ESONET and EuroSITES. The demonstration mission MODOO (funded by ESONET) will be implemented in 2010 at the EuroSITES PAP observatory. Field work will include deployment of a seafloor lander system with various sensors which will send data to shore in real
Two-stage fixed-bed gasifier with selectable middle gas off-take point
Strickland, Larry D.; Bissett, Larry A.
1992-01-01
A two-stage fixed bed coal gasifier wherein an annular region is in registry with a gasification zone underlying a devolatilization zone for extracting a side stream of high temperature substantially tar-free gas from the gasifier. A vertically displaceable skirt means is positioned within the gasifier to define the lower portion of the annular region so that vertical displacement of the skirt means positions the inlet into the annular region in a selected location within or in close proximity to the gasification zone for providing a positive control over the composition of the side stream gas.
Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji
2012-09-01
We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.
Antila, Hanne S; Salonen, Emppu
2015-04-15
The Thole induced point dipole model is combined with three different point charge fitting methods, Merz-Kollman (MK), charges from electrostatic potentials using a grid (CHELPG), and restrained electrostatic potential (RESP), and two multipole algorithms, distributed multipole analysis (DMA) and Gaussian multipole model (GMM), which can be used to describe the electrostatic potential (ESP) around molecules in molecular mechanics force fields. This is done to study how the different methods perform when intramolecular polarizability contributions are self-consistently removed from the fitting done in the force field parametrization. It is demonstrated that the polarizable versions of the partial charge models provide a good compromise between accuracy and computational efficiency in describing the ESP of small organic molecules undergoing conformational changes. For the point charge models, the inclusion of polarizability reduced the the average root mean square error of ESP over the test set by 4-10%.
Investigations on Two Co-C Fixed-Point Cells Prepared at INRIM and LNE-Cnam
NASA Astrophysics Data System (ADS)
Battuello, M.; Florio, M.; Sadli, M.; Bourson, F.
2011-08-01
INRIM and LNE-Cnam agreed to undertake a collaboration aimed to verify, through the use of metal-carbon eutectic fixed-point cells, methods and facilities used for defining the transition temperature of eutectic fixed points and manufacturing procedures of cells. To this purpose and as a first step of the cooperation, a Co-C cell manufactured at LNE-Cnam was measured at INRIM and compared with a local cell. The two cells were of different designs: the INRIM cell of 10 cm3 inner volume and the LNE-Cnam one of 3.9 cm3. The external dimensions of the two cells were noticeably different, namely, 40 mm in length and 24 mm in diameter for the LNE-Cnam cell 3Co4 and 110 mm in length and 42 mm in diameter for the INRIM cell. Consequently, the investigation of the effect of temperature distributions in the heating furnace was undertaken by implementing the cells inside single-zone and three-zone furnaces. The transition temperature of the cell was determined at the two institutes making use of different techniques: at INRIM radiation scales at 900 nm, 950 nm, and 1.6 μm were realized from In to Cu and then used to define T 90(Co-C) by extrapolation. At LNE-Cnam, a radiance comparator based on a grating monochromator was used for the extrapolation from the Cu fixed point. This paper presents a comparative description of the cells and the manufacturing methods and the results in terms of equivalence between the two cells and melting temperatures determined at INRIM and LNE-Cnam.
Kleinert, H; Pelster, A; Bachmann, M
1999-09-01
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating functionals are calculated explicitly for the harmonic oscillator with time-dependent frequency, and used to derive a smearing formula for correlation functions of polynomial and nonpolynomial functions of time-dependent positions and momenta. This formula summarizes the effect of quantum fluctuations, and serves to derive generalized Wick rules and Feynman diagrams for perturbation expansions of nonpolynomial interactions.
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
Kainz, K; Prah, D; Ahunbay, E; Li, X
2014-06-01
Purpose: A novel modulated arc therapy technique, mARC, enables superposition of step-and-shoot IMRT segments upon a subset of the optimization points (OPs) of a continuous-arc delivery. We compare two approaches to mARC planning: one with the number of OPs fixed throughout optimization, and another where the planning system determines the number of OPs in the final plan, subject to an upper limit defined at the outset. Methods: Fixed-OP mARC planning was performed for representative cases using Panther v. 5.01 (Prowess, Inc.), while variable-OP mARC planning used Monaco v. 5.00 (Elekta, Inc.). All Monaco planning used an upper limit of 91 OPs; those OPs with minimal MU were removed during optimization. Plans were delivered, and delivery times recorded, on a Siemens Artiste accelerator using a flat 6MV beam with 300 MU/min rate. Dose distributions measured using ArcCheck (Sun Nuclear Corporation, Inc.) were compared with the plan calculation; the two were deemed consistent if they agreed to within 3.5% in absolute dose and 3.5 mm in distance-to-agreement among > 95% of the diodes within the direct beam. Results: Example cases included a prostate and a head-and-neck planned with a single arc and fraction doses of 1.8 and 2.0 Gy, respectively. Aside from slightly more uniform target dose for the variable-OP plans, the DVHs for the two techniques were similar. For the fixed-OP technique, the number of OPs was 38 and 39, and the delivery time was 228 and 259 seconds, respectively, for the prostate and head-and-neck cases. For the final variable-OP plans, there were 91 and 85 OPs, and the delivery time was 296 and 440 seconds, correspondingly longer than for fixed-OP. Conclusion: For mARC, both the fixed-OP and variable-OP approaches produced comparable-quality plans whose delivery was successfully verified. To keep delivery time per fraction short, a fixed-OP planning approach is preferred.
NASA Astrophysics Data System (ADS)
Slamnoiu, G.; Radu, O.; Surdu, G.; Roşca, V.; Damian, R.; Pascu, C.; Curcă, E.; Rădulescu, A.
2016-08-01
The paper has as its main objectives the presentation and the analysis of the numerical analysis results for the study of a fixed point anchoring system for a hydroacoustic sensor when measuring the hydroacoustic signature of divers and ships in real sea conditions. The study of the mechanical behavior of this system has as main objectives the optimization of the shape and weight of the anchorage ballast for the metallic structure while considering the necessity to maintain the sensor in a fixed point and the analysis of the sensor movements and the influences on the measurements caused by the sea current streams. The study was focused on the 3D model of metallic structure design; numerical modeling of the water flow around the sensor anchoring structure using volume of fluid analysis and the analysis of the forces and displacements using FEM when needed for the study. In this paper we have used data for the sea motion dynamics and in particular the velocity of the sea current streams as determined by experimental measurements that have been conducted for the western area of the Black Sea.
Low-energy fixed points of the σ-τ and the O(3) symmetric Anderson models
NASA Astrophysics Data System (ADS)
Bulla, R.; Hewson, A. C.; Zhang, G.-M.
1997-11-01
We study the single-channel (compactified) models, the σ-τ model, and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low-energy behavior of the isotropic and anisotropic two-channel Kondo systems. These models display both Fermi-liquid and marginal-Fermi-liquid behavior and an understanding of the nature of their low-energy fixed points may give some general insights into the low-energy behavior of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi-liquid fixed point of the σ-τ model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak-coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak- and strong-coupling regimes and show that the χ/γ ratio is 8/3 (χ is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.
NASA Astrophysics Data System (ADS)
Liang, Yanfeng; Naqvi, Syed Mohsen; Chambers, Jonathon A.
2012-12-01
Fast fixed-point independent vector analysis (FastIVA) is an improved independent vector analysis (IVA) method, which can achieve faster and better separation performance than original IVA. As an example IVA method, it is designed to solve the permutation problem in frequency domain independent component analysis by retaining the higher order statistical dependency between frequencies during learning. However, the performance of all IVA methods is limited due to the dimensionality of the parameter space commonly encountered in practical frequency-domain source separation problems and the spherical symmetry assumed with the source model. In this article, a particular permutation problem encountered in using the FastIVA algorithm is highlighted, namely the block permutation problem. Therefore a new audio video based fast fixed-point independent vector analysis algorithm is proposed, which uses video information to provide a smart initialization for the optimization problem. The method cannot only avoid the ill convergence resulting from the block permutation problem but also improve the separation performance even in noisy and high reverberant environments. Different multisource datasets including the real audio video corpus AV16.3 are used to verify the proposed method. For the evaluation of the separation performance on real room recordings, a new pitch based evaluation criterion is also proposed.
Typical Orbits of Quadratic Polynomials with a Neutral Fixed Point: Brjuno Type
NASA Astrophysics Data System (ADS)
Cheraghi, Davoud
2013-09-01
We describe the topological behavior of typical orbits of complex quadratic polynomials {P_{α}(z) = e^{2 π α {i}} z + z2}, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.
Construction of Home-Made Tin Fixed-Point Cell at TUBITAK UME
NASA Astrophysics Data System (ADS)
Kalemci, M.; Arifovic, N.; Bağçe, A.; Aytekin, S. O.; Ince, A. T.
2015-08-01
TUBITAK UME Temperature Laboratory initiated a new study which focuses on the construction of a tin freezing-point cell as a primary temperature standard. The design is an open-cell type similar to the National Institute of Standards and Technology design. With this aim, a brand new vacuum and filling line employing an oil diffusion pump and two cold traps (liquid nitrogen and dry ice) was set-up. The graphite parts (crucible, thermometer well, etc.) have been baked at high temperature under vacuum. Each cell was filled with approximately 1 kg of high-purity tin (99.9999 %) in a three-zone furnace. Then several melting and freezing curves were obtained to assess the quality of the home-made cell, and also the new cell was compared with the existing reference cell of the laboratory. The results obtained are very close to the reference cell of UME, indicating that the method used for fabrication was promising and satisfactory and also seems to meet the requirements to have a primary level temperature standard.
A Phase-Field Solidification Model of Almost Pure ITS-90 Fixed Points
NASA Astrophysics Data System (ADS)
Large, M. J.; Pearce, J. V.
2014-07-01
A two-dimensional axisymmetric phase-field model of thermo-solutal solidification in freezing-point cells used for calibrating standard platinum resistance thermometers for realization and dissemination of the International Temperature Scale of 1990 is presented. The cell is essentially a graphite crucible containing an ingot of very pure metal (of order 99.9999 %). A graphite tube is inserted along the axis of the ingot to enable immersion of the thermometer in the metal. In this study, the metal is tin (freezing temperature of ). During the freezing of these cells, a steady, reproducible temperature is realized, with a defined temperature that can be used to calibrate thermometers with uncertainties mK. The model is applied to understand the effect of experimental parameters, such as initiation technique and furnace homogeneity, on the measured freezing curve. Results show that freezing curves whose behavior is consistent with the Scheil theory of solidification can be obtained with a specific furnace temperature profile, and provided that the freeze is of a long duration, the results are consistent with previous one-dimensional models and experiments. Morphological instability is observed with the inner interface initiation technique, causing the interface to adopt a cellular structure. This elevates the measured temperature, in accordance with the Gibbs-Thomson effect. In addition, the influence of initiation techniques on the solidification behavior is examined. The model indicates that an initially smooth inner mantle can `de-wet' from the thermometer well-forming agglomerated solid droplets, following recalescence, under certain conditions. This manifests as a measured temperature depression due to the Gibbs-Thomson effect, with a magnitude of to in simulations. The temperature rises to that of the stable outer mantle as freezing progresses and the droplets re-melt. It is demonstrated that the effect occurs below a critical mantle thickness. A physical
Selbig, William R.; Bannerman, Roger T.
2011-01-01
The U.S Geological Survey, in cooperation with the Wisconsin Department of Natural Resources (WDNR) and in collaboration with the Root River Municipal Stormwater Permit Group monitored eight urban source areas representing six types of source areas in or near Madison, Wis. in an effort to improve characterization of particle-size distributions in urban stormwater by use of fixed-point sample collection methods. The types of source areas were parking lot, feeder street, collector street, arterial street, rooftop, and mixed use. This information can then be used by environmental managers and engineers when selecting the most appropriate control devices for the removal of solids from urban stormwater. Mixed-use and parking-lot study areas had the lowest median particle sizes (42 and 54 (u or mu)m, respectively), followed by the collector street study area (70 (u or mu)m). Both arterial street and institutional roof study areas had similar median particle sizes of approximately 95 (u or mu)m. Finally, the feeder street study area showed the largest median particle size of nearly 200 (u or mu)m. Median particle sizes measured as part of this study were somewhat comparable to those reported in previous studies from similar source areas. The majority of particle mass in four out of six source areas was silt and clay particles that are less than 32 (u or mu)m in size. Distributions of particles ranging from 500 (u or mu)m were highly variable both within and between source areas. Results of this study suggest substantial variability in data can inhibit the development of a single particle-size distribution that is representative of stormwater runoff generated from a single source area or land use. Continued development of improved sample collection methods, such as the depth-integrated sample arm, may reduce variability in particle-size distributions by mitigating the effect of sediment bias inherent with a fixed-point sampler.
A Note on Laplace's Expansion Theorem
ERIC Educational Resources Information Center
Janji, Milan
2005-01-01
A short proof of Laplace's expansion theorem is given. The proof is elementary and can be presented at any level of undergraduate studies where determinants are taught. It is derived directly from the definition so that the theorem may be used as a starting point for further investigation of determinants.
Fogle, W.E.; Hornung, E.W.; Mayberry, M.C.; Phillips, N.E.
1981-08-01
Comparison of a powdered CMN thermometer with an NBS fixed point device demonstrates an internal inconsistency in the T/sub c/'s assigned to the fixed point device. T/sub c/'s between 100 and 200 mK are in excellent agreement with a temperature scale interpolated between He vapor pressure temperatures and nuclear orientation temperatures, but there is a discrepancy of 8% at the 15 mK point. Evidence for different susceptibility-temperature relations for superficially similar CMN thermometers is also presented.
Noether’s second theorem and Ward identities for gauge symmetries
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-04
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less
NASA Astrophysics Data System (ADS)
Dong, W.; Machin, G.; Bloembergen, P.; Lowe, D.; Wang, T.
2016-11-01
Extensive studies of platinum–carbon eutectic alloy based high temperature fixed point cells have shown that this alloy has extremely good metrological potential as a temperature reference. However, it’s possible adoption as an accepted reference standard means that its eutectic temperature value will soon be agreed with an uncertainty less than most radiation thermometry scales at that temperature. Thus it will lack credibility if used as a future scale comparison artefact. To avoid this, the fixed-point cell can be deliberately doped with an impurity to change its transition temperature by an amount sufficient to test the accuracy of the scales of the institutes, involved in the comparison. In this study dopants of palladium and iridium were added to platinum–carbon to produce ternary alloy and quaternary alloy fixed-point cells. The stability of these artefacts was demonstrated and the fixed-point cells were used to compare the ITS-90 scales of NIM and NPL. It was found that the fixed point temperatures could be changed by an appreciable amount while retaining the stability and repeatability required for comparison artefacts.
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
NASA Astrophysics Data System (ADS)
Siegel, J.; Siegel, Edward Carl-Ludwig
2011-03-01
Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!
A generalization of averaging theorems for porous medium analysis
NASA Astrophysics Data System (ADS)
Gray, William G.; Miller, Cass T.
2013-12-01
The contributions of Stephen Whitaker to the rigorous analysis of porous medium flow and transport are built on the use of temporal and spatial averaging theorems applied to phases in representative elementary volumes. Here, these theorems are revisited, common point theorems are considered, extensions of existing theorems are developed to include the effects of lower dimensional entities represented as singularities, and a unified form of the theorems for phases, interfaces, common curves, and common points is established for both macroscale and mixed macroscale-megascale systems. The availability of the full set of theorems facilitates detailed analysis of a variety of porous medium systems. Explicit modeling of the physical processes associated with interfaces, common curves, and common points, as well as the kinematics of these entities, can be undertaken at both the macroscale and megascale based on these theorems.
NASA Astrophysics Data System (ADS)
McEvoy, H. C.; Sadli, M.; Bourson, F.; Briaudeau, S.; Rougié, B.
2013-12-01
The silver and copper fixed-point blackbody sources of NPL were directly compared with those of LNE-Cnam using an IKE LP3 and an IKE LP5 at three wavelengths (650 nm, 795 nm and 903 nm). The two silver fixed points and the two copper fixed points were in excellent agreement with each other, with a difference of 11 mK for the silver and within 16 mK for the copper, with an expanded measurement uncertainty of between 10 mK and 20 mK depending on the pyrometer used. The temperature interval between the silver and copper freezing points was also measured using combinations of all four fixed points. The results with the NPL LP3 gave a value for the silver-copper temperature interval of 122.89 °C with an expanded uncertainty of 30 mK those with the LNE-Cnam LP5 gave a temperature interval of 122.87 °C also with an expanded uncertainty of 30 mK this compares with the ITS-90 value of 122.84 °C.
Hahl, Sayuri K.; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
Hahl, Sayuri K.; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
Hahl, Sayuri K; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
Hahl, Sayuri K; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
ERIC Educational Resources Information Center
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of…
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
La, Moonwoo; Park, Sang Min; Kim, Dong Sung
2015-01-01
In this study, a multiple sample dispenser for precisely metered fixed volumes was successfully designed, fabricated, and fully characterized on a plastic centrifugal lab-on-a-disk (LOD) for parallel biochemical single-end-point assays. The dispenser, namely, a centrifugal multiplexing fixed-volume dispenser (C-MUFID) was designed with microfluidic structures based on the theoretical modeling about a centrifugal circumferential filling flow. The designed LODs were fabricated with a polystyrene substrate through micromachining and they were thermally bonded with a flat substrate. Furthermore, six parallel metering and dispensing assays were conducted at the same fixed-volume (1.27 μl) with a relative variation of ±0.02 μl. Moreover, the samples were metered and dispensed at different sub-volumes. To visualize the metering and dispensing performances, the C-MUFID was integrated with a serpentine micromixer during parallel centrifugal mixing tests. Parallel biochemical single-end-point assays were successfully conducted on the developed LOD using a standard serum with albumin, glucose, and total protein reagents. The developed LOD could be widely applied to various biochemical single-end-point assays which require different volume ratios of the sample and reagent by controlling the design of the C-MUFID. The proposed LOD is feasible for point-of-care diagnostics because of its mass-producible structures, reliable metering/dispensing performance, and parallel biochemical single-end-point assays, which can identify numerous biochemical.
La, Moonwoo; Park, Sang Min; Kim, Dong Sung
2015-01-01
In this study, a multiple sample dispenser for precisely metered fixed volumes was successfully designed, fabricated, and fully characterized on a plastic centrifugal lab-on-a-disk (LOD) for parallel biochemical single-end-point assays. The dispenser, namely, a centrifugal multiplexing fixed-volume dispenser (C-MUFID) was designed with microfluidic structures based on the theoretical modeling about a centrifugal circumferential filling flow. The designed LODs were fabricated with a polystyrene substrate through micromachining and they were thermally bonded with a flat substrate. Furthermore, six parallel metering and dispensing assays were conducted at the same fixed-volume (1.27 μl) with a relative variation of ±0.02 μl. Moreover, the samples were metered and dispensed at different sub-volumes. To visualize the metering and dispensing performances, the C-MUFID was integrated with a serpentine micromixer during parallel centrifugal mixing tests. Parallel biochemical single-end-point assays were successfully conducted on the developed LOD using a standard serum with albumin, glucose, and total protein reagents. The developed LOD could be widely applied to various biochemical single-end-point assays which require different volume ratios of the sample and reagent by controlling the design of the C-MUFID. The proposed LOD is feasible for point-of-care diagnostics because of its mass-producible structures, reliable metering/dispensing performance, and parallel biochemical single-end-point assays, which can identify numerous biochemical. PMID:25610516
Brückner, Hans-Peter; Spindeldreier, Christian; Blume, Holger
2013-01-01
A common approach for high accuracy sensor fusion based on 9D inertial measurement unit data is Kalman filtering. State of the art floating-point filter algorithms differ in their computational complexity nevertheless, real-time operation on a low-power microcontroller at high sampling rates is not possible. This work presents algorithmic modifications to reduce the computational demands of a two-step minimum order Kalman filter. Furthermore, the required bit-width of a fixed-point filter version is explored. For evaluation real-world data captured using an Xsens MTx inertial sensor is used. Changes in computational latency and orientation estimation accuracy due to the proposed algorithmic modifications and fixed-point number representation are evaluated in detail on a variety of processing platforms enabling on-board processing on wearable sensor platforms. PMID:24110597
Pythagoras Theorem and Relativistic Kinematics
NASA Astrophysics Data System (ADS)
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
A variational proof of Thomson's theorem
NASA Astrophysics Data System (ADS)
Fiolhais, Miguel C. N.; Essén, Hanno; Gouveia, Tomé M.
2016-08-01
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…
The Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Miyazoe, Terumi; Anderson, Terry
2010-01-01
This paper examines the key issues regarding The Interaction Equivalency Theorem posited by Anderson (2003a), which consists of the three interaction elements found in formal education courses among teacher, student, and content. It first examines the core concepts of the theorem and argues that two theses of different dimensions can be…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
Co-C and Pd-C Fixed Points for the Evaluation of Facilities and Scales Realization at INRIM and NMC
NASA Astrophysics Data System (ADS)
Battuello, M.; Wang, L.; Girard, F.; Ang, S. H.
2014-04-01
Two hybrid cells for realizing the Co-C and Pd-C fixed points and constructed at Istituto Nazionale di Ricerca Metrologica (INRIM) were used for an evaluation of facilities and procedures adopted by INRIM and National Metrology Institute of Singapore (NMC) for the realization of the solid-liquid phase transitions of high-temperature fixed points and for determining their transition temperatures. Four different furnaces were used for the investigations, i.e., two single-zone furnaces, one of them of the direct-heating type, and two identical three-zone furnaces. The transition temperatures were measured at both institutes by adopting different procedures for realizing the radiation scales, i.e., at INRIM a scheme based on the extrapolation of fixed-point interpolated scales and an International Temperature Scale of 1990 (ITS-90) approach at NMC. The point of inflection (POI) of the melting curves was determined and assumed as a practical representation of the melting temperature. Different methods for deriving the POI were used, and differences as large as some hundredths of a kelvin were found with the different approaches. The POIs of the different melting curves were analyzed with respect to the different possible operative conditions with the aim of deriving reproducibility figures to improve the estimated uncertainty. As regard to the institutes inter-comparison, differences of 0.13 K and 0.29 K were found between INRIM and NMC determinations at the Co-C and Pd-C points, respectively. Such differences are compatible with the combined standard uncertainties of the comparison, which are estimated to be 0.33 K and 0.36 K at the Co-C and Pd-C points, respectively.
Shimamoto, Akira; Yamashita, Keitaro; Inoue, Hirofumi; Yang, Sung-Mo; Iwata, Masahiro; Ike, Natsuko
2013-04-01
Destructive tests are generally applied to evaluate the fixed strength of spot-welding nuggets of zinc-plated steel (which is a widely used primary structural material for automobiles). These destructive tests, however, are expensive and time-consuming. This paper proposes a nondestructive method for evaluating the fixed strength of the welded joints using surface electrical resistance. A direct current nugget-tester and probes have been developed by the authors for this purpose. The proposed nondestructive method uses the relative decrease in surface electrical resistance, α. The proposed method also considers the effect of the corona bond. The nugget diameter is estimated by two factors: R Quota, which is calculated from variation of resistance, and a constant that represents the area of the corona bond. Since the maximum tensile strength is correlated with the nugget diameter, it can be inferred from the estimated nugget diameter. When appropriate measuring conditions for the surface electrical resistance are chosen, the proposed method can effectively evaluate the fixed strength of the spot-welded joints even if the steel sheet is zinc-plated.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
NASA Astrophysics Data System (ADS)
Sasajima, N.; Yoon, H. W.; Gibson, C. E.; Khromchenko, V.; Sakuma, F.; Yamada, Y.
2006-04-01
The National Institute of Standards and Technology (NIST) has initiated a project on novel high-temperature fixed-points by use of metal (carbide)-carbon eutectics to lower uncertainties in thermodynamic temperature measurement. As the first stage of the NIST eutectic project, a comparison of Co-C, Pt-C and Re-C eutectic fixed-point cells was conducted between the NIST and the National Metrology Institute of Japan (NMIJ) at the NIST to verify the quality of the NIST eutectic cells in addition to checking for possible furnace and radiation thermometer effects on the eutectic fixed-point realizations. In the comparison, two high-temperature furnaces, two radiation thermometers and one gold-point blackbody were used. A Nagano M furnace and a Linear Pyrometer 3 radiation thermometer were transferred from NMIJ and were used in conjunction with a Thermo Gauge furnace and an Absolute Pyrometer 1 radiation thermometer of NIST to check the dependence on the measurement equipment. The results showed that Co-C cells agreed to 73 mK. The melting temperature of the NIST Pt-C cell was approximately 270 mK lower than that of the NMIJ cell, with a comparison uncertainty of roughly 110 mK (k = 2), due to the poor purity of Pt powder. Although the Re-C comparison showed instability of the comparison system, they agreed within 100 mK. Though further improvement is necessary for the Pt-C cell, such as the use of higher purity Pt, the filling and measuring technique has been established at the NIST.
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Plaisted, David A
2014-03-01
Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:26304304
NASA Astrophysics Data System (ADS)
Grigor'ev, K. G.; Zapletina, E. V.; Zapletin, M. P.
1992-06-01
The paper presents an analysis and results of a numerical solution, based on the maximum principle, of three types of problems concerning the optimal launching of a space vehicle with a high-thrust rocket engine from the lunar surface to a fixed point on the circular orbit of a lunar artificial satellite. Attention is given to the problems of the fastest possible launching time, launching with minimal mass expenditure, and minimal trade-off functional (a compromise between expenditures for launch time and mass). The shooting method is used to obtain exact numerical solutions for the appropriate maximum principle boundary problems.
NASA Astrophysics Data System (ADS)
Lowe, Dave; Kodwani, Darsh
2015-11-01
Re-calibration of a thermocouple after it has been installed in a process is often not practical. In situ monitoring of performance is desirable and can be done with built-in reference standards based on melting or freezing phase transitions. Binary alloys with a monotectic reaction frequently have two invariant melt/freeze phase transitions taking place in the same material over a range of compositions. This makes them potentially well suited to be in situ temperature calibration artifacts, enabling correction for thermocouple drift without the need to disturb the thermocouple. A zinc-bismuth fixed-point cell was constructed and has been shown to be stable with two well-defined melting plateaus at nominally 255°C and 415°C. Two miniature fixed-point cells (each designed to be permanently installed with a thermocouple) based on zinc-bismuth and aluminum-indium alloys were made. Measurements have shown that the phase transitions can be identified despite the small quantity of metals used and that the alloys were sufficiently stable to have the potential to provide improved long-term confidence in process control and monitoring.
NASA Astrophysics Data System (ADS)
Renaot, E.; Martin, C.
2011-08-01
In order to improve the uncertainty on the aluminum fixed point, a study was launched by Laboratoire Commun de Métrologie LNE-CNAM in the frame of the EURAMET Project 732 "Toward more accurate temperature fixed points" (coordinating laboratory: France, 17 partner countries). An earlier study completed in this laboratory showed that in regular realization of the melting-freezing plateaus, there is no diffusion of impurities in the thickness of the ingot, or the diffusion is excessively slow and cannot allow a uniform distribution of the impurities. On the other hand, it is frequently noticed that the experimental conditions before the freezing plateau have an impact on its characteristics (value, slope,…). Up to now, no systematic study was performed on the influence of this parameter. So, the objective of the task started recently in this laboratory is to investigate the influence of the time spent in the liquid phase on the phase transition. As a final result, it is demonstrated that in order to reach the equilibrium of the concentration of impurities, it is necessary to ensure that the metal remains in the liquid phase at least 24 h before initiating the freeze. At the end of the process, the aluminum ingot was chemically analyzed. The analyses reveal large contaminations of the surface of the ingot (sodium, sulfur, and phosphorus). One of the important outputs of this study is that the conditions of usage of the cells should be given important attention since large contaminations can be brought by the furnace.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
Generalizations of the abstract boundary singularity theorem
NASA Astrophysics Data System (ADS)
Whale, Ben E.; Ashley, Michael J. S. L.; Scott, Susan M.
2015-07-01
The abstract boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of abstract boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from C1 curves to locally Lipschitz curves.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
NASA Astrophysics Data System (ADS)
Mambrini, Y.; Moultaka, G.
2002-06-01
We investigate the one-loop renormalization-group evolution of extended sectors of Yukawa-type couplings. It is shown that Landau poles, which usually provide the necessary low-energy upper bounds that saturate quickly with increasing initial value conditions, lead in some cases to the opposite behavior: some of the low-energy couplings decrease and become vanishingly small for increasingly large initial conditions. We write down the general criteria for this to happen in typical situations, highlighting a concept of repulsive quasifixed points, and illustrate the case both within a two-Yukawa toy model as well as in the minimal supersymmetric standard model with R-parity violation. In the latter case, we consider the theoretical upper bounds on the various couplings, identifying regimes where λkl3,λ'kkk,λ″3kl are dynamically suppressed due to the Landau pole. We stress the importance of considering a large number of couplings simultaneously. This leads altogether to a phenomenologically interesting seesaw effect in the magnitudes of the various R-parity violating couplings, complementing and in some cases improving the existing limits.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
''CPT Theorem'' for Accelerators
Vladimir Shiltsev
2004-08-05
In this paper we attempt to reveal common features in evolution of various colliders' luminosity over commissioning periods. A simplified formula, ''CPT theorem'' or CP = T, is proposed which relates the time needed for commissioning T, the ''complexity'' of the machine C and performance increase goal P.
A Schwinger disentangling theorem
Cross, Daniel J.; Gilmore, Robert
2010-10-15
Baker-Campbell-Hausdorff formulas are exceedingly useful for disentangling operators so that they may be more easily evaluated on particular states. We present such a disentangling theorem for general bilinear and linear combinations of multiple boson creation and annihilation operators. This work generalizes a classical result of Schwinger.
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
Weinberg, Steven
2008-09-15
It is shown that the generating function for tree graphs in the ''in-in'' formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson-Walker background.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Discovering the Theorem of Pythagoras
NASA Technical Reports Server (NTRS)
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
ERIC Educational Resources Information Center
Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila
2009-01-01
In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
NASA Astrophysics Data System (ADS)
Greaves, Hilary; Thomas, Teruji
2014-02-01
We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.
NASA Astrophysics Data System (ADS)
Sarbicki, Gniewomir; Chruściński, Dariusz; Mozrzymas, Marek
2016-07-01
We analyse linear maps of operator algebras {{ B }}H({ H }) mapping the set of rank-k projectors onto the set of rank-l projectors surjectively. A complete characterisation of such maps for prime n={dim} { H } is provided. A particular case corresponding to k=l=1 is well known as Wigner’s theorem. Hence our result may be considered as a generalisation of this celebrated Wigner’s result.
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-01-01
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-01-01
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-07-08
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields. PMID:11414885
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
NASA Astrophysics Data System (ADS)
Kawaguchi, Y.; Inoue, J.; Nishino, S.
2015-12-01
A fixed-point observation using the R/V Mirai was conducted in the ice-free northern Chukchi Sea of the Arctic Ocean during September of 2013. During the program the authors performed repeated microstructure measurements to reveal the temporal evolution of the surface mixed layer and mixing processes in the upper water column. The shelf region was initially characterized by a distinct two-layer system comprising a warmer/ fresher top layer and a colder/saltier bottom layer. During the two-week observation period, the top-layer water showed two types of mixing processes: near-surface turbulence due to strong wind forcing and subsurface mixing due to internal gravity waves. In the first week, when the top layer was stratified with fresh sea ice meltwater, turbulent energy related to internal waves propagated through the subsurface stratification, resulting in a mechanical overturning near the pycnocline, followed by enhanced mixing there. In the second week, gale winds directly stirred up the upper water and then established a deeper homogenous layer. The combination of internal wave mixing and wind-driven turbulence may contribute to releasing the oceanic heat into the atmosphere, consequently promoting the preconditioning of surface water freezing.
NASA Astrophysics Data System (ADS)
Pearce, J. V.; Elliott, C. J.; Lowe, D. H.; Failleau, G.; Deuzé, T.; Bourson, F.; Sadli, M.; Machin, G.
2014-04-01
A series of high-temperature fixed points (HTFPs) Pt-C (1738 , and Ru-C (1953 ) have been constructed at the National Physical Laboratory (NPL) and the Laboratoire National de métrologie et d'Essais and Conservatoire national des arts et métiers (LNE-Cnam). These are required for the calibration of high-temperature thermocouples in the framework of work package 6 of the European Metrology Research Programme IND01 project "HiTeMS." The goal of this work package is to establish a European capability that can determine low-uncertainty reference functions of non-standard high-temperature thermocouples. For reference functions to be widely applicable, measurements must be performed by more than one institute and preferably by more than one method. Due to the high price of the ingot materials, miniature HTFP cells are used. NPL and LNE-Cnam constructed their HTFP cells with different designs; these are described here, together with the performance of the cells using both radiation thermometry and thermocouples. The melting temperature of the Ru-C cells (for thermocouple calibrations) was determined using radiation thermometry at both NPL and LNE-Cnam, and the two results are compared. The suitability of the cells for calibration of W-Re and Rh-Ir thermocouples is evaluated, and some results are presented. Some discussion is given regarding the materials challenges when calibrating Rh-Ir thermocouples up to 2000 C.
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
A theorem in relativistic electronics
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1990-04-01
This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
NASA Astrophysics Data System (ADS)
Liu, Jianzhou; Zhang, Juan
2011-08-01
In this article, applying the properties of M-matrix and non-negative matrix, utilising eigenvalue inequalities of matrix's sum and product, we firstly develop new upper and lower matrix bounds of the solution for discrete coupled algebraic Riccati equation (DCARE). Secondly, we discuss the solution existence uniqueness condition of the DCARE using the developed upper and lower matrix bounds and a fixed point theorem. Thirdly, a new fixed iterative algorithm of the solution for the DCARE is shown. Finally, the corresponding numerical examples are given to illustrate the effectiveness of the developed results.
Nagai, Satoshi; Hida, Kohsuke; Urushizaki, Shingo; Onitsuka, Goh; Yasuike, Motoshige; Nakamura, Yoji; Fujiwara, Atushi; Tajimi, Seisuke; Kimoto, Katsunori; Kobayashi, Takanori; Gojobori, Takashi; Ototake, Mitsuru
2016-02-01
In this study, we investigated the influence of diurnal sampling bias on the community structure of plankton by comparing the biodiversity among seawater samples (n=9) obtained every 3h for 24h by using massively parallel sequencing (MPS)-based plankton monitoring at a fixed point conducted at Himedo seaport in Yatsushiro Sea, Japan. The number of raw operational taxonomy units (OTUs) and OTUs after re-sampling was 507-658 (558 ± 104, mean ± standard deviation) and 448-544 (467 ± 81), respectively, indicating high plankton biodiversity at the sampling location. The relative abundance of the top 20 OTUs in the samples from Himedo seaport was 48.8-67.7% (58.0 ± 5.8%), and the highest-ranked OTU was Pseudo-nitzschia species (Bacillariophyta) with a relative abundance of 17.3-39.2%, followed by Oithona sp. 1 and Oithona sp. 2 (Arthropoda). During seawater sampling, the semidiurnal tidal current having an amplitude of 0.3ms(-1) was dominant, and the westward residual current driven by the northeasterly wind was continuously observed during the 24-h monitoring. Therefore, the relative abundance of plankton species apparently fluctuated among the samples, but no significant difference was noted according to G-test (p>0.05). Significant differences were observed between the samples obtained from a different locality (Kusuura in Yatsushiro Sea) and at different dates, suggesting that the influence of diurnal sampling bias on plankton diversity, determined using the MPS-based survey, was not significant and acceptable.
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
NASA Astrophysics Data System (ADS)
De Carlo, E. H.; Mousseau, L.; Passafiume, O.; Drupp, P. S.; Gattuso, J.
2011-12-01
The purpose of the Service d'Observation de la Rade de Villefranche-sur-Mer (SO-RADE) is to study the temporal variability of hydrological conditions as well as the abundance and composition of holo- and meroplankton at a fixed station in the bay of Villefranche-sur-Mer, North West Mediterranean. The weekly data collected at this site, designated as "Point B (43° 41.10'N - 7° 18.94'E), since 1957 are recognized as a long-term time series describing the evolution of the hydrological conditions in a coastal environment. Since 2007, historical measurements of hydrological and biological conditions have been complemented by measurements of the CO2-carbonate system parameters. In this contribution we present CO2-carbonate system parameters and ancillary data for the period 2007-2010. The data are evaluated in the context of the physical and biogeochemical processes that contribute to the fluxes of CO2 between the ocean and atmosphere. Seasonal cycles of seawater pCO2 are controlled principally by variations in temperature, showing maxima in the summer and minima during the winters. Normalization of pCO2 to the mean seawater temperature (18oC) results in an apparent reversal of the seasonal cycle with maxima observed in the winters and minima in the summers, consistent with a control of pCO2 by primary productivity. Calculations of "instantaneous fluxes" of CO2 between the ocean and atmosphere show this area to be primarily a weak source of CO2 to the atmosphere during the summer and a weak sink during the winter and near neutral overall (range: -0.3 to +0.3 mmol CO2 m-2 h-1, average: 0.02 mmol CO2 m-2 h-1). We will also provide projections of errors incurred from the estimation of annualized fluxes of CO2 based on weekly measurements relative to daily and high-frequency (3 h) data such as those obtained at the Hawaii Kilo Nalu coastal time series station, which shows similar behavior to the Point B location despite significant differences in climate and hydrological
On the generalized virial theorem for systems with variable mass
NASA Astrophysics Data System (ADS)
Ganghoffer, Jean-François; Rahouadj, Rachid
2016-03-01
We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields.
Pan, Xiao-Yin; Sahni, Viraht
2015-11-01
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Subsubleading soft theorems of gravitons and dilatons in the bosonic string
NASA Astrophysics Data System (ADS)
Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin
2016-06-01
Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.
Nonrenormalization Theorems without Supersymmetry.
Cheung, Clifford; Shen, Chia-Hsien
2015-08-14
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]_{i}≥w[over ¯]_{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally. PMID:26317712
Nonrenormalization Theorems without Supersymmetry.
Cheung, Clifford; Shen, Chia-Hsien
2015-08-14
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w,w[over ¯])=(n-h,n+h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_{i} can only be renormalized by an operator O_{j} if w_{i}≥w_{j} and w[over ¯]_{i}≥w[over ¯]_{j}, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Kharitonov's theorem: Generalizations and algorithms
NASA Technical Reports Server (NTRS)
Rublein, George
1989-01-01
In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837
Noether’s theorem for dissipative quantum dynamical semi-groups
Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G.
2015-02-15
Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quantum setting of quantum Markov dynamics. For finite-dimensional Hilbert spaces, we construct a mapping from observables to completely positive maps that leads to the natural analogue of their criterion of commutativity with the infinitesimal generator of the Markov dynamics. Using standard results on the relaxation of states to equilibrium under quantum dynamical semi-groups, we are able to characterise the constants of the motion under quantum Markov evolutions in the infinite-dimensional setting under the usual assumption of existence of a stationary strictly positive density matrix. In particular, the Noether constants are identified with the fixed point of the Heisenberg picture semi-group.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Bell's theorem on arbitrary causal structures
NASA Astrophysics Data System (ADS)
Fritz, Tobias
2014-03-01
Bell's theorem is a gedankenexperiment with an underlying causal structure in the form of the letter ``M.'' I will describe how such a Bell scenario is a special case of a vastly larger class of scenarios, in which the causal structure of the ``M'' is replaced by an arbitrary directed acyclic graph (or, equivalently, by a causal set). In this formalism, the apparent difference between the notions of ``choice of setting,'' ``source,'' and ``measurement'' disappears completely and all of these become special cases of the general notion of ``event.'' I will explain how this relieves Bell's theorem of the philosophical baggage associated with free will and also present several mathematical results about these more general scenarios obtained by various people. This formalism is expected to have applications in many other areas of science: it is relevant whenever a system is probed at certain points in space and time, and at each of these points there may be hidden information not observed by the probes.
A "fundamental theorem" of biomedical informatics.
Friedman, Charles P
2009-01-01
This paper proposes, in words and pictures, a "fundamental theorem" to help clarify what informatics is and what it is not. In words, the theorem stipulates that a person working in partnership with an information resource is "better" than that same person unassisted. The theorem is applicable to health care, research, education, and administrative activities. Three corollaries to the theorem illustrate that informatics is more about people than technology; that in order for the theorem to hold, resources must be informative in addition to being correct; and that the theorem can fail to hold for reasons explained by understanding the interaction between the person and the resource.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
Equivalence theorem and infrared divergences
Torma, T.
1996-08-01
We look at the equivalence theorem as a statement about the absence of polynomial infrared divergences when {ital m}{sub {ital W}}{r_arrow}0. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to couplings between light particles. {copyright} {ital 1996 The American Physical Society.}
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Fluctuation theorem and mesoscopic chemical clocks.
Andrieux, David; Gaspard, Pierre
2008-04-21
The fluctuation theorems for dissipation and the currents are applied to the stochastic version of the reversible Brusselator model of nonequilibrium oscillating reactions. It is verified that the symmetry of these theorems holds far from equilibrium in the regimes of noisy oscillations. Moreover, the fluctuation theorem for the currents is also verified for a truncated Brusselator model. PMID:18433234
Fluctuation theorem and mesoscopic chemical clocks
NASA Astrophysics Data System (ADS)
Andrieux, David; Gaspard, Pierre
2008-04-01
The fluctuation theorems for dissipation and the currents are applied to the stochastic version of the reversible Brusselator model of nonequilibrium oscillating reactions. It is verified that the symmetry of these theorems holds far from equilibrium in the regimes of noisy oscillations. Moreover, the fluctuation theorem for the currents is also verified for a truncated Brusselator model.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Pigeons' choices in situations of diminishing returns: fixed- versus progressive-ratio schedules.
Wanchisen, B A; Tatham, T A; Hineline, P N
1988-11-01
In two different discrete-trial procedures, pigeons were faced with choices between fixed-ratio and progressive-ratio schedules. The latter schedules entail diminishing returns, a feature analogous to foraging situations in the wild. In the first condition (no reset), subjects chose between a progressive-ratio schedule that increased in increments of 20 throughout a session and a fixed-ratio schedule that was constant across blocks of sessions. The size of the fixed ratio was varied parametrically through an ascending and then a descending series. In the reset condition, the same fixed-ratio values were used, but each selection (and completion) of the fixed ratio reset the progressive-ratio schedule back to its minimal value. In the no-reset procedure, the pigeons tended to cease selecting the progressive ratio when it equaled or slightly exceeded the fixed-ratio value, whereas in reset, they chose the fixed ratio well in advance of that equality point. These results indicate sensitivity to molar as well as to molecular reinforcement rates, and those molar relationships are similar to predictions based on the marginal value theorem of optimal foraging theory (e.g., Charnov, 1976). However, although previous results with monkeys (Hineline & Sodetz, 1987) appeared to minimize responses per reinforcement, the present results corresponded more closely to predictions based on sums-of-reciprocals of distance from point of choice to each of the next four reinforcers. Results obtained by Hodos and Trumbule (1967) with chimpanzees in a similar procedure were intermediate between these two relationships. Variability of choices, as well as median choice points, differed between the reset and no-reset conditions.(ABSTRACT TRUNCATED AT 250 WORDS)
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Nonuniqueness of optical theorem detectors.
Marengo, Edwin A
2015-11-01
We demonstrate and discuss the multitude of ways in which the extinct power of a scatterer can be measured. To tie some of the developed results to the classical statement of the optical theorem involving the imaginary part of the forward-scattering amplitude, particular attention is given to plane wave excitation. On the other hand, the general results apply to more general probing fields including near fields carrying evanescent components. Novel optical theorem detectors are derived that are based on the Kirchhoff-Helmholtz and Rayleigh-Sommerfeld-based formulations of diffraction, backpropagation, and boundary-value problems as well as on the canonical multipole expansion. The derived detectors also lead to novel expressions for the extinct power in terms of the incident and scattered fields. Applications of the derived results to scattering power sensing with near-field data are also discussed.
NASA Astrophysics Data System (ADS)
Leibovich, N.; Barkai, E.
2015-08-01
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I (t ) is related to its correlation function ⟨I (t )I (t +τ )⟩ . We consider nonstationary processes with the widely observed aging correlation function ⟨I (t )I (t +τ )⟩˜tγϕEA(τ /t ) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕEA(x ) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1 /f -type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms.
NASA Astrophysics Data System (ADS)
Lavin, Alicia; Cano, Daniel; González-Pola, Cesar; Tel, Elena; Rodriguez, Carmen; Ruiz, Manuel; Somavilla, Raquel
2015-04-01
, but Dissolved Oxygen sensor is also problematic. Periods of realistic smooth variations present strong offset that is corrected based on the Winkler analysis of water samples. The incorporation of these observatories on larger scale research programs, as done in 2003 in the framework of the VACLAN and COVACLAN projects, is important in order to provide them with a larger spatial dimension and maximize its utility for process-oriented studies. In 2003, the Santander section was extended 90 miles offshore in the framework of a large-scale hydrographic and circulation monitoring program. Partnerships in a large EU project as FixO3 has provided tools for coordination, homogenization and data validation as well as improve the use of chemical-biological data.
A Miniaturisation of Ramsey's Theorem
NASA Astrophysics Data System (ADS)
de Smet, Michiel; Weiermann, Andreas
We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
On the matching method and the Goldstone theorem in holography
NASA Astrophysics Data System (ADS)
Bajc, Borut; Lugo, Adrián R.
2013-07-01
We study the transition of a scalar field in a fixed AdS d+1 background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at q 2 = 0 in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.
Lin, C.; Kalyuzhnyi, Y.V. |; Stell, G.
1998-04-01
A multidensity integral-equation theory for polymerization into freely jointed hard-sphere homonuclear chain fluids proposed earlier [J. Chem. Phys. {bold 106}, 1940 (1997)] is extended to the case of multicomponent heteronuclear chain polymerization. The theory is based on the analytical solution of the polymer Percus{endash}Yevick (PPY) approximation for the totally flexible sticky two-point (S2P) model of associating fluids. The model consists of an n-component mixture of hard spheres of different sizes with species 2,{hor_ellipsis},n{minus}1 bearing two sticky sites A and B, randomly distributed on its surface, and species 1 and n with only one B and A site per particle, respectively. Due to some specific restrictions imposed on the possibility of forming bonds between particles of various species, the present version of the S2P model represents an associating fluid that is able to polymerize into a mixture of heteronuclear chain macromolecules. The structural properties of such a model are studied in the complete-association limit and compared with computer-simulation results for homonuclear hard-sphere chain mixtures, symmetrical diblock copolymers, alternating copolymers, and homonuclear hard-sphere chains in a hard-sphere solvent. Some results for the case of partial association are also presented. The PPY theory represents a quantitatively successful theory for the mixtures of short homonuclear chains and the short copolymer systems studied here. We also expect that the theory will prove to be of the same order of accuracy in investigating the case of partial association. {copyright} {ital 1998 American Institute of Physics.}
The Helmholtz theorem and retarded fields
NASA Astrophysics Data System (ADS)
Heras, Ricardo
2016-11-01
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.
Applications of the theorem of Pythagoras in R3
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2010-01-01
Three distinct points ? and ? with ? are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in ? Using the converse of the theorem of Pythagoras, it is shown that the triangle ? can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed.
Existence of best proximity pairs and equilibrium pairs
NASA Astrophysics Data System (ADS)
Kim, Won Kyu; Lee, Kyoung Hee
2006-04-01
In this paper, using the fixed point theorem for Kakutani factorizable multifunctions, we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies, which include the previous fixed point theorems and equilibrium existence theorems.
Fluctuation theorem for partially masked nonequilibrium dynamics.
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations. PMID:25679593
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem
NASA Astrophysics Data System (ADS)
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem.
An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem
NASA Astrophysics Data System (ADS)
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.
Fixed memory least squares filtering
NASA Technical Reports Server (NTRS)
Bierman, G. J.
1975-01-01
Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.
Alarm points for fixed oxygen monitors
Miller, G.C.
1987-05-01
Oxygen concentration monitors were installed in a vault where numerous pipes carried inert cryogens and gases to the Mirror Fusion Test Facility (MFTF-B) experimental vessel at Lawrence Livermore National Laboratory (LLNL). The problems associated with oxygen-monitoring systems and the reasons why such monitors were installed were reviewed. As a result of this review, the MFTF-B monitors were set to sound an evacuation alarm when the oxygen concentration fell below 18%. We chose the 18% alarm criterion to minimize false alarms and to allow time for personnel to escape in an oxygen-deficient environment.
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
NASA Astrophysics Data System (ADS)
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION.
Meerschaert, M M; Scheffler, H-P
2013-04-01
Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
Double soft theorem for perturbative gravity
NASA Astrophysics Data System (ADS)
Saha, Arnab Priya
2016-09-01
Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
Euler and the Fundamental Theorem of Algebra.
ERIC Educational Resources Information Center
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems.
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions. PMID:26395692
Construction of solutions for some nonlinear two-point boundary value problems
NASA Technical Reports Server (NTRS)
Pennline, J. A.
1982-01-01
Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.
The Scope and Generality of Bell's Theorem
NASA Astrophysics Data System (ADS)
Weatherall, James Owen
2013-09-01
I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.
Magnetic Corrections to the Soft Photon Theorem.
Strominger, Andrew
2016-01-22
The soft photon theorem, in its standard form, requires corrections when the asymptotic particle states carry magnetic charges. These corrections are deduced using electromagnetic duality and the resulting soft formula conjectured to be exact for all Abelian gauge theories. Recent work has shown that the standard soft theorem implies an infinity of conserved electric charges. The associated symmetries are identified as "large" electric gauge transformations. Here the magnetic corrections to the soft theorem are shown to imply a second infinity of conserved magnetic charges. The associated symmetries are identified as large magnetic gauge transformations. The large magnetic symmetries are naturally subsumed in a complexification of the electric ones. PMID:26849586
The infrared limit of the SRG evolution and Levinson's theorem
NASA Astrophysics Data System (ADS)
Arriola, E. Ruiz; Szpigel, S.; Timóteo, V. S.
2014-07-01
On a finite momentum grid with N integration points pn and weights wn (n = 1 , … , N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff λ on energy differences, steadily driving the starting Hamiltonian in momentum space Hn,m0 = pn2 δn,m +Vn,m to a diagonal form in the infrared limit (λ → 0), Hn,mG, λ → 0 =E π (n)δn,m, where π (n) is a permutation of the eigenvalues En which depends on G. Levinson's theorem establishes a relation between phase-shifts δ (pn) and the number of bound-states, nB, and reads δ (p1) - δ (pN) =nB π. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon-nucleon (NN) interaction in the S10 and S31 channels.
Undecidability Theorem and Quantum Randomness
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
2005-04-01
As scientific folklore has it, Kurt Godel was once annoyed by question whether he sees any link between his Undecidability Theorem (UT) and Uncertainty Relationship. His reaction, however, may indicate that he probably felt that such a hidden link could indeed exist but he was unable clearly formulate it. Informational version of UT (G.J.Chaitin) states impossibility to rule out algorithmic compressibility of arbitrary digital string. Thus, (mathematical) randomness can only be disproven, not proven. Going from mathematical to physical (mainly quantum) randomness, we encounter seemingly random acts of radioactive decays of isotopes (such as C14), emission of excited atoms, tunneling effects, etc. However, our notion of quantum randomness (QR) may likely hit similarly formidable wall of physical version of UT leading to seemingly bizarre ideas such as Everett many world model (D.Deutsch) or backward causation (J.A.Wheeler). Resolution may potentially lie in admitting some form of Aristotelean final causation (AFC) as an ultimate foundational principle (G.W.Leibniz) connecting purely mathematical (Platonic) grounding aspects with it physically observable consequences, such as plethora of QR effects. Thus, what we interpret as QR may eventually be manifestation of AFC in which UT serves as delivery vehicle. Another example of UT/QR/AFC connection is question of identity (indistinguishability) of elementary particles (are all electrons exactly the same or just approximately so to a very high degree?).
Exchange fluctuation theorem for correlated quantum systems.
Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio
2015-10-01
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem. PMID:26565174
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
Douma, Huub; Vasconcelos, Ivan; Snieder, Roel
2011-05-01
By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields. PMID:21568381
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
There is No Quantum Regression Theorem
Ford, G.W.; OConnell, R.F.
1996-07-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. {copyright} {ital 1996 The American Physical Society.}
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
No-hair theorem for the Galileon.
Hui, Lam; Nicolis, Alberto
2013-06-14
We consider a Galileon field coupled to gravity. The standard no-hair theorems do not apply because of the Galileon's peculiar derivative interactions. We prove that, nonetheless, static spherically symmetric black holes cannot sustain nontrivial Galileon profiles. Our theorem holds for trivial boundary conditions and for cosmological ones, and regardless of whether there are nonminimal couplings between the Galileon and gravity of the covariant Galileon type.
Jebsen-Birkhoff theorem in alternative gravity
Faraoni, Valerio
2010-02-15
We discuss the validity, or lack thereof, of the Jebsen-Birkhoff theorem in scalar-tensor theories by generalizing it and regarding the Brans-Dicke-like scalar as effective matter. Both the Jordan and Einstein frames are discussed and an apparent contradiction between static spherical solutions of scalar-tensor gravity and Hawking's theorem on Brans-Dicke black holes is clarified. The results are applied to metric and Palatini f(R) gravity.
Gleason's Theorem for Rectangular JBW-Triples
NASA Astrophysics Data System (ADS)
Edwards, C. Martin; Rüttimann, Gottfried T.
A JBW*-triple B is said to be rectangular if there exists a W*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice of projections in A such that B is isomorphic to the JBW*-triple pAq. Any weak*-closed injective operator space provides an example of a rectangular JBW*-triple. The principal order ideal of the complete *-lattice of centrally equivalent pairs of projections in a W*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete lattice of weak*-closed inner ideals in B and to the complete lattice of structural projections on B. Although not itself, in general, orthomodular, possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e2,f2) and (e2,f2) of elements of . This is defined and characterized in terms of properties of . A W*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W*-algebras pAp and qAq of A has a weak*-closed ideal of Type I2, such measures are precisely those that are the restrictions of
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Generalized fluctuation theorems for classical systems
NASA Astrophysics Data System (ADS)
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
Shirzad, A.
2007-08-15
Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system enables us to use either a full gauge, in which all gauged degrees of freedom are determined, or a partial gauge, in which some first class constraints remain as subsidiary conditions to be imposed on the solutions of the equations of motion. We also show that the number of constants of motion depends on the level in a constraint chain in which the gauge fixing condition is imposed. The relativistic point particle, electromagnetism, and the Polyakov string are discussed as examples and full or partial gauges are distinguished.
Adding Some Perspective to de Moivre's Theorem: Visualising the "n"-th Roots of Unity
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2015-01-01
Traditionally, "z" is assumed to be a complex number and the roots are usually determined by using de Moivre's theorem adapted for fractional indices. The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius. The "n"-th roots of unity always include the real number 1, and…
Limit Theorems for Monomer-Dimer Mean-Field Models with Attractive Potential
NASA Astrophysics Data System (ADS)
Alberici, Diego; Contucci, Pierluigi; Fedele, Micaela; Mingione, Emanuele
2016-09-01
The number of monomers in a monomer-dimer mean-field model with an attractive potential fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
The optical theorem for local source excitation of a particle near a plane interface
NASA Astrophysics Data System (ADS)
Eremin, Yuri; Wriedt, Thomas
2015-11-01
Based on classic Maxwell's theory and the Gauss Theorem we extended the Optical Theorem to the case of a penetrable particle excited by a local source deposited near a plane interface. We demonstrate that the derived Extinction Cross-Section involves the total point source radiating cross-section and some definite integrals responsible for the scattering by the interface. The derived extinction cross-section can be employed to estimate the quantum yield and the optical antenna efficiency without computation of the absorption cross-section.
Hidden symmetry of the beam spread function resulting from the reciprocity theorem
NASA Astrophysics Data System (ADS)
Dolin, Lev S.
2016-09-01
It is shown that the optical reciprocity theorem imposes certain constraints on the radiation field structure of a unidirectional point source (beam spread function (BSF)) in a turbid medium with spatially uniform optical properties. To satisfy the reciprocal relation, the BSF should have an additional symmetry property along with axial symmetry. This paper mathematically formulates the BSF symmetry condition that follows from the reciprocity theorem and discusses test results of some approximate analytical BSF models for their compliance with the symmetry requirement. A universal method for eliminating symmetry errors of approximate BSF models is proposed.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime. PMID:17813892
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
Lie symmetry theorem of fractional nonholonomic systems
NASA Astrophysics Data System (ADS)
Sun, Yi; Chen, Ben-Yong; Fu, Jing-Li
2014-11-01
The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert—Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.
Asymptotic symmetries and subleading soft graviton theorem
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
Jarzynski's theorem for lattice gauge theory
NASA Astrophysics Data System (ADS)
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
Note on the theorems of Bjerknes and Crocco
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1946-01-01
The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.
Answering Junior Ant's "Why" for Pythagoras' Theorem
ERIC Educational Resources Information Center
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
Local theorems in strengthened form for lattice random variables.
NASA Technical Reports Server (NTRS)
Mason, J. D.
1971-01-01
Investigation of some conditions which are sufficient for a sequence of independent integral-valued lattice random variables to satisfy a local theorem in strengthened form. A number of theorems giving the conditions under which the investigated sequence satisfies a local theorem in strengthened form are proven with the aid of lemmas derived by Kruglov (1968).
Moving mirrors and the fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Stargen, D. Jaffino; Kothawala, Dawood; Sriramkumar, L.
2016-07-01
We investigate the random motion of a mirror in (1 +1 )-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition. Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value. From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror. Using the fluctuation-dissipation theorem, we compute the mean-squared displacement of the mirror at finite and zero temperature. We clarify a few points concerning the various limiting behavior of the mean-squared displacement of the mirror. While we recover the standard result at finite temperature, we find that the mirror diffuses logarithmically at zero temperature, confirming similar conclusions that have been arrived at earlier in this context. We also comment on a subtlety concerning the comparison between zero temperature limit of the finite temperature result and the exact zero temperature result.
Sahoo- and Wayment-type integral mean value theorems
NASA Astrophysics Data System (ADS)
Tiryaki, Aydin; Çakmak, Devrim
2010-06-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment [An integral mean value theorem, Math. Gazette 54 (1970), pp. 300-301] and Sahoo [Some results related to the integral mean value theorem, Int. J. Math. Ed. Sci. Tech. 38(6) (2007), pp. 818-822]. The importance of our results are illustrated by interesting examples.
NASA Astrophysics Data System (ADS)
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
The Bjerknes' Circulation Theorem: A Historical Perspective.
NASA Astrophysics Data System (ADS)
Thorpe, Alan J.; Volkert, Hans; Ziemianski, Micha J.
2003-04-01
Two lines of thinking concerning fluid rotation-using either vorticity or circulation-emerged from the nineteenth-century work of Helmholtz and Thomson (Lord Kelvin), respectively. Vilhelm Bjerknes introduced an extension of Kelvin's ideas on circulation into geophysics. In this essay a historical perspective will be given on what has become known as the "Bjerknes circulation theorem." Bjerknes wrote several papers on this topic, the first being in 1898. As Bjerknes noted, a Polish physicist, Ludwik Silberstein, had previously published an equivalent result concerning vorticity generation in 1896. Silberstein's work had built on an earlier paper by J. R. Schütz in 1895. In his 1898 paper Bjerknes describes many possible applications of the theorem to meteorology and oceanography including to extratropical cyclones, a subject that made his "Bergen School" famous.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Locomotion in complex fluids: Integral theorems
NASA Astrophysics Data System (ADS)
Lauga, Eric
2014-08-01
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. Building on classical work on the transport of particles in viscoelastic fluids, we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics in a non-Newtonian fluid. These theorems correspond to three situations of interest, namely, (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of swimmer geometry, surface kinematics, and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Thermodynamics of biochemical networks and duality theorems
NASA Astrophysics Data System (ADS)
De Martino, Daniele
2013-05-01
One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Wigner-Araki-Yanase theorem on distinguishability
Miyadera, Takayuki; Imai, Hideki
2006-08-15
The presence of an additive-conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, perfect repeatability and distinguishability of the apparatus cannot be attained simultaneously. Instead of repeatability, in this paper, the distinguishability in both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. An inequality shows that perfect distinguishability of both systems cannot be attained simultaneously.
3D Image Reconstructions and the Nyquist-Shannon Theorem
NASA Astrophysics Data System (ADS)
Ficker, T.; Martišek, D.
2015-09-01
Fracture surfaces are occasionally modelled by Fourier's two-dimensional series that can be converted into digital 3D reliefs mapping the morphology of solid surfaces. Such digital replicas may suffer from various artefacts when processed inconveniently. Spatial aliasing is one of those artefacts that may devalue Fourier's replicas. According to the Nyquist-Shannon sampling theorem the spatial aliasing occurs when Fourier's frequencies exceed the Nyquist critical frequency. In the present paper it is shown that the Nyquist frequency is not the only critical limit determining aliasing artefacts but there are some other frequencies that intensify aliasing phenomena and form an infinite set of points at which numerical results abruptly and dramatically change their values. This unusual type of spatial aliasing is explored and some consequences for 3D computer reconstructions are presented.
Coherent cyclotron motion beyond Kohn's theorem
NASA Astrophysics Data System (ADS)
Maag, T.; Bayer, A.; Baierl, S.; Hohenleutner, M.; Korn, T.; Schüller, C.; Schuh, D.; Bougeard, D.; Lange, C.; Huber, R.; Mootz, M.; Sipe, J. E.; Koch, S. W.; Kira, M.
2016-02-01
In solids, the high density of charged particles makes many-body interactions a pervasive principle governing optics and electronics. However, Walter Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons is independent of the seemingly inescapable Coulomb interaction between electrons. Although this surprising theorem has been exploited in sophisticated quantum phenomena, such as ultrastrong light-matter coupling, superradiance and coherent control, the complete absence of nonlinearities excludes many intriguing possibilities, such as quantum-logic protocols. Here, we use intense terahertz pulses to drive the cyclotron response of a two-dimensional electron gas beyond the protective limits of Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four- and six-wave mixing signatures occur, which our theory links to dynamic Coulomb effects between electrons and the positively charged ion background. This new context for Kohn's theorem unveils previously inaccessible internal degrees of freedom of Landau electrons, opening up new realms of ultrafast quantum control for electrons.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
30 CFR 56.11026 - Protection for inclined fixed ladders.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Protection for inclined fixed ladders. 56.11026... § 56.11026 Protection for inclined fixed ladders. Fixed ladders 70 degrees to 90 degrees from the... point not more than seven feet from the bottom of the ladders....
30 CFR 56.11026 - Protection for inclined fixed ladders.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Protection for inclined fixed ladders. 56.11026... § 56.11026 Protection for inclined fixed ladders. Fixed ladders 70 degrees to 90 degrees from the... point not more than seven feet from the bottom of the ladders....
Finite volume QCD at fixed topological charge
Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya
2007-09-01
In finite volume the partition function of QCD with a given {theta} is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a 1/V expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.
Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group
NASA Astrophysics Data System (ADS)
Minguzzi, E.
2013-02-01
This work is devoted to the relativistic generalization of Chasles' theorem, namely, to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity. The acceleration and angular velocity can be chosen either aligned or perpendicular, and in the latter case the angular velocity can be chosen equal or smaller than the acceleration. We start reviewing the classical Euler's and Chasles' theorems both in the Lie algebra and group versions. We recall the relativistic generalization of Euler's theorem and observe that every (infinitesimal) transformation can be recovered from information of algebraic and geometric type, the former being identified with the conjugacy class and the latter with some additional geometric ingredients (the screw axis in the usual non-relativistic version). Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in detail. We prove its exponentiality and identify a causal semigroup and the corresponding Lie cone. Through the identification of new Ad-invariants we classify the conjugacy classes, and show that those which admit a causal representative have special physical significance. These results imply a classification of the inequivalent Killing vector fields of Minkowski spacetime which we express through simple representatives. Finally, we arrive at the mentioned generalization of Chasles' theorem.
Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)
NASA Astrophysics Data System (ADS)
Badino, M.
2011-11-01
An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.
Applications of the Theorem of Pythagoras in R[superscript 3
ERIC Educational Resources Information Center
Srinivasan, V. K.
2010-01-01
Three distinct points A = (a, 0, 0) B = (0, b, 0) and (c, 0, 0) with abc not equal to 0 are taken, respectively on the "x", "y" and the "z"-axes of a rectangular coordinate system in R[superscript 3]. Using the converse of the theorem of Pythagoras, it is shown that the triangle [delta]ABC can never be a right-angled triangle. The result seems to…
[Advantages of fixed combinations].
Lachkar, Y
2008-07-01
Fixed combinations are indicated in the treatment of glaucoma and ocular hypertension when monotherapy does not sufficiently reduce IOP. Fixed combinations show better efficacy than the instillation of each separate component and are at least equivalent to the administration of both components in a separate association. They simplify treatment, increase compliance and quality of life, and decrease exposure to preservatives. Although they are less aggressive for patients when a new drug needs to be added, the use of fixed combinations should not decrease the follow-up. PMID:18957922
Fatou type theorems for series in Mittag-Leffler functions
NASA Astrophysics Data System (ADS)
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
A unified optical theorem for scalar and vectorial wave fields.
Wapenaar, Kees; Douma, Huub
2012-05-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers. PMID:22559339
A unified optical theorem for scalar and vectorial wave fields.
Wapenaar, Kees; Douma, Huub
2012-05-01
The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
Flory Theorem for Structurally Asymmetric Mixtures
NASA Astrophysics Data System (ADS)
Dobrynin, Andrey; Sun, Frank; Shirvanyants, David; Rubinstein, Gregory; Rubinstein, Michael; Sheiko, Sergei; Lee, Hyung-Il; Matyjaszewski, Krzysztof
2008-03-01
The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization of the surrounding linear chains, NB, but also by the degree of polymerization of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N^2
Disentangling theorem and monogamy for entanglement negativity
NASA Astrophysics Data System (ADS)
He, Huan; Vidal, Guifre
2015-01-01
Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems A ,B , and C factorizes into a product state for parts A B1 and B2C ; and a monogamy relation conjecture based on entanglement negativity, which states that if A is very entangled with B , then A cannot be simultaneously very entangled also with C .
Bayes` theorem and quantitative risk assessment
Kaplan, S.
1994-12-31
This paper argues that for a quantitative risk analysis (QRA) to be useful for public and private decision making, and for rallying the support necessary to implement those decisions, it is necessary that the QRA results be ``trustable.`` Trustable means that the results are based solidly and logically on all the relevant evidence available. This, in turn, means that the quantitative results must be derived from the evidence using Bayes` theorem. Thus, it argues that one should strive to make their QRAs more clearly and explicitly Bayesian, and in this way make them more ``evidence dependent`` than ``personality dependent.``
Fixed Exit Monochromator with fixed Rotation Axis
Caliebe, W.A.; Cheung, S.; Lenhard, A.; Siddons, D.P.
2004-05-12
A new simple design for a fixed-exit monochromator has been developed. The set-up uses a linear slide to couple the rotation of the crystals to a translation of the second one to compensate for the 2hcos{theta} dependence of the beam-offset in a double crystal monochromator. This set-up requires just one motor for the rotation of the monochromator, and three piezo-actuators to tune the second crystal.The monochromator has been tested for Bragg-angles between 7 deg. and 70 deg.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
NASA Astrophysics Data System (ADS)
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
NASA Astrophysics Data System (ADS)
Woolgar, Eric; Wylie, William
2016-02-01
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
NASA Astrophysics Data System (ADS)
Benincasa, Dionigi M. T.
2011-07-01
We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Randomized central limit theorems: A unified theory
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Energy theorem for (2+1)-dimensional gravity.
NASA Astrophysics Data System (ADS)
Menotti, P.; Seminara, D.
1995-05-01
We prove a positive energy theorem in (2+1)-dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson loops and show that the energy-momentum of the enclosed subsystem is a future directed time-like vector whose mass is an increasing function of the loop, until it reaches the value 1/4G corresponding to a deficit angle of 2π. At this point the energy-momentum of the system evolves, depending on the nature of a zero norm vector appearing in the evolution equations, either into a time-like vector of a universe which closes kinematically or into a Gott-like universe whose energy momentum vector, as first recognized by Deser, Jackiw, and 't Hooft (1984) is space-like. This treatment generalizes results obtained by Carroll, Fahri, Guth, and Olum (1994) for a system of point-like spinless particle, to the most general form of matter whose energy-momentum tensor satisfies the dominant energy condition. The treatment is also given for the anti-de Sitter (2+1)-dimensional gravity.
Computer Algebra Systems and Theorems on Real Roots of Polynomials
ERIC Educational Resources Information Center
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
Note on two theorems in nonequilibrium statistical mechanics
Cohen, E.G.D.; Gallavotti, G.
1999-09-01
An attempt is made to clarify the difference between a theorem derived by Evans and Searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2008-03-01
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
The logical status of thermodynamic proofs of mathematical theorems
NASA Astrophysics Data System (ADS)
Deakin, M. A. B.; Troup, G. J.
1981-06-01
The logical status of such thermodynamic proofs of mathematical theorems as Landsberg's derivation of the inequality of arithmetic and geometric means is considered. The status is not as absolute as the rigorous demonstration of a mathematical theorem. Many axiomatic accounts of thermodynamics use this inequality to reduce the number of physical assumptions required.
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
Rotation of Axes and the Mean Value Theorem
ERIC Educational Resources Information Center
Price, David
2004-01-01
This article provides a proof of the Mean Value Theorem by rotating a coordinate system through a specified angle. The use of this approach makes it easy to visualize why the Mean Value Theorem is true. An instructor can use the proof as another illustration of the rotation of axis technique in addition to the standard one of simplifying equations…
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…
Systematic Approaches to Experimentation: The Case of Pick's Theorem
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…
Discovering Theorems in Abstract Algebra Using the Software "GAP"
ERIC Educational Resources Information Center
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Optimal Keno Strategies and the Central Limit Theorem
ERIC Educational Resources Information Center
Johnson, Roger W.
2006-01-01
For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
NASA Astrophysics Data System (ADS)
Ho, Man-Ho
2016-09-01
In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace's theorem revisited
NASA Astrophysics Data System (ADS)
Jacobs, Michel H. G.; de Jong, Bernard H. W. S.
2005-12-01
Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure-temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.
Technical note: Revisiting the geometric theorems for volume averaging
NASA Astrophysics Data System (ADS)
Wood, Brian D.
2013-12-01
The geometric theorems reported by Quintard and Whitaker [5, Appendix B] are re-examined. We show (1) The geometrical theorems can be interpreted in terms of the raw spatial moments of the pore structure within the averaging volume. (2) For the case where the first spatial moment is aligned with the center of mass of the averaging volume, the geometric theorems can be expressed in terms of the central moments of the porous medium. (3) When the spatial moments of the pore structure are spatially stationary, the geometrical theorems allow substantial simplification of nonlocal terms arising in the averaged equations. (4) In the context of volume averaging, the geometric theorems of Quintard and Whitaker [5, Appendix B] are better interpreted as statements regarding the spatial stationarity of specific volume averaged quantities rather than an explicit statement about the media disorder.
Sampling theorems and compressive sensing on the sphere
NASA Astrophysics Data System (ADS)
McEwen, Jason D.; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2011-09-01
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.
A Berger-type theorem for metric connections with skew-symmetric torsion
NASA Astrophysics Data System (ADS)
Reggiani, Silvio
2013-03-01
We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere, then the space must be locally isometric to a Lie group with a bi-invariant metric or its symmetric dual (we assume the space to be locally irreducible). We also prove that a (simple) Lie group with a bi-invariant metric admits only two flat metric connections with skew-symmetric torsion: the two flat canonical connections. In particular, we get a refinement of a well-known theorem of Cartan and Schouten. Finally, we show that the holonomy group of a metric connection with skew-symmetric torsion on these spaces generically coincides with the Riemannian holonomy.
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
NASA Astrophysics Data System (ADS)
Lehrer, G. I.; Zhang, R. B.
2016-08-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension (m|2n) and the Brauer algebra with parameter m - 2n. The result may be interpreted either in terms of the group scheme OSp(V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ} . We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit
2012-11-15
Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties. - Highlights: Black-Right-Pointing-Pointer New method for analytically finding Dirac points. Black-Right-Pointing-Pointer Novel relation of level crossings to singularity theory. Black-Right-Pointing-Pointer More precise version of the von-Neumann-Wigner theorem for arbitrary smooth families of Hamiltonians of fixed size. Black-Right-Pointing-Pointer Analytical proof of the existence of Dirac points for the Gyroid wire network.
Virial Theorem in Nonlocal Newtonian Gravity
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
The Birkhoff theorem and string clouds
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Kim, S.-W.; Skvortsova, M. V.
2016-10-01
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., {(\\partial r)}2 = 0). It is shown that solutions to the Einstein equations with r={const} contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with {(\\partial r)}2 = 0 but r\
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Globally optimal impulsive transfers via Green's theorem
NASA Astrophysics Data System (ADS)
Hazelrigg, G. A., Jr.
1984-08-01
For certain classes of trajectories the cost function (characteristic velocity) can be written as a 'quasilinear' function of the change in state. In the case presented, impulsive transfers between coplanar, coaxial orbits with transfer time and angle unrestricted, Green's theorem can be used to determine the optimal transfer between given terminal states. This is done in a manner which places no restrictions on the number of impulses used and leads to globally optimal results. These results are used to show that the Hohmann transfer and the biparabolic transfer provide global minima in their respective regions. The regions in which monoelliptic and biparabolic trajectories are globally optimal are also defined for elliptic terminal states. The results are applicable to the case in which restrictions are placed on the radius of closest approach or greatest recession from the center of the force field.
Generalization of Kummer's second theorem with applications
NASA Astrophysics Data System (ADS)
Kim, Yong Sup; Rakha, M. A.; Rathie, A. K.
2010-03-01
The aim of this research paper is to obtain single series expression of e^{ - x/2} _1 F_1 (α ;2α + i;x) for i = 0, ±1, ±2, ±3, ±4, ±5, where 1 F 1(·) is the function of Kummer. For i = 0, we have the well known Kummer second theorem. The results are derived with the help of generalized Gauss second summation theorem obtained earlier by Lavoie et al. In addition to this, explicit expressions of _2 F_1 [ - 2n,α ;2α + i;2]and_2 F_1 [ - 2n - 1,α ;2α + i;2] each for i = 0, ±1, ±2, ±3, ±4, ±5 are also given. For i = 0, we get two interesting and known results recorded in the literature. As an applications of our results, explicit expressions of e^{ - x} _1 F_1 (α ;2α + i;x) × _1 F_1 (α ;2α + j;x) for i, j = 0, ±1, ±2, ±3, ±4, ±5 and (1 - x)^{ - a} _2 F_1 left( {a,b,2b + j; - tfrac{{2x}} {{1 - x}}} right) for j = 0, ±1, ±2, ±3, ±4, ±5 are given. For i = j = 0 and j = 0, we respectively get the well known Preece identity and a well known quadratic transformation formula due to Kummer. The results derived in this paper are simple, interesting, easily established and may be useful in the applicable sciences.
NASA Technical Reports Server (NTRS)
Lynnes, Chris
2014-01-01
Three current search engines are queried for ozone data at the GES DISC. The results range from sub-optimal to counter-intuitive. We propose a method to fix dataset search by implementing a robust relevancy ranking scheme. The relevancy ranking scheme is based on several heuristics culled from more than 20 years of helping users select datasets.
Neal, Daniel R.
2000-01-01
A rigid mount and method of mounting for a wavefront sensor. A wavefront dissector, such as a lenslet array, is rigidly mounted at a fixed distance relative to an imager, such as a CCD camera, without need for a relay imaging lens therebetween.
Fermat's point from five perspectives
NASA Astrophysics Data System (ADS)
Park, Jungeun; Flores, Alfinio
2015-04-01
The Fermat point of a triangle is the point such that minimizes the sum of the distances from that point to the three vertices. Five approaches to study the Fermat point of a triangle are presented in this article. First, students use a mechanical device using masses, strings and pulleys to study the Fermat point as the one that minimizes the potential energy of the system. Second, students use soap films between parallel planes connecting three pegs. The tension on the film will be minimal when the sum of distances is minimal. Third, students use an empirical approach, measuring distances in an interactive GeoGebra page. Fourth, students use Euclidean geometry arguments for two proofs based on the Torricelli configuration, and one using Viviani's Theorem. And fifth, the kinematic method is used to gain additional insight on the size of the angles between the segments joining the Fermat point with the vertices.
Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities
NASA Astrophysics Data System (ADS)
Akkelin, S. V.; Sinyukov, Yu. M.
2016-07-01
Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using a recurrence relation for the partition function. Within such a model we investigate the validity of the thermal Wick's theorem and its applicability for decomposition of the two-particle distribution function. The dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A +A and p +p collisions with selected (fixed) multiplicity.
Global stabilization using LSS-Theorem: Applications to Robotics and Aerospace Vehicles
NASA Astrophysics Data System (ADS)
Selman, AbdulRazzak
Underactuated mechanical systems are gaining interest as they can sometimes provide the desired motion or functionality at reduced cost due to their using fewer expensive actuators. The term "underactuated" refers to the fact that such mechanical systems have fewer actuators than degrees of freedom, which makes them very difficult to control. Moreover, underactuated robots have nonlinear dynamics which must be tackled with nonlinear control techniques. Furthermore, control theory for underactuated mechanical systems has been an active area of research for the past 15-20 years. Most of the research has focused on local and global asymptotic stabilization by feedback. Underactuated systems can either possess nonminimum phase or minimum phase characteristics. For minimum phase underactuated systems, the stabilization problem is rather simple and many existing control design methodologies have been proved powerful in providing a solution to this problem. For nonminimum phase underactuated systems, asymptotic stabilization problem has been, and still is, an attractive subject to the researchers in the field of nonlinear control system and theory. In particular, global asymptotic stabilization (GAS) at a desired equilibrium point of such systems by means of a single smooth static or dynamic state feedback law is still largely an open problem in the literature. In this thesis, the problem of GAS via a smooth static state feedback law is addressed for a class of an underactuated nonlinear system that is affine (possibly non affine) in the control, partially feedback linearizable, nonminimum phase and (possibly) has a non-integrable acceleration constraint. The core result of the thesis is formulated through a theorem that the author refers to through this thesis as the Legend of Salah Salman (LSS) Theorem. LSS theorem states the existence of a smooth static state feedback law that globally asymptotically stabilizes the origin of the nonlinear underactuated system that is
Schema theory for genetic programming with one-point crossover and point mutation.
Poli, R; Langdon, W B
1998-01-01
We review the main results obtained in the theory of schemata in genetic programming (GP), emphasizing their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP, which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation, this concept of schema has been used to derive an improved schema theorem for GP that describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
On Pythagoras Theorem for Products of Spectral Triples
NASA Astrophysics Data System (ADS)
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
The global Utiyama theorem in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Bruzzo, Ugo
1987-09-01
A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry.
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
Central limit theorem for reducible and irreducible open quantum walks
NASA Astrophysics Data System (ADS)
Sadowski, Przemysław; Pawela, Łukasz
2016-07-01
In this work we aim at proving central limit theorems for open quantum walks on {mathbb {Z}}^d. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.
Applying the multivariate time-rescaling theorem to neural population models
Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon
2011-01-01
Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436
NASA Astrophysics Data System (ADS)
Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga
2016-02-01
We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.
Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function
Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhás, Pavol; Billinge, Simon J.L.
2011-12-07
We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Lumley, J. L.; Abid, R.
1994-01-01
A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.
New Fermionic Soft Theorems for Supergravity Amplitudes.
Chen, Wei-Ming; Huang, Yu-Tin; Wen, Congkao
2015-07-10
Soft limits of a massless S matrix are known to reflect the symmetries of the theory. In particular, for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this Letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider the Akulov-Volkov theory and demonstrate that the double-soft limit of Goldstinos yields the supersymmetry algebra. More surprisingly, we also find that amplitudes in 4≤N≤8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogous to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by supersymmetry Ward identities and may impose nontrivial constraints on the possible counterterms for supergravity theories.
A stem cell niche dominance theorem
2011-01-01
Background Multilevelness is a defining characteristic of complex systems. For example, in the intestinal tissue the epithelial lining is organized into crypts that are maintained by a niche of stem cells. The behavior of the system 'as a whole' is considered to emerge from the functioning and interactions of its parts. What we are seeking here is a conceptual framework to demonstrate how the "fate" of intestinal crypts is an emergent property that inherently arises from the complex yet robust underlying biology of stem cells. Results We establish a conceptual framework in which to formalize cross-level principles in the context of tissue organization. To this end we provide a definition for stemness, which is the propensity of a cell lineage to contribute to a tissue fate. We do not consider stemness a property of a cell but link it to the process in which a cell lineage contributes towards tissue (mal)function. We furthermore show that the only logically feasible relationship between the stemness of cell lineages and the emergent fate of their tissue, which satisfies the given criteria, is one of dominance from a particular lineage. Conclusions The dominance theorem, conceived and proven in this paper, provides support for the concepts of niche succession and monoclonal conversion in intestinal crypts as bottom-up relations, while crypt fission is postulated to be a top-down principle. PMID:21214945
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
Information-disturbance theorem for mutually unbiased observables
Miyadera, Takayuki; Imai, Hideki
2006-04-15
We derive a version of information-disturbance theorems for mutually unbiased observables. We show that the information gain by Eve inevitably makes the outcomes by Bob in the conjugate basis not only erroneous but random.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
Fixed target facility at the SSC
Loken, S.C.; Morfin, J.G.
1985-01-01
The question of whether a facility for fixed target physics should be provided at the SSC must be answered before the final technical design of the SSC can be completed, particularly if the eventual form of extraction would influence the magnet design. To this end, an enthusiastic group of experimentalists, theoreticians and accelerator specialists have studied this point. The accelerator physics issues were addressed by a group led by E. Colton whose report is contained in these proceedings. The physics addressable by fixed target was considered by many of the Physics area working groups and in particular by the Structure Function Group. This report is the summary of the working group which considered various SSC fixed target experiments and determined which types of beams and detectors would be required. 13 references, 5 figures.
Strong no-go theorem for Gaussian quantum bit commitment
Magnin, Loieck; Magniez, Frederic; Leverrier, Anthony
2010-01-15
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.
a New Look at GOLDSTONE’S Theorem
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Doplicher, Sergio; Longo, Roberto; Roberts, John E.
The appearance of spontaneously broken symmetries and its bearing on the physical mass spectrum are analyzed in the algebraic setting of local quantum field theory. Within this setting, a generalization of Goldstone’s Theorem is established which does not rely on the existence of conserved currents. Continuous symmetries not satisfying the premises of the theorem can be spontaneously broken even in the presence of a mass gap.
Some functional limit theorems for compound Cox processes
NASA Astrophysics Data System (ADS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
No-broadcasting theorem and its classical counterpart.
Kalev, Amir; Hen, Itay
2008-05-30
Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
Liouville`s theorem and phase-space cooling
Mills, R.L.; Sessler, A.M.
1993-09-28
A discussion is presented of Liouville`s theorem and its consequences for conservative dynamical systems. A formal proof of Liouville`s theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur.
Localising Dehn's lemma and the loop theorem in 3-manifolds
NASA Astrophysics Data System (ADS)
Aitchison, I. R.; Hyam Rubinstein, J.
2004-09-01
We give a new proof of Dehn's lemma and the loop theorem. This is a fundamental tool in the topology of 3-manifolds. Dehn's lemma was originally formulated by Dehn, where an incorrect proof was given. A proof was finally given by Papakyriakopolous in his famous 1957 paper where the fundamental idea of towers of coverings was introduced. This was later extended to the loop theorem, and the version used most frequently was given by Stallings.
Generalized Panofsky-Wenzel theorem and hybrid coupling
NASA Astrophysics Data System (ADS)
Smirnov, A. V.
2001-08-01
The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.
Levinson theorem for Aharonov-Bohm scattering in two dimensions
Sheka, Denis D.; Mertens, Franz G.
2006-11-15
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
The Hartogs extension theorem for holomorphic vector bundles and sprays
NASA Astrophysics Data System (ADS)
Andrist, Rafael B.; Shcherbina, Nikolay; Wold, Erlend F.
2016-10-01
We give a detailed proof of Siu's theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in {C}n, n ≥3, is not subelliptic.
22. VIEW OF FIXED SPAN SUBSTRUCTURE, EAST SPAN, SHOWING CANTILEVEREDBEAM ...
22. VIEW OF FIXED SPAN SUBSTRUCTURE, EAST SPAN, SHOWING CANTILEVERED-BEAM SIDEWALK SUPPORTS, LONGITUDINAL GIRDER AND TRANSVERSE ROADBED BEAMS, LOOKING SOUTHEAST - Congress Street Bascule Bridge, Spanning Fort Point Channel at Congress Street, Boston, Suffolk County, MA
Analysis of point fabrication model for near-field photolithography with experimental study.
Lin, Zone-Ching; Yang, Ching-Been
2006-01-01
For the Gaussian beam, the power density distribution of the aluminum-coated optical tapered fiber probe is discussed and a theoretical fixed-point fabrication model for near-field photolithography is established. The energy density theorem is used to explore the surface exposure of photoresist, which is divided into multiple grids to evaluate the changes in the concentration of photoactive compounds at specific nodes of the interior layer. The full width at half maximum (FWHM) and the contour of the photolithograph following development are then calculated. The fixed-point lithographic experiment and aperture verification of the optic fiber probe are performed to confirm the reliability of the present model, and Dill A, B, C parameters are first measured in this article. According to the experimental results, a better image of the probe aperture can be achieved by increasing the conductivity of the measured articles and reducing the electric charges during the image taken by field-emission scanning electron microscope. The FWHM measured is 166.6 nm, while the measured average probe aperture size is 317.4 nm and the FWHM simulated by the proposed model is 151.3 nm. The error between experiment and simulation is <-9.2%. It is thus concluded that the proposed theoretical model is reasonable and acceptable. PMID:16502624
On a variational theorem in acousto-elastodynamics
NASA Astrophysics Data System (ADS)
Thompson, B. S.
1982-08-01
A variational theorem is presented which may be used as a basis for developing the equations of motion and the boundary conditions appropriate for studying the vibrational behavior of flexible bodied systems and the surrounding acoustic medium. The theorem is a generalization of two theorems which are both based on the principle of virtual work; the first governs the elastodynamics of the mechanical system and the second governs the behavior of the fluid medium. Lagrange multipliers are used in the development of the two basic theorems and they are also employed to incorporate the constraints at the solid-fluid interface within the functional for the acousto-elastodynamic theorem. When independent arbitrary variations of the system parameters are permitted, this theorem yields as characteristic equations the equations of motion for each member of the mechanical system, the acoustic wave equation, the compatibility conditions at the mechanical joints, the compatibility conditions at the interface and also the mixed boundary conditions for the complete system. As an illustrative example, the derivation of the problem statement for a flexible slider crank mechanism operating in a perfect gas is presented in which it is assumed that the flexural motion of the links is governed by the Timoshenko beam theory.
Event parameters - fixed target
Poskanzer, A.; Ritter, H.G.; Ludewigt, B.; Foley, K.; Borenstein, S.; Platner, E.; Love, W.; Keane, D.; Plasil, F.
1984-06-15
This subgroup has focussed on detectors for fixed target experiments which have full azimuthal coverage. The general scope of the working group was to consider (1) the configuration of an idealized detector, and (2) various configurations of practical detectors that could be implemented on a relatively short time scale. The second category includes possible upgrades and modifications of existing experimental facilities. Beams of both 15 GeV/A sulphur at the AGS and 200 GeV/A oxygen at the SPS were considered.
The theorem of Greenberg and Robinson for two-dimensional quantum field theories
NASA Astrophysics Data System (ADS)
Baumann, Klaus
1989-10-01
In two space-time dimensions there are quantum fields φ obeying ⧠φ=0, which nevertheless have nonvanishing higher truncated n-point functions. Such fields show up if one wants to adapt the theorem of Greenberg and Robinson to 1+1 space-time dimensions. Using the Jost-Lehmann-Dyson representation we show that if either (a) φ˜(p)=0 for spacelike momenta or (b) W˜φ+φ(p) decreases at least like exp(-p2), then the field φ is the sum of two local fields A and B, where A is a generalized free field and B satisfies ⧠B=0.
Fixed sagittal plane imbalance.
Savage, Jason W; Patel, Alpesh A
2014-12-01
Study Design Literature review. Objective To discuss the evaluation and management of fixed sagittal plane imbalance. Methods A comprehensive literature review was performed on the preoperative evaluation of patients with sagittal plane malalignment, as well as the surgical strategies to address sagittal plane deformity. Results Sagittal plane imbalance is often caused by de novo scoliosis or iatrogenic flat back deformity. Understanding the etiology and magnitude of sagittal malalignment is crucial in realignment planning. Objective parameters have been developed to guide surgeons in determining how much correction is needed to achieve favorable outcomes. Currently, the goals of surgery are to restore a sagittal vertical axis < 5 cm, pelvic tilt < 20 degrees, and lumbar lordosis equal to pelvic incidence ± 9 degrees. Conclusion Sagittal plane malalignment is an increasingly recognized cause of pain and disability. Treatment of sagittal plane imbalance varies according to the etiology, location, and severity of the deformity. Fixed sagittal malalignment often requires complex reconstructive procedures that include osteotomy correction. Reestablishing harmonious spinopelvic alignment is associated with significant improvement in health-related quality-of-life outcome measures and patient satisfaction.
[Health care systems and impossibility theorems].
Penchas, Shmuel
2004-02-01
results are Kurt Godel's seminal paper in 1931: "Ueber formal unentscheidbare Saetze der Principia Mathematica and verwandter System I" and Arrow's Nobel Prize winning "Impossibility Theorem" (Social Choice and Individual Values, 1951). Godel showed, unequivocally, that there is an enormous gap between what is being perceived as truth and what in fact can be proven as such. Arrow showed that the translation of individual preferences into a social order is impossible--except in a dictatorship. The unsolved controversies concerning the desirable or ideal structure of health care systems are impinged upon by these findings generally, and, in the case of the impossibility theorem, also directly. There is the impossibility of aggregating preferences and, at a deeper level, the impossibility of defining certain fundamental values, coupled with the problematic use of certain words, the absence of the possibility of creating, on a logically defined base, a complex system, complete and comprehensive in its own right. This is added to the fact that according to the elaboration by Stephen Wolfram in "A New Kind of Science", it is not easy to reduce complicated systems to simple components and to predict the continuation of their development even from simple basic laws without complicated calculations. All of these factors impede the construction of satisfying health care systems and leave obvious problems which overshadow the structure and the operation of health care systems. PMID:15143703
Fixed and Sunk Costs Revisited.
ERIC Educational Resources Information Center
Wang, X. Henry; Yang, Bill Z.
2001-01-01
Attempts to clarify the concepts of, and the link between, fixed costs and sunk costs. Argues that the root of confusion is the inconsistency in defining the term fixed costs. Consistently defines fixed and sunk costs, and describes how instructors must teach under these definitions. (RLH)
Subexponential estimates in Shirshov's theorem on height
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-04-30
Suppose that F{sub 2,m} is a free 2-generated associative ring with the identity x{sup m}=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F{sub 2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x{sup d}=0 is smaller than {Psi}(d,d,l), where {Psi}(n,d,l)=2{sup 18}l(nd){sup 3log}{sub 3}{sup (nd)+13}d{sup 2}. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d{>=}n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than {Psi}(n,d,l) are either n-divisible or contain x{sup d}; a word W is n-divisible if it can be represented in the form W=W{sub 0}W{sub 1} Horizontal-Ellipsis W{sub n} so that W{sub 1},...,W{sub n} are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<{Phi}(n,l) over the set of words of degree {<=}n-1, where {Phi}(n,l)=2{sup 87}l{center_dot}n{sup 12log}{sub 3}{sup n+48}. Bibliography: 40 titles.
Stability analysis of fixed points via chaos control.
Locher, M.; Johnson, G. A.; Hunt, E. R.
1997-12-01
This paper reviews recent advances in the application of chaos control techniques to the stability analysis of two-dimensional dynamical systems. We demonstrate how the system's response to one or multiple feedback controllers can be utilized to calculate the characteristic multipliers associated with an unstable periodic orbit. The experimental results, obtained for a single and two coupled diode resonators, agree well with the presented theory. (c) 1997 American Institute of Physics. PMID:12779684
Using a Card Trick to Illustrate Fixed Points and Stability
ERIC Educational Resources Information Center
Champanerkar, Jyoti; Jani, Mahendra
2015-01-01
Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…
ERIC Educational Resources Information Center
Dobbs, David E.
2005-01-01
The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…
Hall, David R.; Bartholomew, David B.; Moon, Justin; Koehler, Roger O.
2009-09-08
An apparatus for fixing computational latency within a deterministic region on a network comprises a network interface modem, a high priority module and at least one deterministic peripheral device. The network interface modem is in communication with the network. The high priority module is in communication with the network interface modem. The at least one deterministic peripheral device is connected to the high priority module. The high priority module comprises a packet assembler/disassembler, and hardware for performing at least one operation. Also disclosed is an apparatus for executing at least one instruction on a downhole device within a deterministic region, the apparatus comprising a control device, a downhole network, and a downhole device. The control device is near the surface of a downhole tool string. The downhole network is integrated into the tool string. The downhole device is in communication with the downhole network.
Nagai, Yoshio
2015-03-01
Many patients with type 2 diabetes mellitus(T2DM) do not achieve satisfactory glycemic control by monotherapy alone, and often require multiple oral hypoglycemic agents (OHAs). Combining OHAs with complementary mechanisms of action is fundamental to the management of T2DM. Fixed-dose combination therapy(FDC) offers a method of simplifying complex regimens. Efficacy and tolerability appear to be similar between FDC and treatment with individual agents. In addition, FDC can enhance adherence and improved adherence may result in improved glycemic control. Four FDC agents are available in Japan: pioglitazone-glimepiride, pioglitazone-metformin, pioglitazone-alogliptin, and voglibose-mitiglinide. In this review, the advantages and disadvantages of these four combinations are identified and discussed. PMID:25812374
He, Huimin; Liu, Sanyang; Chen, Rudong
2016-01-01
The aim of this paper is to study a finite family of H-accretive operators and prove common zero point theorems of them in Banach space. The results presented in this paper extend and improve the corresponding results of Zegeye and Shahzad (Nonlinear Anal 66:1161-1169, 2007), Liu and He (J Math Anal Appl 385:466-476, 2012) and the related results. PMID:27386385
NASA Astrophysics Data System (ADS)
Cornaglia, Bruno; Young, Gavin; Marchetta, Antonio
2015-12-01
Fixed broadband network deployments are moving inexorably to the use of Next Generation Access (NGA) technologies and architectures. These NGA deployments involve building fiber infrastructure increasingly closer to the customer in order to increase the proportion of fiber on the customer's access connection (Fibre-To-The-Home/Building/Door/Cabinet… i.e. FTTx). This increases the speed of services that can be sold and will be increasingly required to meet the demands of new generations of video services as we evolve from HDTV to "Ultra-HD TV" with 4k and 8k lines of video resolution. However, building fiber access networks is a costly endeavor. It requires significant capital in order to cover any significant geographic coverage. Hence many companies are forming partnerships and joint-ventures in order to share the NGA network construction costs. One form of such a partnership involves two companies agreeing to each build to cover a certain geographic area and then "cross-selling" NGA products to each other in order to access customers within their partner's footprint (NGA coverage area). This is tantamount to a bi-lateral wholesale partnership. The concept of Fixed Access Network Sharing (FANS) is to address the possibility of sharing infrastructure with a high degree of flexibility for all network operators involved. By providing greater configuration control over the NGA network infrastructure, the service provider has a greater ability to define the network and hence to define their product capabilities at the active layer. This gives the service provider partners greater product development autonomy plus the ability to differentiate from each other at the active network layer.
Dose fractionation theorem in 3-D reconstruction (tomography)
Glaeser, R.M.
1997-02-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens.
Colligative Properties of Solutions: I. Fixed Concentrations
NASA Astrophysics Data System (ADS)
Alexander, Kenneth S.; Biskup, Marek; Chayes, Lincoln
2005-05-01
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent--solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing-point depression. The limit of infinitesimal concentrations is described in a subsequent paper.
A Theorem for Two Nucleon Transfer
NASA Astrophysics Data System (ADS)
Zamick, Larry; Mekjian, Aram
2004-05-01
We use the short notation for a unitary 9j symbol U9j(Ja,Jb)=<(jj)Ja(jj)Ja|(jj)Jb(jj)Jb>I=0 The wave fcn of a state of 44Ti with ang momentum I can be written as sum D(Jp,Jn) [(jj)Jp (jj)Jn]I. For the I=0 ground stae Jp=Jn. We found a new relationship SumJp U9j(Jp,Jx) D(Jp,Jp)= 1/2 D(Jx,Jx) for T=0 and =-D(Jx,Jx) for T=2. We could explain this by regarding U9j for even Jp,Jx as a square matrix hamiltonian, which, when diagonalized has eigenvalues of 1/2(triply degenerate) and -1(singly degenerate) corresponding to T=0 and T=2 respectively.*This theorem is useful,in the context of 2 nucleon transfer, for counting the number of pairs of particles in 44Ti with even Jx.The expressions simplifies to 3|D(Jx,Jx|^2,thus eliminating a complex 9jsymbol A deeper understanding of this result arises if we consider the strange interplay of angular momentum and isospin. Consider the interaction 1/4-t(1).t(2),which is unity for T=0 states and zero for T=1. For n nucleons with isospin T the eigenvalues are n^2/8+n/4-T(T+1)/2 But if we evaluate this with the usual Racah algebra then we note that in the single j shell the interaction can also be written as <(jj)Ia V (jj)Ia>= (1-(-1)^Ia)/2 i.e. the interaction acts only in odd J states since they have isospin T=0.In 44Ti the matrix element of the hamiltonian is [2+2U9j(Jp,Jx)].Connecting this with the isospin expression gives us the eigenvalues above for U9j. * L.Zamick, E. Moya de Guerra,P.Sarriguren,A.Raduta and A. Escuderos, preprint.
Simulation of biological evolution and the NFL theorems.
Meester, Ronald
2009-09-01
William Dembski (No free lunch: why specified complexity cannot be purchased without intelligence, 2002) claimed that the NFL theorems from optimization theory render darwinian biological evolution impossible. Häggström (Biology and Philosophy 22:217-230, 2007) argued that the NFL theorems are not relevant for biological evolution at all, since the assumptions of the NFL theorems are not met. Although I agree with Häggström (Biology and Philosophy 22:217-230, 2007), in this article I argue that the NFL theorems should be interpreted as dealing with an extreme case within a much broader context. This broader context is in fact relevant for scientific research of certain evolutionary processes; not in the sense that the theorems can be used to draw conclusions about any intelligent design inference, but in the sense that it helps us to interpret computer simulations of evolutionary processes. As a result of this discussion, I will argue that from simulations, we do not learn much about how complexity arises in the universe. This position is in contrast with certain claims in the literature that I will discuss.
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Formalization of the Integral Calculus in the PVS Theorem Prover
NASA Technical Reports Server (NTRS)
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Temporal control in fixed-interval schedules.
Zeiler, M D; Powell, D G
1994-01-01
The peak procedure was used to study temporal control in pigeons exposed to seven fixed-interval schedules ranging from 7.5 to 480 s. The focus was on behavior in individual intervals. Quantitative properties of temporal control depended on whether the aspect of behavior considered was initial pause duration, the point of maximum acceleration in responding, the point of maximum deceleration, the point at which responding stopped, or several different statistical derivations of a point of maximum responding. Each aspect produced different conclusions about the nature of temporal control, and none conformed to what was known previously about the way ongoing responding was controlled by time under conditions of differential reinforcement. Existing theory does not explain why Weber's law so rarely fit the results or why each type of behavior seemed unique. These data fit with others suggesting that principles of temporal control may depend on the role played by the particular aspect of behavior in particular situations.
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.
On the role of sharp chains in the transport theorem
NASA Astrophysics Data System (ADS)
Falach, L.; Segev, R.
2016-03-01
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to follow a continuous succession of Lipschitz embedding so that the spatial gradient may be nonexistent in a subset of the domain with zero measure. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in Rn. A time-dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains, the properties are shown to be locally represented by an r-form. Using these notions, a generalized transport theorem is presented.
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937
Model Checking Failed Conjectures in Theorem Proving: A Case Study
NASA Technical Reports Server (NTRS)
Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo
2004-01-01
Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry. PMID:20418506