22,419 results
Search Results
2. Analyses of Scissors Cutting Paper at Superluminal Speeds
- Author
-
Robert J. Nemiroff and Neerav Kaushal
- Subjects
Superluminal motion ,Blade (geometry) ,05 social sciences ,Mathematical analysis ,050301 education ,General Physics and Astronomy ,FOS: Physical sciences ,Angular velocity ,Popular Physics (physics.pop-ph) ,Special relativity ,Physics - Popular Physics ,01 natural sciences ,Education ,Simple (abstract algebra) ,Simplicity (photography) ,0103 physical sciences ,Perpendicular ,010306 general physics ,Constant (mathematics) ,0503 education ,Mathematics - Abstract
A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true., 6 pages, 9 figures, accepted for publication in Physics Education (un-copyedited version)
- Published
- 2019
3. Paper folding and conic sections
- Author
-
Smith, Scott G.
- Subjects
Paper -- Tests, problems and exercises ,Mathematical analysis ,Education ,Mathematics - Abstract
Problems that offer multiple revelations during its investigations and that can be approached mathematically in more than one way often involve paper folding and conic sections. These problems can be easily demonstrated with a sheet of wax paper or emulated by the geometer's sketchpad.
- Published
- 2003
4. A discussion on the paper 'Determination of mortar setting times using shear wave velocity evolution curves measured by the bender element technique'
- Author
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Jerome Carette and Stéphanie Staquet
- Subjects
Ultrasonic actuator ,Shear (geology) ,Métallurgie et mines ,Wave velocity ,Mathematical analysis ,Urbanisme et architecture [génie civil] ,Curve fitting ,General Materials Science ,Building and Construction ,Mortar ,Bâtiments génie civil transports ,Mathematics - Abstract
In a recent paper, Zhu et al. used bender element-type ultrasonic actuator in order to generate S-waves transmission through mortar samples. New criteria for determining the initial and final setting are proposed. The developed methodology leads to the conclusion that these criteria are more reliable than previously published material. Several points would require further discussion, such as the consideration of the effect of temperature, the shear wave onset detection algorithm, or the curve fitting strategy. These considerations might undermine the reliability of the suggested method, and explain the divergence of results obtained in contrast with previously published material., SCOPUS: no.j, info:eu-repo/semantics/published
- Published
- 2019
5. Remarks on a Paper by Leonetti and Siepe
- Author
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Hongya Gao, Hong Tian, and Chao Liu
- Subjects
Pure mathematics ,Generalization ,Applied Mathematics ,Mathematical analysis ,Boundary (topology) ,Monotonic function ,Type (model theory) ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Boundary value problem ,Anisotropy ,Analysis ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type { ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = 0 , x ∈ Ω , u ( x ) = θ ( x ) , x ∈ ∂ Ω . Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum θ forces solutions u to have higher integrability as well. In the present paper, we consider K ψ , θ ( p i ) -obstacle problems of the nonhomogeneous anisotropic elliptic equations ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = ∑ i = 1 n D i f i ( x ) under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe.
- Published
- 2018
6. Withdrawn Paper
- Author
-
Z. Tangxiaotao and D.-C. Gong
- Subjects
Transformation (function) ,Mathematical analysis ,Rational function ,Algorithm ,Image based ,Mathematics ,Image (mathematics) - Abstract
delete
- Published
- 2018
7. On a paper of Hasse concerning the Eisenstein reciprocity law.
- Author
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Vostokov, S., Ivanov, M., and Pak, G.
- Subjects
- *
RECIPROCITY theorems , *MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *MATHEMATICAL combinations - Abstract
In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ and $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ in the cyclotomic field ℚ(ζ n), 2 ∤ n, for a ∈ ℤ, ( a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
8. A note on the paper on the controllability of a coupled system of two korteweg-de vries equations
- Author
-
Ademir F. Pazoto and Eduardo Cerpa
- Subjects
Dispersionless equation ,Controllability ,Nonlinear system ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Calculus ,Boundary (topology) ,Soliton ,Spatial domain ,Korteweg–de Vries equation ,Mathematics - Abstract
This note concerns the paper "On the controllability of a coupled system of two Korteweg–de Vries equations" by Micu et al. [2]. They study a nonlinear coupled system of two Korteweg–de Vries equations and prove that the system is controllable by using four boundary controls. Here, we prove that in some cases it is possible to get the controllablity of the system by using only two controls. This can be done depending on both the spatial domain and the control time.
- Published
- 2011
9. How paper folds: bending with local constraints
- Author
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Martin Michael Müller and Jemal Guven
- Subjects
Statistics and Probability ,Surface (mathematics) ,Mean curvature ,Statistical Mechanics (cond-mat.stat-mech) ,Deformation (mechanics) ,Bending (metalworking) ,Mathematical analysis ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Condensed Matter - Soft Condensed Matter ,Curvature ,Constraint (information theory) ,Condensed Matter - Other Condensed Matter ,symbols.namesake ,Modeling and Simulation ,Lagrange multiplier ,Metric (mathematics) ,symbols ,Soft Condensed Matter (cond-mat.soft) ,Mathematical Physics ,Condensed Matter - Statistical Mechanics ,Other Condensed Matter (cond-mat.other) ,Mathematics - Abstract
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone., 20 pages, 1 figure
- Published
- 2007
10. Plenary Papers A Priori Truncation Error Bounds for Continued Fractions
- Author
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Lisa Lorentzen
- Subjects
Sequence ,40A15 ,convergence ,Truncation error (numerical integration) ,General Mathematics ,Mathematical analysis ,complementary error function ,incomplete gamma function ,30B10 ,Upper and lower bounds ,Limit periodic continued fractions ,Combinatorics ,Error function ,truncation error estimates ,Fraction (mathematics) ,Limit (mathematics) ,Incomplete gamma function ,Gamma function ,Mathematics - Abstract
Most of the known continued fraction expansions of special functions are limit periodic. This means that the classical approximants S n (0) are normally not the best ones to use for approximations. In this paper we suggest a number of approximants S n (w n ) which converge faster. The estimation of the improvement and bounds for the error |f - Sn(wn)| (which we still call the truncation error) are mainly obtained by means of Thron's parabola sequence theorem and the oval sequence theorem.
- Published
- 2003
11. Estimation of curvature along curves with application to fibres in 3D images of paper
- Author
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David Coeurjolly, Stina Svensson, Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2), Centrum för bildanalys (CBA), Uppsala University, and Coeurjolly, David
- Subjects
Multigrid convergence ,Bending (metalworking) ,Property (programming) ,Computation ,Mathematical analysis ,Estimator ,Geometry ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Space (mathematics) ,computer.software_genre ,Curvature ,[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV] ,Voxel ,[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0210 nano-technology ,computer ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Space curves can be used to represent elongated objects in 3D images and furthermore to facilitate the computation of shape measures for the represented objects. In our specific application (fibres in 3D images of paper), we want to analyze the fibre network on a voxel level with respect to elongation and bending. For this purpose, it is of interest to estimate the curvature in each voxel along a curve. We present a new discrete curvature estimator fulfilling the multigrid convergence property. Moreover, we present results from a study where curvature together with other shape measures are used to analyze the fibre network.
- Published
- 2003
12. A remark on a paper of F. Luca and A. Sankaranarayanan.
- Author
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I. Kátai
- Subjects
- *
SET theory , *MATHEMATICAL analysis , *MATHEMATICS , *MATHEMATICAL logic - Abstract
Abstract  We generalize a result of F. Luca and A. Sankaranarayanan by proving that the set of n for which Ï(1) â Ï(n) is squareful is of zero density. A similar statement holds for Ï (n) instead of Ï(n) and for some other multiplicative functions. [ABSTRACT FROM AUTHOR]
- Published
- 2008
13. Some remarks on a paper by L. Carlitz
- Author
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Dominici, Diego
- Subjects
- *
POLYNOMIALS , *ALGEBRA , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
14. Addendum to the paper 'A note on weighted Bergman spaces and the Cesàro operator'
- Author
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Stevo Stević and Der-Chen Chang
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Weighted Bergman space ,Addendum ,01 natural sciences ,Bergman space ,0103 physical sciences ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,46E15 ,0101 mathematics ,polydisk ,Cesàro operator ,Mathematics ,Bergman kernel ,47B38 - Abstract
Let H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such thatwhere Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .
- Published
- 2005
15. Selected Papers of Takeyuki Hida
- Author
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K Saitô, H H Kuo, Nobuaki Obata, Luigi Accardi, Ludwig Streit, and Si Si
- Subjects
Harmonic analysis ,symbols.namesake ,Random field ,General theory ,Feynman integral ,Gaussian ,Mathematical analysis ,symbols ,Calculus of variations ,White noise ,Rotation group SO ,Mathematics ,Mathematical physics - Abstract
General theory of white noise functionals Gaussian and other processes infinite dimensional harmonic analysis and rotation group quantum theory Feynman integrals and random fields variational calculus and random fields application to biology.
- Published
- 2001
16. A note on Rosay's paper
- Author
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Armen Edigarian
- Subjects
Pure mathematics ,Closed manifold ,Stein manifold ,Plurisubharmonic function ,General Mathematics ,Mathematical analysis ,Liouville manifold ,Complex manifold ,Mathematics ,plurisubharmonic function - Published
- 2003
17. Remarks on the paper "On some new inequalities for convex functions" by M. Tunç.
- Author
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WITKOWSKI, Alfred
- Subjects
- *
MATHEMATICAL inequalities , *CONVEX functions , *GENERALIZATION , *ARITHMETIC mean , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
18. Comments about the paper entitled 'A generalized boundary integral equation for isotropic heat conduction with spatially varying thermal conductivity' by A.J. Kassab and E. Divo
- Author
-
Massimo Guiggiani, Marc Bonnet, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica, and Università degli Studi di Siena = University of Siena (UNISI)
- Subjects
Applied Mathematics ,Mathematical analysis ,Isotropy ,General Engineering ,Boundary (topology) ,02 engineering and technology ,Thermal conduction ,01 natural sciences ,Integral equation ,Connection (mathematics) ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,Thermal conductivity ,Character (mathematics) ,0203 mechanical engineering ,[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph] ,Fundamental solution ,0101 mathematics ,Analysis ,Mathematics - Abstract
An integral formulation for heat conduction problems in non-homogeneous media has recently been proposed by Kassab and Divo [Engineering Analysis with Boundary Elements 1996;18:273]. The goal of this communication is to revisit and clarify two key features of the formulation of Kassab and Divo. First, the contention that the integral equation formulation proposed by them does not possess the desired boundary-only character is made and substantiated; it is shown in particular that Eq. (10) therein does not hold owing to the fact that a crucial requirement for the fundamental solution, Eqs. (5c) and (5d) therein, is actually not met. Second, the limiting process associated with a vanishing neighbourhood in connection with the particular kernel function used therein is revisited.
- Published
- 1998
19. Preparation of Papers.
- Subjects
- *
PERIODICAL publishing , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *SIMULATION methods & models , *MATHEMATICS , *PERIODICALS - Abstract
This article provides instructions in preparing a paper for publication in the "Journal of Optimization Theory and Applications." Some of these guidelines are the following: 1)submission of manuscripts in triplicate; 2) reference to English as the official language of the journal; 3) inclusion of an abstract of at least 50 to 100 words in each contribution; and, 4) the abstract should be followed by a list of four to five key words identifying the subject.
- Published
- 2005
- Full Text
- View/download PDF
20. Correction to my paper 'Closed-form solutions of some partial differential equations via quasi-solutions II'
- Author
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Lee A. Rubel
- Subjects
Stochastic partial differential equation ,Elliptic partial differential equation ,Linear differential equation ,Differential equation ,General Mathematics ,Mathematical analysis ,First-order partial differential equation ,35C05 ,35A25 ,Symbol of a differential operator ,Mathematics ,Separable partial differential equation ,Numerical partial differential equations - Published
- 1995
21. Remarks to our former paper 'uniform distribution of some special sequences'
- Author
-
Kazuo Goto and Takeshi Kano
- Subjects
Uniform distribution (continuous) ,General Mathematics ,Mathematical analysis ,Mathematics - Published
- 1992
22. Mathematic Analyses about Error Bars using SD, SE and CI in Psychological Research Results (Updated June 20, 2024).
- Subjects
PSYCHOLOGICAL research ,MATHEMATICAL analysis ,MONADS (Mathematics) - Abstract
This article discusses the use of error bars in psychological research papers and raises questions about the differences between error bars using the Standard Deviation (SD), the Standard Error (SE), and the Confidence Interval (CI). The paper aims to clarify misconceptions and confusions in error bar applications through mathematical theory analyses. The article acknowledges that controversies over error bar applications have been an unsettled issue in the psychological field and other scientific domains. However, it is important to note that this preprint has not been peer-reviewed. [Extracted from the article]
- Published
- 2024
23. High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach.
- Author
-
Sato, Shun
- Subjects
MATHEMATICAL analysis ,MATRIX multiplications ,ORDINARY differential equations ,QUADRATIC forms ,MATHEMATICS ,NUMERICAL integration - Abstract
This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Comments on a paper “A Hermitian Morita theorem for algebras with anti-structure”
- Author
-
Dasgupta, Bhanumati
- Subjects
- *
ALGEBRA , *MATHEMATICS , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
25. Some remarks on my paper 'On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots', (Schrödinger equations and generalizations, I)
- Author
-
Jiro Takeuchi
- Subjects
Cauchy problem ,symbols.namesake ,Cauchy's convergence test ,35A99 ,Mathematical analysis ,symbols ,Applied mathematics ,Cauchy principal value ,Initial value problem ,Cauchy's integral theorem ,Cauchy matrix ,Mathematics ,Schrödinger equation - Published
- 1984
26. Intellectual humility in mathematics.
- Author
-
Rittberg, Colin Jakob
- Subjects
HUMILITY ,MATHEMATICAL analysis ,MATHEMATICS ,VIRTUES ,VIRTUE - Abstract
In this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
27. Generalized Euclidean Distances for Elasticity Tensors
- Author
-
Pierre Gilormini, Katell Derrien, Léo Morin, Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies, and HESAM Université (HESAM)-HESAM Université (HESAM)
- Subjects
Matériaux [Sciences de l'ingénieur] ,Short paper ,02 engineering and technology ,elasticity tensor ,01 natural sciences ,[SPI.MAT]Engineering Sciences [physics]/Materials ,0203 mechanical engineering ,Closest isotropic tensor - Elasticity tensor - Log-Euclidean distance ,Euclidean geometry ,medicine ,General Materials Science ,0101 mathematics ,Elasticity (economics) ,Elasticity tensor ,Mathematics ,Mechanical Engineering ,Log-Euclidean distance ,Mathematical analysis ,Stiffness ,Isotropic tensor ,010101 applied mathematics ,020303 mechanical engineering & transports ,Mechanics of Materials ,Closest isotropic tensor ,medicine.symptom ,Dimensionless quantity - Abstract
International audience; The aim of this short paper is to provide, for elasticity tensors, generalized Euclidean distances that preserve the property of invariance by inversion. First, the elasticity law is expressed under a non-dimensional form by means of a gauge, which leads to an expression of elasticity (stiffness or compliance) tensors without units. Based on the difference between functions of the dimensionless tensors, generalized Euclidean distances are then introduced. A subclass of functions is proposed, which permits the retrieval of the classical log-Euclidean distance and the derivation of new distances, namely the arctan-Euclidean and power-Euclidean distances. Finally, these distances are applied to the determination of the closest isotropic tensor to a given elasticity tensor
- Published
- 2020
28. The Small-Noise Limit of the Most Likely Element is the Most Likely Element in the Small-Noise Limit.
- Author
-
Selk, Zachary and Honnappa, Harsha
- Subjects
STOCHASTIC differential equations ,GAUSSIAN distribution ,ALGEBRA ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measures. The Onsager-Machlup function can serve as a density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the "most likely element". The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the "most likely element". This leads to a conundrum - what is the relationship between these two functions? We show both pointwise and G-convergence (which is essentially the convergence of minimizers) of the Onsager-Machlup function under the small-noise limit to the Freidlin-Wentzell function - and give an expression for both. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to path-dependent stochastic differential equations and the law of an infinite system of random algebraic equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Equivalence of Coefficients Extraction of One-loop Master Integrals
- Author
-
Yang An, Zi-ang Hu, Xiang Lv, Yi Li, and Zhongjie Huang
- Subjects
High Energy Physics - Theory ,Physics and Astronomy (miscellaneous) ,Unitarity ,010308 nuclear & particles physics ,Bubble ,Mathematical analysis ,Short paper ,FOS: Physical sciences ,01 natural sciences ,Scattering amplitude ,Amplitude ,High Energy Physics - Theory (hep-th) ,0103 physical sciences ,010306 general physics ,Equivalence (measure theory) ,Mathematics - Abstract
Now there are many different methods to do the PV-reduction for the one loop amplitudes. Two of them are unitarity cut method and generalized unitarity cut method. In this short paper, we present an explicit connection of these two methods, especially how the extractions of triangle and bubble coefficients are equivalent to each other., 18 pages, 1 figures
- Published
- 2018
30. Application of the nonlinear methods in pneumocardiogram signals
- Author
-
K. Gediz Akdeniz, Mahmut Akıllı, Tamer Zeren, Nazmi Yılmaz, Mustafa Ozbek, Department of Physics, Koç University, Istanbul, Turkey, Nonlinear Science Working Group, Istanbul, Turkey, Department of Physiology, Manisa Celal Bayar University Medical School, Manisa, Turkey, and Department of Biophysics, Manisa Celal Bayar University Medical School, Manisa, Turkey
- Subjects
0301 basic medicine ,Entropy ,Biophysics ,Complex system ,Lyapunov exponent ,01 natural sciences ,Electrocardiography ,03 medical and health sciences ,symbols.namesake ,0103 physical sciences ,Animals ,Molecular Biology ,Mathematics ,Original Paper ,Signal processing ,010304 chemical physics ,Entropy (statistical thermodynamics) ,Mathematical analysis ,Reproducibility of Results ,Wavelet transform ,Signal Processing, Computer-Assisted ,Cell Biology ,Atomic and Molecular Physics, and Optics ,Rats ,Nonlinear system ,030104 developmental biology ,Nonlinear Dynamics ,Aperiodic graph ,Calibration ,Boltzmann constant ,symbols - Abstract
In this work, the pneumocardiogram signals of nine rats were analysed by scale index, Boltzmann Gibbs entropy and maximum Lyapunov exponents. The scale index method, based on wavelet transform, was proposed for determining the degree of aperiodicity and chaos. It means that the scale index parameter is close to zero when the signal is periodic and has a value between zero and one when the signal is aperiodic. A new entropy calculation method by normalized inner scalogram was suggested very recently. In this work, we also used this method for the first time in an empirical data. We compared the both methods with maximum Lyapunov exponents and observed that using together the scale index and the entropy calculation method by normalized inner scalogram increases the reliability of the pneumocardiogram signal analysis. Thus, the analysis of the pneumocardiogram signals by those methods enables to compare periodical and/or nonlinear aspects for further understanding of dynamics of cardiorespiratory system. © 2020, Springer Nature B.V.
- Published
- 2020
31. A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers–Wannier Duality.
- Author
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Al-Bashabsheh, Ali and Vontobel, Pascal O.
- Subjects
TOPOLOGY ,MATHEMATICS ,MATHEMATICAL analysis ,GRAPH theory ,COMPUTER science ,COMPUTER engineering - Abstract
Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. Modelling Creativity: Identifying Key Components through a Corpus-Based Approach.
- Author
-
Jordanous, Anna and Keller, Bill
- Subjects
CREATIVE ability ,NATURAL language processing ,ONTOLOGY ,MATHEMATICAL analysis ,QUANTITATIVE research - Abstract
Creativity is a complex, multi-faceted concept encompassing a variety of related aspects, abilities, properties and behaviours. If we wish to study creativity scientifically, then a tractable and well-articulated model of creativity is required. Such a model would be of great value to researchers investigating the nature of creativity and in particular, those concerned with the evaluation of creative practice. This paper describes a unique approach to developing a suitable model of how creative behaviour emerges that is based on the words people use to describe the concept. Using techniques from the field of statistical natural language processing, we identify a collection of fourteen key components of creativity through an analysis of a corpus of academic papers on the topic. Words are identified which appear significantly often in connection with discussions of the concept. Using a measure of lexical similarity to help cluster these words, a number of distinct themes emerge, which collectively contribute to a comprehensive and multi-perspective model of creativity. The components provide an ontology of creativity: a set of building blocks which can be used to model creative practice in a variety of domains. The components have been employed in two case studies to evaluate the creativity of computational systems and have proven useful in articulating achievements of this work and directions for further research. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
33. LETTER TO THE EDITOR: ON BORWEIN'S PAPER, 'ADJOINT PROCESS DUALITY'
- Author
-
Zălinescu, Constantin
- Subjects
DUALITY theory (Mathematics) ,ALGEBRA ,MATHEMATICAL analysis ,TOPOLOGY ,GEOMETRY ,SET theory ,ADJOINT differential equations ,DIFFERENTIAL equations ,MATHEMATICS - Abstract
We give counterexamples for some statements of Borwein and sufficient conditions for the validity of these. [ABSTRACT FROM AUTHOR]
- Published
- 1986
34. Measurement errors when estimating the vertical jump height with flight time using photocell devices: the example of Optojump
- Author
-
Ahmed Attia, Del P. Wong, Wissem Dhahbi, Johnny Padulo, Karim Chamari, and A Chaouachi
- Subjects
Physical Therapy, Sports Therapy and Rehabilitation ,law.invention ,03 medical and health sciences ,Vertical jump ,0302 clinical medicine ,law ,Physiology (medical) ,Orthopedics and Sports Medicine ,lcsh:Sports medicine ,lcsh:QH301-705.5 ,Simulation ,Reliability (statistics) ,Mathematics ,Original Paper ,Observational error ,Photoresistor ,Mathematical analysis ,Performance analysis ,030229 sport sciences ,Flight time ,Standard error ,Reaction ,lcsh:Biology (General) ,Muscle power ,Jump ,lcsh:RC1200-1245 ,030217 neurology & neurosurgery - Abstract
Common methods to estimate vertical jump height (VJH) are based on the measurements of flight time (FT) or vertical reaction force. This study aimed to assess the measurement errors when estimating the VJH with flight time using photocell devices in comparison with the gold standard jump height measured by a force plate (FP). The second purpose was to determine the intrinsic reliability of the Optojump photoelectric cells in estimating VJH. For this aim, 20 subjects (age: 22.50±1.24 years) performed maximal vertical jumps in three modalities in randomized order: the squat jump (SJ), counter-movement jump (CMJ), and CMJ with arm swing (CMJarm). Each trial was simultaneously recorded by the FP and Optojump devices. High intra-class correlation coefficients (ICCs) for validity (0.98-0.99) and low limits of agreement (less than 1.4 cm) were found; even a systematic difference in jump height was consistently observed between FT and double integration of force methods (-31% to -27%; p1.2). Intra-session reliability of Optojump was excellent, with ICCs ranging from 0.98 to 0.99, low coefficients of variation (3.98%), and low standard errors of measurement (0.8 cm). It was concluded that there was a high correlation between the two methods to estimate the vertical jump height, but the FT method cannot replace the gold standard, due to the large systematic bias. According to our results, the equations of each of the three jump modalities were presented in order to obtain a better estimation of the jump height.
- Published
- 2016
35. Global strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain
- Author
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Fucai Li and Jishan Fan
- Subjects
Applied Mathematics ,010102 general mathematics ,Short paper ,Mathematical analysis ,Nuclear Theory ,Mathematics::Analysis of PDEs ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,Strong solutions ,Viscosity ,Mathematics - Analysis of PDEs ,Bounded function ,FOS: Mathematics ,Compressibility ,Navier stokes ,0101 mathematics ,Analysis of PDEs (math.AP) ,Mathematics ,35Q30, 35Q35, 76N10 - Abstract
In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier–Stokes system with vacuum in a bounded domain Ω ⊂ R 3 by the bootstrap argument provided that the viscosity coefficients λ and μ satisfy that 7 λ > 9 μ and the initial data ρ 0 and u 0 satisfy that ‖ ρ 0 ‖ L ∞ ( Ω ) and ‖ ρ 0 | u 0 | 5 ‖ L 1 ( Ω ) are sufficiently small.
- Published
- 2017
36. Studying the Effectiveness of Online Homework for Different Skill Levels in a College Algebra Course.
- Author
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Mathai, Elizabeth and Olsen, Darlene
- Subjects
ALGEBRA ,INTERNET in education ,MATHEMATICAL analysis ,MATHEMATICS ,UNIVERSITIES & colleges - Abstract
A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill level measured by a departmental placement test. The data suggests that online homework was beneficial to the incoming higher-skilled group, whereas, the lower-skilled students did not benefit from online homework. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
37. A Perturbation Method for the 3D Finite Element Modeling of Electrostatically Driven MEMS
- Author
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Mohamed Boutaayamou, Ruth V. Sabariego, and Patrick Dular
- Subjects
Computer science ,Computation ,finite element method ,Mechanical engineering ,Perturbation (astronomy) ,electrostatic field distortions ,Topology ,MEMS ,lcsh:Chemical technology ,Biochemistry ,Source field ,Analytical Chemistry ,Electrostatic field distortions ,Polygon mesh ,lcsh:TP1-1185 ,Electrical and Electronic Engineering ,Instrumentation ,Electrical conductor ,Mathematics ,Microelectromechanical systems ,Full Paper ,perturbation method ,Mathematical analysis ,Atomic and Molecular Physics, and Optics ,Finite element method ,Conductor ,Classical mechanics ,Mesh generation - Abstract
In this paper, a finite element (FE) procedure for modeling electrostatically actu- ated MEMS is presented. It concerns a perturbation method for computing electrostatic field distortions due to moving conductors. The computation is split in two steps. First, an un- perturbed problem (in the absence of certain conductors) is solved with the conventional FE method in the complete domain. Second, a perturbation problem is solved in a reduced re- gion with an additional conductor using the solution of the unperturbed problem as a source. When the perturbing region is close to the original source field, an iterative computation may be required. The developed procedure offers the advantage of solving sub-problems in re- duced domains and consequently of benefiting from different problem-adapted meshes. This approach allows for computational efficiency by decreasing the size of the problem. ispartof: Sensors vol:8 issue:2 pages:994-1003 ispartof: location:Switzerland status: published
- Published
- 2008
38. REMARKS ON THE STABILITY OF THE 3–VARIABLE FUNCTIONAL INEQUALITIES OF DRYGAS.
- Author
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JEDSADA SENASUKH and SATIT SAEJUNG
- Subjects
MATHEMATICS ,STABILITY constants ,FUNCTIONAL equations ,MATHEMATICAL analysis ,STATISTICS - Abstract
We give some remarks on the recent paper [J. Math. Inequal. 13 (4) (2019), 1235– 1244]. Some misleading conclusions of their stability results are carefully discussed and corrected. Moreover, we reestablish their results with a more general assumption and a stronger conclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. A Multiscale Wavelet-Based Test for Isotropy of Random Fields on a Regular Lattice
- Author
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Marc Geilhufe, Kevin Thon, and Donald B. Percival
- Subjects
maximal overlap discrete wavelet transform ,Random field ,wavelet variance ,isotropy ,Mathematical analysis ,Isotropy ,Wavelet Analysis ,anisotropy ,Rejection rate ,Paper density ,VDP::429 ,Computer Graphics and Computer-Aided Design ,Nominal level ,Wavelet ,Lattice (order) ,Image Processing, Computer-Assisted ,Humans ,random fields ,Anisotropy ,Software ,Algorithms ,Mathematics ,Mammography - Abstract
A test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed. The test is based on wavelet theory, and can operate on the horizontal and vertical scale of choice, or on any combination of scales. Scale is introduced through the wavelet variances (sometimes referred to as the wavelet power spectrum), which decompose the variance over different horizontal and vertical spatial scales. The method is more general than existing tests for isotropy, since it handles intrinsically stationary random fields as well as second-order stationary fields. The performance of the method is demonstrated on samples from different (an)isotropic random fields, and compared to three existing methods. It is competitive with or outperforms existing methods since it consistently rejects close to the nominal level for isotropic fields while having a rejection rate for anisotropic fields comparable to the existing methods in the stationary case, and superior in the intrinsic case. As practical examples, paper density images of handsheets and mammogram images are analyzed.
- Published
- 2014
40. Introduction – from type theory and homotopy theory to univalent foundations.
- Author
-
AWODEY, STEVE, GAMBINO, NICOLA, and PALMGREN, ERIK
- Subjects
HOMOTOPY theory ,UNIVALENT functions ,MATHEMATICS ,MATHEMATICAL analysis ,TOPOLOGY - Abstract
We give an overview of the main ideas involved in the development of homotopy type theory and the univalent foundations of Mathematics programme. This serves as a background for the research papers published in the special issue. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
41. Forthcoming Papers.
- Subjects
MATHEMATICAL logic ,MATHEMATICS ,ALGEBRA ,MATHEMATICAL analysis - Abstract
The article presents abstracts related to mathematics including the equivalent of P to NP-intersect, the application of default logic variants in default logic, and basics of specification.
- Published
- 2005
- Full Text
- View/download PDF
42. Ill-Posedness Issue on a Multidimensional Chemotaxis Equations in the Critical Besov Spaces.
- Author
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Li, Jinlu, Yu, Yanghai, and Zhu, Weipeng
- Subjects
CHEMOTAXIS ,MATHEMATICS ,DIFFERENTIAL equations ,MATHEMATICAL analysis ,MATHEMATICAL models - Abstract
In this paper, we aim to solving the open question left in [Nie, Yuan: Nonlinear Anal 196 (2020); J. Math. Anal. Appl 505 (2022) and Xiao, Fei: J. Math. Anal. Appl 514 (2022)]. We prove that a multidimensional chemotaxis system is ill-posedness in B ˙ 2 d , r - 3 2 × ( B ˙ 2 d , r - 1 2 ) d when 1 ≤ r < d due to the lack of continuity of the solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Idempotents, group membership and their applications.
- Author
-
Porubský, Štefan
- Subjects
RING theory ,IDEMPOTENTS ,MATHEMATICS ,SEMIGROUPS (Algebra) ,MATHEMATICAL analysis - Abstract
Š. Schwarz in his paper [SCHWARZ, Š.: Zur Theorie der Halbgruppen, Sborník prác Prírodovedeckej fakulty Slovenskej univerzity v Bratislave, Vol. VI, Bratislava, 1943, 64 pp.] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups [SCHWARZ, Š.: Contribution to the theory of torsion semigroups, Czechoslovak Math. J. 3(1) (1953), 7–21]. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
44. Theoretical Foundations for the Alpha-Beta Associative Memories: 10 Years of Derived Extensions, Models, and Applications.
- Author
-
Yáñez-Márquez, Cornelio, López-Yáñez, Itzamá, Aldape-Pérez, Mario, Camacho-Nieto, Oscar, Argüelles-Cruz, Amadeo José, and Villuendas-Rey, Yenny
- Subjects
ASSOCIATIVE memory (Psychology) ,ASSOCIATIVE learning ,COMPUTATIONAL geometry ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
The current paper contains the theoretical foundation for the off-the-mainstream model known as Alpha-Beta associative memories (αβ
model). This is an unconventional computation model designed to operate as an associative memory, whose main application is the solution of pattern recognition tasks, particularly for pattern recall and pattern classification. Although this model was devised, proposed and created in 2002, it is worth noting that its theoretical support remains unpublished to this day. This is despite the fact that more than a hundred scientific articles have been published with applications, improvements, and new models derived from the αβ model. The present paper includes all the required definitions, and the rigorous mathematical demonstrations of the lemmas and theorems, explaining the operation of the αβ model, as well as the original models it has inspired or that have been derived from it. Also, brief descriptions of 60 selected articles related to the αβ model are presented. These latter works illustrate the competitiveness (and sometimes superiority) of several extensions and models derived from the original αβ model, when compared against some models and paradigms present in the mainstream current scientific literature. [ABSTRACT FROM AUTHOR] - Published
- 2018
- Full Text
- View/download PDF
45. On the scattered field generated by a ball inhomogeneity of constant index in dimension three
- Author
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George Leadbetter, Andrew Parker, Yves Capdeboscq, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Mathematical Institute [Oxford] (MI), and University of Oxford [Oxford]
- Subjects
Helmholtz equation ,010102 general mathematics ,Short paper ,Mathematical analysis ,Scalar (mathematics) ,01 natural sciences ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,Mathematics - Classical Analysis and ODEs ,Broadband ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Ball (mathematics) ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a ball of radius $\eps$ and another one outside. In this short paper, we report that the results recently obtained in the two dimensional case in [1] can be easily extended to three dimensions. In particular, we provide sharp estimates of the size of the scattered field caused by this ball inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with $\eps$., 17 pages
- Published
- 2012
46. AN ALMOST SCHUR THEOREM ON 4-DIMENSIONAL MANIFOLDS
- Author
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Guofang Wang, Yuxin Ge, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), and Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Short paper ,01 natural sciences ,Schur's theorem ,Computer Science::Computers and Society ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Ricci-flat manifold ,0103 physical sciences ,Sectional curvature ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Schur product theorem ,Mathematics ,Scalar curvature - Abstract
International audience; In this short paper we prove that the almost Schur theorem, introduced by De Lellis and Topping, is true on 4-dimensional Riemannian manifolds of nonnegative scalar curvature and discuss some related problems on other dimensional manifolds.
- Published
- 2012
47. Representing Smoothed Spectrum Estimate with the Cauchy Integral
- Author
-
Ming Li
- Subjects
Signal processing ,Quantitative Biology::Neurons and Cognition ,Article Subject ,Physics::Instrumentation and Detectors ,lcsh:Mathematics ,General Mathematics ,Astrophysics::High Energy Astrophysical Phenomena ,Short paper ,Mathematical analysis ,Spectrum (functional analysis) ,General Engineering ,Spectral density ,lcsh:QA1-939 ,Computer Science::Numerical Analysis ,lcsh:TA1-2040 ,Physics::Space Physics ,lcsh:Engineering (General). Civil engineering (General) ,Cauchy's integral formula ,Mathematics - Abstract
Estimating power spectrum density (PSD) is essential in signal processing. This short paper gives a theorem to represent a smoothed PSD estimate with the Cauchy integral. It may be used for the approximation of the smoothed PSD estimate.
- Published
- 2012
- Full Text
- View/download PDF
48. On Lie point symmetries in differential games
- Author
-
Arsen Palestini
- Subjects
TheoryofComputation_MISCELLANEOUS ,Pure mathematics ,Computer Science::Computer Science and Game Theory ,jel:C72 ,Mathematical analysis ,jel:C73 ,Ode ,TheoryofComputation_GENERAL ,Differential Game ,Closed-Loop Nash Equilibrium ,Lie Point Symmetry ,Infinitesimal Generator ,First Integral ,Lie point symmetry ,SECS-P/01 Economia politica ,C72 ,symbols.namesake ,C73 ,Quaderni - Working Paper DSE ,Nash equilibrium ,Differential game ,Homogeneous space ,ddc:330 ,symbols ,Point (geometry) ,Infinitesimal generator ,Differential (mathematics) ,Mathematics - Abstract
A technique to determine closed-loop Nash equilibria of n-player differential games is developed when their dynamic state-control system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems.
- Published
- 2010
49. On the Topics of “Mathematical Optimization in Modern Medicine and Engineering” Symposium 2019.
- Author
-
Pater, Flavius, Herban, Sorin, and Rosu, Serban
- Subjects
MATHEMATICAL optimization ,APPLIED mathematics ,MATHEMATICAL analysis ,ENGINEERING ,MATHEMATICS ,MATHEMATICAL economics ,NORMED rings - Published
- 2020
- Full Text
- View/download PDF
50. On Factor Prime Factorizations for n-D Polynomial Matrices.
- Author
-
Mingsheng Wang
- Subjects
MATRICES (Mathematics) ,POLYNOMIAL rings ,COMMUTATIVE rings ,ALGORITHMS ,RING theory ,ALGEBRA ,FACTORIZATION ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
This paper investigates the problem of factor prime factorizations for n-D polynomial matrices and presents a criterion for the existence of factor prime factorizations for an important class of n-D polynomial matrices. As a by-product, we also obtain an algebraic algorithm to check n-D factor primeness in some important cases which partially solves the long-standing open problem of recognizing n-D factor prime matrices. Some problems related to the factorization methods are also studied. Several exam- pies are given to illustrate the results. The results presented in this paper are true over any coefficient field. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
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