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Kolmogorov's ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems 被引量:1
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作者 Sheng Fan ZHOU Qiu Li JIA Wei SHI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第2期313-320,共8页
We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dis... We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov's ε-entropy of the global attractor for lattice systems. 展开更多
关键词 Kolmogorov's ε-entropy discrete space dissipative lattice system global attractor
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Discrete state space method and modal extension method based impact sound synthesis model
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作者 Xu-Hua Tian Ke-An Chen +2 位作者 Yan-Ni Zhang Han Li Jian Xu 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第11期270-277,共8页
The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on dis... The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space(DSS) method and modal extension method(MEM). This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures. 展开更多
关键词 impact sound synthesis discrete state space contact force
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Minimax designs for linear regression models with bias in a reproducing kernel Hilbert space in a discrete set
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作者 ZHOU Xiao-dong YUE Rong-xian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第3期361-378,共18页
Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the mod... Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the model bias comes from a reproducing kernel Hilbert space. Two different design criteria are proposed by applying the minimax approach for estimating the parameters of the regression response and extrapolating the regression response to points outside of the design space. A simulated annealing algorithm is applied to construct the minimax designs. These minimax designs are compared with the classical D-optimal designs and all-bias extrapolation designs. Numerical results indicate that the simulated annealing algorithm is feasible and the minimax designs are robust against bias caused by model misspecification. 展开更多
关键词 62K05 62K25 62J05 minimax design reproducing kernel Hilbert space discrete design space simulated annealing algorithm
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A DISCRETE CHARACTERIZATION OF BESOV SPACES
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作者 Anna Kamont 《Analysis in Theory and Applications》 1997年第2期63-77,共15页
The characterization of isotropic Besov spaces for in terms of progressive differences of a function on dyadic points is obtained. Moreover, for withan analogous characterization of anisotropic Besov spaces is presented.
关键词 A discrete CHARACTERIZATION OF BESOV spaceS
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F_(p) as a Discrete Metric Space
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作者 Zezhou Zhang 《Algebra Colloquium》 SCIE CSCD 2024年第1期165-180,共16页
We define a metric that makes the algebraic closure of a finite field F_(p) into a UDBG(uniformly discrete with bounded geometry)metric space.This metric stems from algebraic properties of F_(p).From this perspective,... We define a metric that makes the algebraic closure of a finite field F_(p) into a UDBG(uniformly discrete with bounded geometry)metric space.This metric stems from algebraic properties of F_(p).From this perspective,for F_(p)we explore common research themes in metric spaces,reveal how peculiar properties naturally arise,and present it as a new type of example for certain well-studied questions. 展开更多
关键词 algebraic closure of finite field discrete metric space non-expanding Falner
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Particle-Wave Duality Resulting from the Granulation of Fields in a Hypercubic Lattice
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作者 Christiaan T. de Groot 《Journal of Modern Physics》 2021年第7期870-886,共17页
The possibility of granulated discrete fields is considered in which there are at least three distinct base granules. Because of the limited size of the granules, the motion of an endlessly extended particle field mus... The possibility of granulated discrete fields is considered in which there are at least three distinct base granules. Because of the limited size of the granules, the motion of an endlessly extended particle field must to be split into an inner and an outer part. The inner part moves gradually in a point particle-like fashion, the outer is moving step-wise in a wave-like manner. This dual behaviour is reminiscent of the particle-wave duality. Field granulation can be caused by deviations of the structure of the lattice at the boundaries of the granule, causing some axes of the granule to be tilted. The granules exhibit relativistic effects, inter alia, caused by the universality of the coordination number of the lattice. 展开更多
关键词 discrete space Granular Fields Hypercubic Lattice Motion in a Lattice Particle-Wave Duality Relativistic Effects
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The Basic Idea behind the Relativistic and the Quantum Concepts
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作者 Ahmed Isam 《Journal of Modern Physics》 2016年第1期139-144,共6页
A new aspect of unification is presented in this paper. This aspect depends on two postulates of our recent theory concerning light propagation in a specific medium. The special theory of relativity is demonstrated as... A new aspect of unification is presented in this paper. This aspect depends on two postulates of our recent theory concerning light propagation in a specific medium. The special theory of relativity is demonstrated as a reflection of our first postulate, regarding the existence of multiple, equivalent rest frames in our medium. The second postulate is concerned with energy forms in nature, and it deals with the quantum behavior of light and wave behavior of matter. By using this postulate, we are able to justify the existence of these two phenomena. As a consequence of this, gravity as described by general relativity is unified as a background-independent interaction under the same postulate. 展开更多
关键词 Sama Aether Theory Theory of Relativity Quantum Theory Light Matter Waves GRAVITY Rest Motion String Theory discrete space
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DISCRETE CHARACTERIZATION OF THE PALEY-WIENER SPACE WITH SEVERAL VARIABLES 被引量:1
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作者 陈广贵 房艮孙 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2000年第4期396-404,共9页
In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn... In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn). 展开更多
关键词 discrete Hilbert transform Paley-Wiener space with several variables discrete Hardy space with several variables
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A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem
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作者 Dawei Wu Zhennan Zhou 《Annals of Applied Mathematics》 2024年第1期71-104,共34页
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its i... The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its invariant measure are of interest.In this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound.With a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains. 展开更多
关键词 Growth-fragmentation model Markov chain numerical approximation space discretization convergence rate
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