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CO-ISOMETRIC SOLUTIONS OF EQUATION CU + U*C = 2D

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Acta Mathematica Scientia 2003年第2期23卷 192-200页

作者：杜拴平侯晋川 department of mathematics Shanxi University department of mathematics Shanxi Teachers University

This note discusses the co-isometric solutions of the operator equation CU + U*C = 2D, establishes a correspondence between such solutions and the self-adjoint solutions of the algebraic Riccati equation X2 - iDX + iXD + D2 - C2 = 0, and gives all possible co-isometric solutions parametrically. Some mistakes of Dobovivsek's results are corrected.

关键词： Co-isometric operator invariant subspace factorization

Growth of RB Population in the Conversion Phase of Chlamydia Life Cycle

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Communications on Applied mathematics and Computation 2024年第1期6卷 90-112页

作者： Frederic Y.M.Wan department of mathematics University of CaliforniaIrvineCA92697-3875USA

Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended period.Available data show only RB units in the infected cells 20 hours post infection(hpi),spanning nearly half way through the development cycle.With data collected every 4 hpi,conversion to the elementary body(EB)form begins abruptly at a rapid rate sometime around 24 hpi.By modeling proliferation and conversion as simple birth and death processes,it has been shown that the optimal strategy for maximizing the total(mean)EB population at host cell lysis time is a bang-bang control qualitatively replicating the observed conversion activities.However,the simple birth and death model for the RB proliferation and conversion to EB deviates in a significant way from the available data on the evolution of the RB population after the onset of RB-to-EB conversion.By working with a more refined model that takes into account a small size threshold eligibility requirement for conversion noted in the available data,we succeed in removing the deficiency of the previous models on the evolution of the RB population without affecting the optimal bang-bang conversion strategy.

关键词： Chlamydia Life cycle Optimal control Maximal infectious spread Specie competitive survival

AN EFFICIENT FINITE DIFFERENCE METHOD FOR STOCHASTIC LINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS DRIVEN BY ADDITIVE WHITE NOISES

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Journal of Computational mathematics 2024年第2期42卷 432-453页

作者： Mahboub Baccouch department of mathematics University of Nebraska at OmahaOmaha NE 68182USA

In this paper,we develop and analyze a finite difference method for linear second-order stochastic boundary-value problems(SBVPs)driven by additive white noises.First we regularize the noise by the Wong-Zakai approximation and introduce a sequence of linear second-order SBVPs.We prove that the solution of the SBVP with regularized noise converges to the solution of the original SBVP with convergence order O(h)in the meansquare sense.To obtain a numerical solution,we apply the finite difference method to the stochastic BVP whose noise is piecewise constant approximation of the original noise.The approximate SBVP with regularized noise is shown to have better regularity than the original problem,which facilitates the convergence proof for the proposed scheme.Convergence analysis is presented based on the standard finite difference method for deterministic problems.More specifically,we prove that the finite difference solution converges at O(h)in the mean-square sense,when the second-order accurate three-point formulas to approximate the first and second derivatives are used.Finally,we present several numerical examples to validate the efficiency and accuracy of the proposed scheme.

关键词： Boundary-value problems Finite-difference method Additive white noise Wiener process Mean-square convergence Wong-Zakai approximation

Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

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Communications on Applied mathematics and Computation 2024年第1期6卷 489-500页

作者： John M.Holmes Barbara Lee Keyfitz department of mathematics The Ohio State UniversityColumbusOH43210USA

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results appl... 详细信息

关键词： Conservation laws Data-to-solution map Nonuniform dependence

Data-Driven Modeling of Partially Observed Biological Systems

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Communications on Applied mathematics and Computation 2024年第1期6卷 739-754页

作者： Wei-Hung Su Ching-Shan Chou Dongbin Xiu department of mathematics The Ohio State UniversityColumbusOH43221USA

We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.

关键词： Deep neural network(DNN) Governing equation discovery Biological system Partial observation

REMARKS ON JOHN DISKS

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Acta Mathematica Scientia 2009年第1期29卷 160-168页

作者：褚玉明程金发王根娣 department of mathematics Huzhou Teachers College department of mathematics Xiamen University

Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.

关键词： John disks Linearly locally connected domains Quasiconformal mappings Quasidisks

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

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Acta Mathematica Scientia 2011年第4期31卷 1377-1382页

作者：刘洋陈志华 department of mathematics Zhejiang Normal University department of mathematics Tongji University

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of ... 详细信息

关键词： Schwarz-Pick estimate holomorphic functions classical domains

Nonsolvable Groups with Three Nonlinear Irreducible Character Codegrees

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Chinese Annals of mathematics,Series B 2024年第2期45卷 173-178页

作者： Dongfang YANG Yu ZENG department of mathematics Changshu Institute of TechnologyChangshu 215500JiangsuChina

For an irreducible characterχof a?nite group G,the codegree ofχis de-?ned as|G:ker(χ)|/χ(1).In this paper,the authors determine?nite nonsolvable groups with exactly three nonlinear irreducible character codegrees,... 详细信息

关键词： Character codegree Nonsolvable group

S-SUPERFLUOUS AND S-ESSENTIAL HOMOMORPHISMS

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Acta Mathematica Scientia 2009年第2期29卷 391-401页

作者：朱海燕丁南庆 department of mathematics Zhejiang University of Technology department of mathematics Nanjing University

Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings... 详细信息

关键词： S-essential monomorphism S-superfluous epimorphism （pre）cover,（pre）envelope