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Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects

APPLIED NUMERICAL MATHEMATICS 2024年 200卷 124-137页

作者： Breda, Dimitri Liessi, Davide Lunel, Sjoerd M. Verduyn Univ Udine CDLab Computat Dynam Lab Dept Math Comp Sci & Phys Via Sci 206 I-33100 Udine Italy Univ Utrecht Math Inst Budapestlaan 6 NL-3584 CD Utrecht Netherlands

In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear periodic equation with one discrete delay and fully characterize the spectrum of its monodromy operator. We perform numerical experiments discretizing the evolution operators via pseudospectral collocation, confirming the theoretical results and giving perspectives on the generalization to systems and to multiple delays. Although we do not attempt to perform a rigorous numerical analysis of the method, we give some considerations on a possible approach to the problem. (c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： evolution operators Monodromy operators Spectral analysis Pseudospectral collocation

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On evolution operators in characteristic 2

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COMMUNICATIONS IN ALGEBRA 2021年第2期49卷 590-613页

作者： Varro, Richard Univ Montpellier CNRS Inst Montpellierain Alexander Grothendieck Pl Eugene Bataillon F-35095 Montpellier France

We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately perio... 详细信息

关键词： Baric algebras Bernstein algebras evolution algebras evolution operators periodic Bernstein algebras plenary train algebras quasi-constant algebras solvable algebras ultimately periodic operator

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Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations

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RICERCHE DI MATEMATICA 2020年第2期69卷 457-481页

作者： Breda, Dimitri Liessi, Davide Univ Udine CDLab Computat Dynam Lab Dept Math Comp Sci & Phys Via Sci 206 I-33100 Udine UD Italy

Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral collocation method to approximate the eigenvalues of the evolution operators of linear coupled equations, providing rigorous error and convergence analyses and numerical tests. The method combines the ideas of the analogous techniques developed separately for renewal equations and for retarded functional differential equations. Coupling them is not trivial, due to the different state spaces of the two classes of equations, as well as to their different regularization properties.

关键词： Renewal equations Retarded functional differential equations Stability Equilibria and periodic solutions evolution operators Eigenvalue approximation Pseudospectral collocation

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APPROXIMATION OF EIGENVALUES OF evolution operators FOR LINEAR RENEWAL EQUATIONS

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2018年第3期56卷 1456-1481页

作者： Breda, Dimitri Liessi, Davide Univ Udine Dept Math Comp Sci & Phys Computat Dynam Lab CDLab Udine Italy

A numerical method based on pseudospectral collocation is proposed to approximate the eigenvalues of evolution operators for linear renewal equations, which are retarded functional equations of Volterra type. Rigorous error and convergence analyses are provided, together with numerical tests. The outcome is an efficient and reliable tool which can be used, for instance, to study the local asymptotic stability of equilibria and periodic solutions of nonlinear autonomous renewal equations. Fundamental applications can be found in population dynamics, where renewal equations play a central role.

关键词： renewal equations Volterra integral equations retarded functional equations evolution operators eigenvalue approximation pseudospectral collocation stability equilibria periodic solutions

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A classification of structural dissipations for evolution operators

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2016年第10期39卷 2558-2582页

作者： D'Abbicco, M. Ebert, M. R. Univ Sao Paulo Dept Comp & Matemat FFCLRP Ave Bandeirantes 3900Campus USP BR-14040901 Ribeirao Preto SP Brazil

In this paper, we study the asymptotic profile of the solution for a sigma-evolution equation with a time-dependent structural damping. We introduce a classification of the damping term, which clarifies whether the solution behaves like the solution to an anomalous diffusion problem. We call this damping effective, whereas we say that the damping is noneffective when the solution shows oscillations in its asymptotic profile that cannot be neglected. Our classification shows a completely new interplay between the strength of the damping and the long time behavior of its coefficient. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： evolution operators effective structural damping decay estimates diffusion phenomena

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On the Dirichlet and Neumann evolution operators in

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POTENTIAL ANALYSIS 2014年第4期41卷 1079-1110页

作者： Angiuli, Luciana Lorenzi, Luca Univ Parma Dipartimento Matemat & Informat I-43124 Parma Italy

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators and associated with a class of nonautonomous elliptic operators (t) with unbounded coefficients defined in Ix (where I is a right-halfline or I=a"e). We also prove the existence and the uniqueness of a tight evolution system of measures associated with , which turns out to be sub-invariant for , and we study the asymptotic behaviour of the evolution operators and in the L (p) -spaces related to the system {mu(N)(t)}(t is an element of I).

关键词： Nonautonomous second-order elliptic operators Unbounded coefficients evolution operators Pointwise and uniform gradient estimates evolution systems of measures Asymptotic behaviour

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Gabor frame decomposition of evolution operators and applications

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JOURNAL OF PSEUDO-DIFFERENTIAL operators AND APPLICATIONS 2014年第2期5卷 277-304页

作者： Berra, Michele Univ Turin Dipartimento Matemat Giuseppe Peano I-10123 Turin TO Italy

We compute the Gabor matrix for Schrodinger-type evolution operators. Precisely, we analyze the heat equation, already presented in Cordero et al. (Gabor representations of evolution operators, 2012), giving the exact expression of the Gabor matrix which leads to better numerical evaluations. Then, using asymptotic integration techniques, we obtain an upper bound for the Gabor matrix in one-dimension for the generalized heat equation, new in the literature. Using Maple software, we show numeric representations of the coefficients' decay. Finally, we show the superexponential decay of the coefficients of the Gabor matrix for the harmonic repulsor, together with some numerical evaluations. This work is the natural prosecution of the ideas presented in Cordero et al. (Gabor representations of evolution operators, 2012) and Cordero et al.

关键词： Pseudodifferential operator Gabor frames Metaplectic operator Heat equation evolution operators

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Well-posedness of nonautonomous abstract Cauchy problems under dissipativity conditions expressed by metric-like functionals

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2025年第1期542卷

作者： Tanaka, Naoki Shizuoka Univ Fac Sci Dept Math Shizuoka 4228529 Japan

Under a dissipativity condition expressed by a metric-like functional, the wellposedness of a nonautonomous abstract Cauchy problem is established. The main result not only extends Martin's result on the generation of an evolution operator in a class of uniformly convex Banach spaces but also can be applied to mixed problems for nonautonomous evolution equations of Kirchhoff type with which Kato's quasilinear theory or the theory of quasi-contractive semigroups cannot directly deal. The main result also gives an affirmative answer to Komura's conjecture that an evolution operator of linear operators with moving domains can be generated even under a weak stability condition rather than Kato's stability condition, and the result provides an effective means for solving degenerate wave equations. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Nonautonomous evolution equation Dissipativity condition expressed by a metric-like functional Subtangential condition Comparison function evolution operators Komura's conjecture

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On principles of emergent organization

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PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS 2024年 1071卷 1-47页

作者： Rupe, Adam Crutchfield, James P. Pacific Northwest Natl Lab Richland WA USA Univ Calif Davis Complex Sci Ctr Complex Sci Ctr One Shields Ave Davis CA 95616 USA Univ Calif Davis Phys & Astron Dept One Shields Ave Davis CA 95616 USA

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization-intrinsic computation and evolution operators-lays out a way to overcome these challenges. Additionally, we show how intrinsic computation and evolution operators combine to produce a general framework showing physical consistency between emergent behaviors and their underlying physics. This statistical mechanics of emergence provides a theoretical foundation for data-driven approaches to organization necessitated by analytic intractability. Taken all together, the result is a constructive path towards principles of organization that builds on the mathematical identification of structure. (c) 2024TheAuthor(s).***-NC-NDlicense(http://***/licenses/by-nc-nd/4.0/).

关键词： Nonequilibrium thermodynamics Pattern formation Self-organization evolution operators Intrinsic computation Entropy production

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Improved whale optimization algorithm and its application in vehicle structural crashworthiness

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INTERNATIONAL JOURNAL OF CRASHWORTHINESS 2023年第2期28卷 202-216页

作者： Qian, Lijun Yu, Luxin Huang, Yuezhu Jiang, Ping Gu, Xianguang Hefei Univ Technol Sch Automobile & Traff Engn Hefei Anhui Peoples R China Hefei Univ Technol Inst Intelligent Mfg Technol Hefei Anhui Peoples R China

Whale optimization algorithm (WOA) is a novel-innovative swarm-based meta-heuristic algorithm with excellent performance, but it may still be trapped into local extremum for troublesome problems. To this end, an improved multi-objective whale optimization algorithm (IMOWOA) is proposed to cover the shortages. Firstly, in the search stage of WOA, individual difference is considered to strengthen the exploration ability, and evolution operators are introduced to regenerate the stagnated population to prevent premature convergence. Next, the performance of IMOWOA is compared with MOWOA and other classical optimization algorithms, and a series of multi-objective test functions are used. The results on the convergence and diversity of Pareto front confirm that IMOWOA has better feasibility and competitiveness. Finally, integrated with the least squares support vector regression (LSSVR) model, IMOWOA is applied to the deterministic optimization of vehicle structural crashworthiness. The conclusion testified the efficiency of IMOWOA in the field of vehicle crashworthiness.

关键词： Improved multi-objective whale optimization individual difference evolution operators vehicle structural crashworthiness

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