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Reiterated homogenization of a laminate with imperfect contact:gain-enhancement of effective properties

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Applied Mathematics and Mechanics(English Edition) 2018年第8期39卷 1119-1146页

作者： F.E.ALVAREZ-BORGES J.BRAVO-CASTILLERO M.E.CRUZ R.GUINOVART-DIAZ L.D.PEREZ-FERNANdeZ R.RODRIGUEZ-RAMOS F.J.SABINA Facultad de matematica y Computacion Departamento de MatematicaUniversidad de La HabanaSan Lazaro y LHabana 4La HabanaCP 10400Cuba departamento de matematicas y Mecanica Universidad Nacional Autonoma de MexicoInstituto de Investigaciones en Matematicas Aplicadas y en Sistemas01000 CDMXAP 20-126M′exico departamento de Engenharia Mecanica Universidade Federal do Rio de JaneiroPolitecnica/COPPECaixa Postal 68503Rio de JaneiroRJCEP 21941-972Brasil departamento de matematica e Estatistica Universidade Federal de PelotasCaixa Postal 354PelotasRio Grande do SulCEP 96010-900Brasil

A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

关键词： reiterated homogenization method(RHM) imperfect contact variational formulation effective coefficient gain

Global multiplicity of solutions to a defocusing quasilinear Schrodinger equation with the singular term

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Science China Mathematics 2023年第8期66卷 1789-1812页

作者： Siyu Chen Carlos Alberto Santos Minbo Yang Jiazheng Zhou department of Mathematics Zhejiang Normal UniversityJinhua 321004China departamento de matematica Universidade de BrasiliaBraslia 70910-900Brazil

We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded mensurable functions,0<α<1<β<2*-1 and k,λ≥0 are two *** establish the global existence and multiplicity results of positive solutions in H^(1)_(0)(Ω)∩L^(∞)(Ω)for appropriate classes of parameters k andλand coefficients a(x)and b(x).

关键词： quasilinear Schrodinger equation singular term square diffusion term

A LOW-COST OPTIMIZATION APPROACH FOR SOLVING MINIMUM NORM LINEAR SYSTEMS AND LINEAR LEAST-SQUARES PROBLEMS

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Journal of Computational Mathematics 2024年第4期42卷 932-954页

作者： debora Cores Johanna Figueroa defense University Center at the Spanish Naval Academy Plaza de Espana36920 MarinPontevedraSpain departamento de matematica Facultad de MatematicaPontificia Universidad Catolica de ChileAv.Vicuna Mackenna 4860San JoaquinSantiago 894000Chile

Recently,the authors proposed a low-cost approach,named Optimization Approach for Linear Systems(OPALS)for solving any kind of a consistent linear system regarding the structure,characteristics,and dimension of the coefficient matrix *** results obtained by this approach for matrices with no structure and with indefinite symmetric part were encouraging when compare with other recent and well-known *** this work,we proposed to extend the OPALS approach for solving the Linear Least-Squares Problem(LLSP)and the Minimum Norm Linear System Problem(MNLSP)using any iterative low-cost gradient-type method,avoiding the construction of the matrices AT A or AAT,and taking full advantage of the structure and form of the gradient of the proposed nonlinear objective function in the gradient *** combination of those conditions together with the choice of the initial iterate allow us to produce a novel and efficient low-cost numerical scheme for solving both ***,the scheme presented in this work can also be used and extended for the weighted minimum norm linear systems and minimum norm linear least-squares *** include encouraging numerical results to illustrate the practical behavior of the proposed schemes.

关键词： Nonlinear convex optimization Gradient-type methods Spectral gradient method Minimum norm solution linear systems Linear least-squares solution

Numerical Approximation of an Axisymmetric Elastoacoustic Eigenvalue Problem

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Communications in Computational Physics 2023年第10期34卷 1420-1438页

作者： J.Querales P.Venegas GIMNAP Departamento de MatematicaUniversidad del Bio-BioConcepcionChile departamento de Ciencias Exactas Facultad de IngenieriaArquitectura y DisenoUniversidad San SebastianConcepcionChile

This paper deals with the numerical approximation of a pressure/displacement formulation of the elastoacoustic vibration problem in the axisymmetric *** propose and analyze a discretization based on Lagrangian finite elements in the fluid and solid *** show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error *** report numerical results to validate the proposed methodology for elastoacoustic vibrations.

关键词： Axisymmetric problem fluid-structure interaction spectral problem finite element method

Maschke Type Theorems for Weak Hopf Quasigroups

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Algebra Colloquium 2020年第2期27卷 213-230页

作者： J.N.Alonso Alvarez J.M.Fernández Vilaboa R.González Rodríguez departamento de matematicas Vniversidade de Vigo Campus Universitario Lagoas-MarcosendeE-36280 VigoSpain departamento de matematicas Universidade de Santiago de Compostela E-15771 Santiago de CompostelaSpain departamento de matematica Aplicada II Universidade de Vigo Campus Universitario Lagoas-MarcosendeE-36310 VigoSpain

In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral,thus extending the theories developed in the Hopf algebra,weak Hopf algebra and non-associative Hopf algebra *** this result we also deduce a version of Maschke’s theorems for right(H,B)-Hopf triples associated to a weak Hopf quasigroup H and a right H-comodule magma B.

关键词： (weak)Hopf algebra (weak)Hopf quasigroup integral Maschke theorem

Study of Branes with Variable Tension

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Communications in Theoretical Physics 2017年第11期67卷 595-599页

作者： Rodrigo Aros Milko Estrada departamento de Ciencias Fisicas Universidad Andres Bello department of Physics Universidad de Antofagasta Instituto de matematica Fisica y Estadistica Universidad de las Americas

In this work we study a brane world model with variable tension, which gives rise to four-dimensional cosmologies. The brane worlds obtained correspond to E?tv?s branes whose(internal) geometry can be casted as either a four-dimensional(A)dS_4 or a standard radiation period cosmology. The matter dominated period is discussed as well.

关键词： Randall–Sundrum brane world de Sitter hierarchy problem brane tension

The Quotient Category of a Graded Morita-Takeuchi Context

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Acta Mathematica Sinica,English Series 2006年第1期22卷 123-130页

作者： F. CASTANO IGLESIAS C. NASTASESCU departamento de Estadistica y Matemdtica Aplicada Universidad de Almeria 04120 Almeria Spain Facultatea de matematica Str. Academiei 14 RO-70109 Bucharest Romania

In this paper, we offer a graded equivalence between the quotient categories defined by any graded Morita-Takeuchi context via certain modifications of the graded cotensor functors. As a consequence, we show a commutative diagram that establish the relation between the closed objects of the categories gr^c and M^C, where C is a graded coalgebra.

关键词： Graded coalgebra Graded Morita context Quotient category

A Note on Expanding Planar Real Cellular Automata

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Acta Mathematica Sinica,English Series 2018年第9期34卷 1371-1378页

作者： Jairo GUZMAN Neptali ROMERO Universidad del Atldntico Facultad de Ciencias Bdsicas Departamento de Matematicas Km 7 antigua via Puerto Colombia Barranquilla Colombia Universidad Centroccidental Lisandro Alvarado Decanato de Ciencias y Tecnologia Departamento de Matematica Nucleo Obelisco Barquisimeto Venezuela

In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value... 详细信息

关键词： Real cellular automata block function expanding map

Nielsen coincidence theory on infra-solvmanifolds of Sol

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Science China Mathematics 2021年第8期64卷 1861-1884页

作者： Jong Bum Lee Karen Regina Panzarin department of Mathematics Sogang UniversitySeoul 121-742Korea departamento de matematica Universidade Federal de Sao CarlosSao CarlosSP 13565-905Brazil

We derive averaging formulas for the Lefschetz coincidence numbers,the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on infra-solvmanifolds modeled on a connected and simply connected solvable Lie group of type(R).As an application,we compare our formula for the Nielsen coincidence numbers with a result of Jezierski(1992)for pairs of maps on some infra-solvmanifolds of *** all the pairs of self-maps of a nonorientable infra-solvmanifold of Sol,we determine the sets of all the possible values of the Nielsen coincidence numbers and the Reidemeister coincidence numbers.

关键词： averaging formula infra-solvmanifold Lefschetz coincidence number Nielsen coincidence number Reidemeister coincidence number Sol-geometry