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Chinese Annals of Mathematics,Series B 2002年第2期23卷 293-310页

作者： J.L.VZQUEZ E.ZUAZUA departamento de matematicas Universidad AutonomaDepartamento de Matematica AplicadaUniversidadComplutense 28049MadridSpain28040 M

The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.

关键词： Asymptotic behaviour Scaling Omega-limit Heat equation Hyperbolic conservation laws

Simple Classical Lie Algebras in Characteristic 2 and Their Gradations, II

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Algebra Colloquium 2014年第2期21卷 207-214页

作者： Alexandre N. Grishkov Marines Guerreiro Instituto de matematica e Estatfstica Universidade de Sao Paulo Sao Paulo-SP Brazil departamento de matematica Universidade Federal de Vicosa Vicosa-MG Brazil

This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2e, C2e, D2e＋1, E7 and Es in terms of some gradations of these al... 详细信息

关键词： Lie algebras characteristic 2 gradations

A Weierstrass Representation Formula for Minimal Surfaces in H_3 and H^2×R

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1603-1612页

作者： Francesco MERCURI StefanoMONTALDO PaolaPIU departamento de matematica.C.P.6065 IMECCUNICAMP UniversitàdegliStudi di Cagliari Dipartimento di Matematica

We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional ... 详细信息

关键词： Minimal immersions Weierstrass representation Heisenberg group Hyperbolic space

On the Spectra of a Family of Geometric Operators Evolving with Geometric Flows

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Communications in Mathematics and Statistics 2021年第2期9卷 181-202页

作者： D.M.Tsonev R.R.Mesquita departamento de matematica UFAMManausAM 69077-070Brazil

In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric *** an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric *** also pose three questions which we consider to be of a general interest.

关键词： Witten-Laplacian Eigenvalues Monotonicity of eigenvalues Ricci flow Ricci–Bourguignon flow Yamabe flow Bochner formula Reilly formula

Immersed Boundary Approach to Biofilm Spread on Surfaces

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Communications in Computational Physics 2022年第1期31卷 257-292页

作者： Ana Carpio Rafael Gonzalez-Albaladejo departamento de matematica Aplicada Universidad Complutense28040 MadridSpain

We propose a computational model to study the growth and spread of bacterial biofilms on interfaces,as well as the action of antibiotics on *** membranes are represented by boundaries immersed in a fluid matrix and subject to interaction ***,division and death of bacterial cells follow dynamic energy budget rules,in response to variations in environmental concentrations of nutrients,toxicants and substances released by the *** this way,we create,destroy and enlarge boundaries,either spherical or *** forces represent details of the interaction between cells,and the interaction with the *** can investigate geometrical arrangements and the formation of porous *** simulations illustrate the evolution of top views and diametral slices of small biofilm seeds,as well as the action of *** show that cocktails of antibiotics targeting active and dormant cells can entirely eradicate a biofilm.

关键词： Hybrid multiscale models immersed boundary methods dynamic energy budget models bacterial biofilm antibiotic resistance

Green's Function for Periodic Solutions in Alternately Advanced and delayed Differential Systems

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 936-951页

作者： Kuo-Shou CHIU departamento de matematica Facultad de Ciencias BasicasUniversidad Metropolitana de Ciencias de la EducacionSantiagoChile

In this paper we investigate the existence of the periodic solutions of a nonlinear differential equation with a general piecewise constant argument,in short dePCAG,that is,the argument is a general step *** consider the critical case,when associated linear homogeneous system admits nontrivial periodic *** of existence of periodic solutions of such equations are *** the process we use the Green?s function for periodic solntions and convert the given dePCAG into an equivalent integral *** we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential *** also use the contraction mapping principle to show the existence of a unique periodic *** examples are given to show the feasibility of our results.

关键词： piecewise constant arguments Green's function periodic solutions hybrid equations fixed point theorems

Morphisms and Elements of Group-like Type in Weak Multiplier Bialgebras

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Algebra Colloquium 2018年第1期25卷 107-132页

作者： Esperanza Lopez-Centella departamento de Didactica de la matematica Universidad de Granada Facultad de Educacion Economfa y Tecnologfa de Ceuta

With the purpose of providing a categorical treatment of weak multiplier bialgebras （introduced by BShm, Gomez-Torrecillas and Ldpez-Centella in 2015）, an ap- propriate notion of morphism for these algebraic objects is proposed. This allows us to define a category wmb of （regular） weak multiplier bialgebras （with a right full comultipli- cation）, containing as a full subcategory the category wba of weak bialgebras defined by BShm, Gomez-Torrecillas and Lopez-Centella in 2014. We present a great source of ex- amples of these morphisms proving that, under some assumption, a functor between small categories induces a morphism of this kind between the natural weak multiplier bialgebra structures carried by the linear spans of the arrow sets of the categories. We explore the notion of elements of group-like type in a weak multiplier bialgebra, proposing a definition in the line of the one by the aforementioned authors for weak bialgebras. We show a big number of its properties and provide more general versions of many results known in the context of weak bialgebras. In particular, in analogy with the classical bialgebra setting （where the set of group-like elements is a monoid）, we prove that the set of these elements possesses a structure of category.

关键词： weak multiplier bialgebra weak bialgebra category group-like element

Comments on "Non-existence of Shilnikov chaos in continuous-time systems"

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Applied Mathematics and Mechanics(English Edition) 2013年第9期34卷 1175-1176页

作者： A.ALGABA F.FERNANdeZ-SANCHEZ M.MERINO A.J.RODRIGUEZ-LUIS departamento de matematicas Centro de Investigacion de Fisica Teorica y Matematica FIMATUniversity of Huelva departamento de matematica Aplicada II E.S.IngenierosUniversity of Sevilla Camino de los Descubrimientos s/n

A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.

关键词： homoclinic chaos heteroclinic chaos non-existence of Shilnikov chaos

DIRECT ITERATIVE METHODS FOR RANK deFICIENT GENERALIZED LEAST SQUARES PROBLEMS

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Journal of Computational Mathematics 2000年第4期18卷 439-448页

作者： Jin-yun Yuan Xiao-qing Jin departamento de matematica Universidade Federal do ParanaCuritibaBrazil Faculty of Science and Technology University of MacaoMacaoChina

The generalized least squares (LS) problem ... (Ax - b)[sup TW[sup -1](Ax - b) appears in, many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m ≥ n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well. [ABSTRACT FROM AUTHOR]

关键词： rank deficient generalized LS problem block SOR method PCG method convergence optimal parameter