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Positive solutions for some almost critical Brezis-Nirenberg type problems in bounded and exterior domains

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Acta Mathematica Sinica,English Series 2024年

作者： Salomón ALARCóN Pablo QUIJADA Departamento de Matemática Universidad Técnica Federico Santa María

We study the equation-Δu=|x|~αu(p_α~*+ε)+λ_ε|x|~βu in Ω,under the condition u=0 on ?Ω,where Ω is a smooth bounded domain in RN,N≥ 5,which is symmetric respect to x1,x2,…,xNand contains the origin,α>-2,-2 0 is a small parameter and λ_ε> 0 depends on ε,with λ_ε→ 0 as ε→ 0.Our main focus lies in finding positive solutions that take the form of a tower of bubbles of order α,exhibiting concentration at the origin as ε tends to zero.Furthermore,we extend our study to the equation-Δu=|x|~αup_α~*-ε+λ_ε|x|~βu in RN\ B1,where B1is the unit ball centered at the origin,under Dirichlet zero boundary condition and an additional vanishing condition at infinity.In this context,we discover positive solutions that take the form of a tower of bubbles of order α,progressively flattening as ε tends to zero.

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Landesman–Lazer Type Conditions and Multiplicity Results for Nonlinear Elliptic Problems with Neumann Boundary Values

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Acta Mathematica Sinica,English Series 2014年第2期30卷 229-250页

作者： Edcarlos Domingos DA SILVA Francisco Odair de PAIVA Universidade Federal de Gois Departamento de Matemtica Universidade Federal de So Carlos Departamento de Matemtica

We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of ... 详细信息

关键词： Neumann-Steklov eigenvalue problems resonance Landesman-Lazer conditions

Generalized Hardy Spaces

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Acta Mathematica Sinica,English Series 2010年第9期26卷 1673-1692页

作者： Alexandre ALMEIDA António M.CAETANO Departamento de Matemática Universidade de Aveiro

Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.

关键词： Generalized Hardy spaces maximal functions Poisson kernel interpolation with function parameter Riesz potentials singular integrals

Singular Integrals with Variable Kernels in Dyadic Settings

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1565-1579页

作者： Hugo AIMAR Raquel CRESCIMBENI Luis NOWAK IMAL-CONICET and UNL Santa FeArgentina Departamento de Matemática FaEAUNCo.and IITCI-CONICETNeuquenArgentina

In this paper we explore conditions on variable symbols with respect to Haar systems,defining Calderón–Zygmund type operators with respect to the dyadic metrics associated to the Haar bases. We show that Petermichl’s dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type.

关键词： Singular integrals spaces of homogeneous type Petermichl’s operator Haar basis

旋转输运速度场积分SPH对流扩散方程解的收敛性

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Acta Mechanica Sinica 2023年第2期39卷 61-70页

作者： Pablo Eleazar Merino-Alonso Fabricio Macià Antonio Souto-Iglesias departamento de Arquitectura Constructión y Sistemas Oceánicos y NovalesUniversidad Politécnica de MadridMadridSpain Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval Universidad Politécnica de MadridMadridSpain

本文在刚性旋转输运速度场的特殊情况下,建立了二维平流扩散方程的积分光滑粒子流体动力学(SPH)解的收敛性.考虑了Morris等人对拉普拉斯算子的近似,在傅里叶空间中建立了SPH解与精确解的收敛性.证明了如果满足核的傅里叶变换的某个条件... 详细信息

本文在刚性旋转输运速度场的特殊情况下,建立了二维平流扩散方程的积分光滑粒子流体动力学(SPH)解的收敛性.考虑了Morris等人对拉普拉斯算子的近似,在傅里叶空间中建立了SPH解与精确解的收敛性.证明了如果满足核的傅里叶变换的某个条件,即我们称之为正条件,则收敛是有保证的.这个条件是核的傅里叶变换其径向轮廓的一阶矩为正,并通过数值验证说明了分析结果.根据L2范数和最大范数,比较了使用不同核包括SPH社区更常用的核(即Wendland核以及三次和线性样条核)获得的数值解.除此之外,提出并测试了一个病理核,该核不满足正条件,导致了非收敛结果.这一事实表明,在对流扩散方程的情况下,正条件不仅是收敛的充分条件,也是必要条件.

关键词： Smoothed particle hydrodynamics Numerical analysis Diffusion Convergence Fourier analysis

Proportionally Modular Diophantine Inequalities and Their Multiplicity

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2059-2070页

作者： José Carlos ROSALES Manuel Batista BRANCO Paulo VASCO departamento de lgebra Universidad de Granada Departamento de Matemática Departamento de Matemática Universidade de Trás-os-Montes e Alto Douro

Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.

关键词： Numerical semigroup Diophantine inequality multiplicity Frobenius number

线型和非线型分子转动光谱强度的统计模型(英文)

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物理化学学报 2011年第5期27卷 1053-1060页

作者： SAIZ Andrés Departamento de Matemática Aplicada Universidad Politécnica de Valencia

In this study, we found regular behavior, from a statistical point of view, in the intensities of rotational spectra for several organic and inorganic molecules at room temperature. Non-linear molecules, for which a common intensity behavior was derived, were especially interesting. We provided theoretical support for the obtained results based on the Boltzmann distribution. Boltzmann power laws were used to reproduce the statistical behavior of the intensities from the spectra of linear and non-linear molecules. We only used statistical arguments and no specific details of any molecule were used. Therefore, these results are applicable to a large class of atoms and molecules and the model is valid when considering similar conditions to those used in this study.

关键词：物理学 RMT JPL 研究

THE EFFECT OF MEMORY TERMS IN DIFFUSION PHENOMENA

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Journal of Computational Mathematics 2006年第1期24卷 91-102页

作者： A. Araújo J.A. Ferreira P. Oliveira Departamento de Matemática Universidade de Coimbra Portugal

In this paper the effect of integral memory terms in the behavior of diffusion phenomena is studied. The energy functional associated with different models is analyzed and stability inequalities are established. Approximation methods for the computation of the solution of the integro-differential equations are constructed. Numerical results are included.

关键词： Heat propagation Integro-differential equation Numerical approximation,Splitting method

Efficient Splitting Methods Based on Modified Potentials:Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation

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Communications in Computational Physics 2023年第4期33卷 937-961页

作者： Sergio Blanes Fernando Casas Cesáreo González Mechthild Thalhammer Universitat Politècnica de València Instituto de Matemática Multidisciplinar46022 ValenciaSpain Universitat Jaume I IMAC and Departament de Matemàtiques12071 CastellónSpain Universidad de Valladolid Departamento de Matemática Aplicada47011 ValladolidSpain Leopold–Franzens–Universität Innsbruck Institut für Mathematik6020 InnsbruckAustria.

We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.

关键词： Schrodinger equation imaginary time propagation parabolic equations operator splitting methods modified potentials