检索结果-南通市图书馆

Journal of Systems Science & Complexity 2020年第1期33卷 100-121页

作者： LI Yongkun MENG Xiaofang Department of Mathematics Yunnan UniversityKunming 650091China

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.

关键词： Almost automorphic solutions exponential stability Hopfield neural networks leakage delays quaternion-valued functions

Mean-square estimate of automorphic L-functions

在线全文

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2020年第1期15卷 205-213页

作者： Weili YAO Department of Mathematics Shanghai UniversityShanghai 200444China

Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We st... 详细信息

关键词： automorphic L-function cusp form Fourier coefficient

A conjecture on the Eichler cohomology of automorphic forms

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2000年第7期43卷 734-742页

作者：王学理 Department of Mathematics Guangzhou Teachers' College Guangzhou 510400 China

We prove partially a conjecture of Knopp about the Eichler cohomology of automorphic forms on H-groups.

关键词： automorphic forms Eichler cohomology H-groups.

Exis tence and st ability of μ-pseudo almost automorphic solutions for stochastic evolution equations

在线全文

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2019年第2期14卷 261-280页

作者： Jing CUI Wenping RONG College of Mathematics and Statistics Anhui Normal University Wuhu 241000 China

We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.

关键词： Stochastic evolution equation μ-pseudo almost automorphic process fixed point theorem

Correlation of zeros of automorphic L-functions

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2 1 School of Mathematics,Shandong University,Jinan 250100, China 2Department of Mathematics,The University of Iowa,Iowa City,IA 52242-1419,USA School of Mathematics Shandong University Jinan China Department of Mathematics The University of Iowa Iowa City USA

We compute the n-level correlation of normalized nontrivial zeros of a product of L-functions:L(s,π1)···L(s,πk), where πj, j=1,...,k, are automorphic cuspidal representations of GLmj(QA). Here the sizes of the groups GLmj(QA) are not necessarily the same. When these L(s,πj) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s,πj) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m1,...,mk 4,but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture

Periods of automorphic forms,poles of L-functions and functorial lifting

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2010年第9期53卷 2215-2238页

作者： GINZBURG David SOUDRY David School of Mathematical Sciences Sackler Faculty of Exact SciencesTel-Aviv University69978Israel

In this paper,we survey our work on period,poles or special values of certain automorphic Lfunctions and their relations to certain types of Langlands functorial transfers.We outline proofs for some results and leave ... 详细信息

关键词： period of automorphic forms L-functions Langlands functoriality

Resonance between automorphic forms and exponential functions

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2010年第9期53卷 2463-2472页

作者： REN XiuMin1,& YE YangBo1,2 1School of Mathematics,Shandong University,Jinan 250100,China 2Department of Mathematics,The University of Iowa,Iowa City,Iowa 52242-1419,USA School of Mathematics Shandong University Jinan China Department of Mathematics The University of Iowa Iowa City USA

Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X 详细信息

Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum Xautomorphic forms for SL2(Z).

关键词： automorphic form exponential sum resonance

Functoriality of automorphic L-functions through their zeros

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2009年第1期52卷 1-16页

作者： LIU JianYa YE YangBo School of Mathematics Shandong UniversityJinan 250100China Department of Mathematics The University of IowaIowa CityIA 52242-1419USA

Let E be a Galois extension of Q of degree , not necessarily solvable. In this paper we first prove that the L-function L(s,π) attached to an automorphic cuspidal representation π of GLm(EA) cannot be factored nontrivially into a product of L-functions over E. Next, we compare the n-level correlation of normalized nontrivial zeros of L(s,π1)···L(s,πk), where πj, j = 1,...,k, are automorphic cuspidal representations of GLmj(QA), with that of L(s,π). We prove a necessary condition for L(s,π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific GLmj(QA), j = 1,...,k. In particular, if π is not invariant under the action of any nontrivial σ∈ GalE/Q, then L(s,π) must equal a single L-function attached to a cuspidal representation of GLm (QA) and π has an automorphic induction, provided L(s,π) can factored into a product of L-functions over Q. As E is not assumed to be solvable over Q, our results are beyond the scope of the current theory of base change and automorphic induction. Our results are unconditional when m,m1,...,mk are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.

关键词： automorphic induction automorphic L-function functoriality zero correlation

The Khuri-Jones Threshold Factor as an automorphic Function

在线全文

学校读者我要写书评

暂无评论

Journal of Modern Physics 2013年第7期4卷 904-910页

作者： B. H. Lavenda Università Degli Studi Camerino Italy

The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.

关键词： Threshold Factor automorphic Function Elliptic and Loxodromic Elements

Group Foliation Method and Functional Separation of Variables to Nonlinear Diffusion Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Chinese Physics Letters 2005年第7期22卷 1563-1566页

作者：屈长征张顺利 CenterforNonlinearStudies NorthwestUniversityXi'an710069 DepartmentofMathematics NorthwestUniversityXi'an710069

Generalized functional separation of variables to nonlinear diffusion equations is studied in terms of the extended group foliation method. A complete classification for the nonlinear diffusion equation with source te... 详细信息

关键词： PDE separable automorphic