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Γ-CONVERGENCE OF INTEGRAl FUNCTIONAlS DEPENDING ON VECTOR-VAlUED FUNCTIONS OVER PARABOlIC DOMAINS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 249-258页

作者： JIAN HUAIYU(department of mathematical sciences, Tsinghua university, Beijing 100084, China.) department of mathematical sciences Tsinghua University Beijing 100084 China

This paper studies Γ-convergence for a sequence of parabolic functionals, where the integrand f is nonconvex, and periodic on the first variable. The author obtains the representation formula of the Γ-limit. The results in this paper support a conclusion which relates Γ-convergence of parabolic functionals to the associated gradiend flows and confirms one of De Giorgi’s conjectures partially.

关键词： Γ-convergence Parabolic-minima Nonconvex functionals Parabolic equations

EXTRAPOlATION AND A-POSTERIORI ERROR ESTIMATORS OF PETROV-GAlERKIN METHODS FOR NON-lINEAR VOlTERRA INTEGRO-DIFFERENTIAl EQUATIONS

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Journal of Computational Mathematics 2001年第4期19卷 407-422页

作者： Shu-hua Zhang (department of mathematical sciences, university of Alberta, Edrmonton, Alberta, Canada T6G 2G1) Tao lin (department of Mathematics, Virginia Tech, Blacksburg VA 24061) Yan-ping lin (department of mathematical sciences, university of Alberta university of Alberta 加拿大 T6G 2G1 Virginia Tech 美国 VA 24061 university of Alberta 加拿大 T6G 2G6

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

关键词： Volterra integro-differential equations Petrov-Galerkin finite element methods Asymptotic expansions Interpolation post-processing A-posteriori error estimators.

Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures

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Science China Mathematics 2010年第4期53卷 895-904页

作者： WANG FengYu 1,2 1 School of mathematical sciences,Beijing Normal university,Beijing 100875,China 2 department of Mathematics,Swansea university,Singleton Park,Swansea SA2 8PP,uk 1. School of mathematical sciences Beijing Normal University Beijing 100875 China2. Department of Mathematics Swansea University Singleton Park Swansea SA2 8PP UK

By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically *** conditions,as well as the ... 详细信息

关键词： intrinsic ultracontractivity intrinsic super-Poincar’e inequality Riemannian manifold diffusion semigroup

THE GlOBAl ARTIFICIAl BOUNDARY CONDITIONS FOR NUMERICAl SIMUlATIONS OF THE 3D FlOW AROUND A SUBMERGED BODY

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Journal of Computational Mathematics 2003年第4期21卷 435-450页

作者： Hou-de Han Xin Wen (department of mathematical sciences, Tsinghua university, Beijing 100084, China) department of mathematical sciences Tsinghua University Beijing 100084 China

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.

关键词： Ship wave Potential flow Global artificial boundary condition Finite element method.

Complete solving of explicit evaluation of Gauss sums in the index 2 case

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Science China Mathematics 2010年第9期53卷 2525-2542页

作者： YANG Jing1,2 & XIA lingli3,1department of mathematical sciences,Tsinghua university,Beijing 100084,China 2Division of mathematical sciences,School of Physical and mathematical sciences,Nanyang Technological university,637371,Singapore 3Basic Courses department,Beijing Union university,Beijing 100101,China 1. department of mathematical sciences Tsinghua University Beijing 100084 China2. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Nanyang Singapore3. Basic Courses Department Beijing Union University Beijing 100101 China

let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo *** χ be a primitive multiplicative character of order N over finite field *** paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case"(i.e.[(Z/NZ):<p>] = 2).Firstly,the classification of the Gauss sums in the index 2 case is ***,the explicit evaluation of Gauss sums G(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 3 is odd) is ***,combining with the researches before,the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.

关键词： Gauss sum Stickelberger’s theorem Stickelberger congruence Davenport-Hasse lifting formula Davenport-Hasse product formula

Maximal regularity of second order delay equations in Banach spaces

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Science China Mathematics 2010年第1期53卷 51-62页

作者： BU ShangQuan ? & FANG Yi department of mathematical sciences, Tsinghua university, Beijing 100084, China department of mathematical sciences, Tsinghua university, Beijing 100084, China 1. department of mathematical sciences Tsinghua University Beijing 100084 China

We give necessary and sufficient conditions of lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on lp([-2π, 0];X)(*** ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).

关键词： maximal regularity second order delay equations lebesgue-Bochner spaces Besov spaces Triebel-lizorkin spaces

Evaluation of Industrial IoT Service Providers with TOPSIS Based on Circular Intuitionistic Fuzzy Sets

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Computers, Materials & Continua 2024年第7期80卷 715-746页

作者： Elif Çalo˘glu Büyükselçuk Industrial Engineering department Fenerbahçe University˙Istanbul34758Turkey

Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product *** platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed *** addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine ***,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital *** this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy *** on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been *** criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and *** evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of *** the evaluation of seven distinct alternatives against these criteria,it was deduced tha

关键词： IIoT manufacturing TOPSIS circular intuitionistic fuzzy sets

Rational points and zeta functions of some curves over finite fields

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Science China Mathematics 2010年第11期53卷 2855-2863页

作者： WANG long1, & lUO JinQuan2,3 1department of mathematical sciences, Tsinghua university, Beijing 100084, China 2School of mathematical sciences, Yangzhou university, Yangzhou 225002, China 3Division of mathematical sciences, School of Physical and mathematical sciences, Nanyang Technology university, 637371, Singapore 1. department of mathematical sciences Tsinghua University Beijing 100084 China2. School of Mathematical Sciences Yangzhou University Yangzhou 225002 China3. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technology University Singapore 637371 Singapore

In this paper we study the number of rational points on some curves over finite fields. Moreover, zeta functions of the associated function fields are evaluated explicitly.

关键词： exponential sum rational point rational place zeta function

REGUlARIZATION OF SINGUlAR SYSTEMS BY OUTPUTFEEDBACK

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Journal of Computational Mathematics 2000年第1期18卷 43-60页

作者： De-lin Chu Da-yong Cai(department of mathematical sciences, Tsinghua university, Beijing 100084, China) 清华大学北京 100084

Presents a study which examined problem of regularization of a singular linear time-invariant system by derivative and proportional output feedback. Reduced form for the system that can be computed using orthogonal tr... 详细信息

关键词： regularization singular systems output feedback