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2-D nonseparable multiscaling function interpolation and approximation with an arbitrary dilation matrix

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Communications in Nonlinear Science and Numerical Simulation 2000年第3期5卷 125-133页

作者： En-Bing LIN and Yi LING(department of math.matics, university of Toledo, Toledo OH 43606, usa e-mail: elin@math. utoledo. edu) department of math.matics University of Toledo Toledo OH 43606 USA

We introduce nonseparable multiscaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. An equivalent condition for approximation accuracy for... 详细信息

关键词： wavelets interpolation approximation accuracy of scaling function nonseparable scaling function

Bounds for Two Classes of Graph Spectrum and Proof of Their Conjectures

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应用数学 1991年第3期 119-120页

作者： Chen Jiansheng (math. department of Hu(?)zhong university of Science & Technology)

Let λbe the kth greatest eigenvalue of forest F (or tree T) on n vertices, then λ=-λ. Hong Yuan proposed the following conjecture: Conjecture 1. Suppose T is a tree with n vertices and edge independence number q. For k≤q, λ(T)≥λ(Swith equality iff T≌S, where Sis formed from a Kand a path Pby joining with an edge a vertex of degree one of Pto the vertex of degree n-2k+1 of K.

关键词： tree Bounds for Two Classes of Graph Spectrum and Proof of Their Conjectures Graph

On the Residues of Binomial Coefficients and Their Products Modulo Prime Powers

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Acta mathematica Sinica,English Series 2002年第2期18卷 277-288页

作者： CAI Tian Xin department of math.matics.Zhejiang university.Hangzhou 310028,P.R.China E-mail:trcai@mail.hz.zj.cnGRANVILLE Andrew department of math.matics,university of Georgia.Athens,GA 30602.usa E-mail:andrew@sophie.math.uga.edu department of math.matics Zhejiang University Hangzhou P. R. China department of math.matics University of Georgia Athens USA

In this paper,we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime powers,e.g.. for any distinct odd primes p and *** discuss the connections with the prime r... 详细信息

关键词： Binomial coefficients Bernoulli numbers Recognizing primes

An Improved Method for Calculating Paleoheat Flow from Vitrinite Reflectance Profiles

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Journal of China university of Geosciences 2001年第4期12卷 337-342页

作者： Tang Zhonghua department of math & Stats, Curtin university of Technology, Perth, W A 6845, Australia Engineering Faculty , China university of Geosciences , Wuhan 430074 Wu Yonghong department of math & Stats, Curtin university of Technology, Perth, W department of math & Stats Curtin University of Technology Perth W A 6845 Australia Engineering Faculty China University of Geosciences Wuhan 430074 department of math & Stats Curtin University of Technology Perth W A 6845 Australia department of math & Stats Curtin University of Technology Perth W A 6845 Australia Faculty of Earth Resources China University of Geosciences Wuhan 430074

Based on the models developed by Lerche et al. (1984) and Pang et al. (1993), an improved model for calculating paleoheat flow into basins is investigated. The new model is an optimization problem with the state variables governed by a thermal conduction equation. A genetic algorithm is used to solve the highly nonlinear optimization problem. As an application, the model is applied to the research into the history of heat flow in the Pearl River Mouth basin located in the South China Sea. The numerical analysis shows that the simulation results are in good agreement with the measured data and indicates that the basin may have undergone three rifting and thermal events. It is also demonstrated that a high R0 gradient reflects a response to high paleoheat flow during the early, rapid subsidence stage, while a low R0 gradient is a result of the thermal decay during the thermal subsidence because of thermal contraction of a cooling lithosphere.

关键词： genetic algorithms paleoheat flow vitrinite reflectance.

A　Fastly　Convergent　Directly　Feasible　Directions　Method　for　Nonlinearly　Inequality　Constrained　Optimization

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Systems Science and Systems Engineering 1997年第1期7卷 5-14页

作者： JIAN Jinbao math. and Information Science department, Guangxi university, Nanning530004, China

In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming nor linear equation need to be sovled. Under mild assumptions, the new algorithm is shown to possess global and superlinear convergence.

关键词： Nonlinearly constrained optimization direct search directions feasible directions method global and superlinear convergence.

SOME REMARKS ABOUT THE R-BOUNDEDNESS

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Chinese Annals of math.matics,Series B 2004年第3期25卷 421-432页

作者： BUSHANGQUAN departmentofmathematicalSciences TsinghuaUniversityBeijing100084China

Let X,Y be UMD-spaces that have property (α), 1< p< ∞ and let M be anR-bounded subset in L(X, Y). It is shown that {T(M_k)_(k∈z): M_k, k(M_(k+l)-M_k) ∈M for k∈Z} is an R-bounded subset of L(L^p (0,2π; X), L^p(0,2π; Y)), where T(M_m)_(k∈zdenotes the L^p-multiplier given by the sequence (M_k)_(k∈z), This generalizes a resultof Venni [10]. The author uses this result to study the strongly L^p-well-posedness ofevolution equations with periodic boundary condition. Analogous results for operator-valued L^p-multipliers on R are also given.

关键词： Operator-valued Fourier multiplier Maximal regularity Rademacher boundedness

The Consistency Indexes and Its Improvement Method in AHP

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Systems Science and Systems Engineering 1994年第1期4卷 89-96页

作者： HAN Xuli(department of Applied math and Mechanics,Central South university of Technology,Changsha 410083,Human)

In this paper,the equivalence conditions about the consistency of positive matrices are *** new consistency indexes are proved. By the results of the random expectment,the reference wines for consistency test are given. The improvement methods of the new indexes and priority values are *** the problem about the consistency test,the reviaion of a comparison matrix and the computation of priority values are related to each other.

关键词： decision theory AHP consistency index

The Full-Discrete Mixed Finite ElementMethods for Nonlinear Hyperbolic Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 152-155页

作者： Yanping CHEN and Yunqing HUANG(department of math.matics, Nanjing university, Najing 210008, China)(Institute of Comp. & Appl. math., Xiangtan university, Xiangtan 411105, China)E-mail: huangyq@*** department of math.matics Nanjing University Najing 210008 China Institute of Comp. and Appl. math. Xiangtan University Xiangtan 411105 China

This article treats mixed finite element methods for second order nonlinear hyperbolic equations. A fully discrete scheme is presented and improved L2-errorestimates are established. The convergence of both the functi... 详细信息

关键词： nonlinear hyperbolic equation mixed finite element methods convergence

A Discrete Singular Integral Operator(In Memory of Professor Long Ruilin)

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Acta mathematica Sinica,English Series 1998年第2期14卷 235-244页

作者： Fan Dashan (department of mathematical Sciences,university of Wisconsin-Milwaukee,Milwaukee,WI 53201,usa)(Email:fan@alpha1.csd.uwm.edu)Lu Shanzhen (department of math.matics,Beijing Normal university,Beijing 100875,China)(Email:lusz@***)Pan Yibiao (department of math.matics and Statistics,university of Pittsburgh,Pittsburgh,PA 15260,usa)(Email:yibiao@tomato.math.pitt.edu) university of Wisconsin-Milwaukee 美国北京师范大学数学系北京 Pittsburgh大学美国

Suppose that {αk}k∞=-∞ is a Lacunary sequence of positive numbers satisfying infαk+1/αk=α>1 and that Ω（y’）is a function in the Besov space B10,1(Sn-1)where Sn-1 is the unit sphere on Rn（n≥2）.We prove that if ∫Sn-1Ω（y’）dσ（y’）=0 then the discrete singular integral operator TΩf（x）=∫(Sn-1)f（x-αky’）Ω（y’）dσ（y’） and the associated maximal operator TΩf（x）=∫Sn-1f（x-αky’）Ω（y’）dσ（y’） are both bounded in the space L2（Rn）. The theorems in this paper improve a result by Duoandikoetxea and Rubio de Francia in the L2 case.

关键词： Singular integral Besov space Rough kernel