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Some Endpoint Estimates for the Multiplier Operator

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Journal of Mathematical Research with Applications 2012年第3期32卷 337-345页

作者： Xiaoli CHEN 1,2 1.department of mathematics,Jiangxi Normal University,Jiangxi 330022,P.R.China 2.department of mathematics,Zhejiang University,Zhejiang 310027,P.R.China department of mathematics Jiangxi Normal University Jiangxi 330022

In this paper,the author proves that Multiplier operator is bounded on BMO（R~n）,LMO（R~n） and CBMOρ,λ（R~n）respectively if some concellation conditions are satisfied.

关键词： multiplier operator BMO space LMO space λ-central BMO space.

Variable Separation Solution for(1+1)-Dimensional Nonlinear Models Related to Schrdinger Equation

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Communications in Theoretical Physics 2004年第10期42卷 568-572页

作者： XU Chang-Zhi~(1,2) ZHANG Jie-Fang~11 Institute of Nonlinear Physics,Zhejiang Normal University,Jinhua 321004,China2 department of Physics and mathematics,Jinhua Educational College,Jinhua 321000,China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China department of Physics and mathematics Jinhua Educational College Jinhua 321000 China

A variable separation approach is proposed and successfully extended to the(1+1)-dimensional *** new exact solution of(1+1)-dimensional nonlinear models related to Schr(?)dinger equation by the entranceof three arbitrary functions is *** special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution,oscillating soliton solution,and periodic soliton solutions are discussed by selecting thearbitrary functions appropriately.

关键词： variable separation approach (1+1)-dimensional nonlinear models solution of soliton

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA

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Acta Mathematica Scientia 2010年第3期30卷 810-818页

作者：周惊雷李庆国 College of mathematics and Econometrics Hunan University department of mathematics Hunan University of Arts and Science

Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain：（i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.

关键词： Complete lattice Heyting algebra linear system minimal covering

On the least primitive root in number fields

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Science China mathematics 2010年第9期53卷 2489-2500页

作者： WANG TianZe1,& GONG Ke21School of mathematics and Information Sciences,North China University of Water Resources and Electric Power,Zhengzhou 450011,China 2department of mathematics,Henan University,Kaifeng 475004,China School of mathematics and Information Sciences North China University of Water Resources and Electric Power Zhengzhou China department of mathematics Henan University Kaifeng China

Let K be an algebraic number field and OK its ring of *** any prime ideal p,the group(OK/p) of the reduced residue classes of integers is *** call any element of a generator of the group(OK/p) a primitive root modulo *** both by Shoup's bound for the rational improvement and Wang and Bauer's generalization of the conditional result of Wang Yuan in 1959,we give in this paper a new bound for the least primitive root modulo a prime ideal p under the Grand Riemann Hypothesis for algebraic number *** results can be viewed as either the improvement of the result of Wang and Bauer or the generalization of the result of Shoup.

关键词： primitive root algebraic number fields Hecke zeta function

Approximation of functions on the Sobolev space with a Gaussian measure

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Science China mathematics 2010年第2期53卷 373-384页

作者： WANG HePing 1, ZHANG YanWei 2 & ZHAI XueBo 1 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China 2 department of mathematics, Zaozhuang University, Zaozhuang 277160, China School of Mathematical Sciences Capital Normal University Beijing China department of mathematics Zaozhuang University Zaozhuang China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure

A counter example for nilpotent groups

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Science China mathematics 2010年第11期53卷 3041-3048页

作者： LIU HeGuo1, ZHANG JiPing2 & LIAO Jun2 1department of mathematics, Hubei University, Wuhan 430062, China 2School of Mathematical Sciences, Peking University, Beijing 100871, China department of mathematics Hubei University Wuhan China School of Mathematical Sciences Peking University Beijing China

Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ J} as ring. Write U = 1 + I, and it is a nilpotent group with class ≤ n - 1. Let G be the subgroup of U which is generated by {1 + xj|j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.

关键词： nilpotency class nilpotent group nilpotent ring Lie ring

A relationship between the nonexistence of generalized bent functions and class groups

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Science China mathematics 2010年第1期53卷 213-222页

作者： LIU FengMei 1,& YUE Qin 21 department of Information Research,College of Information Engineering,Information Engineering University,Zhengzhou 450002,China 2 department of mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China department of Information Research College of Information Engineering Information Engineering University Zhengzhou China department of mathematics Nanjing University of Aeronautics and Astronautics Nanjing China

A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations. At the same time,a method is given which can be used to simplify the known results. Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.

关键词： generalized bent function integral basis class group genus theory

Y_CΩ_(2n)are easy terms

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Chinese Science Bulletin 1998年第20期43卷 1707-1709页

作者： ZHAO Xishun 1 and WANG Ju 2 1. department of mathematics, Nanjing University, Nanjing 210093, China 2. Institute of Software, Chinese Academy of Sciences, Beijing 100080, China department of mathematics Nanjing University Nanjing China Institute of Software Chinese Academy of Sciences Beijing China

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λ***...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini’s conjecture: Y CΩ n is an easy term for any natural number n≥2.

关键词： λβ-calculus Kuper’s theorem easy term.

The several transformation formula in several complex variables and its applications

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Science China mathematics 2010年第6期53卷 1541-1553页

作者： HUANG YuSheng1,& LIN LiangYu2 1department of mathematics,Putian College,Putian 351100,China 2School of Mathematical Sciences,Xiamen University,Xiaman 361005,China department of mathematics Putian College Putian China School of Mathematical Sciences Xiamen University Xiaman China

In this paper,by the method of global analysis,the authors give a new global integral transformation formula and obtain the Plemelj formula with Hadamard principal value of higher-order partial derivatives for the integral of Bochner-Martinelli type on a closed piecewise smooth orientable manifold ***,the authors obtain the composition formula,Poincar'e-Bertrand extended formula of the corresponding singular *** the application of some results,the authors also study a higher-order Cauchy boundary problem and a regularization problem of higher-order linear complex differential singular integral equation with variable coefficients.

关键词： integral transformation Bochner-Martinelli type integral higher-order partial derivative Plemelj formula composition formula Poincar’e-Bertrand formula