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On (2.m + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2.(m-1)

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Science china Mathematics 2009年第1期52卷 17-28页

作者： LIAO QunYing1, LIU Feng2.& FENG KeQin2.1 College of Mathematics and Software sciences, Sichuan normal {2., Chengdu 610066, china 2.Department of mathematical sciences, Tsinghua {2., Beijing 100084, china College of Mathematics and Software sciences Sichuan Normal University Chengdu 610066 China Department of mathematical sciences Tsinghua University Beijing 100084 China

All (2. +1)-variable symmetric Boolean functions with submaximal algebraic immunity 2.-1 are described and constructed. The total number of such Boolean functions is 32.·2.m-3 +3m-2.· 2. - 2.for m≥2.

关键词： symmetric Boolean function algebraic immunity cryptography

Perfect reconstruction image modulation based on BEMD and quaternionic analytic signals

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Science china(Information sciences) 2011年第12期54卷 2622-2634页

作者： QIAO LiHong 1 , NIU KaiFu 2., WANG Ning 2.& PENG LiZhong 2.1 College of Information Science and Engineering, Henan university of Technology, Zhengzhou 450001, china {2., Peking university, Beijing 100871, china 1. College of Information Science and Engineering Henan University of Technology Zhengzhou 450001 China2. School of Mathematical Sciences Peking University Beijing 100871 China

Image modulation represents image by meaningful characters such as image instantaneous amplitude and instantaneous frequency. A perfect reconstruction image modulation method is proposed. In detail, the bidimensional empirical mode decomposition (BEMD) is first improved to adaptively decompose image into monocomponents. Then by the quaternionic analytic method, suitable analytic signals is acquired. A new polar form is further proposed to modulate images, then seven characters are derived including instantaneous amplitude and instantaneous frequencies. We demonstrate the techniques on both synthetic and natural images, depict the needle program of the estimated frequencies and obtain the reconstructions that are the same with the original images. The applications in image segmentation and separation establish the validity of characterizing images of this type as sums of locally narrow band modulated components.

关键词： perfect reconstruction image modulation AM-FM representation BEMD quaternionic analytic signals

The relative generalized Hamming weight and the semilinear equivalence of codes

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Science china(Information sciences) 2011年第4期54卷 787-794页

作者： LIU ZiHui 1 & WANG Jie 2.1 Department of Mathematics,Beijing Institute of Technology,Beijing 100081,china 2.school of mathematical sciences,Beijing {2.,Beijing 100871,china 1. Department of Mathematics Beijing Institute of Technology Beijing 100081 China2. School of Mathematical Sciences Beijing University Beijing 100871 China

Certain equivalent conditions are given for the semilinear equivalence of linear codes by using the relative generalized Hamming weight and the value function.

关键词： value function semilinear equivalence support weight relative generalized Hamming weight

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 {2.,Beijing 100084,china 2.ivision of mathematical sciences,school of Physical and mathematical sciences,Nanyang Technological {2.,637371,Singapore 3Basic Courses Department,Beijing Union {2.,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):] = 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 = 2.·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

Entropy Assessment on Environmental Influence of Condense Heat in Recovery System in Air-Conditioning Refrigerating Machine

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湖南大学学报（自然科学版） 2009年第S1期36卷 96-101页

作者： TANG Wen-wu1,2.WANG Han-qing1,2.1.school of Energy Science and Engineering,Central South university,Changsha,Hunan 410083,{2. 2.school of Civil Engineering,Hunan university of Technology,Zhuzhou,Hunan 412.08,{2.) school of Energy Science and Engineering Central South University Changsha 410083 China school of Civil Engineering Hunan University of Technology Zhuzhou 412008 China

This paper presented an entropy evaluation method for the influences of condense heat recovery system on the *** at the damage of the condense heat to the environment,an entropy of resource loss and an emission entropy from the condense heat recovery system in the air conditioning refrigerating machine were *** the evaluation of the entropies,we developed a new algorithm for the parameter identification,called the composite influence coefficient,based on the Least Squares Support Vector Machine *** simulation,the numerical experiments shows that the Least Squares Support Vector Machine method is one of the powerful methods for the parameter identification to compute the damage entropy of the condense heat,with the largest training error being-0.02.(the relative error being-3.56%),and the biggest test error being 0.015(the relative error being 2.5%).

关键词： air-conditioning refrigerating machine condense heat entropy evaluation LS-SVM

Universal approximation of polygonal fuzzy neural networks in sense of K-integral norms

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Science china(Information sciences) 2011年第11期54卷 2307-2323页

作者： WANG GuiJun 1 & LI XiaoPing 2.1 school of Mathematics Science,Tianjin normal {2.,Tianjin 300387,china 2.school of Management,Tianjin normal {2.,Tianjin 300387,china 1. school of Mathematics Science Tianjin Normal University Tianjin 300387 China2. School of Management Tianjin Normal University Tianjin 300387 China

In this paper,we introduce polygonal fuzzy numbers to overcome the operational complexity of ordinary fuzzy numbers,and obtain two important inequalities by taking advantage of their fine *** presenting an actual example,we demonstrate that the approximation capability of polygonal fuzzy numbers is ***,the concepts of K-quasi-additive integrals and K-integral norms are *** the polygonal fuzzy numbers space satisfies separability,the density problems for several functions spaces can be studied,by means of fuzzy-valued simple functions and fuzzy-valued Bernstein *** establish that the class of the integrally-bounded fuzzy-valued functions spans a complete and separable metric space in the K-integral ***,in the sense of K-integral norms,the universal approximation of fourlayer regular polygonal fuzzy neural networks for fuzzy-valued simple functions is ***,we show that this type of networks also possesses universal approximation for the class of integrally-bounded fuzzyvalued *** result indicates that the approximation capability which regular polygonal fuzzy neural networks for continuous fuzzy systems can be extended as for general integrable systems.

关键词： polygonal fuzzy numbers K-quasi-additive integrals K-integral norms polygonal fuzzy neural networks universal approximations

On the local wellposedness of 3-D water wave problem with vorticity

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Science china Mathematics 2007年第8期50卷 1065-1077页

作者： Ping ZHANG~1 Zhi-fei ZHANG~2.1 Academy of Mathematics and Systems Science,Chinese Academy of sciences,Beijing 100080,china {2.,Peking university,Beijing 100871,china Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China school of mathematical {2. Peking University Beijing 100871 China

In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption that $\frac{{\partial p}}{{\partial n}}(\xi )\left| {_{t = 0} } \right. \leqslant - 2._0 < 0$ being restricted to the initial surface.

关键词： water-waves free boundary incompressible Euler equations primary 35Q35 76B03 secondary 35J67 35L80

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 2.2. of mathematical sciences, Peking university, Beijing 100871, china 1. Department of Mathematics Hubei University Wuhan 430062 China2. School of Mathematical Sciences Peking University Beijing 100871 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

Effects of salinity on methane gas hydrate system

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Science china Earth sciences 2007年第11期50卷 1733-1745页

作者： YANG DingHui1 & XU WenYue2.1 Department of mathematical sciences, Tsinghua {2., Beijing 100084, china 2.school of Earth & Atmospheric sciences, Georgia Institute of Technology, Atlanta, GA 30332. USA 1. Department of mathematical sciences Tsinghua University Beijing 100084 China 2. school of Earth & Atmospheric sciences Georgia Institute of Technology Atlanta GA 30332 USA

Using an approximately analytical formation, we extend the steady state model of the pure methane hydrate system to include the salinity based on the dynamic model of the methane hydrate system. The top and bottom boundaries of the methane hydrate stability zone (MHSZ) and the actual methane hy-drate zone (MHZ), and the top of free gas occurrence are determined by using numerical methods and the new steady state model developed in this paper. Numerical results show that the MHZ thickness becomes thinner with increasing the salinity, and the stability is lowered and the base of the MHSZ is shifted toward the seafloor in the presence of salts. As a result, the thickness of actual hydrate occur-rence becomes thinner compared with that of the pure water case. On the other hand, since lower solubility reduces the amount of gas needed to form methane hydrate, the existence of salts in sea-water can actually promote methane gas hydrate formation in the hydrate stability zone. Numerical modeling also demonstrates that for the salt-water case the presence of methane within the field of methane hydrate stability is not sufficient to ensure the occurrence of gas hydrate, which can only form when the methane concentration dissolved in solution with salts exceeds the local methane solubility in salt water and if the methane flux exceeds a critical value corresponding to the rate of diffusive methane transport. In order to maintain gas hydrate or to form methane gas hydrate in marine sedi-ments, a persistent supplied methane probably from biogenic or thermogenic processes, is required to overcome losses due to diffusion and advection.

关键词： methane gas hydrate,solubility,stability of hydrate,salinity,phase equilibrium