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The maximal super-singular integral operators on product spaces

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Science China mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2.3. 1department of {2., Xidian University, Xi’an 710071, China 2.1} of {2., Zhejiang Normal University, Jinhua 3.1004, China 3.0} of {2., Zhejiang University, Hangzhou 3.002., China 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2.0｜∫｜u｜〉ε1,｜v｜〉ε2.b1（｜u｜）b2.｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2.∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

Gas Turbulence Modulation Model for Gas-Solid Flows in Two-Fluid Approach

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Journal of Shanghai Jiaotong university(Science) 2010年第4期15卷 428-433页

作者：曾卓雄潘阳周力行 Aircraft Engineering College Nanchang Hangkong University School of Civil Engineering and Architecture East China Jiaotong University department of Engineering Mechanics Tsinghua University

Turbulence enhancement by particle wake effect is studied by numerical simulation of gas turbulent flows passing over particle under various particle sizes, inlet gas velocities, gas viscosity, gas density and the distance of particles. By performing dimension analysis and using the form of gas-particle interaction source term for reference, a new semi-empirical turbulence enhancement model by the particle-wake effect is proposed. The turbulence model is then incorporated into second-order moment model for simulating gas-particle flows in a horizontal channel with different wall roughness and a sudden-expansion chamber. The results show that this model is with higher calculating accuracy than another two turbulence models in comparison with the experimental results.

关键词： gas-particle flows turbulence modulation particle wake effect

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science China Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. department of mathematics, Beijing Normal University, Beijing 100875, China 2. Institute of Applied Physics and Computational mathematics, Beijing 100080, China 1. department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Algorithm of graph isomorphism with threedimensional DNA graph structures

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Progress in Natural Science:Materials International 2005年第2期15卷 86-89页

作者： LIU Guangwu 1,2., YIN Zhixiang 1,3. XU Jin1 and DONG Yafei1(1. department of Control Science and Engineering, Hua Zhong University of Science and Technology, Wuhan 43.074, China 2. College of Transportation, Wuhan University of Technology, Wuhan 43.063. China 3. department of mathematics and Physics, Anhui University of Science and Technology, Huainan 2.0}001, China) department of Control Science and Engineering Hua Zhong University of Science and Technology Wuhan 430074 China. College of Transportation Wuhan University of Technology Wuhan 430063 China. department of mathematics and Physics Anhui University of Science and Technology Huainan 232001 China

An algorithm for solving the graph isomorphism problem with 3.D DNA structures is proposed in this paper. The k-armed branched junction molecules are used to code k-degree vertices. Double stranded molecules are used to code edges. Then the molecules are mixed in a tube to be ligated. The result can be detected by gel electrophoresis. The time complexity of the algorithm is O(n2., where n is the number of vertices of the graph.

关键词： DNA computing DNA graph structure graph isomorphism

Non-isothermal Melt Crystallization Kinetics of Anhydrite-Filled Polypropylene Composites

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Journal of Wuhan University of Technology(Materials Science) 2010年第1期25卷 12-19页

作者：王少会 department of Chemistry and Chemical Engineering East China JiaoTong University

The non-isothermal crystallization kinetics of polypropylene （PP）, PP/anhydrite composites were investigated by differential scanning calorimetry （DSC） with various cooling rates. The Avrami analysis modified by Jeziorny and a method developed by Mo were employed to describe the non-isothermal crystallization process of these samples. The difference in the exponent n between PP and PP/anhydrite composites indicated that non-isothermal kinetic crystallization corresponded to tri-dimensional growth with heterogeneous nucleation. The values of half-time, Zc and F（T） showed that the crystallization rate increased with the increasing of cooling rates for PP and PP/anhydrite composites, but the crystallization rate of PP/anhydrite composites was faster than that of PP at a given cooling rate. The method developed by Ozawa did not describe the non-isothermal crystallization process of PP very well. Moreover, the method proposed by Kissinger was used to evaluate the activation energy of the mentioned samples. The result showed that the activation energy of PP/anhydrite was greatly larger than that of PP.

关键词： polypropylene anhydrite composites non-isothermal crystallization kinetics

Simultaneously inducing synthesis of semiconductor selenium multi-armed nanorods and nanobars through bio-membrane bi-templates

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Science China Chemistry 2004年第6期47卷 507-511页

作者： LI Li1, WU Qingsheng1 DING Yaping2.& LI Ping3.1. department of Chemistry, Tongji University, Shanghai 2.0092. China 2. department of Chemistry, Shanghai University, Shanghai 2.043., China 3. department of Food, Anhui Agricultural University, Hefei 2.0}03., China 1. department of Chemistry Tongji University 200092 Shanghai China 2. department of Chemistry Shanghai University 200436 Shanghai China 3. department of Food Anhui Agricultural University 230036 Hefei China

Multi-armed nanorods and nanobars of semiconductor selenium were simultane- ously synthesized in the light of biomineralization process through bio-membrane bi-templates of rush at room temperature. The multi-armed nanorods are 60 nm in diameter and 1.5 μm in length; the nanobars are 150 nm in diameter and 1000—1100 nm in length. The XRD pattern indicates that these nanocrystals were crystallized in the hexagonal structure with lattice constants a = 0.43. nm, c = 0.495 nm. The possible formation mechanism was investigated.

关键词： selenium, multi-armed nanorods, nanobars, bio-membrane, bi-templates.

Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

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Chinese Science Bulletin 1997年第1期42卷 8-11页

作者： LI Gang and MA Jipu1. department of mathematics, Yangzhou Normal College, Yangzhou 2.5002. China 2. department of mathematics, Nanjing University, Nanjing 2.0093. China department of mathematics Yangzhou Normal College Yangzhou China department of mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-Lipschitzian mapping.

A low frequency piezoelectric power harvester using a spiral-shaped bimorph

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Science China(Physics,Mechanics & Astronomy) 2006年第6期49卷 649-659页

作者： HU Yuantai1,2.HU Hongping2.& YANG Jiashi3.1. Institute of Mechanics and Sensing Technology,Central South University,Changsha 410083.China 2. {2. of Mechanics,Huazhong University of Science and Technology,Wuhan 43.074,China 3. {2. of Engineering Mechanics,University of Nebraska,Lincoln,NE 68588-052.,USA 1. Institute of Mechanics and Sensing Technology Central South University Changsha 410083 China 2. department of Mechanics Huazhong University of Science and Technology Wuhan 430074 China 3. department of Engineering Mechanics University of Nebraska Lincoln NE 68588-0526 USA

We propose a spiral-shaped piezoelectric bimorph power harvester operating with coupled flexural and extensional vibration modes for applications to low frequency energy sources. A theoretical analysis is performed and the computational results show that the spiral structure has relatively low operating frequency compared to beam power harvesters of the same size. It is found that to optimize the performance of a piezoelectric spiral-shaped harvester careful design is needed.

关键词： spiral-shaped bimorph,piezoelectric harvester,power density.

Algorithms for computing the global infimum and minimum of a polynomial function

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Science China mathematics 2012年第4期 875-885页

作者： XIAO ShuiJing & ZENG GuangXing department of mathematics,{2. University,{2. 3.003.,China

By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial *** a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is *** the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval *** usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is *** the design of our algorithm,Wu’s well-known method plays an important role.

关键词： polynomial optimization global infimum global minimum strictly critical point Transfer prin- ciple Wu’s method rational univariate representation