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| 1 | Existence of periodic and subharmonic solutions for second-order superlinear difference equations显示文摘By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations △2xn-1 + f(n,xn) = 0,some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z. | 郭志明 庾建设 | 2003 | Science China Mathematics2003，46，4： | 51 |
| 2 | Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions显示文摘The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a 'compatibility equation' is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper. | 徐明瑜 谭文长 | 2003 | Science China(Physics,Mechanics & Astronomy)2003，46，2： | 25 |
| 3 | Lie bialgebras of generalized Witt type显示文摘In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W (x) W) is trivial. | SONG Guang’ai & SU Yucai College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China | 2006 | Science China Mathematics2006，49，4： | 22 |
| 4 | Concatenating construction of the multisymplectic schemes for 2+1-dimensional sine-Gordon equation显示文摘In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes. | WANG Yushun, WANG Bin & QIN MengzhaoLASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China School of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China | 2004 | Science China Mathematics2004，47，1： | 17 |
| 5 | Boundary value problems of discrete generalized Emden-Fowler equation显示文摘By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established. | YU Jianshe GUO Zhiming | 2006 | Science China Mathematics2006，49，10： | 14 |
| 6 | Boundary element-free method for elastodynamics显示文摘The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given. | CHENG Yumin1 & PENG Miaojuan2 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China 2. Department of Civil Engineering, Shanghai University, Shanghai 200072, China | 2005 | Science China(Physics,Mechanics & Astronomy)2005，48，6： | 12 |
| 7 | Thermal decomposition kinetics of titanium hydride and Al alloy melt foaming process显示文摘A temperature programmed decomposition (TPD) apparatus with metal tube struc- ture, in which Ar is used as the carrier gas, is established and the TPD spectrum of titanium hy- dride is acquired. Using consulting table method (CTM), spectrum superposition method (SSM) and differential spectrum technique, TPD spectrum of titanium hydride is separated and a set of thermal decomposition kinetics equations are acquired. According to these equations, the rela- tionship between decomposition quantity and time for titanium hydride at the temperature of 940 K is obtained and the result well coincides with the Al alloy melt foaming process. | YANG Donghui*1, HE Deping*1& YANG Shangrun*2 1. Department of Materials Science and Engineering, Southeast University, Nanjing 210096, China 2. Department of Chemistry, Nanjing University, Nanjing 210093, China | 2004 | Science China Chemistry2004，47，6： | 12 |
| 8 | New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ显示文摘An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations. | YAN Zhen-Ya | 2002 | Communications in Theoretical Physics2002，，8： | 9 |
| 9 | New direction of computational fluid dynamics and its applications in industry显示文摘For the past ten years there has been much progress in computational fluid dy- namics (CFD), among which the formation and development of the lattice Boltz- mann method (LBM) are an important new direction. We give a review on the main aspect and the latest development of this method in this article, and at the same time we also discuss the related development of scientific software and its impact on the real-world applications in industry. | CHEN YaoSong1, SHAN XiaoWen2 & CHEN HuDong2 1 Department of Mechanics, Peking University, Beijing 100871, China 2 Exa Corporation, Burlington, MA 01803 USA | 2007 | Science China(Technological Sciences)2007，50，5： | 8 |
| 10 | Monotone method for initial value problem for fractional diffusion equation显示文摘Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation. | ZHANG Shuqin | 2006 | Science China Mathematics2006，49，9： | 7 |
| 11 | Multiplier ideal sheaves in complex and algebraic geometry显示文摘The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed. | Yum-Tong Siu | 2005 | Science China Mathematics2005，48，z1： | 7 |
| 12 | How does innovation's tail risk determine marginal tail risk of a stationary financial time series?显示文摘We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance. | YU Bosco W. T. PANG W. K. | 2004 | Science China Mathematics2004，47，3： | 7 |
| 13 | Large range step method for acoustic waveguide with two layer media显示文摘A numerical method is developed for solving the two-dimensional Helmholtz equation in a two-layer region bounded by a flat top, a flat bottom and a curved interface. A better local orthogonal transformation is used to flatten the curved interface of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implemetation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. | ZHU Jianxin and LU Yayan(1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China 2. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China) | 2002 | Progress in Natural Science:Materials International2002，12，11： | 7 |
| 14 | Limit theorem and uniqueness theorem of backward stochastic differential equations显示文摘This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0)≡0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation εg; this paper also proves that if a filtration consistent expectation ε can be represented as a g-expectation εg, then the corresponding generator g must be unique. | JIANG Long Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China Institute of Mathematics, Fudan University, Shanghai 200433, China School of Mathematics and System Sciences, Shandong University, Jinan 250100, China | 2006 | Science China Mathematics2006，49，10： | 6 |
| 15 | On a nonlinear elliptic problem with critical potential in R^2显示文摘Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexistence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem. | SHEN Yaotian YAO Yangxin HEN Zhihui | 2004 | Science China Mathematics2004，47，5： | 6 |
| 16 | Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation显示文摘The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS. | LI Zhihui1,2, ZHANG Hanxin1 & FU Song2 ⒈ National Laboratory for CFD, Hypervelocity Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China 2.Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China | 2005 | Science China(Physics,Mechanics & Astronomy)2005，48，4： | 6 |
| 17 | Entropy equilibrium equation and dynamic entropy production in environment liquid显示文摘The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications. | HU Yinqiao(Cold and Arid Regions Environment and Engineering Institute, Chinese Academy of Sciences, Lanzhou 730000, China) | 2002 | Progress in Natural Science:Materials International2002，12，3： | 5 |
| 18 | Research on the method for retrieving soil moisture using thermal inertia model显示文摘In order to improve accuracy of soil moisture inversion using remote sensing, a new thermal inertia model is proposed in this paper. The improved model needs only surface maximum temperature as the temperature parameter input instead of input of the surface temperature difference, as well as the surface sensible and latent fluxes are introduced into boundary conditions of thermal conductivity equation. Furthermore, surface soil conductive heat transfer equation of two-layer model is used to solve the soil thermal inertia so that the remote sensing thermal inertia method can be ap- plied to regions with better-covered vegetation, but usually only for the bare areas or worse vegetation covered areas. The model has been tested at several locations in the area of west Inner Mongolia. Comparing the simulation of the new model with the measurements obtained by apparent thermal inertia and by field test, the result shows that the inertia thermal model can be used to estimate soil moisture in more reasonable accuracy. | LIU Zhenhua1 & ZHAO Yingshi2 1. Information College, South China Agricultural University, Guangzhou 510642, China 2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China | 2006 | Science China Earth Sciences2006，49，5： | 5 |
| 19 | Abundant Multisoliton Structures of the Generalized Nizhnik-Novikov-Veselov Equation显示文摘Using the extended homogenous balance method, we obtainabundant exact solution structures ofa (2+1)dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order termanalysis, the nonlinear transformations of generalized Nizhnik-Novikov-Veselov equation are given first, and then somespecial types of single solitary wave solution and the multisoliton solutions are constructed. | ZHANG Jie-Fang CHEN Feng-Juan | 2002 | Communications in Theoretical Physics2002，，10： | 4 |
| 20 | A distributed hydrological model with its application to the Jinghe watershed in the Yellow River Basin显示文摘For the purpose of water resources management in the Yellow River Basin with highly spatial difference, a daily distributed hydrological model was proposed, of which the determination of spatially-distributed parameters and model inputs processing were performed by means of GIS/RS. In the model, the computation of runoff yield was based on the topography index method and flow routing was modeled by Maskingum method. The operation of the model is followed by means of “command structure” technique based upon the topography of river network. A case study using the model was conducted for the Jinghe watershed, which locates at the middle Yellow River Basin. The simulation of the hydrological processes in 1996 has shown that water quantity balance errors were less than 5% and the Nash-Sutcliffe coefficient arrived at 0.7, indicating that the model structure is justifiable, and the precision of the model can satisfy the purpose of water resources management. | WANG Zhonggen1, ZHENG Hongxing1, LIU Changming1, , WU Xianfeng2 2 & ZHAO Weimin3 1. Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Science and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China 2. Institute of Environmental Science, Beijing Normal University, Beijing 100875, China 3. Water Resources Conservation Committee of Yellow River, Zhengzhou 450003, China | 2004 | Science China(Technological Sciences)2004，47，z1： | 4 |
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