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| 1 | Characterization for commutators of n-dimensional fractional Hardy operators显示文摘In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 < p1 <∞, 0 ≤β< n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained. | Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China ~2 Department of Mathematics,Linyi Normal University,Linyi 276005,China ~3 Department of Mathematics,China University of Mining and Technology (Beijing),Beijing 100083,China | 2007 | Science China Mathematics2007，50，10： | 39 |
| 2 | Transition prediction of a hypersonic boundary layer over a cone at small angle of attack——with the improvement of e^N method显示文摘The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5o,and the angle of attack is 1o. The conventional eN method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the eN method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS. | SU CaiHong1 & ZHOU Heng1,2 1 Department of Mechanics, Tianjin University, Tianjin 300072, China 2 Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, China | 2009 | Science China(Physics,Mechanics & Astronomy)2009，52，1： | 26 |
| 3 | The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode显示文摘Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition. | HUANG Zhangfeng 1, CAO Wei 1,2 & ZHOU Heng 1,2 1. Department of Mechanics, Tianjin University, Tianjin 300072, China 2. Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, China | 2005 | Science China(Physics,Mechanics & Astronomy)2005，48，5： | 23 |
| 4 | Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree显示文摘In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree. | HUANG HuiLin~1 YANG WeiGuo~(2+) 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China 2 Faculty of Science,Jiangsu University,Zhenjiang 212013,China | 2008 | Science China Mathematics2008，51，2： | 23 |
| 5 | A three level linearized compact difference scheme for the Cahn-Hilliard equation显示文摘This article is devoted to the study of high order accuracy difference methods for the Cahn-Hilliard equation.A three level linearized compact difference scheme is derived.The unique solvability and unconditional convergence of the difference solution are proved.The convergence order is O(τ 2 + h 4 ) in the maximum norm.The mass conservation and the non-increase of the total energy are also verified.Some numerical examples are given to demonstrate the theoretical results. | LI Juan 1,2 ,SUN ZhiZhong 1,& ZHAO Xuan 1 1 Department of Mathematics,Southeast University,Nanjing 210096,China 2 Yingtian College,Nanjing 210046,China | 2012 | Science China Mathematics2012，55，4： | 22 |
| 6 | On coeffcient estimates for a class of holomorphic mappings显示文摘Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results. | XU QingHua1 & LIU TaiShun2 1 College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330027, China 2 Department of Mathematics, Huzhou Teacher’s College, Huzhou 313000, China | 2009 | Science China Mathematics2009，52，4： | 18 |
| 7 | Geometric construction of energy-minimizing Bézier curves显示文摘Modeling energy-minimizing curves have many applications and are a basic problem of Geometric Modeling.In this paper,we propose the method for geometric design of energy-minimizing B′ezier curves.Firstly,the necessary and sufficient condition on the control points for B′ezier curves to have minimal internal energy is derived.Based on this condition,we propose the geometric constructions of three kinds of B′ezier curves with minimal internal energy including stretch energy,strain energy and jerk energy.Given some control points,the other control points can be determined as the linear combination of the given control points.We compare the three kinds of energy-minimizing B′ezier curves via curvature combs and curvature plots,and present the collinear properties of quartic energy-minimizing B′ezier curves.We also compare the proposed method with previous methods on efficiency and accuracy.Finally,several applications of the curve generation technique,such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed. | XU Gang 1,4,5,WANG GuoZhao 2 & CHEN WenYu 2,3 1 Institute of Graphics and Image,Hangzhou Dianzi University,Hangzhou 310018,China 2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 3 School of Computer Engineering,Nanyang Technological University,639798,Singapore 4 Galaad,INRIA Sophia-Antipolis,2004 Route des Lucioles,06902,France 5 State Key Lab of CAD & CG,Zhejiang University,Hangzhou 310027,China | 2011 | Science China(Information Sciences)2011，54，7： | 15 |
| 8 | Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation显示文摘Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision. | CHEN LiQun1,2 & DING Hu2 1 Department of Mechanics, Shanghai University, Shanghai 200444, China 2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200070, China | 2008 | Science China(Physics,Mechanics & Astronomy)2008，51，11： | 15 |
| 9 | Empirical likelihood confidence regions of the parameters in a partially linear single-index model显示文摘In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method. | XUE Liugen~1 & ZHU Lixing~2 1. College of Applied Sciences,Beijing University of Technology,Beijing 100022,China 2. Department of Mathematics,Hong Kong Baptist University,Hong Kong,China | 2005 | Science China Mathematics2005，48，10： | 13 |
| 10 | A blow-up criterion for classical solutions to the compressible Navier-Stokes equations显示文摘In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, the initial vacuum is allowed in our case. | HUANG XiangDi 1 & XIN ZhouPing 2, 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 2 Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China | 2010 | Science China Mathematics2010，53，3： | 13 |
| 11 | An unconstrained optimization method using nonmonotone second order Goldstein's line search显示文摘In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed. By using the negative curvature information from the Hessian,the sequence generated is shown to converge to a stationary point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency of our new method. | Wen-yu SUN~(1+) Qun-yan ZHOU~(1,2) ~1 School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China ~2 Department of Basic Courses,Jiangsu Teachers University of Technology,Changzhou 213001,China | 2007 | Science China Mathematics2007，50，10： | 12 |
| 12 | Semigroup Method for a Mathematical Model in Reliability Analysis显示文摘The system which consists of a reliable machine, an unreliable machine and a storage buffer with infinite many workpieces has been studied. The existence of a unique positive time-dependent solution of the model corresponding to the system has been obtained by using C 0-semigroup theory of linear operators in functional analysis. | Geni Gupur 1,3 , LI Xue-zhi 2,3 1.Department of Mathematics, Xinjiang University, Urumqi 830046,China2. Department of Mathematics, Xinyang Teachers College, Henan 464000, China3. Academy of Mathematics and System Sciences, Chinese Academy of Sci | 2001 | Journal of Systems Science and Systems Engineering2001，13，2： | 12 |
| 13 | Eigenvalue approximation from below using non-conforming finite elements显示文摘This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems. | YANG YiDu 1 ,ZHANG ZhiMin 2 & LIN FuBiao 11 School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China 2 Department of Mathematics,Wayne State University,Detroit,MI 48202,USA | 2010 | Science China Mathematics2010，53，1： | 12 |
| 14 | 2-Cocycles of original deformative Schrdinger-Virasoro algebras显示文摘Both original and twisted Schrdinger-Virasoro algebras, and also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim at determining the 2-cocycles of original deformative Schrdinger-Virasoro algebras. | LI JunBo1, 2 , SU YuCai3 & ZHU LinSheng21 Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China 2 Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China 3 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China | 2008 | Science China Mathematics2008，51，11： | 12 |
| 15 | Smoothness for the collision local times of bifractional Brownian motions显示文摘Let BHi,Ki={BtHi,Ki,t≥0},i=1,2 be two independent bifractional Brownian motions with respective indices H i ∈(0,1) and K i ∈(0,1].One of the main motivations of this paper is to investigate the smoothness of the collision local time,introduced by Jiang and Wang in 2009,lT = integral(δ(BsH1,K1-BsH2,K2)ds) from n=0 to T,T > 0,where δ denotes the Dirac delta function.By an elementary method,we show that T is smooth in the sense of the Meyer-Watanabe if and only if min{H1K1,H2K2} <1/3. | SHEN GuangJun 1,2,& YAN LiTan 3 1 Department of Mathematics,East China University of Science and Technology,Shanghai 200237,China 2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China 3 Department of Mathematics,Donghua University,Shanghai 201620,China | 2011 | Science China Mathematics2011，54，9： | 12 |
| 16 | Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries显示文摘This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented. | Ling-hua KONG~(1+) Ming-xin WANG~(2,3) 1 Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China 2 Department of Mathematics,Southeast University,Nanjing 210018,China 3 Department of Mathematics,Xuzhou Normal University,Xuzhou 221116,China | 2007 | Science China Mathematics2007，50，9： | 11 |
| 17 | Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices显示文摘We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results. | FU JingLi1, CHEN LiQun2 & CHEN BenYong3 1 Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China 2 Department of Mechanics, Shanghai University, Shanghai 200072, China 3 Faculty of Mechanical-Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China | 2010 | Science China(Physics,Mechanics & Astronomy)2010，53，3： | 11 |
| 18 | The attractor of the stochastic generalized Ginzburg-Landau equation显示文摘The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H01. | GUO BoLing~1 WANG GuoLian~(2+) Li DongLong~3 1 Institute of Applied Physics and Computational Mathematics,P.O.Box 8009,Beijing 100088,China 2 The Graduate School of China Academy of Engineering Physics,P.O.Box 2101,Beijing 100088,China 3 Department of Information and Computer Science,Guangxi University of Technology,Liuzhou 545006,China | 2008 | Science China Mathematics2008，51，5： | 11 |
| 19 | Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets显示文摘This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and proves that D and E areLipschitz equivalent if and only if there are positive integers m and n such that rm1= rn3. | Li-feng XI~(1+) Huo-jun RUAN~2 1 Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China 2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China | 2007 | Science China Mathematics2007，50，11： | 11 |
| 20 | Extension of isometries on the unit sphere of l^p (Γ) space显示文摘In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley's problem. | FANG XiNian 1,& WANG JianHua 2 1 School of Mathematics and Statistics,Nanjing Audit University,Nanjing 210029,China 2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China | 2010 | Science China Mathematics2010，53，4： | 10 |
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