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| 1 | A CLASS OF NONLOCAL BOUNDARY VALUE PROBLEMS OF NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS显示文摘The nonlocal boundary value problems for nonlinear elliptic systems in the unbounded domain are considered. Under suitable conditions the existence of solution and comparison theorem for the boundary value problems are studied. | 莫嘉琪 欧阳成 | 2001 | Acta Mathematica Scientia2001，21，1： | 64 |
| 2 | Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations显示文摘This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems. | PENG ShiGe Institute of Mathematics,Shandong University,Jinan 250100,China | 2009 | Science China Mathematics2009，52，7： | 54 |
| 3 | ON THE EXISTENCE OF POSITIVE SOLUTIONS TO SECOND ORDER PERIODIC BVPS显示文摘The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u’(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u’(0) = u’(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii. | 蒋达清 | 1998 | Acta Mathematica Scientia1998，18，S1： | 28 |
| 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 | Rank theorems of operators between Banach spaces显示文摘Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis. | MA JipuDepartment of Mathematics, Nanjing University, Nanjing 210093, China | 2000 | Science China Mathematics2000，43，1： | 22 |
| 6 | Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds显示文摘Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds. | 马吉溥 | 2000 | Science China Mathematics2000，43，12： | 23 |
| 7 | An Application of a Mountain Pass Theorem | ZHOU Huan Song Laboratory of Mathematical Physics. Wuhan Institute of Physics and Mathematics. Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071. P. R. China | 2002 | Acta Mathematica Sinica,English Series2002，18，1： | 18 |
| 8 | Theory of truth degrees of propositions in two-valued logic显示文摘By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic. | 王国俊 傅丽 宋建社 | 2002 | Science China Mathematics2002，45，9： | 18 |
| 9 | Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces显示文摘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 | LI Gang and MA Jipu1. Department of Mathematics, Yangzhou Normal College, Yangzhou 225002, China 2. Department of Mathematics, Nanjing University, Nanjing 210093, China | 1997 | Chinese Science Bulletin1997，42，1： | 16 |
| 10 | A general central limit theorem under sublinear expectations显示文摘Under some weaker conditions,we give a central limit theorem under sublinear expectations,which extends Peng's central limit theorem. | LI Min & SHI YuFeng School of Mathematics,Shandong University,Jinan 250100,China | 2010 | Science China Mathematics2010，53，8： | 15 |
| 11 | Lattice-Valued Proposition Logic(Ⅱ)显示文摘Lattice-ValuedPropositionLogic(Ⅱ)QinKeyun;XuYang(Dept.ofAppl.Mathematics,SouthwestJiaotongUniversity)Chengdu610031,ChinaLatti... | Qin Keyun Xu Yang( Dept. of Appl. Mathematics, Southwest Jiaotong University)Chengdu 610031,China | 1994 | Journal of Modern Transportation1994，11，1： | 13 |
| 12 | Growth theorem of convex mappings on bounded convex circular domains显示文摘The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex. | 刘太顺 任广斌 | 1998 | Science China Mathematics1998，41，2： | 13 |
| 13 | KKM TYPE THEOREMS AND COINCIDENCE THEOREMS ON L-CONVEX SPACES显示文摘Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature. | 丁协平 | 2002 | Acta Mathematica Scientia2002，22，3： | 13 |
| 14 | A view on big data and its relation to Informetrics显示文摘Purpose:Big data offer a huge challenge.Their very existence leads to the contradiction that the more data we have the less accessible they become,as the particular piece of information one is searching for may be buried among terabytes of other data.In this contribution we discuss the origin of big data and point to three challenges when big data arise:Data storage,data processing and generating insights.Design/methodology/approach:Computer-related challenges can be expressed by the CAP theorem which states that it is only possible to simultaneously provide any two of the three following properties in distributed applications:Consistency(C),availability(A)and partition tolerance(P).As an aside we mention Amdahl’s law and its application for scientific collaboration.We further discuss data mining in large databases and knowledge representation for handling the results of data mining exercises.We further offer a short informetric study of the field of big data,and point to the ethical dimension of the big data phenomenon.Findings:There still are serious problems to overcome before the field of big data can deliver on its promises.Implications and limitations:This contribution offers a personal view,focusing on the information science aspects,but much more can be said about software aspects.Originality/value:We express the hope that the information scientists,including librarians,will be able to play their full role within the knowledge discovery,data mining and big data communities,leading to exciting developments,the reduction of scientific bottlenecks and really innovative applications. | Ronald ROUSSEAU | 2012 | Chinese Journal of Library and Information Science2012，，3： | 13 |
| 15 | Age-dependent branching processes in random environments显示文摘We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R+, and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. | LI YingQiu LIU QuanSheng | 2008 | Science China Mathematics2008，51，10： | 12 |
| 16 | A class of strong deviation theorems and an approach of Laplace transformation显示文摘The limit properties of the dependent sequence of absolutely continuous random variables are investigated by using the notion of likelihood ratio, and a class of strong limit theorems, represented by inequalities, i.e. the strong deviation theorems, are obtained. In the proof an approach of applying the Laplace transformation to the investigation of the strong limit theorems is proposed. | LIU Wen Hebei University of Technology, Tianjin 300130, China | 1998 | Chinese Science Bulletin1998，43，19： | 12 |
| 17 | MULTIPLE POSITIVE SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER ODES显示文摘This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0. | 蒋达清 | 2002 | Acta Mathematica Scientia2002，22，2： | 11 |
| 18 | The multi-dimension RSA and its low exponent security显示文摘Using a well-known result of polynomial over the finite field , we show that the Euler-Fermat theorem holds in N[ x]. We present a multi-dimension RSA cryptosystem and point out that low exponent algorithm of attacking RSA is not suitable for the multi-dimension RSA. Therefore, it is believed that the security of the new cryptosystem is mainly based on the factorization of large integers. | 曹珍富 | 2000 | Science China(Technological Sciences)2000，43，4： | 10 |
| 19 | Theory of Σ-(α-tautologies) in revised Kleene systems显示文摘That there are only three different kinds of α_ tautologies in revised Kleene systems is proved first; then in finite case the diversity theorem of α_ tautologies with α’ s larger than the mid_value is established. Lastly, also in finite case, a representation theorem of α_ tautologies by means of tautologies is given. | 王国俊 | 1998 | Science China(Technological Sciences)1998，41，2： | 9 |
| 20 | Singular values, quasiconformal maps and the Schottky upper bound显示文摘Some properties and asymptotically sharp bounds are obtained for singular values of Ramanujan’s generalized modular equation, from which infinite_product representations of the Hersch_Pfluger φ distortion function φ K(r) and the Agard η distortion function η K(t) follow. By these results, the explicit quasiconformal Schwarz lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ(K) is proved to be true. | 裘松良 | 1998 | Science China Mathematics1998，41，12： | 9 |
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