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| 1 | On adjacent-vertex-distinguishing total coloring of graphs显示文摘In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree. | ZHANG Zhongfu, CHEN Xiang’en, LI Jingwen, YAO Bing, LU Xinzhong & WANG Jianfang College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China Department of Computer, Lanzhou Normal College, Lanzhou 730070, China Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China College of Information and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China | 2005 | Science China Mathematics2005，48，3： | 173 |
| 2 | Design of a new dynamical core for global atmospheric models based on some efficient numerical methods显示文摘A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme todesign the global adiabatic model of atmospheric dynamics ispresented. This scheme includes a method of weighted equal-areamesh and a fully discrete finite difference method with quadraticand linear conservations for solving the primitive equationsystem. Using this scheme, we established a new dynamical corewith adjustable high resolution acceptable to the availablecomputer capability, which can be very stable without anyfiltering and smoothing. Especially, some important integralproperties are kept unchanged, such as the anti-symmetries of thehorizontal advection operators and the vertical convectionoperator, the mass conservation, the effective energy conservationunder the standard stratification approximation, and so on. Somenumerical tests on the new dynamical core, respectively regardingits global conservations and its integrated performances inclimatic modeling, incorporated with the physical packagesfrom the Community Atmospheric Model Version 2 (CAM2) of NationalCenter for Atmospheric Research (NCAR), are included. | WANG Bin, WAN Hui, Jl Zhongzhen, ZHANG Xin, YU Rucong, YU Yongqiang & LIU HongtaoState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China Department of Computational Mathematics, Academy of Mathematics and System Sciences, Peking University, Beijing 100871, China | 2004 | Science China Mathematics2004，47，z1： | 92 |
| 3 | SINGULAR PERTURBATION FOR A CLASS OF NONLINEAR REACTION DIFFUSION SYSTEMS显示文摘This paper deals with the initial-bounndary value problem for the wider nonlinear reaction diffusion system: where Leading into the variables of multiple scales, we obtained a uniformly valid asymptotic solution to any degree of precision by using comparison theorem. | 莫嘉琪 | 1989 | Science China Mathematics1989，32，11： | 213 |
| 4 | On the adjacent-vertex-strongly-distinguishing total coloring of graphs显示文摘For any vertex u∈V(G), let TN(U)={u}∪{uv|uv∈E(G), v∈v(G)}∪{v∈v(G)|uv∈E(G)}and let f be a total k-coloring of G. The total-color neighbor of a vertex u of G is the color set Cf(u)={f(x)|x∈TN(U)}. For any two adjacent vertices x and y of V(G)such that Cf(x)≠Cf(y), we refer to f as a k-avsdt-coloring of G('avsdt'is the abbreviation of'adjacent-vertex-strongly- distinguishing total'). The avsdt-coloring number of G, denoted by Xast(G), is the minimal number of colors required for a avsdt-coloring of G. In this paper, the avsdt-coloring numbers on some familiar graphs are studied, such as paths, cycles, complete graphs, complete bipartite graphs and so on. We proveΔ(G)+1≤Xast(G)≤Δ(G)+2 for any tree or unique cycle graph G. | ZHANG ZhongFu CHENG Hui YAO Bing LI JingWen CHEN XiangEn XU BaoGen | 2008 | Science China Mathematics2008，51，3： | 74 |
| 5 | The weighted Herz-type Hardy space and its applications显示文摘A certain weighted Herz-type Hardy space is introduced and its atom-decomposition theory is established. As applications of this theory, a boundedness theorem of sublinear operators and an interpolation theorem of linear operators on these spaces are given. | 陆善镇 杨大春 | 1995 | Science China Mathematics1995，38，6： | 69 |
| 6 | D(β)-vertex-distinguishing total coloring of graphs显示文摘A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented. | ZHANG Zhongfu,LI Jingwen,CHEN Xiang’en,YAO Bing, WANG Wenjie & QIU Pengxiang Institute of Applied Mathematic, Lanzhou Jiaotong University, Lanzhou 730070, China College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China College of Information and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China | 2006 | Science China Mathematics2006，49，10： | 54 |
| 7 | 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 |
| 8 | 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 |
| 9 | A CLASS OF SINGULARLY PERTURBEDBOUNDARY VALUE PROBLEMS FOR NONLINEARDIFFERENTIAL SYSTEMS显示文摘The singularly perturbed nonlinear problem εy' = f(x, y’)y + g(x, y’), 0 | MO Jiaqi (Department of Mathematics, Anhui Normal University, Wuhu 241000, China) | 1999 | Systems Science and Mathematical Sciences1999，12，1： | 51 |
| 10 | Weighted composition operators between μ-Bloch spaces on the unit ball显示文摘In this paper, necessary and sufficient conditions are given for the weighted composition operator Tψ,ψ to be bounded or compact from the spaceβμ to βv, (or βμ,o to βv,o) on the unit ball of Cn. At the same time, a series of corollaries are also obtained. | ZHANG Xuejun~1 & XIAO Jianbin~2 1. College of Mathematics and Computer Science,Hunan Normal University,Changsha 410006,China(email:xuejunttt@263. net) 2. The School of Science,Hangzhou Dianzi University,Hangzhou 310037,China | 2005 | Science China Mathematics2005，48，10： | 49 |
| 11 | The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space显示文摘Let E and F be Hilbert spaces with unit spheres S1(E) and S1(F). Suppose that V0 S1(E)→S1(F) is a Lipschitz mapping with Lipschitz constant k=1 such that -V0[S1(E)] V0[S1(E)]. Then V0 can be extended to a real linear isometric mapping V from E into F. In particular, every isometric mapping from S1(E) onto S1(F) can be extended to a real linear isometric mapping from E onto F. | 定光桂 | 2002 | Science China Mathematics2002，45，4： | 48 |
| 12 | Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails显示文摘This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances. | LIU Li School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China | 2010 | Science China Mathematics2010，53，6： | 44 |
| 13 | Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications显示文摘In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables. | YUAN DeMei AN Jun | 2009 | Science China Mathematics2009，52，9： | 50 |
| 14 | Moment inequalities and weak convergence for negatively associated sequences显示文摘A probability inequality for Sn and some pth moment (p≥2) inequalities for | Sn| and max 1≤k≤n |Sk|are established. Here Sn is the partial sum of a negatively associated sequence Based on these inequalities, a weak in variance principle for strictly stationary negatively associated sequences is proved under some general | 苏淳 赵林城 王岳宝 | 1997 | Science China Mathematics1997，40，2： | 44 |
| 15 | The decomposition of weighted Herz space on R^n and its applications显示文摘The decompositional characterizations of the weighted Herz spaces on Rn are established. Using this decomposition, the boundedness on the weighted Herz spaces for a large class of sublinear operators is studied. | 陆善镇 杨大春 | 1995 | Science China Mathematics1995，38，2： | 42 |
| 16 | Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications显示文摘Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite. | ZHANG LiXin | 2016 | Science China Mathematics2016，59，4： | 46 |
| 17 | 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 |
| 18 | NONLINEARIZATION OF THE LAX SYSTEM FOR AKNS HIERARCHY显示文摘The Lax system for the AKNS vector field is nonlinearized and becomes naturally compatible under the constraint induced by a relation (q,r) = f(ψ) between reflectionless potentials and the eigenfunctions of the Zakharov-Shabat eigenvalue problem (ZS). The spatial part (ZS) is nonlinearized as a completely integrable system in the Liouville sense with the Hamiltonian:H = <iZψ1, ψ2> + 1/2<ψ1,ψ1><ψ2,ψ2>in the symplectic manifold (R2N, dψ1(?)dψ2), whose solution variety (?) is an invariant set of the S-flow defined by the nonlinearized time part. Moreover, f maps (?) into the solution variety of a stationary AKNS equation, and maps the S-flow on (?) into the AKNS-flow on f((?)). | 曹策问 | 1990 | Science China Mathematics1990，33，5： | 38 |
| 19 | Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm显示文摘Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances. | ZHANG LiXin | 2016 | Science China Mathematics2016，59，12： | 38 |
| 20 | Classification of hypersurfaces with parallel Mobius second fundamental form in S^(n+1)显示文摘Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form. | HU Zejun LI Haizhong Department of Mathematics, Zhengzhou University Zhengzhou 450052, China Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China | 2004 | Science China Mathematics2004，47，3： | 33 |
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