一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.     

Sign-based Test for Mean Vector in High-dimensional and Sparse Settings

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.     

Multiple Positive Solutions for One Dimensional Third Order p-Laplacian Equations with Integral Boundary Conditions

In this paper,we consider the one dimensional third order p-Laplacian equation■u^′′(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.     

中国数学会举行第十次全国代表大会

中国数学会第十次全国代表大会暨2007学术年会11月2日在北京航空航天大学开幕,这是中国数学会历史上规模最大的一次全国代表大会.教育部副部长吴启迪、中国科协书记处书记冯长根、北京航空航天大学校长李未及中科院、科技部等单位的相关领导、嘉宾出席开幕式.     

Bayesian Approach for Recovering Piecewise Constant Viscoelasticity from MRE Data

This paper deals with an inverse problem for recovering the piecewise constant viscoelasticity of a living body from MRE(Magnetic Resonance Elastography)data.Based on a scalar partial differential equation whose solution can approximately simulate MRE data,our inverse coefficient problem is considered as a statistical inverse problem of reconstructing the posterior distribution of unknown viscoelastic modulus.For sampling this distribution,one usually can use the Metropolis-Hastings Markov chain Monte Carlo(MHMCMC)algorithm.However,without an appropriate"proposal"distribution given artificially,the MH-MCMC algorithm is hard to draw samples efficiently.To avoid this,a so-called slice sampling algorithm is introduced in this paper and applied for solving our problem.The performance of these statistical inversion algorithms is numerically tested basing on simulated data.     

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|²-2uv-τu(|u|²)x=0 vtt+vxx-β(|u|^x)xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

针对一维空间分数阶扩散方程的一个新的最大模近似公式

Based on the maximum principle,the difference formula defined on a non-integral node is given to approximate the fractional Riemann-Liouville derivative and the finite difference scheme for solving one-dimensional space fractional diffusion equations(FDEs) with variable coefficients is presented.Furthermore,using the maximum principle the scheme is proved unconditionally stable and secondorder accuracy in spatial grid size.Several numerical examples are given to verify the efficiency of the scheme.     

可圈的一个充分条件

本文我们证明如下结果:设G=(V,E)是一个n(n≥3)阶k-连通(k≥2)图,记X1,X2,…,Xk为V的子集,X=X1∪X2∪…∪Xk.若对每个I,I=1,2,…,k,满足:对任意的u,v∈Xi,有d(u) d(v)≥n或|N(u)∪N(v)|≥n-δ或|N(u)∩N(v)|≥α,这里δ是G的最小度,α是G的独立数,则G是X-可圈的.     

长圈的邻域交条件的推广

证明了若G为一个k(k≥2)连通简单图,独立数为α,V(G)=n≥3,X1,X2,…,Xk是顶点集合V的子集,X=X1∪X2∪…∪Xk,且对于Xi(i=1,2,…,k)中任意两个不相邻点u,v,|N(u)∩N(v)|≥α,则X在G中可圈,并给出几个相关推论.     

若干并图的优美标号

证明了,对任意大于1的自然数m,n,p,非连通图(■ V ■)∪K_(n,p)是优美图;当k≤p,m=kn+3或m=kn+1时,非连通图(P_2 V ■)∪K_(n,p)是优美图;当p≥2,m=3k+1时,非连通图(P_2 V ■)∪K_(3,p)是优美图;对任意正整数n,p,非连通图(P_1 V P_(2n+2))∪_(n,p)是优美图.     

由n次幂等矩阵确定的交换幺半群

设R是含幺结合环,n≥2为自然数.对所有的k≥1,本文给出了n次幂等矩阵集Pk^n（R）={P｜P^n=P∈Mk（R）}上的一种等价关系,证明了P^n（R）=∪k=1^∞Pk^n（R）中的等价类在给定的加法运算下构成一个交换幺半群.     

有限个互素因子链上幂GCD矩阵与幂LCM矩阵的行列式的整除性

设S={x1,x2,...,xn}是由n个不同的正整数组成的集合,并设a为正整数.如果一个n阶矩阵的第i行j列元素是S中元素xi和xj的最大公因子的a次幂(xi,xj)a,则称该矩阵为定义在S上的a次幂最大公因子(GCD)矩阵,用(Sa)表示;类似定义a次幂LCM矩阵[Sa].如果存在{1,2,...,n}上的一个置换σ使得xσ(1)|xσ(2)|···|xσ(n),则称S为一个因子链.如果存在正整数k,使得S=S1∪S2∪···∪Sk,其中每一个Si(1ik)均为一个因子链,并且对所有的1i=jk,Si中的每个元素与Sj中的每个元素互素,则称S由有限个互素因子链构成.本文中,设S由有限个互素的因子链构成,并且1∈S.我们首先给出幂GCD矩阵与幂LCM矩阵的行列式的公式,然后证明:如果a|b,则det(Sa)|det(Sb),det[Sa]|det[Sb],det(Sa)|det[Sb].最后我们指出:如果构成S的有限个因子链不互素,则此结论一般不成立.     

Cantor集并的自相似性(英文)

本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.     

P_n~k的均匀全染色

设G(V,E)是一个简单图,f是G的一个k-正常全染色,若f满足||Vi∪Ei|-|Vj∪Ej||≤1(i≠j),其中Vi∪Ei={v|f(v)=i}∪{e|f(e)=i},则称f为G的k-均匀全染色,简记为k-ETC.并称eχT(G)=min{k|G存在k-均匀全染色}为G的均匀全染色数.本文将通过很好的全染色方法得到eχT(Pkn)=5(n≥2k+1),并证明了对Pkn,[5]中猜想是正确的.     

若干图的广义Mycielski图的边色数

设图G(V,E)为简单图,V(Mn(G))={v01,v02,…,v0p;v11,v12,…,v1p;…,vn1,vn2,…,vnp}EMn(G))=E(G)∪vijv(i+1)kv0 jv0k∈E(G),1 j,k p,i=0,1,…,n-1称Mn(G)为G的n串广义M ycielsk i图,其中n为自然数,V(G)={v01,v02,…,v0p}.本文得到了路、圈、扇、轮、星图的广义M ycielsk i图的边色数.     

On the Gracefulness of Graph $(jC_{4n}) ∪ P_m$

The present paper deals with the gracefulness of unconnected graph $(jC_{4n}) ∪ P_m$, and proves the following result: for positive integers $n$, $j$ and $m$ with $n ≥ 1$, $j ≥ 2$, the unconnected graph $(jC_{4n}) ∪ P_m$ is a graceful graph for $m = j − 1$ or $m ≥ n + j$, where $C_{4n}$ is a cycle with $4n$ vertexes, $P_m$ is a path with $m + 1$ vertexes, and $(jC_{4n}) ∪ P_m$ denotes the disjoint union of $j − C_{4n}$ and $P_m$.     

路和圈多重联图的邻点可区别E-全染色

设G（V,E）是一个简单图,k是一个正整数,f是一个V（G）∪E（G）到{1,2,...,k}的映射.如果u,v∈E（G）,则f（u）=f（v）,f（u）=f（uv）,f（v）=f（uv）,C（u）=C（v）,其中C（u）={f（u）}∪{f（uv）｜uv∈E（G）}.称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数.讨论了路和圈的多重联图的邻点可区别E-全色数。