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.     

Degree-Continuous Graphs

A graph G is degree-continuous if the degrees of every two adjacent vertices of G differ by at most 1. A finite nonempty set S of integers is convex if k S for every integer k with min(S)kmax(S). It is shown that for all integers r > 0 and s 0 and a convex set S with min(S) = r and max(S) = r+s, there exists a connected degree-continuous graph G with the degree set S and diameter 2s+2. The minimum order of a degree-continuous graph with a prescribed degree set is studied. Furthermore, it is shown that for every graph G and convex set S of positive integers containing the integer 2, there exists a connected degree-continuous graph H with the degree set S and containing G as an induced subgraph if and only if max(S)(G) and G contains no r-regular component where r = max(S).     

Independence number,connectivity, and r-factors

We show that if r ? 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ? (r + 1)²/2 and (r + 1)²α(G) ? 4rk(G), then G has an r-factor; if r ? 2 is even and G is a graph with k(G) ? r(r + 2)/2 and (r + 2)α(G) ? 4k(G), then G has an r-factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).     

A note on the bichromatic numbers of graphs

For a pair of integers k, l≥0, a graph G is (k, l)‐colorable if its vertices can be partitioned into at most k independent sets and at most l cliques. The bichromatic number χ^b(G) of G is the least integer r such that for all k, l with k+l=r, G is (k, l)‐colorable. The concept of bichromatic numbers simultaneously generalizes the chromatic number χ(G) and the clique covering number θ(G), and is important in studying the speed of hereditary properties and edit distances of graphs. It is easy to see that for every graph G the bichromatic number χ^b(G) is bounded above by χ(G)+θ(G)?1. In this article, we characterize all graphs G for which the upper bound is attained, i.e., χ^b(G)=χ(G)+θ(G)?1. It turns out that all these graphs are cographs and in fact they are the critical graphs with respect to the (k, l)‐colorability of cographs. More specifically, we show that a cograph H is not (k, l)‐colorable if and only if H contains an induced subgraph G with χ(G)=k+1, θ(G)=l+1 and χ^b(G)=k+l+1. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 263–269, 2010     

The Mayer-Erdös phenomenon

Two rational numbers r and r′ are said to be similarly ordered if r = a/q, r′ = a′/q′, gcd(a, q) = gcd(a′, q′) = 1, and (a − a′) (q − q′) ? 0. We investigate the problem of similar ordering of chains of consecutive Farey fractions.     

Some 3‐connected 4‐edge‐critical non‐Hamiltonian graphs

Let γ(G) be the domination number of graph G, thus a graph G is k‐edge‐critical if γ (G) = k, and for every nonadjacent pair of vertices u and υ, γ(G + uυ) = k?1. In Chapter 16 of the book “Domination in Graphs—Advanced Topics,” D. Sumner cites a conjecture of E. Wojcicka under the form “3‐connected 4‐critical graphs are Hamiltonian and perhaps, in general (i.e., for any k ≥ 4), (k?1)‐connected, k‐edge‐critical graphs are Hamiltonian.” In this paper, we prove that the conjecture is not true for k = 4 by constructing a class of 3‐connected 4‐edge‐critical non‐Hamiltonian graphs. © 2005 Wiley Periodicals, Inc.     

Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k, r) at most ten

This paper is a further contribution to the classification of linetransitive finite linear spaces. We prove that if ? is a non-trivial finite linear space such that the Fang-Li parameter gcd(k, r) is 9 or 10, and the group G ? Aut(?) is line-transitive and point-imprimitive, then ? is the Desarguesian projective plane PG(2, 9).     

On numerical experiments with symmetric semigroups generated by three elements and their generalization

We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4,6+4k,87−4k) and S(9,3+9k,85−9k) generated by three elements. We present a generalization of these sequences by numerical semigroups S(r₁²,r₁r₂+r₁²k,r₃-r₁²k)\mathsf{S}(r_{1}^{2},r_{1}r_{2}+r_{1}^{2}k,r_{3}-r_{1}^{2}k), k∈ℤ, r ₁,r ₂,r ₃∈ℤ⁺, r ₁≥2 and gcd(r ₁,r ₂)=gcd(r ₁,r ₃)=1, and calculate their universal Frobenius number Φ(r ₁,r ₂,r ₃) for the wide range of k providing semigroups be symmetric. We show that this type of semigroups admit also nonsymmetric representatives. We describe the reduction of the minimal generating sets of these semigroups up to {r₁²,r₃-r₁²k}\{r_{1}^{2},r_{3}-r_{1}^{2}k\} for sporadic values of k and find these values by solving the quadratic Diophantine equation.     

Coloring of universal graphs

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH (G) _r ¹ . Answering a question of A. Hajnal we show that countably universal graphU ₃ satisfiesU ₃ (U₃) _r ¹ for every finiter.     

Generalized degree conditions for graphs with bounded independence number

We consider a generalized degree condition based on the cardinality of the neighborhood union of arbitrary sets of r vertices. We show that a Dirac-type bound on this degree in conjunction with a bound on the independence number of a graph is sufficient to imply certain hamiltonian properties in graphs. For K_1,m-free grphs we obtain generalizations of known results. In particular we show: Theorem. Let r ≥ 1 and m ≥ 3 be integers. Then for each nonnegative function f(r, m) there exists a constant C = C(r, m, f(r, m)) such that if G is a graph of order n (n ≥ r, n > m) with δ_r(G) ≥ (n/3) + C and β (G) ≥ f(r, m), then (a) G is traceable if δ(G) ≥ r and G is connected; (b) G is hamiltonian if δ(G) ≥ r + 1 and G is 2-connected; (c) G is hamiltonian-connected if δ(G) ≥ r + 2 and G is 3-connected. © 1995 John Wiley & Sons, Inc.     

Undecidability of Winkler′s r-Neighborhood Problem for Covering Digraphs

Consider the following decision problem which P. Winkler and V. Bulitko (independently) showed was undecidable: Given a finite set Φ of rooted graphs and a positive integer r, is there a graph G such that Φ represents, up to isomorphism, the set of all r-neighborhoods of G? We show the undecidability of the related problem in which G is required to be the covering digraph of a partial ordering. Our construction shows that the problem remains undecidable (for certain fixed r) even when G is also required to be planar and bipartite.