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.     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

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.     

Indefinite Least Squares Problem with Quadratic Constraint and Its Condition Numbers

In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,mixed,and componentwise condition numbers for solution and residual of this problem are derived.Numerical example is also provided to illustrate these results.     

Statistical Analysis and Evaluation of Macroeconomic Policies: A Selective Review

In this paper,we highlight some recent developments of a new route to evaluate macroeconomic policy effects,which are investigated under the framework with potential outcomes.First,this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program evaluation.Secondly,primary attention goes to the focus on causal effect estimation of macroeconomic policy with single time series data together with some extensions to multiple time series data.Furthermore,we examine the connection of this new approach to traditional macroeconomic models for policy analysis and evaluation.Finally,we conclude by addressing some possible future research directions in statistics and econometrics.     

Recovering Unbounded Rough Surfaces with a Direct Imaging Method

In this paper,we consider the inverse acoustic scattering problem by an unbounded rough surface.A direct imaging method is proposed to reconstruct the rough surfaces from scattered-field data for incident plane waves and the performance analysis is also presented.The reconstruction method is very robust to noises of measured data and does’t need to know the type of the boundary conditions of the surfaces in advance.Finally,numerical examples are carried out to illustrate that our method is fast,accurate and stable even for the case of multiple-scale profiles.     

Modeling and targeting an essential metabolic pathway of Plasmodium falciparum in apicoplast using Petri nets

Petri net(PN) is one of the promising computational and mathematical formalisms used to represent and study the behavior of complex metabolic networks. The various available analysis techniques of PN could be used to validate and analyze the network in different scenarios. Plasmodium falciparum is one of the threatening parasites which causes malaria, a deadly disease affecting a large number of today’s world population. The development of antimalarial drug resistance is an emerging global threat, highlighting the need to discover novel antimalarial targets. The fatty acid biosynthesis of malarial parasite is one of the essential metabolic pathways required for its growth and is present in apicoplast, a non-photosynthetic plastid. The malarial parasite obtains fatty acids by using type two fatty acid synthase(FAS II) enzyme,which is different from type one enzyme used by human host, making it an ideal drug target.This article proposes and studies the PN model of the parasite’s FAS II pathway to analyze the mechanism of potential drug targets in this pathway. The proposed PN model can serve as a base for further findings in the field of antimalarial drug targets to decrease the malaria mortality rate.     

HYBRID REGULARIZED CONE-BEAM RECONSTRUCTION FOR AXIALLY SYMMETRIC OBJECT TOMOGRAPHY

In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis,so that the density of the whole object can be recovered layer by layer.Considering the relationship between different layers,we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results.In view of the anisotropy of classical discrete total variations,a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model.Furthermore,considering that the object density consists of continually changing parts and jumps,a high-order regularization term is introduced.The final hybrid regularization model is solved using the alternating proximal gradient method,which was recently applied in image processing.Density reconstruction results are presented for simulated radiographs,which shows that the proposed method has led to an improvement in terms of the preservation of edge location.     

Gibbs Measure for the Higher Order Modified Camassa-Holm Equation

This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.     

AN EFFICIENT ADER DISCONTINUOUS GALERKIN SCHEME FOR DIRECTLY SOLVING HAMILTON-JACOBI EQUATION

This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.     

Low dimensional modules over quantum complete intersections in two variables

We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations.     

中国的数学课程标准——在第四届世界华人数学家大会中学数学教育论坛上的发言

我们国家自隋朝开科举之初就有算学考试,考中了可以做负责丈量土地,计算排水工程量等事物的从九品官员(相当于副科级),这种考试到明朝被取消了.那个时代自然科学的地位不高.