一类消失项带有时间导数的对流方程

本文在Duijn等的基础上研究了方程ht f(h)x=εhxx ε2τ1hxxt ε2τhxxx的行波解,其中f(h)∈C2(R)是满足所谓凹凸性的任意已知函数,得出了在不同的τ1,τ2条件下,该方程行波解的存在性条件和唯一性条件,并利用行波解得到上述方程的解,从而得到了对流方程的弱解,并分析了对流方程的多解性.     

奇素数的三项方幂和中的平方数

研究了一类基本而又重要的指数Diophantine方程,利用广义Ramanujan-Nagell方程的性质证明了这类方程有非负整数解的充要条件,并得出这类方程的全部非负整数解.     

非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

研究了具有非线性记忆项的Euler-Poisson-D arboux-Tricomi方程在次临界情况下解的爆破现象.利用泛函分析方法结合修正的Bessel方程推出了其柯西问题解的迭代框架和第一下界,然后通过迭代技巧,获得了其解的全局非存在性以及解的生命跨度上界估计.     

具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题:u_t=u_(xx) (u~n)_x,(x,t)∈S=R×(0,∞),u(x,0)=δ(x),x∈■在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n_0=3.当0≤n相似文献   

具任意次非线性项的Camassa-Holm方程的双孤子新解

给出辅助方程、函数变换与变量分离解相结合的方法,构造了具任意次非线性项的Camassa-Holm方程的双孤子和双周期新解.首先,通过两个辅助方程、函数变换与变量分离解,将具任意次非线性项的Camassa-Holm方程的求解问题转化为非线性代数方程的求解问题.然后,借助符号计算系统Mathematica求出该方程组的解,并用辅助方程的相关结论,构造了双周期解和双孤子新解.     

带非均匀项的MKdV方程

本文讨论了带非均匀项的MKdV方程：ut 6u^2ux uxxx βu (α βx)ux=0（1.1）它与特征值问题Vx＝QV（1.3）相联系，文章推导了方程（1.3）的散射数据的演化规律，得到了方程（1.1）的反散射解－孤子解。最后还讨论了单孤子解和双孤子解。     

具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题ut=uxx+(un)x, (x,t)∈S=R×(0,∞),u(x,0)=δ(x), x∈R在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n0=3.当0≤n＜n0时,方程源型解存在且唯一;当n≥n0时,方程不存在源型解;当0≤n＜2时,方程的源型解在原点附近渐近行为恰似热传导方程的基本解;应用量纲分析技巧,证明了当且仅当n=2时,方程存在唯一相似源型解,并求出了其解析表达式.研究结果表明了这类抛物型方程对流项的存在对扩散项产生重要影响的物理事实.     

一类带强色散项DGH方程的精确解

利用改进的F-展开法,求出了一类带强色散项DGH方程的一系列类孤子解,三角函数周期解和有理数解,方程结合了KdV方程的线性色散项和C-H方程的非线性色散项.而且改进的F-展开法在借助于计算机符号系统Mathematica(Maple)下,操作方便,适用于大量的非线性偏微分方程(组),并有助于发现新解.     

含变系数或强迫项的KdV方程的新解

Jacobi椭圆函数展开法被推广并用于求解另一种形式的KdV方程的新的精确解,所求解的这类KdV方程包括一种典型的变系数的KdV方程和具有强迫项（随机项）的KdV方程．用这种方法得到的新的类周期解在极限条件下可以退化为类孤立波解或类冲击波解．     

关于带非均匀项KdV方程的求解

本文研究带非均匀项的KdV方程(1)的反散射解。得到了当Schr(?)din ger方程的位势u按方程(1)演化时,它的散射量随时间t的演化规律。并利用反散射方法求出了方程(1)的孤子解。     

服务管理差距与服务质量差距之间关系模型的研究

在服务质量差距分析模型的基础上,基于服务管理差距和服务质量差距测评体系,运用结构方程建模方法,建立了企业内部服务管理差距与顾客感知服务质量差距之间的关系路径图和关系模型,定量研究了四个服务管理差距对服务质量差距的影响关系、服务管理差距测评指标对相应的四个服务管理差距的影响关系,为顾客感知服务质量差距的测量和评价提供了技术和方法.结合某外语培训学校服务管理实际进行了案例研究,为企业服务质量的诊断和改进提供了科学依据.     

中国邮递员问题50年

首先介绍一般邮递员问题, 涉及费用、服务侧、衔接费用、次序等要素. 然后简要综述过去50年来中国邮递员问题、有向图上中国邮递员问题、带风向的邮递员问题、混合图上邮递员问题以及乡村邮递员问题等一般邮递员问题的特殊情况的研究进展, 突出问题的线性规划描述及相应的组合多面体结构, 着重讨论问题的模型、精确算法及其时间复杂度、NP-困难情形下的近似算法及其性能比.     

Laplace-Beltrami differentiability of positive definite kernels on the sphere

This contribution gives results on the action of the Laplace-Beltrami derivative on sufficiently smooth kernels on the sphere, those defined by absolutely and uniformly expansions generated by a family of at least continuous functions. Among other things, the results show that convenient Laplace-Beltrami derivatives of positive definite kernels on the sphere are positive definite too. We also include similar results on the action of the Laplace-Beltrami derivative on condensed spherical harmonic expansions.     

Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping

In this paper, based on some mesh-dependent estimates on the extreme eigenvalues of a general finite element system defined on a simplicial mesh, novel and sharp bounds on the permissible time step size are derived for the mass lumping finite element approximations of parabolic equations. The bounds are dependent not only on the mesh size but also on the mesh shape. These results provide guidance to the stability of numerical solutions of parabolic problems in relation to the unstructured geometric meshing. Numerical experiments on both uniform meshes and adaptive meshes are presented to validate the theoretical analysis.     

VonMises分布表的一种插值方法

本文给出ＶｏｎＭｉｓｅｓ分布表的一种插值方法     

Compactness of composition operators on BMOA and VMOA

We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].     

A note on stability results for scattered data interpolation on Euclidean spheres

The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated sampling nodes and construct strongly localized polynomials on spheres. Numerical results illustrate our theoretical findings. Dedicated to Professor Manfred Tasche on the occasion of his 65th birthday.     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

一类分数次次线性算子及其交换子在齐型空间上的弱Morrey-Herz空间上的有界性

本文研究了一类次线性算子及其交换子在齐型空间上的弱有界性的问题.利用齐型空间的基本性质以及给出的一类次线性算子及其分别与BMO函数,Lipschitz函数生成的交换子在L~p(X)上的弱有界性,证明了其在齐型空间上Morrey-Herz空间中的弱有界性.推广了该类算子在Morrey-Herz空间中的强有界性这一结果.