单调序列的非齐次GM(1,1)模型

GM(1,1)模型的白化解为齐次指数形式,而一般数据呈非齐次指数形式,存在形式上的差异.本文运用非齐次级比与非齐次指数函数的对应关系,对原始序列中相邻数据做差处理,得到新的序列,将非齐次指数序列转换为齐次指数序列,再建立GM(1,1)模型.实例表明,运用初值优化和非齐次化能提高GM(1,1)模型的精度.     

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

<正>In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.     

N维多重非齐次调和方程及其边界积分方程

对n维多重非齐次调和方程△~((k))u=f(x),x∈R~n,给出了基本解的递推公式以及多重调和函数的积分关系式.在非齐次项f(x)为m次调和的情形下将域上的积分转化为沿边界的积分,进而应用直接法给出了基本边界积分方程.对f(x)为一般光滑函数的情形,给出了用泰勒多项式逼近时相应的误差估计并证明了含误差项的积分是收敛的.     

ON RIEMANN BOUNDARY VALUE PROBLEM FOR POLYANALYTIC FUNCTIONS ON THE REAL AXIS

In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained.     

亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

三阶微分方程解的增长性

In this paper,the precise estimation of the order and hyper-order of solutions of a class of three order homogeneous and non-homogeneous linear differential equations are obtained. The results of M. Ozawa (1980), G. Gundersen (1988) and J. K. Langley ( 1986 ) are improved.     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

The Einstein-K(a)hler metric on Hua construction of the first type

Let HCI be the Hua construction of the first type. We describe the EinsteinKahler metric for HCI. We reduce the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X(z, w, ζ). This differential equation can be solved to give an implicit function in X(z,w,ζ). For some cases, we obtained the solution of the differential equation and the explicit forms of the complete Einstein-Kahler metrics on HCI which are the non-homogeneous domains.     

A STABILITY RESULT ON SOLUTIONS TO CERTAIN FOURTH ORDER NON-HOMOGENEOUS DIFFERENTIAL EQUATIONS

In this paper,we study the fourth order non-homogeneous differential equations x(4) + f1()+ f2() + f3(■) + f4(x) = p(t,x,■,,x),and obtain suffcient conditions,under which the solutions to the system tend to zero as t →∞.     

The construction of markov processes in random environments and the equivalence theorems

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec. 2, we construct the Markov process in random enviromment and skew product Markov process by p -m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.     

非齐次树上m重非齐次马氏链的一类强偏差定理

研究给出了非齐次树上m重非齐次马氏链的一类强偏差定理.     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点:一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系.     

一类二阶非齐次线性微分方程解的复振荡

研究了一类二阶非齐次线性微分方程f″+Ae~(az~n)f′+(B_1e~(bz~n)+B_0e~(dz~n))f=F(z)解的增长性和零点分布,其中F为级小于n的非零整函数,A,B1,B0为非零多项式.在复数a,b,d满足一定条件下,得到该方程的每一个解的超级和二级零点收敛指数的精确估计.     

On a non-homogeneous bi-layer shallow-water problem: smoothness and uniqueness results

In this paper, we present several results for a non-homogeneous bi-layer shallow-water model in depth-mean velocity formulation. The homogeneous case was studied in (Nonlinear Anal.: Real World Appl. 4(1) (2003) 139–171). In (On a non-homogeneous bi-layer shallow water problem: an existence theorem, Diff. and Integral Equations 17 (9–10) (2004) 1175–1200) we proved the existence of a solution for the non-homogeneous problem and now we give some smoothness and uniqueness results. The main difficulties in the non-homogeneous case arise from the treatment of the boundary terms.     

Boundary value problems for multi-term fractional differential equations

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.     

The Einstein-Kahler metrics on Cartan-Hartogs domain of the first type

Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K =mn+1/m+n,m>1, the explicit forms of the complete Einstein-Kahler metrics are obtained.     

非齐次树上m重非齐次马氏信源的一个强偏差定理

研究给出了非齐次树上m重非齐次马氏信源的一个强偏差定理.     

On novel grey forecasting model based on non-homogeneous index sequence

To solve the problem that traditional grey models were constructed on the hypothesis that the original data sequence is in accord with homogeneous index trend rather than non-homogeneous index trend. A novel grey forecasting model based on non-homogeneous index sequence approximately (abbreviated as NDGM) is proposed. It is proved that the models based on homogeneous index sequence are all special cases that of non-homogeneous index sequence. The recursive function of the NDGM model is proposed and the forecasting precision of the model based on pure non-homogeneous index sequence is discussed and the affine properties of the model are further studied. Finally, one numerical case is used to show the effective results of the proposed model.     

Thermo-magneto-dynamic stresses and perturbation of magnetic field vector in a non-homogeneous hollow cylinder

An analytical method is presented to investigate thermo-magneto-elastic stresses and perturbation of the magnetic field vector in a conducting non-homogeneous hollow cylinder under thermal shock. The interaction between the deformation and the magnetic field vector in a non-homogeneous hollow cylinder is considered by adding a Lorentz’s electro-magneto-force into the equation of thermo-elastic motion of the non-homogeneous hollow cylinder in an axial magnetic field. The exact solution for magneto-thermo-dynamic stresses and perturbation responses of an axial magnetic field vector in a conducting non-homogeneous hollow cylinder was obtained by using finite integral transforms. From numerical calculations, the dynamic characteristics on both thermo-magneto-stresses and perturbation of the axial magnetic field vector in the conducting non-homogeneous hollow cylinder is revealed and discussed.