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解表达式
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  expression of solution
     The process for working out the particular solution of the difference equation yt+1+ayt=b1cos鵷+b2sin鵷 (t=0,1,2,…) can be simplified and brought about a simple and clear particular expression of solution.
     差分方程y_(t+1)+ay_t=b_1coswt+b_2sinwt(t=0,1,2,…)的特解的推导过程可以被简化,并可以推导出一个简洁的特解表达式
短句来源
     Starting from a Bcklund transformation and taking a special ansatz for the function f,we can obtain a much more general expression of solution that include some variable separated functions for the higher order Broer-Kaup system.
     始于一Backlund变换和取函数f的一特殊拟解,可以得到高阶Broer-Kaup系统中含有若干变量分离函数的一个较一般的解表达式
短句来源
     Starting from a Bcklund transformation and taking a special ansatz for the function f,we can obtain a much more general expression of solution that include some variable separated functions for the higher order Broer-Kaup system.
     始于一Bácklund变换和取函数f的一特殊拟解,我们可以得到高阶Broer-Kaup系统中含有若干变量分离函数的一个较一般的解表达式
短句来源
  solution formula
     Based on the point set base solutions, the approximate solution formula of single drainage hole in the finite element has been ascertained by the superposition principle.
     应用叠加原理 ,在点汇基本解的基础上 ,推导出了有限元单元内单个排水孔的近似解表达式
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  “解表达式”译为未确定词的双语例句
     In this paper we study bifurcation from the branch of trivial solutions for a class of semilinear elliptic equations, Δu+λu+f(x,u)=0  u  n=0 at the second eigenvalue of the Laplacian in [0,π]×[0,π] .
     本文主要讨论在方形区域[0,π]×[0,π]内,当f满足一定条件时Neumman边值问题Δu+λu+f(x,u)=0 u n=0在平凡解(λ2,0)处产生的分歧解表达式.
短句来源
     Through this method the expressions of periodic solutions with more accuracy are gotten and the relations curves between amplitude-frequency and transmissibility-frequency are also obtained.
     应用这一方法,获得了精度较高的周期解表达式、振幅与频率关系曲线以及位移传递率与频率关系曲线;
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     We introduce some new concepts of differential and integral in discrete time system.
     引入了离散时间系统中微分与积分的新概念,讨论了该系统中一阶微分方程的建立与求解的方法,给出了相应的解表达式.
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     To design thermo-optic photoelectric devices, the awareness of thermal behavior in the devices is the foundation.
     了解热光型器件的热学行为是设计热光型光电器件的基础,本文根据热传导理论,得到了温度场的瞬态解表达式
     In this paper,the exact solution of the following reaction-diffusing equation ut-auxx+b(u3+cu2+du)=0 are constructed by using a generalized homogeneous balance method. In particular,we obtain the solitary wave solutions.
     用推广的齐次平衡方法求出了一类非线性发展方程ut-auxx+b(u3+cu2+du)=0(a,b,c,d为常数)的精确解表达式,从而物理上许多著名的方程,如:Chaffee-Infane方程,Huxley方程等,都可以作为该方程的特殊情形,并求得了相应的孤立波解.
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  相似匹配句对
     THE GENERAL EXPRESSION OF FEASIBLE SOLUTION
     可行的一般表达式
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     The Expressions of Solution of Some Differential Equations
     一类微分方程表达式
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     PROCESS EXPRESSION
     加工表达式
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     The expression for V is new.
     V 的表达式是新的。
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     The Solution of Inversion Eqation
     逆序方程的
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  expression of solution
In this paper we consider the construction of asymptotic expression of solution for general boundary value problem for higher order elliptic equation containing two parameters.
      
By using the method of two-parameter expression, asymptotic expression of solution and estimation corresponding to the remainder term are given.
      
We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.
      
By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics.
      
In [1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm.
      
  solution formula
Some problems arisen in the computation of analytical solution formula are also analysed.
      
Some problems arisen in the computation of analytical solution formula are also analysed.
      
A solution formula for the linearized problem is derived, and Lp estimates for solutions of the linearized problem are obtained for 2≤p≤∞.
      
It is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary Stokes problem in some Lp spaces; and, as a result, a solution formula for the nonstationary Stokes problem is obtained.
      
We use the heat kernel and Ukai's solution formula for the Stokes equations.
      
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In the first part of this paper we consider the partial differential equa-tion as a generalized Euler-Poisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(x-y)~ρυ(x,y)is...

In the first part of this paper we consider the partial differential equa-tion as a generalized Euler-Poisson equation:(?) (1.1)where β,β′are constants, and a(x,y),b(x,y),c(x,y),d(x,y)are all regularfunctions in Hadamard's sense.Therefore x=y is the singular line of thecoefficients.The behaviors of the solutions of(1.1)in the neighborhood ofthe singular line x=y are described by introducing the concepts of“index”and the“regular part”:Let ρ be a constant and υ(x,y)be a regularfunction(υ(x,x)≠0)such thatu(x,y)=(x-y)~ρυ(x,y)is a solution of(1.1),then the constant ρ is said to be the“index”andρ(x,y)the“regular part”of the solution.It is shown that all the possibleindexes must satisfy the indicial equation(?)and if F(ρ+1)≠0,then the normal derivative of the regular part on thesingular line x=y is determined completely by the value itself,i.e.(?)The regular part υ(x,y)satisfies the equation of a particular form of(1.1),in which γ=0,and therefore it is sufficient to study the equation of theform(?) (?) (3.2)We define the singular Cauchy prob em as follows:to find a functionυ(x,y)continuous together with its first derivatives and twice differentiablein the region ACBD(cf.figure 1 p.518),and satisfying the equation(3.2)in the region ACBD,except the singular line AB,on which it takes anygiven regular funtion u_0(2x)as its initial value.We give the existence proof of such singular Cauchy problem in thegeneral case(β+β′≠0),and it follow that,the solution of the equation(1.1)may,in general,be expressed as.(?)where ρ_1 and ρ_2 are different roots of the indicial equation;or(?)where ρ_1 is the double root of indicial equation.The second part of this paper,deals with the singular equation in spa-ce,especially the equation of the following form:(?) (15.5)where A_σ is any linear operator which (?)epends only on the variables σ==(σ_1,…,σ_n),such that,the Cauchy problem for the associated regular equation(?) (15.6)and the initial data(?)has a unique soluion υ(x,σ_,…,σ_n).The solution of singular Cauchy pro-blem for equation(15.5),with initial data(?)can be expressed by υ(x,σ_1,…,σ_n)in the form(?)where K(τ,t)is a kernel well defined by the operator(?)For example,the kerne for Euler-Poisson-Darboux opera-tor(?)is(?). The same method can be applied to solve the Cauchy problem for thegeneralized Chapligin equation(?)(where K(t)is an increasing function,and K(0)=0),with initial data(?)The solution is given explicitly by(17.12).(p.550).

本文的第一部分研究了含奇线方程的解在奇线附近的性质;引进了“指数”的概念,从而给出了关于这类方程的“奇型郭西问题”的正确提法;并且通过一种特殊的积分-征分方程的研究,证明了这种“奇型郭西问题”的解的存在性,并且给出其近似解法;最后,就一般的情形,给出了方程一般解的表达式,从而说明了在β+β′<0时,郭西问题的多解性。本文的第二部分研究了空间含奇面方程(?)其中 A_σ是任一祇与变元σ=(σ_1…,σ_n)有关的算子,并且关于(15.5)的奇型郭西问题的解可以用关于方程(不合奇面)(?)(15.6)的郭西问题的解表示出来。同样的方法可用来解决空间却普里金方程(17.1)的郭西问题。

It is efficient to compute long-period and secular perturbations by numerical in-tegration, but the classical analytic solution may be used to calculate the short-period perturbations.

用数值积分来计算长周期和长期摄动,而用经典分析解的表达式来计算短周期摄动,这是很有效的。

In this paper we discuss the singular perturbations of first boundary value problem for higher order elliptic equations, considering both the perturbation of operator and that of boundary. We discuss the problem:??Here ε, μ denote positive small parameters, Ω_μ denotes the perturbated region, n denotes the inner normal vecter of the boundary ?Ω_μ of Ω_μ, L_0、L_1 represent strong elliptic operators of order 2m and 2(m+l) respectively. The asymptotic approximation involving two parameters is constructed and the...

In this paper we discuss the singular perturbations of first boundary value problem for higher order elliptic equations, considering both the perturbation of operator and that of boundary. We discuss the problem:??Here ε, μ denote positive small parameters, Ω_μ denotes the perturbated region, n denotes the inner normal vecter of the boundary ?Ω_μ of Ω_μ, L_0、L_1 represent strong elliptic operators of order 2m and 2(m+l) respectively. The asymptotic approximation involving two parameters is constructed and the error is estimated in L_2 - norm. Some results in [1~3] are included in our result as special cases.

本文研究算子和区域边界双摄动的高阶椭圆型方程第一边值问题的奇摄动,建立含两个参数的渐近解表达式,导出求形式渐近解的迭代过程,并对余项进行估计,拓广了?和?J.G.Besjes、林宗池等人的工作.

 
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