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空间变量
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  spatial variable
     Then,we consider the integrable (2+1)dimensional M(modified)HF model, and give the corresonding geometrical equivalent counterparts,such as the (2+1)-dimensional nonlinear Schrodinger equation and the coupled (2+1)-dimensional integrable equations,through the motion of Minkowski space curves endowed with an addi-toional spatial variable.
     之后进一步讨论可积的(2+1)维M(修正的)HF模型,首先用延拓结构理论对该模型进行分析,并通过赋予在闵氏空间中运动的空间曲线新的空间变量y,得到(2+1)维非线性薛定谔方程以及成对的(2+1)维可积方程。
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     In this method, three shell displacements are first expanded in Fourier series in the circumferential direction, then an infinite number of decoupled partial differential equations containing a spatial variable and a time variable are obtained.
     壳体的三个位移函数首先沿环向展开为Fourier级数,由此得到解耦的偏微分方程,它包括一个空间变量和一个时间变量。
短句来源
     The spatial variable of the time-dependent Schrdinger equation was discretized,and the time-dependent part was treated by using the time average technique,then the time evolution of the system was simulated by the precise intergration method.
     首先对含时薛定谔方程的空间变量进行离散,而后对含时部分进行时间平均处理,采用精细积分方法模拟其随时间的演化过程.
短句来源
     This paper discusses the system of hyperbolic equations(Et+∧x+C(x)V=Φ(x,t)f(x) in the condition of known matrix∧,C(x),Φ(x,t) and the inverse problem,boundary condition determines the right-hand member f(x).It also talks about the reverse problem. Right-hand member f(x,y) is determined by system of hyperbolic equations of great spatial variable quantity.
     讨论了双曲方程组(E t+∧x+C(x)V=Φ(x,t)f(x)在矩阵∧,C(x),Φ(x,t)为已知的情况下,由边界条件确定右端项的f(x)一类反问题.进而讨论了空间变量较大数量的双曲方程组确定右端项f(x,y)的一类反问题.
短句来源
     In this paper,we provide Galerkin algorithm and nonlinear Galerkin algorithm for solving the nonlinear evolution equations,where the spatial variable discretization is performed by Galerkin spectral element method and nonlinear Galerkin spectral element method and the time variable discretization is made by Euier explicit scheme Moreover,we analyse the boundedness,stability and convergence accuracy of these algorithms By comparison,we come to the condusion that under the same convergence accuracy,the computational time and stability of nonlinnear Galerkin algorithm are prior to the ones of Galerkin algorithm
     给出了数值求解非线性发展方程的Galerkin算法和非线性Galerkin算法,其中空间变量用谱元法离散,时间变量用Euier显式格式离散。 此外,我们分析了两种算法的有界性、稳定性和收敛精度估计。
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  space variable
     By changing space variable, introducing elliptic projection and using other priori estimate technique for differential equation , the optimal L2-norm and H1-norm convergence results are obtained.
     应用空间变量代换、引入椭圆投影及其他微分方程先验估计技巧,得到了最优阶的L~2模及H~1模收敛结果。
短句来源
     By changing space variable, introducing elliptic projection and using other priori i error estimate technique for nonlinear differential equation, the optimal L 2 norm and H 1 norm convergence results are obtained.
     通过进行空间变量代换、引入椭圆投影,以及采用其它非线性微分方程先验误差估计技巧,得到了最优阶的L2模和H1模收敛结果。
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     Space Variable Transform Method for Free Vibration Analysis of Thick Cylindrical Shelf with Arbitrary Boundary Conditions
     任意边界条件下圆柱厚壳自由振动分析的空间变量变换法
短句来源
     We prove that the solutions of the three dimensional Leray-Alpha equations with periodic boundary condition are analytic in time with values in a Gevrey class of functions(for the space variable).
     本文考查了三维周期边界条件下的Leray-Alpha方程,证明了在Gevrey函数类(关于空间变量)中取值的方程的解关于时间是解析的。
短句来源
     This paper is concerned with the numerical simulation of the unsteady Navier-Stokes equations by full discrete two-grid method (time variable is discreteized by Eular implicit difference scheme, and space variable is discreteized by mixed finite element method).
     本文采用全离散双重网格算法(时间变量采用Eular全隐式格式离散,空间变量采用混合有限元离散),对非定常Nayier-Stokes(N—S)方程进行数值模拟。
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  spatial variables
     This result means that the solutions are real analytic functions in spatial variables.
     这个结果说明解关于空间变量是实解析函数.
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     With the method of dynamic programming,two spatial variables,the expected utility andthe Probability of success for each offense,are used to model the criminal' s lacation choicesin urban areas.
     本文以犯罪期望效用和成功概率为空间变量,用数学动态规划方法建立模型模拟罪犯在城市内选择犯罪区位的一般规律。
短句来源
     With the method of dynamic programming,two spatial variables,the expected utility andthe Probability of success for each offense,are used to model the criminal' s lacation choicesin urban areas.
     本文以犯罪期望效用和成功概率为空间变量,用数学动态规划方法建立模型模拟罪犯在城市内选择犯罪区位的一般规律。
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     By utilizing a polynomial interpolation for the time variable in a partitioned small interval and boundary element approximation for the spatial variables,a new analyzing technique for transient heat conduction problems is presented in this paper.
     对时间变量在小区间内应用多项式插值,对空间变量采用边界元求解,提出一种新的分析瞬态热传导问题的计算格式。
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     The results show that the opd versus x and i has nice linearity in the case of cut - angle being not too big, and larger maximum of opd could be gotten with suitable element parameters and spatial variables being used.
     模拟结果表明在切割角不太大的条件下,光程差与入射点和入射角的关系具有较好的线性,只要相关的元件参数和空间变量选取的合适,也可以得到较大的最大光程差。
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  “空间变量”译为未确定词的双语例句
     In this paper, we discussed an inverse problem for finding unkown coeffident k(x) in the parabolic equation u_t-( k(x) u_x)_x+B(x) u_x+c(x) u=0 in the domain x>0, t>0. The uniqueness and existence of the local solution are given.
     本文讨论了抛物型方程μ_i-(k(x)u_x)_x+B(x)u_x+c(x)u=0确定和空间变量有关的未知系数k(x)的反问题,给出了反问题解的存在性,唯一性。
短句来源
     The wedged liquid crystal cell and the director of liquid crystal as the function of two special variable measurement x and z are considered, namely θ=θ(x,z).
     考虑楔形液晶盒,液晶指向矢倾角θ是两个空间变量x,z的函数,即θ=θ(x,z)。
短句来源
     Mixed finite element method , characteristic method and discontinuous Galerkin methods are combined to one dimensional KdV equations. The characteristic mixed discontinuous finite element scheme and the modified method of characteristics with adjusted advection (MMOCAA) are given. Namely, the characteristic method in time and discontinuous finite element method in space are used.
     对一维KdV方程利用混合有限元方法,特征线方法和间断有限元方法相结合的技巧,给出方程的特征线混合间断有限元离散方案和修正的特征线混合间断有限元离散格式,即对时间导数离散采用特征线方法,空间变量离散采用间断有限元方法,证明了有限元解的存在唯一性,稳定性和误差估计。
短句来源
     On the Choices of Phase Space Variables in the Study of Anomalous Scaling in High Energy Multiparticle Production
     高能多粒子产生反常标度性研究中的相空间变量选择
短句来源
     Firstly, the solution of the time domain electric flied integral equation (TD-EFIE) is based on the method of moments (MoM) and using the marching-on-in-time (MOT) technique, in which both explicit solution scheme and implicit solution scheme are used, to calculate the scattering form arbitrary shaped conducting structure.
     首先,对于时域电场积分方程,通过时间步进法(MOT,marching-on-in-time),即空间变量部分用矩量法(MoM)离散,时间变量部分则采用差分法,求解任意形状导体结构的瞬态散射问题,其中,显式解法和隐式解法分别都被采用进行计算分析。
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  spatial variable
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed.
      
Depending on the character of the salinization and the water-physical properties of the soil at the moving boundary, there are given either the values of the sought function or of its derivative with respect to the spatial variable.
      
The characteristic feature of this region is its "elongatedness" in the direction of the timet-axis in thex, t-plane (x being the spatial variable).
      
We consider the solution of a linear second-order parabolic equation with one spatial variable and a zero right side.
      
We prove that since the solution decreases quite rapidly in the spatial variable as it approaches a particular point, it vanishes on the part of the characteristic joining the point to the boundary of the region in which the solution is defined.
      
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  space variable
The method employed is that of fitting with respect to a space variable in which the system of equations of motion is hyperbolic, using the computing scheme of V.
      
A new method for solving nonlinear nonstationary equations (case of one space variable)
      
It is shown that in the case of small initial data there exists a unique classical solution of this problem, and an asymptotics of this solution uniform in the space variable is given.
      
Estimates of the perturbations of the exact solution due to the approximate conditions are obtained for a model problem with one space variable.
      
Analytical expressions for the dependence of the material parameters on the space variable and possibly on the time variable are obtained.
      
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  spatial variables
The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work.
      
The present paper considers the case of an arbitrary dependence of the velocity profile of the basic flow on two spatial variables.
      
The discretization of the problem is carried out in the spatial variables using Galerkin's method, and in the time variable using Euler's implicit method.
      
The first mixed boundary value problem for a parabolic difference-differential equation with shifts with respect to the spatial variables is considered.
      
Similar problems are studied for the cases of an exciting force of the form depending on time and of an external force rapidly oscillating with respect to the spatial variables or with respect to time .
      
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In this paper, finite element approximation solution is cstablished dy finite element discret1e of space variable, and by characteristic function expansion of time variable for hyperbolic and parabolic equations. This is so called semi-discrete method. Meanwhile the L~2- error estimation of approximation (?)lution is obtained.The result(?) of computation by tne semi-discrete method are then compared with the correct solution.

本文对双曲型方程与抛物型方程的空间变量进行有限元离散化,对时间变量用特征函数展开法,即用半离散化法来构造有限元逼近解.同时还得到了逼近解的L~2——误差估计.通过算例及图示,将所得到的结果与精确解进行了比较。

The purpose of this paper is to find some regularities of numerical simulation for metal metal mould castings with equiaxed grains. Three computation methods-explicit difference, I. A. D. and finite element were used for the same castings with identical initial and boundary conditions and thermal physical parameters. Advantages and shortcomngs of these methcds were compared. Questions such as how to treat heat of fusion, thermal properties of the casting/mould interfaces and initial conditions etc. were analyzed...

The purpose of this paper is to find some regularities of numerical simulation for metal metal mould castings with equiaxed grains. Three computation methods-explicit difference, I. A. D. and finite element were used for the same castings with identical initial and boundary conditions and thermal physical parameters. Advantages and shortcomngs of these methcds were compared. Questions such as how to treat heat of fusion, thermal properties of the casting/mould interfaces and initial conditions etc. were analyzed in order to improve the accuracy of computation. Three modified specific huat functions were used to simulate the release of fusion heat during the solidification stage. Each parameter of casting/mould interface is adjusted for observing their influence on the temperature field.

本文目的是探讨金属型铸件在获得等轴晶的条件下数值模拟的一些规律。对于同一铸件,在获得等轴晶的相同条件下,采用有限差分交替方向隐式(I.A.D)、有限差分显式和有限元三种方法进行了计算,并对三种方法的优缺点作了比较。为了提高计算精度,对如何处理凝固潜热,铸件—铸型界面热性质和初始条件等问题进行了分析。采用了三种不同折合比热函数来模拟凝固阶段潜热的释放。调整了界面的各种参数观察其对温度场的影响。符号表 T 温度 (℃) b 蓄热系数 (cal/cm~2·S·1/2·℃) t 时间 (s) v 表面换热系数 c 比热 (cal/g℃) M =△τ·k/c·p·(△x)~2 p 容重 (g/cm~3) k 在T的右上角表示时间步长数 k 导热系数 (cal/s·cm·℃) i r或x方向空间步长数 J 潜热 (cal/g) j r或x方向空间步长数 f_B 凝固阶段固相析出量与总量之比 m 液相线斜率 cj =(-J)()(cal·/g·℃) C_o 溶质浓度 x,y 直角坐标系中空间变量 T_L 液相线温度(℃) r,z 柱坐标系中空间变量 T_s 固相线温度(℃) n 边界法线方向坐标变量...

本文目的是探讨金属型铸件在获得等轴晶的条件下数值模拟的一些规律。对于同一铸件,在获得等轴晶的相同条件下,采用有限差分交替方向隐式(I.A.D)、有限差分显式和有限元三种方法进行了计算,并对三种方法的优缺点作了比较。为了提高计算精度,对如何处理凝固潜热,铸件—铸型界面热性质和初始条件等问题进行了分析。采用了三种不同折合比热函数来模拟凝固阶段潜热的释放。调整了界面的各种参数观察其对温度场的影响。符号表 T 温度 (℃) b 蓄热系数 (cal/cm~2·S·1/2·℃) t 时间 (s) v 表面换热系数 c 比热 (cal/g℃) M =△τ·k/c·p·(△x)~2 p 容重 (g/cm~3) k 在T的右上角表示时间步长数 k 导热系数 (cal/s·cm·℃) i r或x方向空间步长数 J 潜热 (cal/g) j r或x方向空间步长数 f_B 凝固阶段固相析出量与总量之比 m 液相线斜率 cj =(-J)()(cal·/g·℃) C_o 溶质浓度 x,y 直角坐标系中空间变量 T_L 液相线温度(℃) r,z 柱坐标系中空间变量 T_s 固相线温度(℃) n 边界法线方向坐标变量α导温系数(cm~2/s) r 定义域的边界线下标含义 m或M 金属或铸件 s 铸型 sm 相对于铸件的铸型界面ms 相对于铸型的铸件界面i 界面

A class of collocation methods is proposed for solving first order hyperbolic equations. The exposing example chosen is of a single equation in one space dimension with constant cofficients and of the quasilinear equation system.Optimal L~∞ error estimates under less conditons are derived for the first example. A Crank-Nicolson type time discretization yields approximation discreted in time with optimal L~∞ error estimates of O(h~(r+1)+τ~2), using the space of continuous piecewise polynomial functions of degree...

A class of collocation methods is proposed for solving first order hyperbolic equations. The exposing example chosen is of a single equation in one space dimension with constant cofficients and of the quasilinear equation system.Optimal L~∞ error estimates under less conditons are derived for the first example. A Crank-Nicolson type time discretization yields approximation discreted in time with optimal L~∞ error estimates of O(h~(r+1)+τ~2), using the space of continuous piecewise polynomial functions of degree r(γ≥1), τ denotes time step and h is the space step. It has been proved that the method is unconditionally stable.Finally, the method is generated to first order quasilinear hyperbolic system. The optimal error estimates are also derived.

本文提出了解一阶双曲型方程的一类配置方法。选择考察的问题是空间变量为一维的常系数方程和拟线性方程组。对第一个例子,若在空间方向使用连续的分片r(r≥1)次多项式,h记空间步长,在时间方向采用Crank-Nicolson类离散化,τ记时间步长,则当真解u∈L~∞(0,T;W_1~(r+2),(?)∈L~∞(0,T;H~(r+1),(?)∈L~2(0,T;H~(r+1)时,配置近似解的L~∞误差估计为O(h~(r+1)+τ~2)。本文还证明了这个计算格式是绝对稳定的。最后,将此方法推广到解一阶拟线性方程组,同样得到了最优阶的误差估计式。

 
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