神经传播方程的特征差分及特征有限元方法

给出矩形域上神经传播方程的两层特征差分及特征有限元格式,并且证明了l2和L2模误差估计是最优的.     

特征2CARTAN型李代数的结合型

本文确定了在特征 2域上的阶化 Cartan型李代数中 (包括本文作者以前所构造的非交错哈密尔顿代数 P( n,m)具有非退化结合型的所有李代数     

利用有限域上特征为2的正交几何构作一类Cartesian认证码

利用了有限域上的特征为2的正交几何构造了一类Cartesian认证码,并且计算了其参数及模仿攻击成功的概率PI和替换攻击成功的概率PS.     

水污染问题特征有限元方法的数值计算及理论分析

本文研究了水污染二维对流占优数学模型特征有限元方法的计算问题，导出的计算格式对时间变量用特征线方法离散，对空间变量用Galerkin有限元方法离散，得到的H^1－模和L^2－模误差估计是最优阶的。     

对数函数的特征点,特征线及其应用

对数函数 ｙ =ｌｏｇａｘ(ａ >0且ａ≠ 1)的图象经过两个点 (1,0 )和 (ａ ,1) ,我们不妨称之为对数函数的两个特征点 .对数函数 ｙ =ｌｏｇａｘ(ａ >0且ａ≠ 1)的图象中 ,直线ｘ =1反映了它的分布特征 ;而直线 ｙ =1与对数函数图象的交点 (ａ ,1)的横坐标则直观地反映了对数函数的底数特征 .我们可以称ｘ =1和ｙ =1为对数函数的两(ａ >1)　　　　　　 ( 0 <ａ <1)图 1　对数函数特征线条特征线 .(如图 1所示 ) .知道了对数函数的特征点、特征线 ,我们在画图象时就能把握住图象的基本特征 ,利用对数函数的特征点、特征线处理一些问题形象、直…     

特征为2的有限正交空间上全奇异子空间的Critical问题

利用特征为2的有限正交空间的性质及计数定理在特征为2的有限正交空间上研究了全奇异子空间的Critical问题,得到了相应的计数公式和Critical指数.     

特征标次数的重数与可解群结构

非线性不可约特征标次数的重数全部为1的有限群的分类是熟知的.对可解群,本文讨论更一般的,即非线性不可约特征标次数的重数都与群阶互素的有限群的纯群论性质.特别地,得到了非线性不可约特征标次数的重数均小于2p的奇阶群G的分类结果.这里p为群阶|G|的最小素因子.     

正交矩阵的特征多项式及特征根

以《高等代数习题解》(杨子胥)的两道习题为理论根据,应用正交矩阵的若干性质,给出了正交矩阵特征多项式系数的规律.     

保特征2域上上三角矩阵群逆的线性映射

设F是一个特征2且至少含有5个元素的域,n≥2是一个正整数．令Mn（F）和Tn（F）分别F上的全矩阵空间和上三角矩阵空间．我们首先刻划从Tn（F）到Mn（F）的保矩阵群逆的所有线性单射，由此从Tn（F）到自身的所有保矩阵群逆的线性双射被刻划．     

不可约特征标和B_π-特征标的对应关系

首先给出 Isaacs著名引理的一个推广 .把其中关于θ和φ分别为 G -不变的和 K -不变的特征标的条件减弱为更为一般的和常见的惯性群关系 IK(θ) =IK(φ) .其次 ,我们证明了当θ为 N的一个 Bπ特征标而φ恰为一个与θ相伴的 Fong特征标时 ,相应的对应关系自动成为 Bπ-特征标和 Fong特征标的对应 .     

A Characteristic Finite Volume Element Method for the Air Pollution Model

In this article, a characteristic finite volume element method is presented for solving air pollution models. The convection term is discretized using the characteristic method and diffusion term is approximated by finite volume element method. Compared with standard finite volume element method, our proposed method is more accurate and efficient, especially suitable to solve convection-dominated problems. The proposed numerical schemes are analyzed for convergence in L ₂ norm. Some numerical results are presented to demonstrate the efficiency and accuracy of the method.     

三维油水运移聚集数值模拟的交替方向格式和分析

研究油气运移聚集史的数值模拟,其数学模型是三维非线性偏微分方程组的初进值问题．我们从实际出发,考虑了重力、毛管力和浮力的作用,同时考虑到三维问题大规模科学和工程计算的特征,提出对流动方程采用大步长的混合元法,而对三维饱和度方程的计算,采用一类交替方向特征有限元法．将其化为连续解三个一维问题,使工程数值计算成为可能．应用张量积计算．负模估计和先验估计理论,得到最佳阶Ｌ~２误差估计．     

对流-扩散问题的特征──块中心差分法

１．引言１９８２年,Ｄｏｕｇｌａｓ和Ｒｕｓｓｅｌｌ［１］提出解对流一扩散问题的特征一差分方法,网格节点为均匀分布,求解区域为直线Ｒ．文中讨论了基于二次插值的特征一差分格式,但其近似解按离散Ｌ２模未达到最优阶误差估计．１９８８年Ｗｅｉｓｅｒ和Ｗｈｅｅｌｅｒ［２］提出解线性椭圆型和线性抛物型方程的块中心差分法,１９９１年王申林［３］讨论了解拟线性双曲型积分微分方程的块中心差分方法,其共同特点为近似解按离散的Ｌ２模达到最优阶误差估计,解的一阶导数的近似解达到超收敛误差估计．１９９３年由同顺［４］讨论了…     

EXPLICITLY SOLVABLE CHARACTERISTIC METHOD FOR CONVECTION DIFFUSION PROBLEMS

In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given.     

Concatenating construction of the multisymplectic schemes for 2+1-dimensional sine-Gordon equation

In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The-method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.     

TWO-GRID CHARACTERISTIC FINITE VOLUME METHODS FOR NONLINEAR PARABOLIC PROBLEMS＊

In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.     

多层非线性渗流耦合系统的特征分数步差分方法

对多层非线性渗流耦合系统提出适合并行计算的特征分数步差分格式, 利用变分形式、能量方法、粗细网格配套、分片双二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶的l₂误差估计. 该方法已成功的应用到多层油资源评估的生产实际中.     

Exponential Time Differencing-Padé Finite Element Method for Nonlinear Convection-Diffusion-Reaction Equations with Time Constant Delay

In this paper, ETD3-Padé and ETD4-Padé Galerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions. An ETD-based RK is used for time integration of the corresponding equation. To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator, the Padé approach is used for such an exponential operator approximation, which in turn leads to the corresponding ETD-Padé schemes. An unconditional $L^2$ numerical stability is proved for the proposed numerical schemes, under a global Lipshitz continuity assumption. In addition, optimal rate error estimates are provided, which gives the convergence order of $O(k^{3}+h^{r})$ (ETD3-Padé) or $O(k^{4}+h^{r})$ (ETD4-Padé) in the $L^2$ norm, respectively. Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.     

奇异伪辛群的Carter子群

设 Fq是特征为 2的有限域 ,本文研究了 Fq上 2 ν+δ+t级奇异伪辛群 Ps2ν+δ+ t(Fq) (δ=1或 2 )的 Carter子群的存在性及结构 .得到的结果为 :若 q>2 ,Ps2ν+δ+ t(Fq)中不含 Carter子群 ,若 q=2 ,Ps2ν+δ+ t(Fq)的 Carter子群为它的 Sylow2 -子群的正规化子 .