At first we give the energy norm and L_2-norm estimates of anisotropic bilinear finite element, then we prove the estimates of semidiscrete form and fulldicrete form of linear parabolic problem. 并用此单元求解线性抛物型方程,给出半离散格式和全离散格式的误差估计。
Using the property of the bilinear and trilinear form, a priori bound for solutions of a weak formulation is given. 利用双线性函数和三线性函数的性质,论述了各子问题的有界性、强制性以及解的先验估计。
In this paper, we use the theory of symmetric bilinear function to solve problems of quadratic form, and finally give a proof of the inertia theorem. 通过建立二次型与对称双线性函数之间的对应关系,在双线性函数的概念下讨论二次型化标准型的问题,最后给出惯性定理的一个证明。
Secondly, for a finite dimensional semisimple Hopf algebra, we prove that the Killing form is an ad-invariant bilinear form, which leads to the further orthogonal relations between the center of Hopf algebras and the kernel of linear mapping induced by a left integral. 其次,证明了有限维半单Hopf代数的Killing型是ad-不变的双线性型,进而得到了Hopf代数的中心与积分所诱导的伴随映射的核在Killing型框架下的正交关系。
A Class of Lie Algebras with a Symmetric Invariant Non-Degenerate Bilinear Form 一类带有非退化对称不变双线性型的李代数
The synthesis problem in the form of bilinear matrix inequalities ( BMI) was transferred into convex optimal problem in the form of linear matrix inequalities ( LMI) by adding equation constraint in the systems. 在系统中增加等式约束,将具有双线性矩阵不等式(BMI)形式的综合问题转换为线性矩阵不等式(LMI)的凸优化问题。
In section 2, we investigate the symmetric bilinear functions and their standard form over the complex ( real) field. 第二部分给出了对称双线性函数的基本概念及其在复(实)数域上的标准型,及它们的分类情况。
First, use the grid-based kd-tree to increase the intersection efficiency, and in interpolation methods, offer the inverse distance interpolation method and implement bilinear/ trilinear interpolation based on form function of finite element method, which is second-order accurate and computationally inexpensive. 在插值方法研究方面详细介绍了逆距离插值方法,并引入有限单元法中的型函数思想实现双线性/三线性插值,这种基于型函数的线性插值方法具有严格二阶精度、计算简单的优点。
It is necessary to simplify the capacity spectrum into bilinear form so as to get characteristic point of hysteretic bone curve ( especially the yield point and the yielded stiffness), ductility and equivalent damping of the structure. 将结构的能力曲线简化为二折线是确定结构的恢复力骨架曲线特征点(屈服点和屈服后刚度)、计算结构延性和等效阻尼比的关键。
A bilinear differential form of the sh-gordon equation SH&GORDON方程的双线性微分形式
In 1998,, Jin Hong constructed a nondegenerate symmetric bilinear form. 1998年,JinHong构造了Borcherds超代数的量子化包络代上的一个非退化对称双线性型。
Formula of the short-term stiffness of prestressed concrete slabs reinforced with PCB is fitted out based on the bilinear form. 采用双折线形式拟合得到配置PC钢棒预应力混凝土板短期刚度计算公式。
It is often bilinear form for those integrable systems. 对于其中的可积系统,往往是双线性形式。
This thesis discusses the optimal control problem of a class of bilinear systems with the worst disturbance rejection. A bilinear system is a nonlinear system which is the simplest in form and most approximate to a linear system. 本文研究了一类具有最坏扰动抑制的双线性系统的最优控制问题。双线性系统是形式上最简单且最接近线性系统的一类非线性系统。
Based on the bilinear form and Backlund transformation, we obtain the Wronskian solutions for the KP-BBM equation. 基于KP-BBM方程的双线性形式和Backlund变换,我们给出了它的Wronskian行列式解。
With the aid of the Hirota method and symbolic computation, the bilinear form and N-soliton solutions for the KP-BBM equation are derived. 借助于Hirota双线性方法和计算机符号计算,我们得到了KP-BBM方程的双线性形式和N-孤子解。