Sparse shape functions for tetrahedral <Emphasis Type="Italic">p</Emphasis>-FEM using integrated Jacobi polynomials

Summary In this paper, we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp-version of the finite element method using a mesh of tetrahedrons. We present several bases based on integrated Jacobi polynomials in which the element stiffness matrix has nonzero entries, where p denotes the polynomial degree. The proof of the sparsity requires the assistance of computer algebra software. Several numerical experiments show the efficiency of the proposed bases for higher polynomial degrees p.      

H∞ ALMOST DISTURBANCE DECOUPLING FOR MIMO BILINEAR SYSTEMS

The H_∞ almost disturbance decoupling problem is considered. In this paper, a nonlinear design is proposed to find a state feedback controller for bilinear systems. The closed‐loop system is internally stable and achieves disturbance attenuation in nonlinear H_∞ sense. We defined a special form of Lyapunov function, which is constructed in terms of one or a set of positive definite constant matrices. If, except of the origin of system, the corresponding polynomial of the positive definite matrix (or several polynomials relevant to the positive definite constant matrices) has (have) no zero on a given subset of state space, then we can construct a controller to solve our problem. It is found that the controller structure could be complicated, but is feasible in computation and may require optimization technique to search the solution. We consider both SIMO and MIMO cases with illustrated examples.     

硝铵装置降膜蒸发存在问题与改进措施

对我公司硝铵装置降膜蒸发工序存在的问题进行分析 ,并通过技术改进 ,使干燥洗涤液全部返回系统 ,造粒塔粘塔问题得到缓解 ,取得可观的经济效益和环保效益     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

一个二阶非线性中立时滞微分方程的正解

研究了一个二阶非线性中立时滞微分方程,给出了关于此方程正解存在的一些充分条件,其优点在于省略了对任意的a〉0,aQ1（t）-Q2（t）都是最终非负的限制条件。最后通过数值例子说明研究结果的优越性。     

深埋型无水芒硝矿床溶采工艺研究

采用本研究成果──钻井两管油垫注热水工艺，能够成功地开采出理深达2200m的无水芒硝矿，较好地解决芒硝卤水采运过程中的结晶堵管及顶板垮塌等技术难题，充分有效地开采地下芒硝资源，并取得较好的经济效益。     

串联CSTR的图解求法

介绍了如何根据（－rA）－xA关系进行串联CSTR的图解法计算，该法简单、应用面广。     

一次同余方程组的一种矩阵解法

同余方程组是数论中一个极为有用的课题。文中考虑的是具有一个未知数而具有不同的模的一次同余方程组。一般可以用中国剩余定理或者递推算法等方法给出一次同余方程组的解法。利用矩阵的初等变换和矩阵的Sm ith标准形给出了求解一次同余方程组的一种矩阵解法。     

Synthesis and Characterization of Nanocapsules of a-Fe(NiCoAl) Solid-solution

α-Fe(NiCoAl) solid-solution nanocapsules were prepared with pure powders of Fe, Ni, Co and Al by the plasma arc-discharging using a copper crucible. The shapes of the nanocapsules are in polyhedrons with the core/shell structure. The body centered cubic (BCC) phase is formed in the core. The size of the nanocapsules is in the range of 10~120 nm and the thickness of the shell is 4~11 nm. Saturation magnetization Js=150 Am2/kg and coercivity iHC=24.3 kA/m are achieved for the nanocapsules.