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。     

氧传感器作用原理及其固体电解质的制备

简要讨论了ZrO2基氧传感器的作用原理及用于氧传感器的钇稳定氧化锆粉体的几种制备方法。     

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.     

丙酸正丁酯绿色合成工艺中固体酸催化剂研制

针对目前酯化工艺过程中存在的环境污染问题,以丙酸正丁酯催化合成为例,对酯化过程清洁生产工艺中固体酸催化剂的制备进行了研究.制备了 SO_4~(2-)/TiO_2固体超强酸催化剂,讨论了各种制备条件对该催化剂的丙酸正丁酯合成催化活性的影响,采用 TG/DTA、FTIR、XRD 等仪器分析手段对催化剂结构进行了表征,实验结果表明,SO_4~(2-)/TiO_2固体超强酸催化剂具有很好的催化活性和选择性,且无腐蚀、反应时间短、后处理简单、重复使用性好.     

关于丢番图方程x^3±1=2Dy^2

给出了当Ｄ含６ｋ＋１型素因子时，方程ｘ＾３±１＝２Ｄｙ＾２无正整数解的充分性条件。