In this paper,we firstly characterize the form of transformation T which preserves both minimal rank and a nonsingular bilinear function from Mn(F) to itself when n≥3.
文中首先刻画n≥3时,Mn(F)到其自身的同时保持极小秩和某一非奇异双线性函数的变换T的形式,然后证明M2(F)到其自身的保持极小秩的线性变换的形式。
In this paper we study the nonsingular discrete Dirichlet boundary value problem for the second-order differential systems one-dimension P-Laplacian,we prove the existence of solutions for these BVPs by using the Leray-Schauder nonlinear alternative theorem and Schauder cone fixed-point theorem.
本文主要研究二阶微分系统一维p-Laplacian非奇异离散Dirichlet边值问题,利用Leray-Schauder非线性抉择定理和Schauder不动点定理证明了此问题的解的存在性定理,推广并改进了已有结果。
The definition of the nonsingularity is presented based on analyzing digital discrete chaotic sequence.
分析结果表明这类算法产生碰撞的原因是其对混沌映射的数字化导致混沌序列的奇异性,因此必须谨慎选择混沌映射的数字化方法以保证混沌序列的非奇异性。
Based on the kernel estimating theory of nonlinear semiparametric models under the least-square principle,this paper proves the nonsingularity of coefficient matrix of normal equation in least-square estimator of non-linear semiparametric models under certain condition.
本文基于非线性半参数模型最小二乘核估计的迭代解法,证明了非线性半参数模型最小二乘类估计法方程系数阵在一定条件下的非奇异性。
The new nonsingularity criteria of matrices and the equivalent representation of M-matrices are presented in this paper.
本文给出了矩阵非奇异性的判定准则和M-矩阵的等价表征,所得结果推广了最近的相关结论。
This paper presents the necessary and sufficient conditions for the nonsingularity of feedback shift registers on the q element finite field, and shows the necessary and sufficient conditions for the nonsingularity of feedback shift registers on q=3,4,5 with the theory of the Groebner basis.
本文给出q元有限域上的反馈移位寄存器非奇异性判定的充分必要条件,并利用Groebner基理论对定理给出的条件进行约化,给出了q=3,4,5时任意次反馈函数非奇异性的充要条件。
PS ring is characterized using nonsingular modules and minijective modules.
利用非奇异模、极小内射模 ,给出 PS环的一些刻画 ,同时刻画了半单环 ,指出右 YJS环、右 DS环与右 PS环之间的关系及它们等价的条
When ring R , as an R module, is YJ injective, this paper gives some equivalent conditions among nonsingular ring, semiprimitive ring, pp ring and regular rings.
利用非奇异环、半本原环、pp环刻画正则环 ,当 R是 YJ内射 R模时 ,给出以上环的等价的几个条件 ,同时给出强正则环及半单环的刻画 。
Some conditions for a weakly regular ring to be right nonsingular ring are discussed.
讨论弱正则环成为右非奇异环的若干条件 ,指出 MERT环上每个奇异单右 R模是 YJ内射模时 ,R为右非奇异环 ;同时给出一个环成为弱正则环的条件 ,证明了每个单右 R 模是 p 内射模时 ,R为弱正则环 。
Also, the expression of the matrix equation s nonsingular solution is given.
在此基础上,进一步讨论了这类矩阵方程有非奇异解的条件,并且给出非奇异解的一般表达形式。
By applying the equivalent normalized form of desected matrix,the article discusses the sufficient and necessary conditions of linear matrix equation A m×n X n×n =B m×n with nonsingular solution,gives out the general expression formula of nonsingular solution,thus generalizing the conclusion of the 4th point in it.
应用分块矩阵的等价标准形 ,讨论了线性矩阵方程Am×nXn×n=Bm×n有非奇异解的充要条件 ,并给出了非奇异解的一般表达式 ,从而推广了文 [4]的结论 。
In this paper, the existence problem is discussed of a nonsingular solution to the matrix equation AX-XB=C, and several sufficient conditions are given for the existence of a nonsingular solution to it.
本文讨论了矩阵方程AX-XB =C非奇异解的存在性问题 ,并给出了该方程非奇异解存在的几个充分条件 。
Finally the nonsingular stress effect in rock fracture is researched.
本文分析了加载系统的刚度对岩石断裂韧性的影响，探讨了岩石断裂韧度的依时性，并对岩石断裂中的非奇应力效应进行了分析。