Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms

Many imaging systems can be modeled by the following linear system of equations Ax = b, （1） where the observed data is b = （b^1…b^M）^T∈K^M and the image is x = （x1…xN）^T∈K^N.     

Necessary and Sufficient Conditions for Oscillations of Neutral Delay Equations with Several Positive and Negative Coefficients

In thisPositive and (l)PaPer,we eonsider thenegative eoeffieients ofoseillations of neutral delay equations with、o山 the form·习k-1十玄。,·(卜r。卜全·,·(卜。,))十 XZ夕.、、d一dtJ.。、x(‘一u、)一名h:x(‘一。:)=o,where the eoeffieients and the delays areequation of(1)15non一negative constants.The Charaeteri“tieN(2)F(几):=‘+‘习。‘e一“·卜‘习r,e一‘’,+习。、e一“”一习h:e一‘’一0. ‘二lj一1论一15,1 our main result 19 the following theorem. Theorem All solutions of(l)oseillate if …     

The Minimax Equality; Sufficient and Necessary Conditions

The paper produces new versions of the minimax theorem based on original conditions. Moreover, we investigate not only the sufficiency, but also the necessity of such conditions. The proofs are very simple and preclude any topological technique.     

Necessary and Sufficient Conditions for the Cohen–Macaulayness of Blowup Algebras

In this paper we provide a complete characterization for when the Rees algebra and the associated graded ring of a perfect Gorenstein ideal of grade three are Cohen–Macaulay. We also treat the case of second analytic deviation one ideals satisfying some mild assumptions. In another set of results we give criteria for an ideal to be of linear type. Finally, we describe the equations defining the Rees algebras of certain Northcott ideals.     

RESEARCH ANNOUNCEMENTS Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms

Many imaging systems can be modeled by the following linear system of equations Ax=b,(1) where the observed data is b=(b~1...b~M)~T∈K~M and the image is x=(x_1…x_N)~T∈K~N.The number field K can be the reals R or the complexes C.The system matrix A=(A_(i,j)) is nonzero and of the dimension M×N matrix.The image reconstruction problem is to reconstruct the     

Necessary and Sufficient Conditions of Existence and Uniqueness of Limit Cycles for a Polynomial System

In this paper, the following polynomial system is discussed:And the necessary and sufficient conditions of existence and uniqueness of limit cyclesare obtained.     

Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.     

Necessary and Sufficient Conditions for the Strong Consistency of Mnltiple Regression Coefficients Undera Restrictive Condition

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判定亚正定矩阵的一个充要条件

给出了一个更一般的判定亚正定矩阵的充要条件.     

复正定矩阵的充要条件

本文研究Hermite正定矩阵、实正定矩阵的推广概念复正定矩阵,给出了复方阵复正定性的一些充分必要条件。     

哈密顿连通图和可迹图的新充分谱条件

令G是一个简单连通图,ρ(G)和q~D(G)分别为图G的邻接谱半径和距离无符号拉普拉斯谱半径.提供了图G是哈密顿连通的两个新的谱充分条件,这两个充分条件分别是以ρ(G)和q~D(G)表示的,其中G是G的补图.进一步地,还给出了以q~D(G)表示的图G是从任意一点出发都是可迹的新的谱充分条件,从而扩展和改进了文献中的结果.     

行半正定矩阵的充要条件及其性质

文章给出行半正定矩阵的概念,并对它进行讨论,获得行半正定矩阵的一些充要条件及其性质。     

Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities

The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional extension of the Theorem of the Alternative.     

Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators

For a compact subset of symmetric with respect to conjugation and a continuous function, we obtain sharp conditions on and that insure that can be approximated uniformly on by polynomials with nonnegative coefficients. For a real Banach space, a closed but not necessarily normal cone with , and a bounded linear operator with , we use these approximation theorems to investigate when the spectral radius of belongs to its spectrum . A special case of our results is that if is a Hilbert space, is normal and the 1-dimensional Lebesgue measure of is zero, then . However, we also give an example of a normal operator (where is unitary and ) for which and .

     

The difference between doubly nonnegative and completely positive matrices

The convex cone of n×n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, for n4 only, every DNN matrix is CP. In this paper, we investigate the difference between 5×5 DNN and CP matrices. Defining a bad matrix to be one which is DNN but not CP, we: (i) design a finite procedure to decompose any n×n DNN matrix into the sum of a CP matrix and a bad matrix, which itself cannot be further decomposed; (ii) show that every bad 5×5 DNN matrix is the sum of a CP matrix and a single bad extreme matrix; and (iii) demonstrate how to separate bad extreme matrices from the cone of 5×5 CP matrices.     

A Kind of Square Matrices and Its Qualities

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几类Lurie型控制系统绝对稳定性充分必要条件

本借助部分变元绝对稳定性的充要条件，得出几类Lurie型控制系统绝对稳定性充分必要条件，这些判据为显式的代数形式，易于验证，也便于在实践中应用。