MARKOV DECISION PROGRAMMING WITH CONSTRAINTS

ＭＡＲＫＯＶＤＥＣＩＳＩＯＮＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＣＯＮＳＴＲＡＩＮＴＳＬＩＵＪＩＡＮＹＯＮＧ（刘建庸）；ＬＩＵＫＥ（刘克）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，...     

A modified Frank-Wolfe algorithm and its convergence properties

ＡＭＯＤＩＦＩＥＤＦＲＡＮＫ－ＷＯＬＦＥＡＬＧＯＲＩＴＨＭＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＣＥＰＲＯＰＥＲＴＩＥＳＷＵＦＡＮＧ（吴方）ＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄ...     

EXTENDED SYSTEM, BIFURCATION PROBLEM AND HIGH ORDER SINGULARITIES

（胡国庆）（李开泰）ＥＸＴＥＮＤＥＤＳＹＳＴＥＭ，ＢＩＦＵＲＣＡＴＩＯＮＰＲＯＢＬＥＭＡＮＤＨＩＧＨＯＲＤＥＲＳＩＮＧＵＬＡＲＩＴＩＥＳ￥ＨｕＧｕｏｑｉｎｇ；ＬｉＫａｉｔａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎＪｉａｏｔｏｎｇＵ...     

NON-ISOMORPHIC GROUPS WITH ISOMORPHICSPECTRAL TABLES AND BURNSIDE MATRICES

ＮＯＮ－ＩＳＯＭＯＲＰＨＩＣＧＲＯＵＰＳＷＩＴＨＩＳＯＭＯＲＰＨＩＣＳＰＥＣＴＲＡＬＴＡＢＬＥＳＡＮＤＢＵＲＮＳＩＤＥＭＡＴＲＩＣＥＳ￥Ｗ．ＫＩＭＭＥＲＬＥ；Ｋ．Ｗ．ＲＯＧＧＥＮＫＡＭＰ（ＭａｔｈｅｍａｔｉｓｃｈｅｓｉｎｓｔｉｔｕｔＢ，Ｕｎｉｖｅｒｓ...     

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

ＣＯＭＰＬＥＴＥＥＸＴＲＥＭＡＬＳＵＲＦＡＣＥＳＯＦＭＩＸＥＤＴＹＰＥＩＮ３－ＤＩＭＥＮＳＩＯＮＡＬＭＩＮＫＯＷＳＫＩＳＰＡＣＥ￥ＧＵＣＨＡＯＨＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００...     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

ＳＯＭＥＫＩＮＤＳＯＦＬＩＡＰＵＮＯＶＦＵＮＣＴＩＯＮＡＬＩＮＳＴＡＢＩＬＩＴＹＴＨＥＯＲＹＯＦＲＦＤＥＤＵＸＵＥＴＡＮＧ（杜雪堂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ４１００...     

USING FINITE GEOMETRIES TO CONSTRUCT 3-PBIB(2) DESIGNS AND 3-DESIGNS

ＵＳＩＮＧＦＩＮＩＴＥＧＥＯＭＥＴＲＩＥＳＴＯＣＯＮＳＴＲＵＣＴ３－ＰＢＩＢ（２）ＤＥＳＩＧＮＳＡＮＤ３－ＤＥＳＩＧＮＳ￥ＹＡＮＧＢＥＮＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｅｎｇｄｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｅｎｇｄｕ...     

ARONSON'S ESTIMATES AND CONDITIONAL DIFFUSION PROCESSES

ＡＲＯＮＳＯＮ＇ＳＥＳＴＩＭＡＴＥＳＡＮＤＣＯＮＤＩＴＩＯＮＡＬＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＱＩＡＮＺＨＯＮＧＭＩＮ（钱忠民）ＷＥＩＧＵＯＱＩＡＮＧ（魏国强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈ...     

PROGRESSING WAVE SOLUTIONS TO QUASI-LINEAR SYSTEMS MIXED PROBLEMS

ＰＲＯＧＲＥＳＳＩＮＧＷＡＶＥＳＯＬＵＴＩＯＮＳＴＯＱＵＡＳＩ－ＬＩＮＥＡＲＳＹＳＴＥＭＳＭＩＸＥＤＰＲＯＢＬＥＭＳ￥ＷＡＮＧＷＥＩＫＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７２，Ｃｈｉｎ...     

THE CONVERGENCE OF GLOWINSKI'S ALGORITHM FOR ELLIPTIC PROBLEMS

ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＡＬＧＯＲＩＴＨＭＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＣＨＵＤＥＬＩＮ（储德林）；ＨＵＸＩＡＮＣＨＥＮＧ（胡显承）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇ－Ｈｕ...     

Generalized inverses of tensors via a general product of tensors

We define the {i}-inverse (i = 1, 2, 5) and group inverse of tensors based on a general product of tensors. We explore properties of the generalized inverses of tensors on solving tensor equations and computing formulas of block tensors. We use the {1}-inverse of tensors to give the solutions of a multilinear system represented by tensors. The representations for the {1}-inverse and group inverse of some block tensors are established.     

Pseudo core inverses in rings with involution

Let R be a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse in R. The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary ?-ring case by Raki?, Din?i? and Djordjevi? in 2014. Our definition of pseudo core inverse extends the notion of core inverse to elements of an arbitrary index in R. Meanwhile, it generalizes the notion of core-EP inverse, introduced by Manjunatha Prasad and Mohana for matrices in 2014, to the case of ?-ring. Some equivalent characterizations for elements in R to be pseudo core invertible are given and expressions are presented especially in terms of Drazin inverse and {1,3}-inverse. Then, we investigate the relationship between pseudo core inverse and other generalized inverses. Further, we establish several properties of the pseudo core inverse. Finally, the computations for pseudo core inverses of matrices are exhibited.     

环Z/pkZ上s次幂等矩阵及矩阵的加权广义逆

设R=Z/pkZ是模pk的有限局部环,其中p是素数,k>1,p≠2.本文确定了R上n阶s(s≥3)次幂等矩阵的伪标准形,得到了R上n阶矩阵A的加权{ , }-广义逆矩阵的计数定理.     

半正定自共轭四元数矩阵广义逆的单调性问题

对于四元数矩阵的Ｌｏｗｎｅｒ偏序，设０≤Ｂ≤Ａ．本文利用（ｎ，≥）中矩阵的同时合同化简，给出了Ｂ｛１；≥；ｓ；≥Ａ（１）｝的表式，以及下面三个单调性结论的特征刻划：ｉ）Ｂ（１）∈Ｂ｛１；＊｝，Ａ｛１；＊；≤Ｂ（１）｝≠；０；ｉｉ）０≤Ｂ（１，２）≤Ｂ（１，２）≤Ａ（１，２）；ｉｉｉ）Ａ（１，２）∈Ａ｛１，２；≥｝，Ｂ｛１，２；≥；≤Ａ（１，２）｝只含一个元素．     

The {2}-inverse with applications in statistics

An inverse G of a given matrix A which satisfies the property GAG = G is known as a {2}-inverse. This paper presents a three-phase inversion procedure for which the {2}-inverse is a special case. We present the geometry of {2}-inverses and show that, starting from {2}-inverses, various types of generalized inverses can be derived. Two examples of the occurrence of {2}-inverses in statistics are given: one concerning the constrained least-squares estimator, the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi-square distribution.     

The Core-EP,Weighted Core-EP Inverse of Matrices and Constrained Systems of Linear Equations

We study the constrained systemof linear equations Ax=b,x∈R(A^k)for A∈C^n×nand b∈Cn,k=Ind(A).When the system is consistent,it is well known that it has a unique A^Db.If the system is inconsistent,then we seek for the least squares solution of the problem and consider min_x∈R(A^k)||b?Ax||2,where||·||2 is the 2-norm.For the inconsistent system with a matrix A of index one,it was proved recently that the solution is A^■b using the core inverse A^■of A.For matrices of an arbitrary index and an arbitrary b,we show that the solution of the constrained system can be expressed as A^■b where A^■is the core-EP inverse of A.We establish two Cramer’s rules for the inconsistent constrained least squares solution and develop several explicit expressions for the core-EP inverse of matrices of an arbitrary index.Using these expressions,two Cramer’s rules and one Gaussian elimination method for computing the core-EP inverse of matrices of an arbitrary index are proposed in this paper.We also consider the W-weighted core-EP inverse of a rectangular matrix and apply the weighted core-EP inverse to a more general constrained system of linear equations.     

一个关于平面图的K-(2,1)-全可选性的结果

设图$G$的一个列表分配为映射$L: V(G)\bigcup E(G)\rightarrow2^{N}$. 如果存在函数$c$使得对任意$x\in V(G)\cup E(G)$有$c(x)\in L(x)$满足当$uv\in E(G)$时, $|c(u)-c(v)|\geq1$, 当边$e_{1}$和$e_{2}$相邻时, $|c(e_{1})-c(e_{2})|\geq1$, 当点$v$和边$e$相关联时, $|c(v)-c(e)|\geq 2$, 则称图$G$为$L$-$(p,1)$-全可标号的. 如果对于任意一个满足$|L(x)|=k,x\in V(G)\cup E(G)$的列表分配$L$来说, $G$都是$L$-$(2,1)$-全可标号的, 则称$G$是 $k$-(2,1)-全可选的. 我们称使得$G$为$k$-$(2,1)$-全可选的最小的$k$为$G$的$(2,1)$-全选择数, 记作$C_{2,1}^{T}(G)$. 本文, 我们证明了若$G$是一个$\Delta(G)\geq 11$的平面图, 则$C_{2,1}^{T}(G)\leq\Delta+4$.     

Drazin谱和算子矩阵的Weyl定理

A∈B(H)称为是一个Drazin可逆的算子,若A有有限的升标和降标．用σ_D(A)={λ∈C：A-λI不是Drazin可逆的)表示Drazin谱集．本文证明了对于Hilbert空间上的一个2×2上三角算子矩阵M_C=■,从σ_D(A)∪σ_D(G)到σ_D(M_C)的道路需要从前面子集中移动σ_D(A)∩σ_D(B)中一定的开子集,即有等式：σ_D(A)∪σ_D(B)=σ_D(M_C)∪G,其中G为σ_D(M_C)中一定空洞的并,并且为σ_D(A)∪σ_D(B)的子集．2×2算子矩阵不一定满足Weyl定理,利用Drazin谱,我们研究了2×2上三角算子矩阵的Weyl定理,Browder定理,a-Weyl定理和a-Browder定理．     

Norm estimations for perturbations of the weighted Moore-Penrose inverse

For a complex matrix $A\in \mathbb{C}^{m\times n}$, the relationship between the weighted Moore-Penrose inverse $A^\dag_{M_1N_1}$ and $A^\dag_{M_2N_2}$ is studied, and an important formula is derived,where $M_1\in \mathbb{C}^{m\times m}, N_1\in\mathbb{C}^{n\times n}$ and $M_2\in \mathbb{C}^{m\times m}, N_2\in\mathbb{C}^{n\times n}$ are different pair of positive definite hermitian matrices. Based on this formula, this paper initiates the study of the perturbation estimations for $A^\dag_{MN}$ in the case that $A$ is fixed, whereas both $M$ and $N$ are variable. The obtained norm upper bounds are then applied to the perturbation estimations for the solutions to the weighted linear least squares problems.     

Generalized Inverses of Matrices over Rings

Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.