Further results on integral generalized inverses of integral matrices

This paper further investigates integral generalized inverses of integral matrices.     

Further results on generalized inverses of tensors via the Einstein product

The notion of the Moore–Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate on this theory by producing a few characterizations of different generalized inverses of tensors. A new method to compute the Moore–Penrose inverse of tensors is proposed. Reverse order laws for several generalized inverses of tensors are also presented. In addition to these, we discuss general solutions of multilinear systems of tensors using such theory.     

On the product of projectors and generalized inverses

We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two projectors is again a projector, and we discuss necessary and sufficient conditions in terms of their kernels and images alone. We give a new representation of the product of generalized inverses that does not require explicit knowledge of the factors. Our approach is based on implicit representations of subspaces via their orthogonals in the dual space. For Fredholm operators, the corresponding computations reduce to finite-dimensional problems. We illustrate our results with examples for matrices and linear ordinary boundary problems.     

Further results on overlarge sets of Kirkman triple systems

In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If there exist both an OLKF（6^k） and a 3-OLGKS（6^k-1,4） for all k ∈{6,7,...,40}／{8,17,21,22,25,26}, then there exists an OLKTS（v） for any v ≡ 3 （mod 6）, v ≠ 21. As well, we obtain the following result： There exists an OLKTS（6u ＋ 3） for u = 2^2n-1 - 1, 7^n, 31^n, 127^n, 4^r25^s, where n ≥ 1,r＋s≥ 1.     

Lipschitzian stability of fully parameterized generalized equations

This paper concerns the study of Lipschitzian stability of fully parameterized generalized equations in which both single-valued and set-valued functions depend on parameters. Various relationships between the Lipschitz-like and metric regularity properties of the solution mapping, the base mapping, or field mapping in the fully perturbed generalized equations are established by using the Dontchev–Hager Fixed Point Theorem. The implicit mapping theorem for metric regularity is also extended to fully parameterized generalized equations.     

基于有限射影平面上(ω,r,d)-CFF(N,T)系统的构作

在有限射影平面上利用有限射影平面的性质构作了(ω,r,d)-CFF(N,T)系统,并利用有限射影平面的性质计算了它的参数.最后利用一个有限点集构作了一个(ω,r,d)-DS(N,T)系统并计算了它的参数.     

On inverses of Vandermonde and confluent Vandermonde matrices III

Summary We derive lower bounds for the norm of the inverse Vandermonde matrix and the norm of certain inverse confluent Vandermonde matrices. They supplement upper bounds which were obtained in previous papers.Sponsored in part by the United States Army under Contract No. DAAG29-75-C-0024 and the National Science Foundation under grant MCS 76-00842A01     

Some results on distance two labelling of outerplanar graphs

Let G be an outerplanar graph with maximum degree △. Let χ（G^2） and A（G） denote the chromatic number of the square and the L（2, 1）-labelling number of G, respectively. In this paper we prove the following results： （1） χ（G^2） = 7 if △= 6; （2） λ（G） ≤ △ ＋5 if △ ≥ 4, and ）,（G）≤ 7 if △ = 3; and （3） there is an outerplanar graph G with △ = 4 such that ）λ（G） = 7. These improve some known results on the distance two labelling of outerplanar graphs.     

Some new results on unimodality of generalized order statistics and their spacings

Because of the importance of ordered random variables and, in general, generalized order statistics (GOSs), in many branches of Statistics, a wide interest has been shown in investigating unimodality and strong unimodality of such random variables. Assuming certain restrictions on the model parameters and distributions, some authors have shown unimodality of GOSs. In this article, we shall provide some new results on unimodality of GOSs based on the population distribution function which contain and strengthen several known findings in this regard. A counterexample is also provided for the cases where the results are not valid in general. Unimodality of arbitrary spacings of GOSs based on exponential distributions is also discussed.     

叠加码的一些新构作

利用集合的并与直积运算建立了新的二元矩阵,从而在已有的叠加码的基础上构作了一些新的叠加码.     

Higher‐order generalized invexity in variational problems

We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd.     

Some results on systems of quasi-variational inclusion problems and systems of generalized quasi-variational inclusion problems

In this paper, we study systems of quasi-variational inclusion problem and systems of quasi-variational disclusion problem. From the existence theorems of solution for these two types of problems, we study various types of systems of quasi-variational inclusion problems, systems of quasi-equilibrium problems, systems of quasi-KKM theorem, abstract economics and system of KKM theorem. We also show their equivalent relations. We study further existence theorems of solution for generalized quasi-variational inclusion problem. Our results are different from any existence result in the literature.     

Generalized Hankel operators and the generalized solution operator to $ \bar \partial $ on the Fock space and on the Bergman space of the unit disc

In this paper we consider Hankel operators = (Id – P ₁) from A ²(?, |z |²) to A ^2,1(?, |z |²)^⊥. Here A ²(?, |z |²) denotes the Fock space A ²(?, |z |²) = {f: f is entire and ‖f ‖² = ∫_? |f (z)|² exp (–|z |²) dλ (z) < ∞}. Furthermore A ^2,1(?, |z |²) denotes the closure of the linear span of the monomials { z ⁿ : n, l ∈ ?, l ≤ 1} and the corresponding orthogonal projection is denoted by P ₁. Note that we call these operators generalized Hankel operators because the projection P ₁ is not the usual Bergman projection. In the introduction we give a motivation for replacing the Bergman projection by P ₁. The paper analyzes boundedness and compactness of the mentioned operators. On the Fock space we show that is bounded, but not compact, and for k ≥ 3 that is not bounded. Afterwards we also consider the same situation on the Bergman space of the unit disc. Here a completely different situation appears: we have compactness for all k ≥ 1. Finally we will also consider an analogous situation in the case of several complex variables. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

n阶仿射平面上d-disjunct矩阵的讨论

分组测试的NGT算法在许多领域有着广泛的应用,它的数学模型是d-disjunct矩阵.近年来,人们借助于复形理论、图理论、空间理论和容错估算等来研究它.介绍了分组测试和仿射平面的基本知识,在n阶仿射平面上构作了d-disjunct矩阵,证明了它的一些性质,与n阶射影平面上的d-disjunct矩阵作了比较.