Construction of hjelmslev planes from (t,k)-nets

A (t, k)-net is an abstract generalization of the incidence structures which occur as the point and line neighborhoods of a finite Hjelmslev plane. A (t, k)-net contains ‘substructures’ which are nets of ordert and degreek. Every (t, r) Hjelmslev plane (brieflyH-plane) can be constructed from a suitable collection of (t, r+1)- and (t, r)-nets. A (t, r)H-plane or (t, k)-net is called extremal provided: each two points which are joined by more than two lines are joined by preciselyt lines and dually. IfB is a ‘properly’ extremal (t, r)H-plane (means both 2 andt≠2 occur among the joining numbers), thent is even; andr=2 orr=1+(t/2). All the 3-uniform [J. Combinat. Theory 9, 267–288 (1970, this Zbl.204, 210)] (4, 2)H-planes are examples. Two further examples are constructed in the paper: an (8, 2) translationH-planeC and an (8, 2) projectiveH-planeD, none of whose affineH-planes are translationH-planes. All point neighborhoods fromC andD and all line neighborhoods fromD are isomorphic to a give (8, 3)-netE;E is constructed by considering the subspaces of a 64-point symplectic geometry overZ ₂.E is also used to answer (affirmatively) the question of the existence of proper fairly near affineH-planes [J. Combinat. Theory 16A, 34–50 (1974)].     

A combinatorial characterization of (t,m,s)-nets in base b

We consider (t,m,s)-nets in base b, which were introduced by Niederreiter in 1987. These nets are highly uniform point distributions in s-dimensional unit cubes and have applications in the theory of numerical integration and pseudorandom number generation. A central question in their study is the determination of the parameter values for which these nets exist. Niederreiter has given several methods for their construction, all of which are based on a general construction principle from his 1987 paper. We define a new family of combinatorial objects, the so-called “generalized orthogonal arrays,” and then discuss a combinatorial characterization of (t.m.s)-nets in base b in terms of these generalized orthogonal arrays. Using this characterization, we describe a new method for constructing (t.m.s)-nets in base b that is not based on the aforementioned construction principle. This method gives rise to some very general conditions on the parameters (involving a link with the theory of orthogonal arrays) that are sufficient to ensure the existence of a (t.m.s)-net in base b. In this way we construct many nets that are new. © 1996 John Wiley & Sons, Inc.     

New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences

In this paper, we derive new general upper bounds on the star discrepancy of $(t,m,s)$ -nets and $(t,s)$ -sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.     

A Note on Geometric Structures of Linear Ordered Orthogonal Arrays and (T,M,S)-Nets of Low Strength

The equivalent geometrical configurations of linear ordered orthogonal arrays are determined when their strengths are 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.     

A 1-(S,T)-edge-connectivity augmentation algorithm

Received January 1995 / Revised version received April 1996 Published online March 16, 1999     

$M$-半群的直觉$(S,T)$-模糊$M$-子半群的性质

K.T.Atanassov在1986年首先引入直觉模糊集的概念,本文利用s-范数和t-范数,引入M-半群的直觉(S,T)-模糊M-子半群的概念,刻画其性质和特征,我们再进一步给出了直觉(S,T)-直积的概念,并由此探讨了一些有意义的相关结论。     

广义逆A_(T,S)~(2)的子式

The explicit expression for the generalized inverse A_(T,S)~2 in [6] is utilized in presenting the minors of the generalized inverse A_(T,S)~(2). Thus, without calculating M-P inverse, weighted M-P inverse, group inverse and Drazin inverse, we are able to find the minors of them. The main results are also the generalization of the results proposed by [5] and [8].     

广义逆A_(T,S)~(2)的子式

１．引 言 设Ａ∈Ｃｍ×ｎ,Ｍ和Ｎ分别为ｍ和ｎ阶Ｈｅｒｍｉｔｅ正定阵,考虑下列方程 （１） ＡＸＡ＝Ａ （２） ＸＡＸ＝Ｘ （３）（ＡＸ）＊＝ＡＸ （４）（ＸＡ）＊＝ＸＡ （３Ｍ）（ＭＡＸ）＊＝ＭＡＸ （４Ｎ）（ＮＸＡ）＊＝ＮＸＡ 如果Ｘ∈Ｃｎ×ｍ满足条件（１）和（２）,则称Ｘ为Ａ的自反广义逆,记作Ｘ＝Ａ（１,２）;如果 Ｘ满足条件（２）,则称Ｘ为 Ａ的｛２｝逆,记作 Ｘ＝Ａ（２）;如果Ｘ满足（１）－（４）,则称Ｘ为 Ａ的 Ｍ－Ｐ逆,记作Ｘ＝Ａ＋;如果Ｘ满足（１）、（２）、（３Ｍ）、（４Ｎ）,则称 Ｘ为 Ａ的加权…     

广义逆A_(T,S)~(2)的一种计算方法

本文给出了利用特征多项式求矩阵广义逆AT,S(2)的一种计算方法,并由此得到了加权M-P逆AM,N+、M-P逆A+、Drazin逆Ad及群逆A9的相应计算方法,推广了文献[2]的结果.     

广义逆A(2)T,S的子式

1.引言 设A∈Cm×n,M和N分别为m和n阶Hermite正定阵,考虑下列方程 (1) AXA = A (2) XAX = X (3) (AX)* = AX (4) (XA)* = XA (3M) (MAX)* = MAX (4N) (NXA)* = NXA 如果X∈Cm×m满足条件(1)和(2),则称X为A的自反广义逆,记作X=A(1,2);如果X满足条件(2),则称X为A的{2}逆,记作X=A(2);如果X满足(1)-(4),则称X为A的M-P逆,记作X=A+;如果X满足(1)、(2)、(3M)、(4N),则称X为A的加权M-P逆,记作A+MN.     

广义逆A(2)T,S的一种计算方法

本文给出了利用特征多项式求矩阵广义逆AT，S^(2)的一种计算方法，并由此得到了加权M—P逆AM，N^ 、M—P逆A^ 、Drain逆Ad及群逆A9的相应计算方法，推广了文献[2]的结果．     

广义逆A(2)T,S的一个特征

给出了矩阵广义逆AT,S^(2)的一个特征，并由此建立了AT,S^(2)的一种算法。     

关于广义逆矩阵AT,S^（2）的极限表示的注记

1引言文[1]中应用广义逆矩阵A_r.s~(2)的一个极限表示给出了计算A_r.s~(2)r嵌入法(imbeddingmethod).但对其主要结果定理1,即A_r.s~(2)的极限表示。并没有给出严格的证明，实际上其证明并不是显然的。本文于此给出A_r.s~(2)的极限表示的一种严格的证明，并叙述许多常用广义逆的极限表示，作为文[1]的补充。     

广义逆A(2)T,S的几种秩关系式

利用矩阵A的广义逆A(2)T,S的Moore-Penrose逆表示式,得到了与广义逆A(2)T,S相关的几种秩等式和不等式,并由此得到了加权Moore-Pensore逆,Moore-Pensore逆,Drazin逆及群逆的相应结论.     

The impact of unknown demand parameters on (R,S)-inventory control performance

For a given inventory control system and a known stationary demand pattern, it is relatively easy to calculate the safety factors needed to satisfy predetermined performance criteria. It is more or less customary to use these standard safety factors in practical situations as well. In practice, however, demand parameters are unknown, causing additional variation. Consequently, the performance of this standard approach generally stays below the desired level. Hence, the safety factors should be increased.This general phenomenon is studied here in some detail for an (R,S)-inventory control system with normal demand, using the two best-known service criteria. Simple exponential smoothing is used to estimate the unknown demand parameters. Using large simulation runs, new (constant) safety factors are found that do satisfy the given service levels.They are not suitable for practical use, however: long series of past observations usually are not available, while stationary demand is rare. Therefore, time-varying safety factors are presented that seem to perform well for normal demand with unknown parameters.     

OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A_(T,S)~(2)

. IntroductionIn this paper we adopt the same notations on generalized inverses of matrices andprojectors as those in [1].Several rePresentations for the generalized inverses of matrices, for example, those forthe Moors-Penrose inverse A and the Drazin inverse A(d), have led to[1--4]:where k = index (A).In order to study the matrix form of the above-mentioned operator represelltations,we denote linear operators by A, B,' ', and their matrices by the corresponding A, B,' '.All of the li…     

计算广义逆A_(T,S)~(2)的迭代法

1引言与引理 文【l}中Ben一Israel与Greville给出了计算矩阵A的Moore一penrose逆的一阶和p阶 迭代法，陈永林图推广了11]的结果，给出了类似的计算矩阵A的具有指定值域T与零 空间s的(z)一逆A级公的一阶迭代法 X* ，=X、 X0(I一AX*)，k=0，1，2，二 刘桂香:计算广义逆A钾:的迭代