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Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and Williamson-type matrices. These latter are four (1,-1) matrices A,B,C,D, of order m, which pairwise satisfy (i) MNT = NMT, M,N ε {A,B,C,D}, and (ii) AAT+BBT+CCT+DDT = 4mIm, where I is the identity matrix. Currently Williamson matrices are known to exist for all orders less than 100 except: 35,39,47,53,59,65,67,70,71,73,76,77,83,89,94. This paper gives two constructions for Williamson matrices of even order, 2n. This is most significant when no Williamson matrices of order n are known. In particular we give matrices for the new orders 2.39,2.203,2.303,2.333,2.689,2.915, 2.1603. [ABSTRACT FROM AUTHOR]

Several authors in recent years investigated the properties of the Moore-Penrose inverse of an arbitrary Boolean relation matrix. The concept of a Moore-Penrose inverse for Boolean relation matrices was discussed first by Rutherford [11] and then independently discovered by Markowsky [8], Plemmons [10], and the author ([3] and [4]). It is natural to inquire whether or not the Moore-Penrose inverse is unique, if it exists. In this paper, the properties of unique Moore-Penrose inverse of an arbitrary Boolean relation matrix are examined in connection with partial order relation and three computational methods for the unique Moore-Penrose inverse for an arbitrary Boolean relation matrix is developed. [ABSTRACT FROM AUTHOR]

Given an n × n grid of n2 points we must select as many as possible so that no three are in a straight line. This paper reviews results concerning the problem and provides a few minor proofs, additions and generalisations. [ABSTRACT FROM AUTHOR]

Many of the operating parameters of semiconductor diode lasers can be related directly to the dielectric wave-guide structure and the carrier injection properties of the junction. Modern lasers virtually all utilize the variable bandgap and refractive index of the GaxAl1−xAs system to control the wave-guide and injection properties, and devices can be designed and made to have specific operating characteristics for given applications. This paper presents a brief review of the important laser characteristics and shows how these can be controlled to achieve the desired performance. The main classes of laser: single heterostructure, double heterostructure, and localized gain region diodes are described, and the performance limitations of each type are discussed under the separate headings of threshold current, efficiency, emission pattern, and peak power limit. [ABSTRACT FROM AUTHOR]

Not only is the equation of state of molecular hydrogen at high density of interest to planetary models and laser fusion, but also the proposals that metallic hydrogen might be a superconductor at high temperature and/or metastable, has recently led to a large amount of theoretical and experimental work. Hydrogen is expected to transform into the metallic phase at a density of about 1 g/cm3, which is 14 times the normal liquid density of the molecular phase. Such a density requires a pressure of several megabars and because of its great compressibility, new approaches to compressing matter are needed. This paper will describe the experimental approaches to obtaining and studying the properties of hydrogen in the megabar region. [ABSTRACT FROM AUTHOR]