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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]

The numerous applications in various fields of chemistry and physics have clearly demonstrated the potential of X-ray photoelectron spectroscopy. A number of interesting experimental projects will be completed in the near future and papers with new and more reliable reference data will appear in the literature. Further refinement of the theoretical models will add to the fundamental understanding of the obtained results. And last, but not least new developments in instrumentation will keep pace with the practical and theoretical experience and open up new areas, which so far could not be penetrated because of resolution, sensitivity or sample handling problems. [ABSTRACT FROM AUTHOR]

There are two general conclusions which can be drawn from the numerical investigations reported in this paper. The equation solved has a very mild non-linearity and yet the solutions exhibit a remarkable variety of possible forms. This fact should perhaps stand as a warning against drawing conclusions from limited amounts of numerical evidence when non-linear equations of the complexity of the Navier-Stokes equations are being solved. In arriving at conclusions about the structure of the solutions of this equation, both analysis and numerical work were needed and the investigation proceeded with a continuous interchange between the two methods of examining the equation. The success of such cooperation in this instance is evidence that more may be achieved by a combination of analytical and numerical techniques than can be obtained by either in isolation. [ABSTRACT FROM AUTHOR]

Non-hydrostatic convection is studied by numerical integration of a Boussinesq system in three space dimensions and time. To simulate cloud convection, parameterized effects of latent heat and small-scale turbulence have been included. In this paper, the results are compared, in simplified cases without the parameterizations, with cell structure observed in Rayleigh-Bénard laboratory convection experiments in air. At a Rayleigh number of 4000, the numerical model successfully simulates the experimentally observed evolution, including some prominent transient features, of the flow from a randomly perturbed conductive initial state to a final state of large-amplitude, steady, two-dimensional rolls. At a Rayleigh number of 9000, the model reproduces the experimentally observed unsteady equilibrium of vertically coherent oscillatory waves superimposed on rolls. In both cases, good quantitative agreement with laboratory data is obtained. [ABSTRACT FROM AUTHOR]

As can be seen from the results presented in this paper, three-dimensional and time-dependent boundary layer flows can be calculated in a reasonable amount of time with the current generation of computers. However, serious individual problems with the initial conditions and uniqueness of the numerical methods still exist, and of course there is the ever-present problem of very few time-dependent and three-dimensional inviscid flow solutions. [ABSTRACT FROM AUTHOR]

This paper presents a review of the charge-transfer mechanisms in charge-transfer devices. Special attention is given to the similarity of the physics of the transfer processes that occur in integrated MOS bucket brigades, surface charge-coupled devices, and bulk charge-coupled devices. The results of theoretical analysis and experimental measurements are used to compare the performances expected from the mentioned devices. The comparison indicates that bulk chargecoupled devices are capable of the highest performance in terms of operating frequency and charge-transfer inefficiency at all possible levels of signal charge. [ABSTRACT FROM AUTHOR]

This paper gives the results of recent experiments on the electrical, magnetic, optical and structural properties of layer type crystals. It deals in particular with the layer type transition metal dichalcogenides, MX2, and representative members are ZrS2, NbSe2, MoS2. These materials have been the subject of fairly intense activity during the past few years. It is argued that in NbSe2, there is a relatively narrow "d" band based on overlap of dz2 orbitals on the Nb atoms lying in the plane of the sandwich, and that it is this band which is the basis of many of the interesting physical properties, Phenomena such as excitons, screening effects, conduction in narrow "d" bands, superconductivity and the metal-insulator transtion are all encountered. Interaction of the MX2 crystals with a variety of organic and inorganic molecules and atoms can lead to quite dramatic changes in the physical properties. Long chain organic amines inserted between the MX2 layers in the van der Waal's gap can separate the layers by large distances approaching 60 Å, and the intercalated crystals still remain superconductors. These experiments, together with those in which superconductivity is found in crystals of NbSe2 a until cell in thickness (c 12 Å), suggests we may be concerned with essentially two dimensional superconductivity, but this is still an open and controversial point. [ABSTRACT FROM AUTHOR]

This paper surveys recent work on the oxide cathode. This work points to a physical model of the oxide cathode in which (1) current is carried through the cathode by semiconduction through the oxide and by pore conduction through the interstices between oxide particles, (2) both conduction process are controlled by the properties of the semiconducting oxide, (3) the oxide is activated by the production of electron donors, (4) the donors, as well as other constituents of the oxide, are mobile at the normal operating temperature of the cathode, and (5) electrolysis of the donors limits the density of free electrons available for conduction near the emitting surface and the density of free electrons available for emission at the emitting surface. [ABSTRACT FROM AUTHOR]

The present paper deals with something about the influence of adsorbed impurity centres on the electrical properties of germanium and silicon. After a historical review and an introduction to the fundamental conceptions (§ 2), the essential properties of semiconductor surfaces are discussed. § 3 deals with surface recombination and after an illustration of the term of surface recombination velocity summarizes measuring methods and experimental results; furtheron, the influence on the electrical behaviour of rectifiers and transistors is discussed, and finally, the effective surface recombination is dealt with. § 4 contains a review of measuring methods and experimental results on work function and contact potential. § 5 describes the surface conduction, particularly the channels. § 6 reviews the surface model of Brattain and Bardeen, commonly used for the explanation of surface properties. In the following chapters, the physical properties of surfaces are, under simplified conditions, treated quantitatively, and, as far as possible, illustrated by experimental examples. In § 7, the occupation of surface terms under thermal equilibrium as a function of density and energy level is derived, and work function and surface conductivity, including field effect, are discussed. § 8 deals with surface recombination, i. e. with electron transitions between surface levels and energy bands. § 9 describes the theory of work function under the influence of ligth as developed by Brattain and Bardeen. Finally, § 10 deals with the special properties of channels, namely, with Schrieffer's theory of carrier mobility in channels, on one side, and the channel conductivity parallel to the surface, on the other. § 11 discusses the influence of channels on the dc and ac behaviour of rectifiers and transistors as far this is possible today. [ABSTRACT FROM AUTHOR]

In this paper, the mutual interactions, leading to additional attractive or repulsive forces, between material lattice defects in (preferentially ionic) crystals are reviewed from the point of view of the theory of thermal disorder founded by Frenkel, Schottky and Wagner. At first the physical nature of the possible forces and their types of force law (wide or low range) are discussed. Of these, Coulomb and chemical (valence) interactions seem to be of much higher importance than those created by different polarizabilities, by elastic distortion of the lattice or by lattice vibrations. Values of binding energies known from detailed calculations or experimental data are reported. Then the methods of calculating the thermal equilibrium of the defects are critically studied. Starting from the well-known concepts of association (especially adapted to low range forces) and of the Debye-Hückel ionic cloud (successful in the theory of strong liquid electrolytes), it is shown that a combination of both will approximate best the real equilibrium of interacting defects in ionic crystals and semiconductors, an exact description lacking until now for higher than "infinitely small" concentrations of defects. This combined theory is essentially identical with one advanced by Bjerrum for aqueous electrolytes. Also in crystals, the Bjerrum critical radius will reasonably separate between associated defects and those belonging to the ionic cloud. Owing to the comparatively small dielectric constant in most of the crystals, the second region here generally is of small importance. To extend the validity of the calculations towards higher defect concentrations seems still highly desirable. After outlining the non-equilibrium states of defects, the methods of experimental detection of defect interactions are briefly described, summarizing the most important results. These methods include ionic conductivity, self diffusion and diffusion of foreign ions, dielectric loss, optical absorption and its successive phenomena (luminescence, photochemical reactions), and magnetic methods (nuclear resonance). [ABSTRACT FROM AUTHOR]

Under certain conditions, an increased contact resistance and rectifier effect not only appears at the boundary between a metal and a semiconductor but—as mainly observed by Joffé—also at the boundary between two semiconductors. These zones, the conductivity of which differs from the interior of the semiconductor, are generally situated on both sides of the boundary. Therefore, this layer is called "Doppelrandschicht" (double-barrier layer) in contradistinction to the barrier layer at the metal-semiconductor boundary. This paper deals with the theory of such double-barrier layers, primarily reported earlier by Gubanow. When two semiconductors of opposite conductivity type (n-type and p-type) are in contact, a difference must be made between the two critical cases in which the electrons and holes either recombine directly at the boundary, or by means of thermal energy pass into the other semiconductor and then recombine in the interior thereof. It is shown that in accordance with the last-mentioned transition mechanism the theory contains Shockley's theory of homogeneous p—n junctions as a special case. Double-barrier layers having one semiconductor adjoining another semiconductor of the same conductivity type are dealt with by applying to this case the method used by Schottky and Spenke for metal-semiconductor contacts with altered boundary conditions. Contacts between two semiconductors may appear also in the boundary region metal-semiconductor by the growing of intermediate layers, e. g. in consequence of diffusion of proper impurities. Two cases of special interest, the theory of which is also given by Gubanow, are discussed: in the first case a metal-semiconductor arrangement, the contact potential of which is so great that in the semiconductor grows an opposite-type zone at the boundary, a so-called inversion layer, and in the second case such an arrangement having a thin opposite-type semiconducting intermediate layer with the same fundamental lattice as the semiconductor, otherwise however, chemically differing from it. Finally, using the theories developed, the question of the barrier mechanism of technical copper oxide and selenium rectifiers is discussed. [ABSTRACT FROM AUTHOR]

The difference between the chemical potentials of the electrons, respectively the Fermi levels in two phases in contact, produces space charge layers at the phase boundaries. At the phase boundary between a semiconductor and a gas, the gas particles are bounded and an electronic equilibrium between adsorbed particles and the solid is produced (chemisorption). The production of a space charge barrier layer at the surface of the solid, which is a consequence of this equilibrium may explain many observed effects involving the interaction of gases and semiconductors. The application of these considerations is limited to the temperature range in which an electron exchange between gas and semiconductor is possible, however, the transportation of ionic impurities in the semiconductor does not take place. The following effects related to chemisorption on semiconductors are tretaed: Change of conductivity, variation of the electron work function, kinetics of chemisorption and influence on luminescence and the electro-optical properties. In the following discussion connections with other papers were maintained, and some arguments, as well as possible extensions of the theoretical foundation, were offered. [ABSTRACT FROM AUTHOR]

The usual treatment of the interaction between electrons and lattice-oscillations using pertubation-theory becomes inapplicable, if the coupling is too strong. An important example is that of an electron moving in a polar medium. If one tries to explain superconductivity with aid of the interaction between electrons and lattice oscillations, such a strong coupling is also to be taken into account. A survey of a number of recent papers is therefore given, in which other methods of approximation better than perturbation-theory have been developed. In the case of an electron in a polar medium the variational calculus predominates. The many-electron problem in superconducters on the other hand is treated by several kinds of special canonical transformations. The connection between the (exactly determined) stationary states of the whole system consisting of electrons and lattice-oscillations and a description using the conception of scattering is treated in some detail. [ABSTRACT FROM AUTHOR]

The most general type of a wave function for an electron ensemble in a periodic lattice is developed and discussed in the paper. Approximate solutions may be built up either from Bloch functions or from atomic functions of the single electrons. The relations between these two representations are discussed for a number of cases and possible extensions are outlined. The principles of the energy term structure of electron ensembles in solids may be understood in this way as well as the limitations in the applicability of the approximations used. Some applications of the results to the theory of ferromagnetism and of ionic crystals are discussed. For further progress it seems necessary to develop a theory which takes into account the Coulomb correlation of the electrons in a more satisfactory way. [ABSTRACT FROM AUTHOR]