Frequency and temperature dependence of a.c. conductivity of vitreous silver phosphate electrolytes

The a.c. conductivity behaviour in the 20–300 K temperature range has been investigated for (Ag₂S)_x(AgPO₃)_1−x and (Ag₂SO₄)_x(AgPO₃)_1−x glasses at various salt contents (x). The temperature dependence at selected frequencies in the radioand micro-wave region displays several relaxational contributions which are indistinct in the frequency domain. The low temperature experimental data are discussed and a proposed ‘new universality’ has been examined.     

Note on a proposed weighted residual method for solving nonlinear differential boundary problems

A proposed iterative method for solving nonlinear differential two-point boundary value problems is generalized and shown to be equivalent to using the standard method of adjoints on a linearized form of the nonlinear boundary-value problem.     

O.R. in the Company Car Fleet: When Simple is Efficient

The management of a large fleet of company vehicles represents a significant administrative activity, particularly when the company is a motor vehicle manufacturer and the fleet consists of its own products. The approach taken by the Operational Research Group was to cross departmental boundaries to smooth vehicle ordering, reduce inventories of vehicles awaiting delivery and optimize resale values. The method steers between two potential pitfalls: that of ‘optimizing’ one affected department to the detriment of others, and that of developing sophisticated scheduling and forecasting algorithms which the users would not understand and therefore not trust.     

Properties of a representation of a basis for the null space

Given a rectangular matrixA(x) that depends on the independent variablesx, many constrained optimization methods involve computations withZ(x), a matrix whose columns form a basis for the null space ofA ^T(x). WhenA is evaluated at a given point, it is well known that a suitableZ (satisfyingA ^T Z = 0) can be obtained from standard matrix factorizations. However, Coleman and Sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously withx; they also suggest several techniques for adapting these schemes so as to ensure continuity ofZ in the neighborhood of a given point.This paper is an extension of an earlier note that defines the procedure for computingZ. Here, we first describe howZ can be obtained byupdating an explicit QR factorization with Householder transformations. The properties of this representation ofZ with respect to perturbations inA are discussed, including explicit bounds on the change inZ. We then introduceregularized Householder transformations, and show that their use implies continuity of the full matrixQ. The convergence ofZ andQ under appropriate assumptions is then proved. Finally, we indicate why the chosen form ofZ is convenient in certain methods for nonlinearly constrained optimization.The research of the Stanford authors was supported by the U.S. Department of Energy Contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; the National Science Foundation Grants MCS-7926009 and ECS-8312142; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-84-K-0156.The research of G.W. Stewart was supported by the Air Force Office of Scientific Research Contract AFOSR-82-0078.     

The effect of stereochemistry on the mass spectra of the bis(trimethyl-silyl) esters of maleic and fumaric acids

The mass spectra of the bis(trimethylsilyl) esters of maleic and fumaric acids provide a simple and particularly striking example of the influence of stereochemistry on the electron-impact-induced fragmentation of organic molecules. The results provide evidence for the structural significance of the m/e 147 ion, which is considerably more intense in the maleate spectrum than in the fumurate spectrum.     

The elastic behaviour of tetrahedral materials with vacant sites

As part of a study of defect tetrahedral structure compounds, the elastic constants of single crystal specimens of Hg₃Ga₂□Te₆ and HgIn₂□Te₄ have been measured between 77 K and room temperature using the pulse superposition technique. These compounds are included in the series HgTe, Hg₅In₂□Te₈, Hg₃In₂□Te₆ and HgIn₂□Te₄ and HgTe, Hg₅Ga₂□Te₈, Hg₃Ga₂□Te₆ where there is a progressive increase in the concentration of vacant sites. While the other compounds studied are cubic, HgIn₂□Te₄ has a tetragonal structure with a $\text{c}\text{a}$ ratio of 2.0. The components of the elastic stiffness tensor of this material at 77 K are (in units of 10¹¹ dyne cm^?2) C₁₁ = 4.31 C₁₂ = 2.54 C₄₄ = 2.14 C₃₃ = 4.47 C₁₃ = 2.18 C₆₆ = 2.41. In a cubic material C₁₁ = C₃₃, C₄₄ = C₆₆ and C₁₂ = C₁₃: the elastic behaviour of this tetragonal compound closely resembles that of a cubic material, as might be anticipated from its structure. This similarity is further illustrated by reference to the symmetry of phase velocity and Young's modulus surfaces. Examination of the elastic constants and reduced elastic constants of these compounds shows a regular trend, the elastic stiffness decreases as the number of vacant sites increases. There is an approximately linear relationship between the reduced bulk modulus and the number of sited vacancies.