The DT-Polynomial Approach to Discrete Time-Varying Network Flow Problems

This paper introduces a polynomial operator called the DT-polynomial as a novel approach to network flow problems. The class of networks dealt with is time-varying in the sense that the capacity, cost, and travel-time of each edge may vary in discrete time. The Dt-polynomial is a polynomial in two operators, D (delay) and T (time), which is used for describing the time-varying transmission characteristics. The paper starts with the mathematics involving the DT-polynomials. A new shortest arrival route algorithm is presented, and its computational complexity is found to be favorable in comparison with others such as Dijkstra's method and the potential method derived from Ford-Fulkerson's technique. Furthermore, a dynamic flow problem is formulated and analyzed in terms of DT-polynomials, and a latest-departure earliest-arrival schedule is given. Finally, a modified DT-polynomial is applied to digital filter networks.     

On Incremental Deformations of Initially Stressed Media with Couple Stresses

A two-dimensional theory for the incremental deformations of an initially stressed continuum with couple stresses is established in this paper. As applications of theory, the problems of internal instability and wave propagation are studied. It is found that the otherwise non-dispersive waves become dispersive, and additional local modes of buckling and vibratory motion are observed. To complete the theory, a stress function formulation of equations is also presented.     

Error Estimation in Numerical Inversion of Laplace Transforms Using Padé Approximation

Uniform asymptotic estimates for the error in the main diagonal and first two subdiagonal Padé approximants for exp(iz) in a sector covering the real z axis are derived. The results are applied to analyze the error in a cerain procedure for the numerical inversion of the Laplace transform.     

An efficient computation of thick microstrip properties on anisotropic substrates

The reproducibility of microwave integrated circuits can be improved by employing substrates which are anisotropic. A method is presented which facilitates the computation of the characteristics of distributed integrated microwave circuits of finite conductor thickness on anisotropic and inhomogeneous substrates. The method is variational and it relies on a quasi-static approach which assumes that the charge distribution on each side of the conductor can be represented by a spatially dependent set of exponential functions.     

Buckling of a continuous beam resting on a tensionless elastic foundation

In this paper, a solution is presented to the buckling problem of a continuous beam resting on a tensionless foundation model that was proposed by Winkler and by Reissner.     

Government programs and the growth of high-technology industries

The research reported in this article was carried out as part of a larger prefect investigating the impact of the US Space Program on the American economy. The author describes the influence of governmental programs in space and defense on the growth of the computer and semiconductor industries. Three types of economic impacts are analyzed: the role of the federal government in financing research and development; the importance of the government as a market, particularly in the early stages of an industry's growth; and the extent to which government policy encouraged the entrance of new firms and permitted the survival of companies that might otherwise have failed. The paper also deals with the contribution of Defense and NASA to the acceleration of technological changes and the development of specialized manpower on which the progress of the industry largely depended.The author concludes that large government programs can play an essential role in the growth of high technology industries. The significance of space-defense programs for US semiconductor and computer firms can only be perceived by reviewing each type of impact-economic, technological and manpower. The government's early R & D support, assured demand during startup periods, encouragement of competition, acceleration of technological progress and its facilitating of professional mobility, are the separate impacts which together greatly aided US firms in their rise to a dominant position in the world semiconductor and computer industries.     

Perforation of Nonlocal Visco- Plastic Plates by a Cylindrical Projectile

This paper is concerned with the analysis of the problem of dynamic perforation of visco-plastic plates by a cylindrical projectile, leading to a failure of the plate by a plug formation. Assuming the behavior of the plate material is nonlocal visco-plastic, the classical theory of visco-plasticity for Bingham solids is generalized to take the non-local effects into consideration. The target plate being thin, it is assumed that only the contributions of vertical shearing stress need be taken into account. The effect of the impact is represented by a uniform velocity distribution over a circular region of the plate surface. The expressions of velocity, strain rate and shear stress are obtained and some particular cases are discussed. Some numerical results concerning stress distributions are also included.     

Modeling of Star-shaped and Parallel-wire Carrier Distribution Systems

It is often desirable to represent carrier distribution systems by networks so that analysis can be made to predict the behavior of these systems. Modeling of two canonical carrier distribution systems, the star-shaped system and the parallel-wire system by networks was carried out in this paper. The representation is given in terms of lumped parameters when the lengths of the carrier lines are short and it is given in terms of lumped and distributed parameters when the lengths of the carrier lines are long.     

The Fourier theorem

It has been tacitly understood that Fourier's representation theorem applies only to a very restricted class of functions. On the contrary, by adopting an appropriate algebraic viewpoint, it is explained in this article how the theorem can be readily extended to include all (non-pathological) functions.