A new algorithm for parallel solution of linear equations

Abstract is not available.

Supersymmetric Solution Of Gauge Hierarchy Problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

On the non-existence of hydrodynamic solution of surface plasmons at the bimetallic interface

It is shown that for an abrupt bimetallic interface a hydrodynamic solution for interface plasmons does not exist. It appears that this result is valid irrespective of the choice of of the additional boundary condition, thereby suggesting a careful look at the use of usual hydrodynamic equations for a bimetallic interface.

On the Solution of Certain Simultaneous Pairs of Dual Integral Equations

Mit einer direkten Methode, bei der der Erdelyi-Kober- und der modifizierte Hankel-Operator Anwendung finden, werden gewisse Systeme aus zwei bzw. drei Paaren dualer Integralgleichungen mit Bessel-Kernen in geschlossener Form gelöst. Für bestimmte Funktionenklassen und Ordnungen der Bessel-Funktionen ist die Vorgehensweise angebrachter und geeigneter als die bereits existierenden Methoden.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.

A new framework for solution of multidimensional population balance equations

A new framework is proposed in this work to solve multidimensional population balance equations (PBEs) using the method of discretization. A continuous PBE is considered as a statement of evolution of one evolving property of particles and conservation of their n internal attributes. Discretization must therefore preserve n + I properties of particles. Continuously distributed population is represented on discrete fixed pivots as in the fixed pivot technique of Kumar and Ramkrishna [1996a. On the solution of population balance equation by discretization-I A fixed pivot technique. Chemical Engineering Science 51(8), 1311-1332] for 1-d PBEs, but instead of the earlier extensions of this technique proposed in the literature which preserve 2(n) properties of non-pivot particles, the new framework requires n + I properties to be preserved. This opens up the use of triangular and tetrahedral elements to solve 2-d and 3-d PBEs, instead of the rectangles and cuboids that are suggested in the literature. Capabilities of computational fluid dynamics and other packages available for generating complex meshes can also be harnessed. The numerical results obtained indeed show the effectiveness of the new framework. It also brings out the hitherto unknown role of directionality of the grid in controlling the accuracy of the numerical solution of multidimensional PBEs. The numerical results obtained show that the quality of the numerical solution can be improved significantly just by altering the directionality of the grid, which does not require any increase in the number of points, or any refinement of the grid, or even redistribution of pivots in space. Directionality of a grid can be altered simply by regrouping of pivots.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Ultrasonic studies in chemically active liquid media (1) aqueous solution of N2O4

Using a pulse method the ultrasonic absorption has been studied in the frequency range of 2 to 10 Mc/s in dilute aqueous solutions of nitrogen tetroxide gas at room temperature. The absorption peaks (αλ vs frequency) observed in this study are attributed to the ionic dissociation reaction of the nitrous acid into its constituent ions. The rate constants of the forward and backward reactions are calculated using the theory of Tabuchi. The variation of the logarithm of the rate constant of the bimolecular ionic reaction, namely, log10 kb, with the square root of ionic strength qualitatively follows Brönsted's theory for ionic reactions in solutions.

Asymtotic solution of the Frieman and Book equation for the pair-correlation function

Using Thomé's procedure, the asymptotic solutions of the Frieman and Book equation for the two-particle correlation in a plasma have been obtained in a complete form. The solution is interpreted in terms of the Lorentz distance. The exact expressions for the internal energy and pressure are evaluated and they are found to be a generalization of the result obtained earlier by others.