Abstract. We propose to look at (a simplified version of) Heisenberg’s fundamental field equation (see [2]) as a relativistic quantum field theory with a fundamental length, as introduced in [1] and give a solution in terms of Wick power series of free fields which converge in the sense of ultrahyperfunctions but not in the sense of distributions. The solution of this model has been prepared in...

An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independ...

Computational and biological systems are often distributed so that processors (cells) jointly solve a task, without any of them receiving all inputs or observing all outputs. Maximal independent set (MIS) selection is a fundamental distributed computing procedure that seeks to elect a set of local leaders in a network. A variant of this problem is solved during the development of the fly's nerv...

Using the tools of semiconvex duality and max-plus algebra, this work derives a new fundamental solution for the matrix differential Riccati equation (DRE) with time-varying coefficients. Such a fundamental solution, is the counterpart of the state transition matrix in linear time-varying differential equations, and can solve the DRE analytically starting with any initial condition. By parametr...

In this paper we describe the fundamental solution of the equation that is obtained linearizing the Uehling-Uhlenbeck equation around the steady state of Kolmogorov type f(k) = k−7/6. Detailed estimates on its asymptotics are obtained.

(1.4) dYt = μYt dt + σYt dBt (Y0 =1). ∗ Network in Mathematical Physics and Stochastics (funded by the Danish National Research Foundation). ∗ Centre for Analytical Finance (funded by the Danish Social Science Research Council). Mathematics Subject Classification 2000. Primary 60J60, 35K15. Secondary 60J65, 35C15.

The present article deals with the study of propagation of plane waves in isotropic generalized thermoelastic diffusion with voids under initial stress. It is found that, for two dimensional model of isotropic generalized thermoelastic diffusion with voids under initial stress, there exists four coupled waves namely, P wave, Mass Diffusion (MD) wave, thermal (T) wave and Volume Fraction (VF) wa...

Gauge theories induced by scalars in the fundamental representation of the U(Nc)gauge×U(Nf )global group are investigated in the large Nc and Nf limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D = 2) and...