The quantization of the electromagnetic field in vacuum is presented without reference to lagrangean quantum field theory. The equal time commutators of the fields are calculated from basic principles. A physical discussion of the commutators suggest that the electromagnetic fields are macroscopic emergent properties of more fundamental physical system: the photons.

This paper deals with systems of fuzzy inequalities. It shows that a system of fuzzy inequalities with piecewise linear membership functions can be converted to a one-constraint nonlinear programming problem by employing the concepts of constraint surrogation and maximum entropy. An augmented Lagrangean algorithm is then applied to solve the resulting problem. Some computational results are inc...

We consider a variational problem, where the Lagrangean is of the form f(∇u)+αu. We introduce an explicit family of solutions to this problem and we prove uniqueness and comparison results. We show that as α tends to zero, the solutions converge to solutions of the limiting variational problem where α = 0.

The quantization of SU(2) Yang-Mills theory reduced to 0 + 1 space-time dimensions is performed in the BRST framework. We show that in the unitary gauge A0 = 0 the BRST procedure has difficulties which can be solved by introduction of additional singlet ghost variables. In the Lorenz gauge Ȧ0 = 0 one has additional unphysical degrees of freedom, but the BRST quantization is free of the problems...

In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian. ∗This work is supported by a grant from CNPQ-Brazil

Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Article A Hierarchical Lagrangean Relaxation Procedure for Solving Midterm Planning Problems Anshuman Gupta, and Costas D. Maranas Ind. Eng. Chem. Res., 1999, 38 (5), 1937-1947• DOI: 10.1021/ie980782t • Publication Date (Web): 26 March 1999 Downloaded from ...

We address the problem of planning the cap~ city augmentation of a packet-switching network with given routing and topology under uncertainty of future costs and traffic requirements. Recent advances in hierarchical planning and lagrangean relaxation techniques allow to minimize the present cost plus the expected value of future costs, without exceeding a specified threshold for the average delay.

Convex nondifferentiable, also known as convex nonsmooth, optimization (NDO) looks at problems where the functions involved are not continuously differentiable. The gradient does not exist, implying that the function may have kinks or corner points, and thus cannot be approximated locally by a tangent hyperplane, or by a quadratic approximation. Directional derivatives still exist because of th...

This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules.