These lectures describe some efforts to understand quark confinement in the context of quantum field theory. First we describe the formation of the SLAC l’bag” (“bubble” or llshell’*) by the strong interaction of an elementary fermion quark field with a quartically self-coupled neutral scalar field. The L%AC bag is derived using a variational approach and a semi-classical (“tree approximation”)...

Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variati...

The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we a discrete field theory Lagrangian density $L_d$ that is modelled as neural network. Careful regularisation the loss function for training necessary obtain suitable numerical computations: derive term optimises solvability Euler--L...

This paper presents an approach which addresses both de-noising and contrast enhancement. In a multiscale wavelet analysis framework, we take advantage of both soft thresholding and hard thresholding wavelet shrinkage techniques to reduce noise. In addition, we carry out nonlinear processing to enhance contrast within structures and along boundaries. Feature restoration and enhancement are acco...

We obtain multiple positive solutions of singular discrete p-Laplacian problems using variational methods.

Abstract We contribute to the field of Ramsey-type equilibrium models with heterogeneous agents. To this end, we state such a model in time-continuous and time-discrete form, which latter case leads finite-dimensional mixed complementarity problem. prove existence solutions problem using theory variational inequalities present further properties its solutions. Finally, compute growth dynamics c...

wetlands as a situ for the growth of native plants, as a habitat for certain species of fish and aquatic birds, and because of their potential economic, cultural and recreational services, are valuable heritage so their protection and conservation is very essential. mostly due to the absence of wetlands services’ valuation, lack of special regulations, and lack of guarantee for these properties...

in this paper, the interaction between an oscillating dipole moment and a silver nanoparticle has been studied. our calculations are based on mie scattering theory and discrete dipole approximation(dda) method.at first, the resonance frequency due to excitingthe localized surface plasmons has been obtained using mie scattering theory and then by exciting a dipole moment in theclose proximity of...