In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital dynamics and Thomas-BMT equations for classical spin vector. We represent the solution of this dynamical system in framework of biorthogonal wavelets via variationa...

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipati...

We discuss in this paper local uniqueness, continuity and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use two types of techniques. One approach consists in formulating variational inequalities in a form of optimization problems, based on regularized gap functions, and applying a general theory of perturbation analys...

this study presents a comparative survey of direct methods for solving variational problems. thisproblems can be used to solve various differential equations in physics and chemistry like rateequation for a chemical reaction. there are procedures that any type of a differential equation isconvertible to a variational problem. therefore finding the solution of a differential equation isequivalen...

the aim of this article is to establish the existence of at least three‎ ‎solutions for a perturbed $p$-biharmonic equation depending on two‎ ‎real parameters‎. ‎the approach is based on variational methods‎.

Variational methods are becoming increasingly popular for the approximate solution of complex probabilistic models in machine learning, computer vision, information retrieval and many other fields. Unfortunately, for every new application it is necessary first to derive the specific forms of the variational update equations for the particular probabilistic model being used, and then to implemen...

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the...