A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, known as the Shortest Vector Problem (SVP). This believed be hard even on quantum computers and thus plays pivotal role post-quantum cryptography. In this work we explore how (efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may used solve SVP. Specifically, map that of finding ground st...

The goal of the paper is to develop a method that will combine use variational techniques with regularization methods in order study existence and multiplicity results for periodic Dirichlet problem associated perturbed Kepler systemx¨=−x|x|3+p(t),x∈Rd, where d≥1, p:R→Rd smooth T-periodic, T>0. critical points action functional proved via non-local change variables inspired by Levi-Civita Kusta...

This article deals with the study of a variational-like inequality problem which involves generalized Cayley operator. We compare our fixed point equation, and based on it we construct an iterative algorithm to obtain solution problem. Convergence analysis as well stability are studied.

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights wh...

VARIATIONAL THEORY: VARIABLE-INDEPENDENCE AND CONSISTENCY Jian-zhong Zhao Geophysics Department, College of Resource, Environment and Earth Sciences, Yunnan University, Kunming, P.R. China 650091 [email protected] Abstract Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper. The problem of variable-independence of variational principles ra...

We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We prove existence and regularity results, and finally show some explicit examples of minimizers. Introduction In this paper we consider a variational p...

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...

In this paper, the bisection of the local mesh refinement in self adaptive finite element is applied to the obstacle problem of elliptic variational inequalities .We try to find the approximated region of the contact in the obstacle problem efficiently .Numerical examples are given for the obstacle problem. Key-Words: obstacle problem, variational inequalities, self adaptive finite element, bis...