We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

This paper addresses a new class of differential variational inequalities that have recently been introduced and investigated in finite dimensions as a new modeling paradigm of variational analysis to treat many applied problems in engineering, operations research, and physical sciences. This new subclass of general differential inclusions unifies ordinary differential equations with possibly d...

In this paper, the conventional level set method is extended as an efficient approach for shape optimization. The motion of the dynamic interface is governed by Stokes equations. Although this method is not specifically designed for topology optimization, it can handle topology changes easily. Furthermore, a relatively smooth evolution can be maintained without re-initialization. The cost of th...

The paper deals with the shape and topology optimization of the elliptic variational inequalities using the level set approach. The standard level set method is based on the description of the domain boundary as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton-Jacobi equation. In the paper a piecewise constant level set metho...

We construct a variational explicit-solute implicit-solvent model for the solvation of molecules. Central in this model is an effective solvation free-energy functional that depends solely on the position of solute-solvent interface and solute atoms. The total free energy couples altogether the volume and interface energies of solutes, the solute-solvent van der Waals interactions, and the solu...

A nonlinear functional is considered in this letter for segmentation and noise removal of piecewise continuous signals containing binary information contaminated with Gaussian noise. A discontinuity is defined as points in time scale that separates two signal segments with different amplitude spectra. Segmentation and noise removal of a piecewise continuous signal are obtained by deriving equat...

The main aim of this paper is to provide a method that could easily delineate the exact location of tumor region from brain MRI images by integrating the fuzzy c-means and level set method. The proposed method smoothly exploits the spatial function during FCM clustering which in turn proves the automaticity of the method by dividing the original image into clusters and then using one cluster fo...

Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute-solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method to determine stable equilibrium confo...