Variational Inequality Models of Restructured Electricity Systems

In this paper we give a new method to find a grayscale image from a color image. The idea is that the structure tensors of the grayscale image and the color image should be as equal as possible. This is measured by the energy of the tensor differences. We deduce an Euler-Lagrange equation and a second variational inequality. The second variational inequality is remarkably simple in its form. Our equation does not involve several steps, such as finding a gradient first and then integrating it. We show that if a color image is at least two times continuous differentiable, the resulting grayscale image is not necessarily two times continuous differentiable.

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Global prospective electricity systems generation to the year 2025

Renewable Energy and Power Quality Journal ◽

10.24084/repqj09.318 ◽

2011 ◽

pp. 294-299

Author(s):

J. Molina ◽

J. Pérez ◽

E. Muela

Keyword(s):

Electricity Systems

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Topological degree and application to a parabolic variational inequality problem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201004306 ◽

2001 ◽

Vol 25 (4) ◽

pp. 273-287 ◽

Cited By ~ 3

Author(s):

A. Addou ◽

B. Mermri

Keyword(s):

Variational Inequality ◽

Topological Degree ◽

Variational Inequality Problem ◽

Maximal Monotone ◽

Maximal Monotone Operators ◽

Monotone Operators ◽

Parabolic Variational Inequality ◽

Inequality Problem ◽

Monotone Map ◽

New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

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On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽

10.3390/math9030266 ◽

2021 ◽

Vol 9 (3) ◽

pp. 266 ◽

Cited By ~ 1

Author(s):

Savin Treanţă

Keyword(s):

Optimal Control ◽

Variational Inequality ◽

Variational Inequalities ◽

Optimal Control Theory ◽

Infinite Dimensional ◽

Nash Games ◽

New Class ◽

Set Valued Mappings ◽

Differential Variational Inequalities ◽

Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

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