The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a differe...

A numerical method for solving the fractional-order logistic differential equation with two different delays FOLE is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the conv...

When underlying financial variables follow a Markov jump-diffusion process, the value function of a derivative security satisfies a partial integro-differential equation (PIDE) for European-style exercise or a partial integro-differential variational inequality (PIDVI) for American-style exercise. Unless the Markov process has a special structure, analytical solutions are generally not availabl...

Recently, Benzoni–Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg’s model for phase-transitional isentropic gas dynamics in terms of convexity of a certain “moment of instability” with respect to wave speed, which is equivalent to variational stability with respect to the associated Hamiltonian ene...

Variational–hemivariational inequalities are useful in applications in science and engineering. This paper is devoted to numerical analysis for an evolutionary variational–hemivariational inequality. We introduce a fully discrete scheme for the inequality, using a finite element approach for the spatial approximation and a backward finite difference to approximate the time derivative. We presen...

Structure-preserving numerical schemes for a nonlinear parabolic fourthorder equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified e...

Preface Variational methods have become more and more important in image processing during the last years. They offer an intuitive way to understand the noise removal and image restoration process as minimisation of an energy functional. This energy functional provides the opportunity to compare the quality of two filtered versions of the same input image and thus can be seen as a quality measu...

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, fractional differential transformation method (CFDTM) and variational iteration (VIM). These models system equation (CFDE) that has no solution. The VIM is based on derivative proved. result revealed both methods in agreement accurate efficient solving ...

Abstract In this paper, we deal with the sensitivity analysis in vector equilibrium problems by using S -derivative of a set-valued mapping. We first investigate on kind gap function for problems. Based these results, estimations perturbed mapping parametric problem are given. Moreover, provide some examples to illustrate obtained results. Finally, derive solutions via variational system.