We present a kinetic version of the Watanabe-Strogatz (WS) transform for vector models in this paper. From generalized WS-transform, we can reduce model into an ODE system. also obtain cross-ratio type constant motion functionals under suitable conditions. sufficient and necessary conditions existence suggested functionals. As application functional, provide instability bipolar states swarm sph...

In this paper we prove that the steepest descent of certain porous-medium type functionals with respect to the quadratic Wasserstein distance over a constrained (but not weakly closed) manifold gives rise to a nonlinear, nonlocal parabolic partial differential equation connected to the study of the asymptotic behavior of solutions for filtration problems. The result by Carlen and Gangbo on cons...

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof PBE generalized-gradient approximation GGA , as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and...

We show existence of an optimal control and a saddlepoint for the zero-sum games associated with payoff functionals of mean-field type, under a dynamics driven by a class of Markov chains of mean-field type.

K. Mehlhorn introduced a class of polynomial time computable operators in order to study poly time reducibilities between functions. This class is deened using a generalization of A. Cobham's deenition of feasibility for type 1 functions to type 2 functionals. Cobham's feasible functions are equivalent to the familiar poly time functions. We generalize this equivalence to type 2 functionals. Th...

About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...

About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of smoothness, K-functionals, realization functi...

In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and Γ-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functiona...

The (PS)-weak lower semicontinuity property has been introduced in Vasiliu and Yan [10] for general continuously differentiable functionals on Sobolev spaces in connection with the Ekeland variational principle and the direct method of calculus of variations. In this paper, we give a necessary and sufficient condition of this property for the functionals in one-dimension of the simple type I(u)...

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect t...