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Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.
A finite sum S
involving inverse powers of cosines has been studied previously by Fisher, who was able to solve the v=1 and v=2 cases exactly and provide the first term of an “asymptotic solution”. The series is re-visited here by using a completely different approach from Fisher’s...
In this paper, we use duality arguments “ à la Michel Pierre” to establish global existence of classic solutions for a class of parabolic reaction-diffusion systems modeling, for instance, the evolution of reversible chemical reactions.
The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous...
In this paper we consider the persistence of lower dimensional invariant tori for a class of reversible systems, and prove that if the average of the linear terms has full rank, then the invariant torus with Diophantine frequencies persists under small perturbations.
In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship...
The paper considers a problem of construction of asymptotically efficient estimators for functionals defined on a class of spectral densities, and bounding the minimax mean square risks. We define the concepts of H- and IK-efficiency of estimators, based on the variants of...
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