This paper presents a novel fast and robust model for active contours to detect objects in an image, based on techniques of curve evolution. The proposed model can detect objects whose boundaries are not necessarily defined by gradient, based on the minimization of a fuzzy energy. This fuzzy energy is used as the model motivation power evolving the active contour, which will stop on the desired...

Problems of optimal control are considered in the neoclassical Bolza format, which centers on states and velocities and relies on nonsmooth analysis. Subgradient versions of the EulerLagrange equation and the Hamiltonian equation are shown to be necessary for the optimality of a trajectory, moreover in a newly sharpened form that makes these conditions equivalent to each other. At the same time...

This paper studies optimal control problems for dynamical systems governed by neutral functional-differential inclusions that linearly depend on delayed velocity variables. Developing the method of discrete approximations, we derive new necessary optimality conditions for such problems in both EulerLagrange and Hamiltonian forms. The results obtained are expressed in terms of advanced generaliz...

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective EulerLagrange extremals.

We study the regularity properties of generalized solutions of the EulerLagrange equation of a functional involving capacity and perimeter, related to a conjecture of Pólya and Szegö.

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

We prove a Lagrangian analogue of the Conley conjecture: given a 1-periodic Tonelli Lagrangian with global flow on a closed configuration space, the associated EulerLagrange system has infinitely many periodic solutions. More precisely, we show that there exist infinitely many contractible periodic solutions with a priori bounded mean action and unbounded integer period.

The Karush–Kuhn–Tucker (KKT) optimality conditions and saddle point optimality conditions in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we have obtained the Fritz John (FJ) constraint qualificat...