We approach uncertainty principles of Cowling-Price-Heis-enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in The optimal constant these is the smallest eigenvalue inverse operator. Euler-Lagrange equations for associated functional provide eigenfunctions operators. As by-product proofs derive gener...

In 1980’s, Lee proposed an energy-preserving discrete mechanics with variable time steps by taking (discrete) time as dynamical variable [2, 3, 4]. On the other hand, motivated by the symplectic property of Lagrangian mechanics, a version of discrete Lagrangian mechanics has been devoloped and variational integrators that preserve discrete symplectic two form have been obtained [11, 12, 15, 16,...

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

We consider the variational inequality, which describes the torsion problem for a long elasto-plastic bar. Using duality methods of the variational calculus, we derive a posteriori estimates of functional type that provide computable and guaranteed upper bounds of the energy norm of the difference between the exact solution and any function from the corresponding energy space that satisfies the...

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis’ entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is amalgamated with Hopfield-like learning rules resulting in an unsupervised learning model. The update rules are formulated with the aid of q-deformed calculus. Num...

This paper demonstrates how discrete exterior calculus tools may be useful in computer vision and graphics. A variational approach provides a link with mechanics.

We prove a DuBois–Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets of nondifferentiable functions. As an application, we obtain a constant of motion for a linear Schrödinger equation. AMS Subject Classifications: 49K05, 49S...