We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...

We analyze a variational time discretization of geodesic calculus on finiteand certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on th...

Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from potentials in the classical sense, and as such they are not always amenable to the standard methods of the calculus of variations. We describe here how the selfd...

This paper presents a novel approach to recovering articulatory trajectories from the speech signal using a variational calculus method and Maeda’s articulatory model. The acoustic-toarticulatory mapping is generally assessed by a double criterion: the acoustic proximity of results to acoustic data and the smoothness of articulatory trajectories. Most of the existing methods are unable to explo...

This chapter introduces a robust mathematical formalism for the definition of deliberative agents implemented using a case-based reasoning system. The concept behind deliberative agents is introduced and the case-based reasoning model is described using this analytical formalism. Variational calculus is introduced in this chapter to facilitate to the agents the planning and replanning of their ...

In this paper, some existence theorems of nonzero solutions for a system of bilinear variational inequalities are proved by using the coincidence degree theory in reflexive Banach spaces. The results presented in this paper improve and extend some known results in the literature. © 2008 Elsevier Ltd. All rights reserved.

The solvability of the generalized weak vector implicit variational inequality problem, generalized strong vector implicit variational inequality problem and generalized vector variational inequality problem are proved by using a generalized Fan’s KKM theorem. Our results extend and unify corresponding results of other authors.

We introduce the relative tail pressure to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail pressure is conserved by the principal extension.

In this paper, with the help of the duality operator and K. Fan’s lemma, we present existence results for strong vector equilibrium problems, under pseudomonotonicity assumptions and without any pseudomonotonicity assumptions, respectively. Then, as an application, the main results allow us to state existence theorems for strong vector variational inequality problems.