Many problems in Calculus of Variations require the use functionals containing several independent and dependent variables. The first part of this report covers the derivation of the Euler-Lagrange equation for the general functional involving multi-variables vectorvalued functions with fixed boundary. Some of its corollaries and applications will be explored. In the second part we focus on an ...

In this paper, we propose a method for automatic term recognition (ATR) which uses the statistical differences of relative frequencies of terms in target domain corpus and elsewhere. Generally, the target terms appear more frequently in target domain corpus than in other domain corpora. Utilizing such characteristics will lead to the improvement of extraction performance. Most of the ATR method...

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x, y) ≤ σ(d(x, z) +d(z, y)) for some constant σ ≥ 1, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in quasimetr...

In many industries, customers are offered free shipping whenever an order placed exceeds a minimum quantity specified by suppliers. This allows the suppliers to achieve economies of scale in terms of production and distribution by encouraging customers to place large orders. In this paper, we consider the optimal policy of a retailer who operates a single-product inventory system under periodic...

The slow motion of a self-gravitating CP 1 lump is investigated in the approximation of geodesic flow on the moduli space of unit degree static solutions M1. It is found that moduli which are frozen in the absence of gravity, parametrizing the lump’s width and internal orientation, may vary once gravitational effects are included. If gravitational coupling is sufficiently strong, the presence o...

Title: Exoskeleton-assisted Gait Training to Improve Gait in Individuals with Spinal Cord Injury: A Pilot Randomized Study Authors: Shuo-Hsiu Chang ([email protected]) Taimoor Afzal ([email protected]) TIRR SCI Clinical Exoskeleton Group TIRR SCI Clinical Exoskeleton Group ([email protected]) Jeffrey Berliner ([email protected]) Gerard Francisc...

In this paper we address the general problem of approximating, in a certain optimal way, non admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider systems modeled by a subriemanni...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...