It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between these polynomials and the corresponding linear operators.

In this paper we study the action of a double infinite matrix A on f ∈ H ν (weighted Banach space, 1 ≤ p ≤ ∞) and on its wavelet coefficients. Also, we find the frame condition for A−transform of f ∈ H ν whose wavelet series expansion is known.

The aim of this note is to demonstrate that Kaplansky–Hilbert lattices and injective Banach lattices may be produced from each other by means of the well known convexification procedure. This is done via the Boolean valued analysis approach. The subject gives a good opportunity to discuss also the relationship between the Kantorovich’s heuristic principle and the Boolean value transfer principl...

Despite the remarkable improvement of hardware and network technology, the inevitable delay from a user's command action to a system response is still one of the most crucial influence factors in user experiences (UXs). Especially for a web video service, an initial delay from click action to video start has significant influences on the quality of experience (QoE). The initial delay of a syste...

In this thesis, we construct an algebraic framework for analyzing committee elections. In this framework, module homomorphisms are used to model positional voting procedures. Using the action of the wreath product group S2[Sn] on these modules, we obtain module decompositions which help us to gain an understanding of the module homomorphism. We use these decompositions to construct some interes...

This article examines the use of action learning sets in a leadership module delivered by a university in south east England. An evaluation research study was undertaking using survey method to evaluate student engagement with action learning sets, and their value, impact and sustainability. Data were collected through a questionnaire with a mix of Likert-style and open-ended questions and qual...

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎. We prove that the semigroup algebra $ell^{1}(S)$ is always‎ ‎$2n$-weakly module amenable as an $ell^{1}(E)$-module‎, ‎for any‎ ‎$nin mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎ ‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎.