We work in set-theory without choice ZF. Given a closed subset F of [0, 1] which is a bounded subset of l(I) (resp. such that F ⊆ l(I)), we show that the countable axiom of choice for finite subsets of I, (resp. the countable axiom of choiceACN) implies that F is compact. This enhances previous results where ACN (resp. the axiom of Dependent Choices DC) was required. Moreover, if I is linearly ...

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

This chapter will discuss attempts to produce formal mathematical models for dynamical simulation of the development process of Free/Open Source Software (F/OSS) projects. First, a brief overview for simulation methods of closed source software development is given. Then, based on empirical facts reported in F/OSS case studies, we describe a general framework for F/OSS dynamical simulation mode...

This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put...

Let R be an integral domain of finite type over Z and let f : X → SpecR be a smooth projective morphism of relative dimension d ≥ 1. We investigate, for a vector bundle E on the total space X , under what arithmetical properties of a sequence (pn, en)n∈N, consisting of closed points pn in SpecR and Frobenius descent data Epn ∼= F n(F) on the closed fibers Xpn , the bundle E0 on the generic fibe...

We show that on a closed smooth manifold M equipped with k fiber bundle structures whose vertical distributions span the tangent bundle, every smooth diffeomorphism f of M sufficiently close to the identity can be written as a product f = f1 · · · fk, where fi preserves the ith-fiber. The factors fi can be chosen smoothly in f . We apply this result to show that on a certain class of closed smo...

Let X and Y be independent 2-dimensional Brownian motions, X(0) = (0, 0), Y (0) = (ε, 0), and let p(ε) = P (X[0, 1] ∩ Y [0, 1] = ∅), q(ε) = {Y [0, 1] does not contain a closed loop around 0}. Asymptotic estimates (when ε → 0) of p(ε), q(ε), and some related probabilities, are given. Let F be the boundary of the unbounded connected component of R2\Z[0, 1], where Z(t) = X(t) − tX(1) for t ∈ [0, 1...

Let X ⊂ R be a closed semialgebraic set and let f P(X) be the ring obtained from the characteristic function of X by the operations +, −, ∗, the half link operator and by the polynomial operations with rational coefficients which preserve finite formal sum of signs. McCrory and Parusiński proved that necessary conditions for X to be semialgebraically homeomorphic to a real algebraic set is that...

A quadrangulation G on a closed surface F 2 is a simple graph embedded in F 2 so that each face of G is quadrilateral. The diagonal slide and the diagonal rotation were defined in [1] as two transformations of quadrangulations. See Fig. 1. We also call the both transformations diagonal transformations in total. If the graph obtained by a diagonal slide is not a simple graph, then we do not appl...

We analyze quasi-stationary distributions {μ}ε>0 of a family of Markov chains {X}ε>0 that are random perturbations of a bounded, continuous map F : M →M , where M is a closed subset of R. Consistent with many models in biology, these Markov chains have a closed absorbing set M0 ⊂ M such that F (M0) = M0 and F (M \ M0) = M \ M0. Under some large deviations assumptions on the random perturbations...