We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...

Let M be a von Neumann algebra with a faithful normal trace τ , and let H∞ be a finite, maximal, subdiagonal algebra of M. Fundamental theorems on conjugate functions for weak∗-Dirichlet algebras are shown to be valid for non-commutative H∞. In particular the Hilbert transform is shown to be a bounded linear map from Lp(M, τ) into Lp(M, τ) for 1 < p < ∞, and to be a continuous map from L1(M, τ)...

We show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in Berkovich’s sense by constructing a continuous section to the tropicalization map. Our main tool is an explicit description of the algebraic coordinate rings of the toric strata of the Grassmannian. We determine the fibers of the tropicalization map and compute the init...

Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some phenomena can depend alternatively of two values of the same parameter. We use the quadratic map xn+1 = 1 − axn when the parameter alternates between two valu...

We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A BC where B is a continuous map and C is a continuous linear weakly compact operator from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Kra...

This paper presents a novel methodology to deal with the problem of trajectory tracking in WMR. This new approach uses the dynamic model of WMR and allows perfect velocities tracking. Generally, the classic control approaches applied to the dynamic model of the robot solve the problem of trajectory tracking in two stages. In the first one is designed a controller that ensures the perfect tracki...

Let D be a non empty set, let us consider k, and let M be a matrix over D. Then M k is a matrix over D. We now state four propositions: (3) For every finite sequence M such that lenM = n+1 holds len(M n+1) = n: (4) Let M be a matrix over D of dimension n+1 m and M1 be a matrix over D. Then (i) if n > 0; then widthM = width(M n+1); and (ii) if M1 = hM(n+1)i; then widthM = widthM1: (5) For every ...

The purpose of this study was to describe the nonlinear pharmacokinetics of piperacillin observed during intermittent infusion and continuous infusion by using a nonparametric population modeling approach. Data were 120 serum piperacillin concentration measurements from eight adult cystic fibrosis (CF) patients. Individual pharmacokinetic parameter estimates during intermittent infusion or cont...

We study the periodic non-linear Schrodinger equation −iu t +u xx = ±|u| p−1 u for initial data which are assumed to be small in some negative order Sobolev space H s (T) (s < 0), but which may have large L 2 mass. In [6], [7] these equations were shown to be ill-posed in H s (T), in the sense that the solution map was not uniformly continuous from H s (T) to itself even for short times and sma...

It is a well-known result of Kadec that every two separable infinite dimensional Banach spaces are homeomorphic. Also in large classes of nonseparable Banach spaces (perhaps all) the density character of a Banach space is its only topological invariant (see the book [2] for details). The situation changes considerably if we consider uniform homeomorphisms. Several results are known which prove ...