Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisyński’s generalisation of the Hille–Yosida theorem and to establish two generalisations of the Trotter–Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in cha...

BACKGROUND Determining the variation of circulating cathodic antigen (CCA) in urine and egg counts variation in stool between days in Schistosoma mansoni (S. mansoni) infected individuals is vital to decide whether or not to rely on a single-sample test for diagnosis of Schistosomiasis. In this study, the magnitude of day-to-day variation in urine-CCA test scores and in faecal egg counts was ev...

Objective To assess the status of intestinal schistosomiasis among preschool-aged (PSAC) and school-aged children (SAC) to compare efficacy praziquantel (PZQ) in both groups. Methods The study was conducted on 400 children; 103 PSAC 297 SAC. Diagnosis Schistosoma mansoni based triplicate Kato-Katz thick smears from a single stool sample. identify missed cases by Kato-Katz, 120 randomly selected...

We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

for all 1,4 E Q(A). Under this hypothesis A + hB is an entire analytic family of type (B) in the sense of Kato [3]. In particular, the theory of Rellich [6] and Kato [2, 31 is applicable: If CL,, is an eigenvalue of A + X,,B which is discrete (i.e., an isolated point of spec(A + &,B)) an o multiplicity K and either k = 1 d f or h, is real, then for h near &, , the only spectrum of A + /\B near ...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...

Introduction Traditionally Schistosoma mansoni infection is diagnosed by the Kato-Katz method. Thick smears from each stool sample are prepared on slides and eggs counted microscopically. Commercially available point-of-care circulating cathodic antigen (POC-CCA) cassette tests detect schistosomiasis antigens urine samples in 20 minutes. POC-CCA results qualitative or semi-quantitative: signal ...

We consider a multidimensional Burgers equation on the torus T and the whole space R . We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of R we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove thes...

We consider here pseudo-differential operators whose symbol σ(x, ξ) is not infinitely smooth with respect to x. Decomposing such symbols into four -sometimes fivecomponents and using tools of paradifferential calculus, we derive sharp estimates on the action of such pseudo-differential operators on Sobolev spaces and give explicit expressions for their operator norm in terms of the symbol σ(x, ...