Lebesgue weighted <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-algebra on locally compact groups

Let G be a locally compact group, ω a weight function on G, and 1<p<∞. We introduce the Lebesgue weighted L ^p -space \({\mathcal{L}}_{\omega}^{1,p}(G)= L^{p}(G,\omega)\cap L^{1}(G)\) as a Banach space and introduce its dual. Furthermore, we consider this space as a Banach algebra with respect to the usual convolution and show that \({\mathcal{L}}_{\omega}^{1,p}(G)\) admits a bounded approximate identity if and only if G is discrete. In addition, we prove that amenability of this algebra implies that G is discrete and amenable. Moreover, we discuss the converse of this result.     

Convolution on L p -spaces of a locally compact group

We have recently shown that, for 2 < p < ∞, a locally compact group G is compact if and only if the convolution multiplication f * g exists for all f, g ∈ L ^p (G). Here, we study the existence of f * g for all f, g ∈ L ^p (G) in the case where 0 < p ≤ 2. Also, for 0 < p < ∞, we offer some necessary and sufficient conditions for L ^p (G) * L ^p (G) to be contained in certain function spaces on G.     

Evaluation of dose rate and photon energy dependence of PASSAG polymer gel dosimeter

Journal of Radioanalytical and Nuclear Chemistry - In the current study, dose rate and photon energy dependence of PASSAG gel dosimeter is evaluated by using MRI technique. The gel samples were...     

On the static and dynamic stability of thin beam conveying fluid

In this paper, numerical investigation of the statical and dynamical stability of aligned and misaligned viscoelastic cantilevered beam is performed with a terminal nozzle in the presence of gravity in two cases: (1) effect of fluid velocity on the flutter boundary of beam conveying fluid and (2) effect of gravity on the buckling boundary of beam conveying fluid. The beam is assumed to have a large width-to-thickness ratio, so the out-of-plane bending rigidity is far higher than the in-plane bending and torsional rigidities. Gravity vector is considered in the vertical direction. Thus, deflection of the beam because of the gravity effect couples the in-plane bending and torsional equations. The beam is modeled by Euler–Bernoulli beam theory, with the flow-induced inertia, Coriolis and centrifugal forces along the beam considered as a distributed load along the beam. Furthermore, the end nozzle is regarded as a lumped mass and modeled as a follower axial force. The extended Hamilton’s principle and the Galerkin method are utilized to derive the bending–torsional equations of motion. The coupled equations of motion are solved as eigenvalue problems. Also, several cases are examined to study the impact of gravity, beam inclination angle, mass ratio, nozzle aspect ratio, bending-to-bending rigidity ratio and bending-to-torsional rigidity ratio on flutter and buckling margin of the system.

     

Pupils,tools and the Zone of Proximal Development

In this article, I use the Vygotskian concept of the Zone of Proximal Development (ZPD) to examine the learning experience of two grade seven pupils as they attempted to solve an addition of fractions problem using fraction strips. The aim is to highlight how tools can facilitate the enactment of a ZPD, within which the tool provides the guidance. Viewing the ZPD as a zone that allows for the emergence of various forms of guided talk and actions, I present a detailed analysis of a short video-recording of the pupils’ participation in a tool-mediated problem-solving activity. I show how their knowing of the concept of fractions and their perceptions of the affordances of the fraction strips marked what they said and did. I conclude by suggesting that the ZPD emerges through participation and interaction, not only between individuals but also between individuals and tools.     

On the strict,uniform and compact-open topologies on an algebra

We introduce and study strict, uniform, and compact-open locally convex topologies on an algebra \({\mathcal {B}},\) by the fundamental system of seminorms of a locally convex subalgebra \(({\mathcal {A},p}_\alpha )\). Moreover, we investigate when \({\mathcal {B}}\) is a locally convex algebra with respect to these topologies. Furthermore, we generalize an essential result related to derivations, from Banach to the Fréchet case. Finally we provide a useful example in this field.     

Weighted <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-conjecture for locally compact groups

Let G be a locally compact group, ω be a weight function on G and 1 < p < ∞. Here, we give a sufficient condition for that the weighted L ^p -space L ^p (G, ω) is a Banach algebra. Also, we get some necessary conditions on G and the weight function ω for L ^p (G, ω) to be a Banach algebra. As a consequence, we show that if G is abelian and L ^p (G, ω) is a Banach algebra, then G is σ-compact.     

Response overshoot: a challenge for the application of polymer gel dosimeters

Journal of Radioanalytical and Nuclear Chemistry - Studies of phosphorus cycling in the ocean have been greatly facilitated by the use of high molar activity 32P- and 33P-labeled phosphate...