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.     

Dose distribution verification in intraoperative radiation therapy using an N-isopropyl acrylamide-based polymer gel dosimeter

The purpose of the current study was to verify the dose distribution of an Intrabeam-50 kV IORT system using polymer gel dosimetry technique. Results of dose distribution evaluation using NIPAM polymer gel dosimetry were compared with those measured using an ionization chamber and simulated using MCNPX code. Results showed the calculated gamma index was less than 1 with 2% dose-difference/2 mm distance-to-agreement for comparison between NIPAM and ionization chamber as well as between NIPAM and MCNPX simulation. It was concluded that the NIPAM polymer gel dosimetry is useful for verifying the dose distribution of low energy X-ray IORT technique.

     

Choline chloride-urea deep eutectic solvent as an efficient media for the synthesis of propargylamines via organocuprate intermediate

A facile method for the synthesis of various propargylamines derivatives with different structural parts has been reported. The reaction has consisted of one-pot coupling between aldehydes, secondary amines and terminal alkynes using CuCl as a catalyst and choline chloride/urea DES as a cheap and biocompatible reaction media. The procedure is free of using toxic solvents and used CuCl as an available, inexpensive and non-toxic catalyst. Using this methodology, 15 different propargylamine derivatives were successfully synthesized at 60 °C in 15 hr, mostly in good yields.     

Optical and MRI investigations of an optimized acrylamide-based polymer gel dosimeter

The first purpose of this research was improvement of sensitivity of the normoxic acrylamide-based polymer gel dosimeter. Another aim of this study was investigation of the absorbance of the irradiated gels as well as their relaxation rate variations. In addition, a new optical parameter, area under the absorbance spectrum (AUS), was investigated. Sensitivity improvement was performed by adding glucose and urea to the previously reported acrylamide-based polymer gel formulation and new formulation was named PAGATUG. The formulation which gives the nearest tissue elemental composition has been determined to be 3 % bis, 3 % AA, 5 % gelatine, 5 mM THPC, 0.01 mM HQ, 8.5 % glucose, and 3 % urea. The differences in electron density, number of electrons per gram and effective atomic number of PAGATUG gel were no more than 1, 0.5, and 0.8 % of the corresponding values for the soft tissue respectively. PAGATUG gels were irradiated by ⁶⁰Co radiotherapy unit photon beams with different doses and imaged using a 1.5T Siemens Avanto MRI scanner for different post irradiation times. In addition, the absorbance of the irradiated gels were evaluated using a double beam spectrophotometer. We found that the R ₂-sensitivity of polymer gel was improved by a factor of more than 2.6 in respect of the previously reported PAGAT polymer gel. Dose–absorbance sensitivity was obtained as 0.89 Au Gy^?1 and the results showed more stable response in respect of R ₂ investigation. An AUS-sensitivity of 107.7 Au nm Gy^?1 indicated to steep response variation. This read out parameter showed an acceptable linearity and dynamic dose range.     

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.     

Existence and uniqueness of a solution for a two dimensional nonlinear inverse diffusion problem

The problem of identifying the coefficient in a square porous medium is considered. It is shown that under certain conditions of data f,g, and for a properly specified class A of admissible coefficients, there exists at least one a∈A such that (a,u) is a solution of the corresponding inverse problem.     

Supply chain performance evaluation using fuzzy network data envelopment analysis: a case study in automotive industry

Supply chain performance evaluation problems are evaluated using data envelopment analysis. This paper proposes a fuzzy network epsilon-based data envelopment analysis for supply chain performance evaluation. In the common data envelopment analysis models which are used for evaluation of decision-maker units efficiency, there are several inputs and outputs. One of the bugs of such models is that the intermediate products and linking activities are overlooked. Considering these intermediate activities and products, the current study evaluates the performance of decision-maker units in an automotive supply chain. There are ten decision-maker units in the supply chain in which there are three suppliers, two manufacturers, two distributors, and four customers. Moreover, the overall efficiency of input-oriented (input-based) model and input-oriented divisional efficiency are calculated. In order to improve the efficiencies, the projections onto the frontiers are obtained by using the outputs of the solved model and Lingo software. In order to show the applicability of the proposed model, it is applied on automotive industry, as a case study, to evaluate supply chain performance. Then, the overall efficiencies of DMUs and each sections (divisions) of DMUs were calculated separately. Therefore, every organization can apply this evaluation method for improving the performance of alternative factors.