On existence and asymptotic behaviour of solutions of a fractional integral equation

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions, defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.     

Reusable Nano-Zirconia-Catalyzed Synthesis of Benzimidazoles and Their Antibacterial and Antifungal Activities

In this article, a zirconia-based nano-catalyst (Nano-ZrO₂), with intermolecular C-N bond formation for the synthesis of various benzimidazole-fused heterocycles in a concise method is reported. The robustness of this reaction is demonstrated by the synthesis of a series of benzimidazole drugs in a one-pot method. All synthesized materials were characterized using ¹HNMR, ¹³CNMR, and LC-MS spectroscopy as well as microanalysis data. Furthermore, the synthesis of nano-ZrO₂ was processed using a standard hydrothermal technique in pure form. The crystal structure of nano-ZrO₂ and phase purity were studied, and the crystallite size was calculated from XRD analysis using the Debye–Scherrer equation. Furthermore, the antimicrobial activity of the synthesized benzimidazole drugs was evaluated in terms of Gram-positive, Gram-negative, and antifungal activity, and the results were satisfactory.     

Thermal stability and UV–Vis-NIR spectroscopy of a new erbium-doped fluorotellurite glass

A new transparent bulk glass from the system 76TeO₂?·?10ZnO?·?9.0PbO?·?1.0PbF₂?·?3.0Na₂O doped with Er³⁺ (TZPPN doped with Er³⁺) has been prepared using the conventional melt-quenching method. Results of differential thermal analysis (DTA) measurements indicate good thermal stability of this glass. The refractive indices at different wavelengths, the optical energy gap, the Sellmeier gap energy and the dispersion energy have been estimated. The Judd–Ofelt parameters, Ω _t (t?=?2,?4,?6) of Er³⁺ were evaluated from optical absorption spectra. Electric dipole, magnetic dipole type transition probabilities, spectroscopic quality factors, branching ratio and radiative lifetimes of several excited states of Er³⁺ have been predicted using intensity Judd–Ofelt parameters. The spectroscopic properties indicate that TZPPN glass doped with Er³⁺ is a promising candidate for laser applications and may be suitable for upconversion fibre optical devices.     

Recent developments in polyetherimide membrane for gas separation

Polyetherimide (PEI) is an extraordinary type of polyimide with excellent thermal and mechanical properties. The polymer is also gas permeable and is considered one of the best membranes for gas separation. Despite the high selectivity, PEI suffers from low permeability due to the trade‐off between phenomena in polymers. To overcome this limitation, fillers are added during the membrane preparation to create voids for better gas transport. In this paper, permeability and selectivity data of PEI membranes for the separation of oxygen, carbon dioxide, and helium are discussed. The paper also summarizes the reported studies for adding fillers to improve the membrane performance.     

68Ga-5, 10, 15, 20-Tetrakis (2, 4, 6-trimethoxy phenyl) porphyrin: a novel radio-labeled porphyrin complex for positron emission tomography

Journal of Radioanalytical and Nuclear Chemistry - Porphyrins and 68Ga have emerged as novel synergic options for PET applications so the idea of preparation of a novel porphyrin complex using this...     

The effect of CdS addition on linear and non-linear refractive indices of glasses in the system TeO2/Nb2O5/ZnO

Glasses in the system TeO₂/Nb₂O₅/ZnO/CdS were studied with respect to the density, molar volume, refractive index, polarizability, molar refraction, metallization and third order non-linear optical susceptibility. The third order non-linear optical susceptibilities, χ⁽³⁾, were measured using degenerate four-wave mixing (DFWM). The addition of CdS to TeO₂-based glasses leads to increasing refractive as well as the non-linear refractive indices. The largest measured value of the third order non-linear optical susceptibility was 7.8 × 10^?13 esu and has been found in the 90TeO₂ · 5Nb₂O₅ · 5ZnO · 0.4 CdS glass. The non-linear optical susceptibility increased with increasing CdS-concentration. In order to estimate the third order non-linear optical susceptibility, the theoretical model of Lines and the empirical equation of Miller were used.     

The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.     

Photoinduced Birefringence in Poly(Methyl Methacrylate) Polymeric Thin Films Doped with Di-Azo Sudan G

Photoinduced birefringence in poly(methyl methacrylate) (PMMA), polymeric thin films doped with di-azo Sudan G was investigated. A pump-probe method was used to study the dynamic behavior of the birefringence. The mechanism for the inducement of birefringence is discussed in terms of the photoisomerization of the di-azo Sudan G molecules. The results showed that the dynamic evolution of the photoinduced birefringence was such that the average birefringence increased, saturated, and then decreased with respect to the laser pump intensity. Also, an exponential-like relationship was observed between both the saturation and the isotropic states of the averaged transmitted probe beam (expressing the residual anisotropy) and the birefringence on one hand, and the intensity amplitudes of the pumping powers on the other hand.