Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations

This paper is devoted to considering the existence and uniqueness results for fuzzy fractional integral equations employing the method of upper and lower solutions. Moreover, the approach is followed to prove the existence of solutions for the fuzzy initial value problem of fractional integrodifferential equations involving Riemann–Liouville differential operators. The method is illustrated by two examples.     

A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization

Two algorithms for establishing a connection between correlations before and after ordinalization under a wide spectrum of nonnormal underlying bivariate distributions are developed by extending the iteratively found normal-based results via the power polynomials. These algorithms are designed to compute the polychoric correlation when the ordinal correlation is specified, and vice versa, along with the distributional properties of latent, continuous variables that are subsequently ordinalized through thresholds dictated by the marginal proportions. The method has broad applicability in the simulation and random number generation world where modeling the relationships between these correlation types is of interest.     

Topical propolis improves wound healing in patients with diabetic foot ulcer: a randomized controlled trial

In this randomized controlled trial, diabetic patients with foot ulcers (Wagner grades 1 and 2) were randomly assigned to conventional therapies for diabetic foot ulcer plus topical propolis ointment (5%; twice daily) or conventional therapies alone. The process of ulcer healing was observed during 4 weeks and compared between the two groups regarding the size, erythema, exudates, white blood cell (WBC) count and erythrocyte sedimentation rate (ESR). The process of ulcer size reduction during the four-week period of study was significantly different between the groups. However, this difference was not significant between the third and fourth weeks. There was no significant difference between two groups regarding erythema and exudate reduction as well as WBC count and ESR. Administration of topical propolis ointment in addition to the conventional treatments of diabetic foot ulcer could reduce the size of ulcers with Wagner grades 1 and 2.     

Synthesis of nanostructured polyaniline via chemical oxidative polymerization: Investigation of morphology and conductivity of the prepared polymers

In this study, nanostructure polyaniline was prepared from aniline monomer via chemical oxidative polymerization in the presence of ammonium persulfate as an oxidizing agent. Interfacial, emulsion, rapid mixing and ultrasonic techniques are used for polymer synthesis. In the interfacial method, chloroform, n-hexane, hexanole and toluene were used as organic solvents and sulfuric acid, methane sulfonic acid and acetic acid were employed as electrolyte solutions. In the emulsion polymerization, dodecyl benzene sulfonic acid and aqueous solution of hydrochloric acid were used as emulsion agent and electrolyte solution respectively. In rapid mixing reaction and ultrasonic method, hydrochloric acid and salicylic acid were used as dopants. The structure, conductivity, morphology and particle size distribution of prepared polymers were investigated after purification and drying by FTIR spectroscopy, scanning electron microscopy and electrical conductivity measurements.     

Existence of energy maximizing vortices in a three-dimensional quasigeostrophic shear flow with bounded height

The existence of an energy maximizer relative to a class of rearrangements of a given function is proved. The maximizers are stationary and stable solutions of the quasigeostrophic equation, which governs the time evolution of large-scale three-dimensional geophysical flow in a vertically bounded domain. The background flow is unidirectional, with linear horizontal shear. The theorem proved implies the existence of a family of stationary and stable vortices that rotate in the same direction as the background shear. It extends an earlier theorem by Burton and Nycander, which is valid for a vertically unbounded domain.     

碱性溶液中电聚酪胺-铜草酸盐纳米复合物修饰铜电极电催化甲醇氧化(英文)

A polytyramine-copper oxalate nanocomposite modified copper(PTCOxNMC) electrode prepared by electropolymerization was examined for electrocatalytic activity towards the oxidation of methanol in alkaline solution using cyclic voltammetry and impedance spectroscopy. The prepared PTCOxNMC electrode showed a significantly high response for adsorbed methanol oxidation. The effects of various parameters such as potential scan rate and methanol concentration on the electrocatalytic oxidation at the surface of the PTCOxNMC electrode were investigated. Spectrometry techniques such as Fourier transform infrared spectroscopy and scanning electron microscopy were used to determine the surface physical characteristics of the modified electrode and revealed that the polytyramine-copper oxalate nanocomposite particles were highly dispersed on the surface of the copper electrode with a narrow size up to 40 nm. The very high current density obtained for the catalytic oxidation may have resulted from the high electrode surface area caused by modification with the poly-tyramine-copper oxalate nanocomposite.     

Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations

In this paper, we introduce new solutions for fuzzy differential equations as mixed solutions, and prove the existence and uniqueness of global solutions for fuzzy initial value problems involving integro-differential operators of Volterra type. One example is also given by applying mixed solution concept to fuzzy linear differential equations for obtaining their global solutions.     

Facile ultrasonic-assisted preparation of Fe<Subscript>3</Subscript>O<Subscript>4</Subscript>/Ag<Subscript>3</Subscript>VO<Subscript>4</Subscript> nanocomposites as magnetically recoverable visible-light-driven photocatalysts with considerable activity

In this work, a facile ultrasonic-assisted method was applied for preparation of Fe₃O₄/Ag₃VO₄ nanocomposites with different compositions. The as-prepared products were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, energy-dispersive analysis of X-rays, UV–Vis diffuse reflectance spectroscopy, Fourier transform infrared spectroscopy, and vibrating sample magnetometery. Photocatalytic degradation of rhodamine B under visible-light irradiation was investigated, and it was found that weight ratio of Fe₃O₄–Ag₃VO₄ has significant influence on the photocatalytic activity and the nanocomposite with 1:4 weight ratio of Fe₃O₄–Ag₃VO₄ has superior activity. In addition, the nanocomposite showed great activities in degradations of methylene blue and fuchsine, which are comparable with activity of the pure Ag₃VO₄. More importantly, this nanocomposite displayed remarkable saturation magnetization, leading to easily and quickly separation of its suspension from treated system by applying a magnetic field.     

Ultrasound-mediated efficient synthesis of dihydrothiopyrano[2,3-<Emphasis Type="Italic">b</Emphasis>]indole-3-carbonitrile derivatives

An efficient one-pot synthesis of fused dihydrothiopyrano[2,3-b]indole-3-carbonitriles has been developed through ultrasound mediated reaction by simply combining malononitrile and various aldehydes with two indoline-2(3H)-thiones. The method has the advantages of high yields, short reaction time, good functional group tolerance and green reaction conditions.