Decay integral solutions for neutral fractional differential equations with infinite delays

Our aim in this work is to find decay integral solutions for a class of neutral fractional differential equations in Banach spaces involving unbounded delays. By constructing a suitable measure of noncompactness on the space of solutions and establishing new estimates for fractional resolvent operators, we prove the existence of a compact set of decay integral solutions to the mentioned problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence Results in a General Equilibrium Problem

In this article, we give sufficient conditions for the existence of solutions of a general model which includes as special cases many generalized vector quasi-equilibrium problems with set-valued maps. The obtained results generalize and improve several earlier results.     

On a Nonlinear Heat Equation Associated with Dirichlet–Robin Conditions

This article is devoted to the study a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo–Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as t → + ∞. Finally, we give numerical results.     

Parallel Algorithms for Solving a Class of Variational Inequalities over the Common Fixed Points Set of a Finite Family of Demicontractive Mappings

Abstract

We propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem.     

Log-concavity of compound distributions with applications in stochastic optimization

Compound distributions come up in many applications (telecommunication, hydrology, insurance, etc.), where some of the typical problems are of optimization type. The log-concavity property is paramount in these respects to ensure convexity. In this paper, we prove the log-concavity of some compound Poisson and other compound distributions.     

Electrochemical sensing of hydroxylamine by gold nanoparticles on single-walled carbon nanotube films

The arrays of gold nanoparticles (AuNPs) were fabricated on flexible and transparent single-walled carbon nanotube (SWCNT) films using the electrochemical deposition method, and the patterned nanotubes were then used as electrodes for hydroxylamine detection. The sizes and densities of the AuNPs could easily be controlled by varying the amount of charge deposited, and the gold-deposited area showed a homogeneous distribution on the exposed SWCNT film surface. X-ray diffraction analysis of the AuNPs shows a face-centered cubic structure that is dominated by the lowest energy {111} facets. The oxidation of the hydroxylamine on the AuNP-deposited SWCNT films depended strongly on the solution pH, and the maximum catalytic current was observed at a pH of 9.0. A linear electrical response was observed for concentrations ranging from 0.016 to 0.210 mM, and the detection limit and the sensitivity were 0.72 μM and 165.90 μAmM^?1 cm^?2, respectively. Moreover, the amperometric response in hydroxylamine showed a stable response for a long time (300 s), during which time it retained 94% of its initial value. In the long-term storage stability test, the current response to hydroxylamine decreased slightly, with only 17% leakage after 30 days.     

Quantitative three-dimensional microstructure of a solid oxide fuel cell cathode

Solid oxide fuel cells (SOFCs) are being actively developed world wide for clean and efficient electrical generation from fuels such as natural gas, hydrogen, coal, and gasoline. The cathode in state of the art SOFCs is typically a porous composite of electronically-conducting La_1?xSr_xMnO₃ (LSM) and ionically-conducting Y₂O₃-stabilized ZrO₂ (YSZ) that facilitates the critical oxygen reduction reaction. Here we describe the three-dimensional characterization and quantification of key structural parameters from an LSM-YSZ cathode, using imaging and volume reconstruction based on focused ion beam – scanning electron microscopy. LSM-YSZ-pore three-phase boundaries (TPBs) were identified. Approximately 1/3 of the TPBs were found to be electrochemically inactive, as they were on isolated LSM particles, yielding an active TPB density of 4.9 μm^?2. Cathode electrochemical modeling, which included a measured YSZ tortuosity of 3.4, yielded an effective TPB resistance of ≈2.5 × 10⁵ Ω cm at 800 °C.     

Tuneable Control of Interfacial Rheology and Emulsion Coalescence

Breaking point: Switchable peptide surfactants are used to demonstrate that the extent of cross‐linking in an interfacial surfactant layer can control the rate of emulsion coalescence. Pictured is the rupture of an aqueous thin film where the peptide layer lacks sufficient strength to prevent hole formation, but nonetheless dramatically slows the rate of hole expansion.

     

A Perron-Frobenius theorem for positive polynomial operators in Banach lattices

In this paper, we extend the Perron-Frobenius theorem for positive polynomial operators in Banach lattices. The result obtained is applied to derive necessary and sufficient conditions for the stability of positive polynomial operators. Then we study stability radii: complex, real and positive radii of positive polynomial operators and show that in this case the three radii coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results.     

Structure of the human telomere in K+ solution: an intramolecular (3 + 1) G-quadruplex scaffold

We present the intramolecular G-quadruplex structure of human telomeric DNA in physiologically relevant K(+) solution. This G-quadruplex, whose (3 + 1) topology differs from folds reported previously in Na(+) solution and in a K(+)-containing crystal, involves the following: one anti.syn.syn.syn and two syn.anti.anti.anti G-tetrads; one double-chain reversal and two edgewise loops; three G-tracts oriented in one direction and the fourth in the opposite direction. The topological characteristics of this (3 + 1) G-quadruplex scaffold should provide a unique platform for structure-based anticancer drug design targeted to human telomeric DNA.