Synthesis and Characterization of CeO2 Nanoparticles via Solution Combustion Method for Photocatalytic and Antibacterial Activity Studies

CeO₂ nanoparticles have been proven to be competent photocatalysts for environmental applications because of their strong redox ability, nontoxicity, long-term stability, and low cost. We have synthesized CeO₂ nanoparticles via solution combustion method using ceric ammonium nitrate as an oxidizer and ethylenediaminetetraacetic acid (EDTA) as fuel at 450 °C. These nanoparticles exhibit good photocatalytic degradation and antibacterial activity. The obtained product was characterized by various techniques. X-ray diffraction data confirms a cerianite structure: a cubic phase CeO₂ having crystallite size of 35 nm. The infrared spectrum shows a strong band below 700 cm⁻¹ due to the Ce−O−Ce stretching vibrations. The UV/Vis spectrum shows maximum absorption at 302 nm. The photoluminescence spectrum shows characteristic peaks of CeO₂ nanoparticles. Scanning electron microscopy (SEM) images clearly show the presence of a porous network with a lot of voids. From transmission electron microscopy (TEM) images, it is clear that the particles are almost spherical, and the average size of the nanoparticles is found to be 42 nm. CeO₂ nanoparticles exhibit photocatalytic activity against trypan blue at pH 10 in UV light, and the reaction follows pseudo first-order kinetics. Finally, CeO₂ nanoparticles also reduce Cr^VI to Cr^III and show antibacterial activity against Pseudomonas aeruginosa.     

Duality,area-considerations,and the Kalai–Smorodinsky solution

We introduce a new solution concept for $2$-person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarc? and Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai–Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom–area-based fairness–and offer three characterizations of the Kalai–Smorodinsky solution in which this axiom plays a central role.     

Incorporating model uncertainty into optimal insurance contract design

In stochastic optimization models, the optimal solution heavily depends on the selected probability model for the scenarios. However, the scenario models are typically chosen on the basis of statistical estimates and are therefore subject to model error. We demonstrate here how the model uncertainty can be incorporated into the decision making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is illustrated by a risk management problem involving the optimal design of an insurance contract.     

On the inheritance of the strongly π-extending property

In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.     

Fundamental solution of the time‐fractional telegraph Dirac operator

In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems.     

A note on Arzela–Ascoli's lemma in almost periodic problems

This paper is concerned with a generalized Arzela–Ascoli's lemma, which has been extensively applied in almost periodic problems by the continuation theorem of degree theory. We give a counter example to show that this lemma is incorrect, and there is a gap in the proof of some existing literature, where the addressed generalized Arzela–Ascoli's lemma was used. Moreover, we make some final comments and introduce an open problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Maxwell's equations in an unbounded structure

This paper is concerned with the mathematical analysis of the electromagnetic wave scattering by an unbounded dielectric medium, which is mounted on a perfectly conducting infinite plane. By introducing a transparent boundary condition on a plane surface confining the medium, the scattering problem is modeled as a boundary value problem of Maxwell's equations. Based on a variational formulation, the problem is shown to have a unique weak solution for a wide class of dielectric permittivity and magnetic permeability by using the generalized Lax–Milgram theorem. Copyright © 2016 John Wiley & Sons, Ltd.     

Blow‐up of the smooth solutions to the compressible Navier–Stokes equations

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.     

Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces

Through solving the problem step by step and by applying the method of a C₀ semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright © 2017 John Wiley & Sons, Ltd.