Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time-Dependent Setting

We obtain lower bounds on blow-up of solutions for the 3D magneto-micropolar equations. More precisely, we establish some estimates for the solution \((\mathbf{u},\mathbf{w},\mathbf{b}) (t)\) in its maximal interval \([0,T^{*})\) provided that \(T^{*}<\infty\), which show for \(\delta\in(0,1)\) that \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) is at least of the order \((T^{*}-t)^{-(\delta s)/(1+2\delta)}\) for \(s\geq1/2+\delta\). In particular, by choosing a suitable \(\delta\), one concludes that \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) is at least of the order \((T^{*}-t)^{-s/4}\), and \((T^{*}-t)^{1/4-s/2}\) for \(s\geq1\), and \(1/2< s<3/2\), respectively. We also show that \((T^{*}-t)^{-s/3}\) is a lower rate for \(\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}\) if \(s>3/2\).     

A theory of finite elastic consolidation

Presented in this paper is a general theory describing the consolidation of a porous elastic soil. The formulation allows for the occurrence of finite geometry changes and finite elastic strains during the consolidation process. The governing equations have been cast in a rate form and the laws which determine deformation and pore fluid flow, i.e. Hooke's law and Darcy's law, are presented in a frame indifferent manner. A numerical technique is described that provides an approximate solution to the governing equations. The theory and the solution technique are illustrated by several examples of practical interest.     

Particle plasmon‐induced charge trapping at heterointerfaces in PCDTBT:PC70BM blends

We investigate the influence of particle plasmons on exciton and charge generation and recombination processes in the blend of poly (9‐(1‐octylnonyl)‐9H‐carbazole‐benzothiadiazole‐4,7‐diyl‐2,5‐thiophenediyl) (PCDTBT) and [6,6]‐phenyl‐C₇₀butyric acid methyl ester (PC₇₀BM). The particle plasmons are generated from gold nanoparticles, which are embedded into PCDTBT:PC₇₀BM blend. For the blend with gold nanoparticles, we observe enhance light harvesting. Despite the enhanced light collection, we find that the quasi‐steady‐state charge generation has not been influenced by the particle plasmons. However, the generation and recombination of long‐lived (sub‐millisecond) polaron paris have been significantly enhanced: from untrapped state in the pristine blend to the trapped state in the gold nanoparticle‐embedded blend. This result implies that the plasmon‐influenced polarons are trapped at the broadband geminate polaron pair (GPP) state. This state acts as an intermediate state, which either leads to the formation of charge transfer excitons (CTXs) or free charge carriers. In our case, the particle plasmon‐influenced polarons are trapped in the GPP state, which leads to the formation of CTXs. For this reason, we do not observe the enhanced charge generation in PCDTBT:PC₇₀BM blend with particle plasmon resonance. Finally, we revealed that the long‐lived polarons mainly resulted from the localization by particle plasmons. The macroscopic modification in the blend film made negligible contributions to this influence. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 940–947     

Pyridinium tribromide catalyzed condensation of indoles and aldehydes to form bisindolylalkanes

An efficient synthetic method for bis(indol-3-yl)alkane derivatives has been developed.In the presence of 5 mol%of pyridinium tribromide(PTB),the condensation of indoles and aldehydes proceeded smoothly under mild conditions,giving rise to the corresponding bis(indol-3-yl)alkanes in good to excellent yields.     

Science Conference Presenters’ Images of Inquiry

Inquiry‐focused professional development and conceptions of inquiry held by eight professional development leaders were investigated within the context of a state science teacher conference. The prominent session format involved session leaders modeling classroom experiences. In all sessions, classroom inquiry was portrayed as a teacher‐guided activity with the primary goal being to increase motivation for engaging students in classroom inquiry. The leaders’ conceptualized inquiry primarily as a teaching approach with various goals, characteristics, and potential barriers. The findings of this study provide evidence of how inquiry, a prominent feature of science education reform, was portrayed in sessions at a conference sponsored by a state affiliate of the National Science Teachers Association and thought about by persons who led these sessions. The findings have implications for teacher learning from conference‐based professional development and its potential influence on science teacher thinking and practice.     

Ferromagnetism study of Co<Subscript>0.2</Subscript>Mg<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript>0.8−<Emphasis Type="Italic">x</Emphasis></Subscript>O films prepared by the sol–gel method

Co_0.2Mg _x Zn_0.8−x O films prepared with different molar ratio of magnesium acetate to zinc acetate were deposited on substrates by the sol–gel technique. X-ray diffraction, photoluminescence (PL) and ferromagnetism measurements were used to characterize the Co_0.2Mg _x Zn_0.8−x O diluted magnetic semiconductors. The acceptor-like defects were determined in the PL band and the intensity of the acceptor-related PL increased with increasing Mg concentration. Therefore, an increase in the number of the acceptor-like defects (zinc vacancies especially) in the Co_0.2Mg _x Zn_0.8−x O film may lead to the enhancement of the magnetic properties. It is worth noting that changes in Mg concentration and the number of the acceptor-like defects are important issues for producing strong ferromagnetism Co_0.2Mg _x Zn_0.8−x O films prepared by the sol–gel method.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.