Optimal control for a population dynamics with age-dependent and diffusion in a periodic environment

Here we consider the optimal harvesting problem for a periodic age-dependent population dynamics with diffusion. Namely, we investigate the model with periodic vital rates and a periodic forcing term that sustains oscillations. By using Mazur’s theorem, we demonstrate existence of solutions of the optimal control problem and by the conception of normal cone, we also obtain the first order necessary conditions of optimality for the problem. Our results extend some known criteria.     

An inverse problem of identifying the coefficient of parabolic equation

This paper studies an inverse problem of identifying the coefficient of parabolic equation when the final observation is given, which has important application in a large fields of applied science. Based on the optimal control framework, the existence and necessary condition of the minimum for the control functional are established. Since the optimal control problem is nonconvex, one may not expect a unique solution. However, in this paper the solution is proved to be locally unique. After the necessary condition is transformed into an elliptic bilateral variational inequality, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the algorithm designed in this paper is stable and that the coefficient is recovered very well.     

Synthesis,crystal structures and photoluminescence of 7-(N,N′-diethylamino)-3-phenylcoumarin derivatives

Two new coumarin derivatives, 7-(N,N′-diethylamino)-3-(4-hydroxyphenyl)-coumarin and 7-(N,N′-diethylamino)-3-(4-bromophenyl)-coumarin, were synthesized successfully. Their structures were verified by single crystal X-ray crystallography. The UV–vis absorption and fluorescence of the compounds were discussed. The compounds exhibit strong blue emission under ultraviolet light excitation. The molecular structures, the lowest energy transitions and the UV–vis spectra of 7-(N,N′-diethylamino)-3-(4-hydroxyphenyl)-coumarin and 7-(N,N′-diethylamino)-3-(4-bromophenyl)-coumarin have been studied with density functional theory (DFT) and time-dependent density functional theory (TD-DFT) at B3LYP/6-31G(d) level.     

新型室温酯化法接枝聚合物改性SiO_2纳米微粒

提出了一种在室温、大气环境等温和条件下通过酯化反应将端羧基聚合物链接枝到纳米SiO2微球表面从而制备有机/无机复合纳米微粒的新方法.该方法通过以下两个步骤得以实现,即第一,用3-环氧丙基三甲氧基硅烷对纳米SiO2微球表面进行改性处理,接着将引入到纳米SiO2表面的环氧基团转化为烷羟基基团;第二,通过引入到纳米SiO2微球表面的烷羟基与聚合物中的端羧基在室温下发生酯化反应,从而将聚合物接枝到纳米SiO2表面制得复合微球.利用XPS、FTIR、TEM和TGA等测试手段对纳米SiO2的改性过程以及聚合物接枝后得到的复合微球进行了表征.研究结果表明,该室温酯化接枝方法具有较高的接枝率,接枝到无机纳米微粒表面的聚合物占复合微球质量的55wt%～70wt%;接枝聚合物后,纳米SiO2微球的粒径从40nm增加到64～75nm,从而得到了以SiO2为核、以聚合物为壳的有机-无机复合微球.     

考虑意外事件对交通流影响的元胞自动机交通流模型

在NaSh模型的基础上,考虑交通事故和养护路段等意外事件对高速公路交通流的影响,建立了有意外事件影响的在车道管制下的高速公路交通流元胞自动机模型,并进行数值模拟. 研究发现:意外事件对高速公路交通流有明显影响,并且意外事件对交通流的影响在某一密度值范围内尤其明显,且意外事件堵塞点在第一车道比在第二车道对交通流的影响小;同时,在该密度值范围内,意外事件堵塞时间和堵塞路段长度越长,对交通流的影响就越大. 关键词： 元胞自动机 交通流 意外事件     

Superhydrophobic alumina surface based on stearic acid modification

A novel superhydrophobic alumina surface is fabricated by grafting stearic acid layer onto the porous and roughened aluminum film. The chemical and phase structure, morphology, and the chemical state of the atoms at the superhydrophobic surface were investigated by techniques as FTIR, XRD, FE-SEM, and XPS, respectively. Results show that a super water-repellent surface with a contact angle of 154.2° is generated. The superhydrophobic alumina surface takes on an uneven flowerlike structure with many nanometer-scale hollows distribute in the nipple-shaped protrusions, and which is composed of boehmite crystal and γ-Al₂O₃. Furthermore, the roughened and porous alumina surface is coated with a layer of hydrophobic alkyl chains which come from stearic acid molecules. Therefore, both the roughened structure and the hydrophobic layer endue the alumina surface with the superhydrophobic behavior.     

Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces

In this paper, we consider a second order evolution equation in a Banach space, which can model an elastic system with structural damping. New forms of the corresponding first order evolution equation are introduced, and their well-posed property is proved by means of the operator semigroup theory. We give sufficient conditions for analyticity and exponential stability of the associated semigroups.     

MULTIPLE POSITIVE SOLUTIONS FOR A FOURTH-ORDER NONLINEAR EIGENVALUE PROBLEM

In this paper, by using the Guo-Krasnoselskii’s fixed-point theorem, we establish the existence and multiplicity of positive solutions for a fourth-order nonlinear eigenvalue problem. The corresponding examples are also included to demonstrate the results we obtained.     

Multiple stability switches and Hopf bifurcation in a damped harmonic oscillator with delayed feedback

This paper takes into consideration a damped harmonic oscillator model with delayed feedback. After transforming the model into a system of first-order delayed differential equations with a single discrete delay, the single stability switch and multiple stability switches phenomena as well as the existence of Hopf bifurcation of the zero equilibrium of the system are explored by taking the delay as the bifurcation parameter and analyzing in detail the associated characteristic equation. Particularly, in view of the normal form method and the center manifold reduction for retarded functional differential equations, the explicit formula determining the properties of Hopf bifurcation including the direction of the bifurcation and the stability of the bifurcating periodic solutions are given. In order to check the rationality of our theoretical results, numerical simulations for some specific examples are also carried out by means of the MATLAB software package.

     

Research progress on Na3V2(PO4)2F3-based cathode materials for sodium-ion batteries

Sodium-ion batteries (SIBs) have received significant attention in large-scale energy storage due to their low cost and abundant resources. To obtain high-performance SIBs, many intensive studies about electrode materials have been carried out, especially the cathode material. As various types of cathode material for SIBs, a 3D open framework structural Na₃V₂(PO₄)₂F₃ (NVPF) with Na superionic conductor (NASICON) structure is a promising cathode material owing to its high operating potential and high energy density. However, its electrochemical properties are severely limited by the poor electronic conductivity due to the insulated [PO₄] tetrahedral unit. In this review, the challenges and strategies for NVPF are presented, and the synthetic strategy for NVPF is also analyzed in detail. Furthermore, recent developments of modification research to enhance their electrochemical performance are discussed, including designing the crystal structure, adjusting the electrode structure, and optimizing the electrolyte components. Finally, further research and application for future development of NVPF are prospected.