The problem of the nonlinear diffusive predator–prey model with the same biotic resource

In recent years, the research on the diffusive predator–prey model has attracted much attention. In these models, the carrying capacity is considered as a constant. In 2013, H. M. Safuan investigated the system of a predator and prey that shares the same biotic resource, where the carrying capacity is a function of the time. The spatial component of ecological interactions has been recognized as an important factor. So, we will discuss the problem of the nonlinear diffusive predator–prey model with the same biotic resource. This model is the system of the nonlinear partial differential equations with zero-flux boundary condition. The main objective of the present paper is to investigate the existence and uniqueness of the solution of this model. In this paper, we also obtain that there is a unique solution of the nonlinear partial differential equations with Dirichlet boundary condition.     

凸函数与半连续函数的关系

通过研究凸函数与半连续函数的关系,给出了凸函数的一个与上半连续性相结合的等价定义.     

Efficient preprocessing of complex geometries for CFD simulations

Preprocessing remains one the main bottlenecks in the computational fluid Dynamics simulations of flows involving complex geometries as advances in the algorithm development, turbulence modelling and parallel computing are made. To this end, two approaches are presented here to efficiently deal with complex geometries in order to reduce the preprocessing time and manual effort. First, a hybrid blocking approach, combining the medial axis-based method with level set iso-surface is presented to aid the block topology generation for subsequent structured meshing of complex 3D external flow domains. Secondly, a hierarchical geometry handling approach is demonstrated which makes use of the lower order modelling, overset meshes and zonal blocking for efficient preprocessing. Typical external aerodynamics cases have been showcased to describe how such techniques can be used to address modern challenges in the preparation of complex geometries for flow simulations.     

Temperature-responsive smart surfaces via rise-and-descent transition: Attachability,durability, and fast sweating

Smart surfaces containing thermo-responsive hydrogels have been investigated for several decades, but the development of mechanically durable and versatile surfaces that can undergo distinct property changes remains a challenging task. Herein, we prepare smart surfaces showing reversible changes in micro-scale roughness, which are attachable to various polymeric substrates. The hydrogel microphase located between silicone phases responsively rise and descend (volcanic-terrain-mimetic transition); as a result, the surface properties reversibly swing from those of the hydrophobic silicone-like ones to those of the wet hydrogel ones. The durability of these surfaces resembles that of silicone, while their fast water release characteristics allow the utilization of the studied materials in self-aligning and artificial sweating applications. The release of the drug molecules loaded into the hydrogel phase is controlled by varying the temperature and composite structure. Thus, the fabricated versatile surfaces utilizing the volume transition of thermo-responsive hydrogels can meet the requirements of various future applications.     

一类具有Dirichlet边界条件的反应扩散方程的爆破解

针对一类具有Dirichlet边界条件的非线性反应扩散方程的爆破问题,通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了解在有限时刻爆破的一个充分条件,并在一定条件下得到了爆破时刻的上界和下界.     

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.     

Photo‐regulated phase transition of poly(ethylene glycol) derivative containing azobenzene group

A photo‐responsive and thermo‐responsive poly(ethylene glycol) derivative containing azobenzene group was synthesized. Its photoisomerization kinetics was investigated by the UV–vis spectra, and the pseudo‐first‐order rate constants (k_t and k_c) were determined to be 1.5 × 10^?2 and 9.3 × 10^?2 s^?1, respectively. It is found that the phase transition behavior can be tuned theoretically through photoirradiation between 26.6°C and 36.7°C. Finally, it is worthy to note that the changes of the lower critical solution temperature occur repeatedly upon successive irradiation of UV and visible light. Copyright © 2012 John Wiley & Sons, Ltd.     

Equilibrium problems techniques in the qualitative analysis of quasi-hemivariational inequalities

In this paper, we investigate the problem of existence of solutions of quasi-hemivariational inequalities. Some concepts of semicontinuity and hemicontinuity on subsets for functions as well as for set-valued mappings are developed and applied for solving quasi-hemivariational inequalities. Generalizations of some old results on the existence of solutions of equilibrium problems are obtained and applications to quasi-hemivariational inequalities are derived.     

Improving Christofides' lower bound for the traveling salesman problem

In 1972 Christofides introduced a lower bound for the Traveling Salesman Problem (TSP). The bound is based on solving repeatedly a Linear Assignment Problem. We relate the bound to the Complete Cycle Problem; as a consequence the correctness of the bound is easier to prove.

Further we give improvements for the bound in the symmetric case and we deal with the influence of the triangle equation together with the identification of non-optimal edges for the TSP. The improvements are illustrated by examples and computational results for large problems.     

非线性项依赖于一阶导数的共振情形下二阶三点边值问题解的存在性和唯一性

本文致力于研究共振情形下二阶三点边值问题x″(t)+ f(t,x(t),x'(t))=0, t∈(0,1),x(0)=0, x(1)=ξx(η),其中f:[0,1]×R2→R是一个连续函数,ξ＞0,0＜η＜1满足ξn=1.运用先验界估计,微分不等式技巧和Leray-Schauder度理论得到了该边值问题解的存在性和唯一性.