具有阶段结构的竞争系统的持久性和稳定性

研究带有时滞和成长阶段的两种群竞争模型,第一个种群分成年和幼年两个阶段,第二个种群不具有阶段结构.本文证明了系统正解的有界性;利用比较原理得到了系统永久生存的充分条件;通过构造Lyapunov函数得到了系统全局渐近稳定的充分条件.     

A unified method for a class of convex separable nonlinear knapsack problems

In this paper, a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems, which are characterized by positive marginal cost (PMC) and increasing marginal loss–cost ratio (IMLCR). By taking advantage of these two characteristics, the proposed algorithm is applicable to the problem with equality or inequality constraints. In contrast to the methods based on Karush–Kuhn–Tucker (KKT) conditions, our approach has linear computation complexity. Numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems.     

模型论简介

本文将模型论介绍为“可定义集的数学”．首先给出“可定义集”的确切定义，并引入处理可定义集的主要工具——一阶公式的概念．然后给出一些例子．最后介绍一些相当于可定义集的组合性质的稳定性理论．     

求解随机微分方程的二级Milstein方法(英文)

In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.     

具有HollingII类型功能反应的3种群捕食时滞模型

研究了具有HollingII类型功能反应的一捕食者有两个食饵的时滞系统,通过构造Lyapunov泛函得到了与时滞有关的系统全局渐近稳定的充分条件.     

First‐principles calculations of the stability and electronic properties of the PbTiO3 (110) polar surface

The structural and electronic properties of five terminations of cubic lead titanate (PbTiO₃) (110) polar surface were investigated by first‐principles total‐energy calculations using a periodic slab model. On the PbTiO termination, an anomalous filling of conduction band was observed, whereas on the O₂ termination, two surface oxygen atoms formed a peroxo group, demonstrating that the electronic structures of the two stoichiometric terminations undergo significant changes with respect to bulk materials. However, for the three nonstoichiometric TiO‐, Pb‐, and O‐terminated surfaces, their electronic structures are very similar to bulk. Charge redistribution results for the five terminations confirmed that electronic structure and surface composition changes are responsible for their polarity compensation. However, which mechanism actually dominates the stabilization process depends upon energetic considerations. A thermodynamic stability diagram suggested that the two stoichiometric terminations are unstable; however, the three nonstoichiometric terminations can be stabilized in some given regions. Furthermore, this study indicates that the very different stabilities and surface states filling behaviors of the PbTiO₃ (110) polar surface with respect to SrTiO₃ and BaTiO₃ ones seem to originate from the partially covalent characteristics of Pb O pairs. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Numerical modelling of unsteady convective–diffusive heat transfer with a control volume hybrid method

Presented in this paper is a numerical methodology for the solution of the parabolic governing partial differential equation that describes unsteady advection–diffusion heat transfer. The formulation presented here is shown to be free from the numerical oscillation commonly associated with advection–diffusion heat transfer regardless of the value of the Peclet number. The formulation involves the absorption of the advection term in the unsteady heat equation into the capacitance term. This process is achieved with the use of a control volume methodology applied to each nodal element on a finite-volume mesh. This is shown to ensure that spurious energy losses and gains are avoided and provides for consistency between temperature and energy change. This approach provides unconditional stability and it is shown that good accuracy is achievable with relatively large time-steps.     

Synthesis and characterization of fluorene‐based rod–coil liquid crystal polymers

A series of fluorene‐based rod–coil liquid crystal polymers with different lengths of the coil segments on backbones were designed and synthesized by a palladium‐catalyzed Suzuki coupling‐reaction. The thermal stability, the UV–Vis absorption and fluorescence spectra in chloroform solution and thin film, the electrochemical properties, thermal behavior, and morphology of these rod–coil polymers were investigated. The thermal stability of these polymers steadily decreased on increasing the length of the coil segments on the backbone; their optical and electrochemical properties did not exhibit noticeable dependence on the weight fraction of the coil segments. However, the shoulder emission and the full width at the half‐maximum (FWHM) in PL spectra of the films increased, whereas the oxidation onset potentials and the corresponding HOMO energy levels decreased with the increase in the weight fraction of the coil segments, which was assigned to microphase separation and formation of folded chain conformation as the weight fraction of the coil segments increased. These polymers displayed a characteristic liquid crystalline texture. The variation of the weight fraction of the coil segments obviously affected the thermal behavior and morphology of these rod–coil polymers. Copyright © 2008 John Wiley & Sons, Ltd.     

Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.     

On the stability of the additive Cauchy functional equation in random normed spaces

Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.