非线性种群反应扩散系统的奇摄动

研究了一类具有非线性种群反应扩散系统奇摄动问题,在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态．     

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction–diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace–Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.     

捕食-被捕食反应扩散方程非线性奇摄动问题

研究了非线性反应扩散方程奇摄问题,在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的一致有效性和渐近性态。     

Pattern Formation in a Nonlinear Membrane Model for Epithelial Morphogenesis

A theoretical model is presented for pattern formation in an epithelium. The epithelial model consists of a thin, incompressible, viscoelastic membrane on an elastic foundation (substrate), with the component cells assumed to have active contractile properties similar to those of smooth muscle. The analysis includes the effects of large strains and material nonlinearity, and the governing equations were solved using finite differences. Deformation patterns form when the cells activate while lying on the descending limb of their total (active + passive) stress-stretch curve. Various one-dimensional and two-dimensional simulations illustrate the effects of spatial and temporal variations in passive stiffness, as well as the effects of foundation stiffness and stretch activation. The model can be used to examine the mechanical aspects of pattern formation in morphogenetic processes such as angiogenesis and myocardial trabeculation.     

非线性种群反应扩散系统奇摄动ROBIN问题

研究了一类具有非线性种群反应扩散系统奇摄动Robin初始边值问题.在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态.     

Formation Conditions and Stability Criteria for Small-Size Cluster Systems

The formation conditions and stability criteria for small-size cluster systems consisting of several particles interacting via an arbitrary isotropic pair potential are considered. Analytical criteria for instability development in horizontal (quasi-two-dimensional) and vertical (chain) structures consisting of three, four, and five charged particles are obtained for the first time. A simple algorithm to search for similar criteria in systems consisting of a larger number of particles is proposed. The obtained relations are verified by numerically solving the problem for Yukawa systems.     

一类捕食-被捕食控制反应扩散方程非线性奇摄动问题

研究了一类非线性反应扩散方程奇摄动问题．在适当的条件下,首先求出了原问题的外部解, 然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的一致有效性和渐近性态．     

An Efficient Two-Tier Causal Protocol for Mobile Distributed Systems

Causal ordering is a useful tool for mobile distributed systems (MDS) to reduce the non-determinism induced by three main aspects: host mobility, asynchronous execution, and unpredictable communication delays. Several causal protocols for MDS exist. Most of them, in order to reduce the overhead and the computational cost over wireless channels and mobile hosts (MH), ensure causal ordering at and according to the causal view of the Base Stations. Nevertheless, these protocols introduce certain disadvantage, such as unnecessary inhibition at the delivery of messages. In this paper, we present an efficient causal protocol for groupware that satisfies the MDS''s constraints, avoiding unnecessary inhibitions and ensuring the causal delivery based on the view of the MHs. One interesting aspect of our protocol is that it dynamically adapts the causal information attached to each message based on the number of messages with immediate dependency relation, and this is not directly proportional to the number of MHs.     

An Efficient Wavelet Analysis Method to Film–Pore Diffusion Model Arising in Mathematical Chemistry

In this paper, we have established an efficient Legendre wavelet based approximation method to solve film–pore diffusion model arising in engineering. Film–pore diffusion model is widely used to determine study the kinetics of adsorption systems. The use of Legendre wavelet based approximation method is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. It is shown that film–pore diffusion model satisfactorily describe kinetics of methylene blue adsorption onto the three low-cost adsorbents, Guava, teak and gulmohar plant leaf powders, used in this study.     

An Efficient Algorithm for Some Highly Nonlinear Fractional PDEs in Mathematical Physics

In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.     

NADH依赖型酶活性检测方法的建立

目的:建立一种NADH依赖型酶活性检测的方法。方法:将FDH、LeuDH串联克隆到表达载体pET-22b(+)中,转化至E.coli,并向培养液中分别添加去离子水、甲酸胺、三甲基丙酮酸,反应一段时间后,检测NADH的吸光度。同时通过测定氨气的产生判断FDH活性;通过薄层层析检测判断LeuDH活性;比较NADH吸光度测定结果与常规方法结果是否一致。结果:通过测定氨气的产生,证明FDH具有活性;此时NADH吸光度上升亦说明FDH具有活性;两种方法结论一致。薄层层析检测,生成叔亮氨酸,证明LeuDH具有活性;此时NADH吸光度下降亦说明LeuDH具有活性;两种方法结论一致。结论:通过检测菌体内部NADH吸光度的变化检测NADH依赖型酶活性的方法可行。     

The Scaling and Shift of Morphogen Gene Expression Boundary in a Nonlinear Reaction Diffusion System

The scaling and shift of the gene expression boundary in a developing embryo are two key problems with regard to morphogen gradient formation in developmental biology. In this study, a bigradient model was applied to a nonlinear reaction diffusion system (NRDS) to investigate the location of morphogen gene expression boundary. In contrast to the traditional synthesis–diffusion–degradation model, the introduction of NRDS in this study contributes to the precise gene expression boundary at arbitrary location along the anterior-posterior axis other than simply midembryo even when the linear characteristic lengths of two morphogens are equal. The scaling location depends on the ratio of two morphogen influxes ( \(w\) ) and concentrations ( \(r\) ) as well as the nonlinear reaction diffusion parameters ( \(\alpha , n\) ). We also formulate a direct relationship between the shift in the gene expression boundary and the influx of morphogen and find that enhancing the morphogen influx is helpful to build up a robust gene expression boundary. By analyzing the robustness of the morphogen gene expression boundary and comparing with the relevant results in linear reaction diffusion system, we determine the precise range of the ratio of the two morphogen influxes with a lower shift in the morphogen gene expression boundary and increased system robustness.     

Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly

Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are “strong” assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic self-assembly systems in the literature.     

PCR鉴定肺炎克雷伯菌的强毒性血清型

目的:了解肺炎克雷伯菌强毒性血清型K1、K2、K54和K57型菌株在我国重庆、北京、深圳三地的分布及流行趋势。方法:采用PCR对310株肺炎克雷伯菌临床分离株进行血清型K1、K2、K54和K57检测。结果:310株菌中,K1、K2、K54和K57血清型分别占14.2%、9.4%、6.5%和4.2%;来自呼吸系统标本分离株中的K1血清型菌株在4种检测的强毒血清型中占首位,为呼吸系统总数的17.4%。结论:310株肺炎克雷伯菌的4种强毒性血清型中,K1血清型菌株所占比例高,较为流行。     

若干具有非线性传染力的传染病模型的稳定性分析

讨论了具有常数迁入和非线性传染力的三类传染病模型,即SIRI模型,SIRI框架下的DS模型及SIR框架下的DI模型。给出了它们基本再生数R0的表达式,证明了R0≤1时无病平衡点是全局稳定的,同时证明了如果地方病平衡点存在,则必是全局稳定的结果（从而必唯一）对第一和第三个模型还给出了R0＞1时地方病平衡点的存在唯一性。     

Using Moment Equations to Understand Stochastically Driven Spatial Pattern Formation in Ecological Systems

Spatial patterns in biological populations and the effect of spatial patterns on ecological interactions are central topics in mathematical ecology. Various approaches to modeling have been developed to enable us to understand spatial patterns ranging from plant distributions to plankton aggregation. We present a new approach to modeling spatial interactions by deriving approximations for the time evolution of the moments (mean and spatial covariance) of ensembles of distributions of organisms; the analysis is made possible by “moment closure,” neglecting higher-order spatial structure in the population. We use the growth and competition of plants in an explicitly spatial environment as a starting point for exploring the properties of second-order moment equations and comparing them to realizations of spatial stochastic models. We find that for a wide range of effective neighborhood sizes (each plant interacting with several to dozens of neighbors), the mean-covariance model provides a useful and analytically tractable approximation to the stochastic spatial model, and combines useful features of stochastic models and traditional reaction-diffusion-like models.     

Structure, Pattern and Mechanisms of Formation of Seed Banks in Sand Dune Systems in Northeastern Inner Mongolia, China

A comparison of structure and pattern of the soil seed bank was made between active and stabilized sand dunes in northeastern Inner Mongolia, China. The objective of this paper was to determine the significance of seed bank in vegetation restoration of sand dunes. The results showed that (1) average seed density decreased from stabilized sand dune to interdune lowland of stabilized sand dune, to interdune lowland of active sand dune, and to active sand dune; (2) horizontally, along the transect from interdune lowland to ecotone and to sand dune top, a ‘V’ shaped pattern was presented in the active dune system, and a reverse ‘V’ shaped pattern in the stabilized sand dune system; (3) vertically, the proportion (accounting for the total seeds) of seeds found in 0–20 mm soil profile decreased from stabilized sand dune to interdune lowland of stabilized sand dune, to interdune lowland of active sand dune, and to active sand dune. The same order was also found in 20–50 mm and 50–100 mm soil profiles; (4) the Sokal and Sneath similarity indices in the species-composition between soil seed bank and above-ground vegetation were ranked as: the stabilized sand dune (24%) > the interdune lowland of active sand dune (21%) > the interdune lowland of stabilized sand dune (18%) > the active sand dune (5%); and (5) vegetation restoration of active sand dunes depends on the dispersal of seeds from nearby plant communities on the interdune lowlands. Much effort must be made to preserve the lowlands, as lowlands are the most important seed reservoir in the active sand dune field.     

An Efficient Soft Set-Based Approach for Conflict Analysis

Conflict analysis has been used as an important tool in economic, business, governmental and political dispute, games, management negotiations, military operations and etc. There are many mathematical formal models have been proposed to handle conflict situations and one of the most popular is rough set theory. With the ability to handle vagueness from the conflict data set, rough set theory has been successfully used. However, computational time is still an issue when determining the certainty, coverage, and strength of conflict situations. In this paper, we present an alternative approach to handle conflict situations, based on some ideas using soft set theory. The novelty of the proposed approach is that, unlike in rough set theory that uses decision rules, it is based on the concept of co-occurrence of parameters in soft set theory. We illustrate the proposed approach by means of a tutorial example of voting analysis in conflict situations. Furthermore, we elaborate the proposed approach on real world dataset of political conflict in Indonesian Parliament. We show that, the proposed approach achieves lower computational time as compared to rough set theory of up to 3.9%.