A geometrical model for the effect of interference on food intake

Interference competition is often due to kleptoparasitism (food stealing). In which case, the attack distance, the distance over which one animal attacks another in an attempt to steal food, determines to a large extent the competitor density range over which interference significantly affects the intake rate of foraging animals.We develop a simple model of kleptoparasitism containing three parameters: attack distance, the density of foraging animals and a single dimensionless parameter α which summarizes the non-geometrical aspects of the interference process. Dominant and subdominant animals are not considered separately. The model predicts that the average intake rate will decrease exponentially with animal density and that a measure of the strength of interference depends on attack distance squared.The simple model is compared with a much more detailed individual-based foraging model from the literature. Simulated average intake rates are indeed well approximated by an exponential decrease with competitor density. Also the measure of interference behaves in the way expected from the simple model. By explaining the shape of the relationship between intake rate and animal density, the simple model provides insight into the behaviour of the detailed behavioural model.Insight into the role of geometry is important in the interpretation of field results and in the further development of detailed foraging models.     

市区性河流水质数学模型研究

本文通过对哈尔滨信义沟的调查和分析，研究了市区性河流的自净规律，将高浓度悬浮物沉降和有机物厌氧分解纳入河流水质模型，从而得出了广义的市区性河流多河段水质数学模型，这种建模的方法对市区性河流具有普遍的意义．     

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

An important research area in life sciences is devoted to modeling, prediction, and dynamics of gene-expression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced gene–environment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, time- discretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene–environment networks with its structural (in)stability. By embedding as a module and investigating CO₂ emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research.