Baseline models of spatial population dynamics

To understand human population dynamics fully, before considering complex human agency it may be useful to construct baseline models to see where such agency may and may not be necessary. In fact, the dynamics of human populations may be amenable to mathematical modeling with relatively parsimonious mechanisms. We review some of the more prominent of such models, namely, the spatial Galton-Watson (GW) model, modifications of the GW model that add migration and immigration, and the Bolker-Pacala model, in which mortality (or birth rate) is affected by competition. We show that change in the distribution of population density over the last century for 12 American rural states may be captured by the simplest of the models, the spatial GW model.     

Infinity-Laplacian type equations and their associated Dirichlet problems

ABSTRACT

In this paper, we study the Dirichlet problem associated with infinity-Laplacian type equations that may exhibit anisotropic character. We identify a broad class of nonlinearities for which the problem may or may not admit viscosity solutions for any continuous boundary data. We also discuss comparison with Finsler cones, which may be of independent interest.     

A Class of Multisided Surface Patches

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On the associativity and commutativity of multiplication of infinite matrices

Unlike the case of finite matrices, the product of two infinite matrices may not exist in general. Moreover, for infinite matrices A, B, C the product A(BC) may exist whereas (AB)C may not and, if it exists, A(BC) may not be equal to (AB)C. In this paper some significant instances of associativity and commutativity of products of infinite matrices are presented and some of their useful consequences are derived.     

Outsourcing and capacity planning in an uncertain global environment

Firms employing offshore outsourcing strategies may face both exchange rate and demand uncertainties. In this paper, we show that the firms may benefit from operational option to switch production by keeping capacities with both domestic and foreign suppliers. The value of the operational option increases as the exchange rate uncertainty or demand uncertainty increases. In addition, when the firms become risk-averse, they may use domestic capacity to hedge against offshore capacity. As a result, the firms may choose to hold local capacity even if it exhibits negative marginal contribution to the profit. Furthermore, risk-averse firms may keep more total capacity than risk-neutral firms.     

弹性厚板的分区广义变分原理

本文提出弹性厚板分区广义变分原理,其要点如下:1.各分区可任意定为势能区或余能区.分区势能、分区余能、分区混合变分原理是它的三种特殊形式.2.每个分区中独立变分变量的个数可任意规定.每个分区可定为单类变量区、二类变量区或三类变量区.3.每个交界线上的位移和力的连接条件可以放宽.这个原理为非协调元的厚板有限元法提供理论基础.各种厚板有限元模型可看作这个原理的特殊应用.特别是弹性厚板分区混合变分原理的提出为分区混合有限元法应用于厚板问题打下了基础.     

SIR epidemic models with general infectious period distribution

We show how epidemics in which individuals’ infectious periods are not necessarily exponentially distributed may be naturally modelled as piecewise deterministic Markov processes. For the standard susceptible–infective–removed (SIR) model, we exhibit a family of martingales which may be used to derive the joint distribution of the number of survivors of the epidemic and the area under the trajectory of infectives. We also show how these results may be extended to a model in which the rate at which an infective generates infectious contacts may be an arbitrary function of the number of susceptible individuals present.     

独立董事的信号作用博弈模型

为了探讨独立董事在我国上市公司中的作用和运作机制,本文构建了一个博弈模型,来反应在大股东与市场上的出资人之间的博弈中,独立董事所发挥的间接的信号作用.模型中,由于出资人不能区分公司大股东是否有侵吞中小股东资产的意图,在没有任何信号（包括独立董事制度）的情况下,无侵吞意图的公司的资产会被低估,而有侵吞意图的公司则会被高估.无侵吞意图的大股东有可能通过聘请较多的独立董事来将自己和有侵吞意图的公司区分开来,使得高的独立董事比例成为一个正的信号,向出资人显示自己没有侵吞中小股东资产的意图.     

Positive solutions for a coupled system of nonlinear fractional differential equations

Using the Krasnoselskii–Zabreiko fixed point theorem, we establish two existence theorems for positive solutions of a coupled system of nonlinear fractional differential equations. Power functions and nonnegative matrices are used to characterize coupling behavior of our nonlinearities, so nonlinearities may grow differently; in fact, one may grow superlinearly, and the other may grow sublinearly. Copyright © 2014 John Wiley & Sons, Ltd.     

Maxwell方程的一类解

本文导出了Maxwell方程的一类含有任意泛复变解析函数的解并简略地分析了它们的物理意义,得到了比经典电磁理论更为广泛的一些性质:1.电磁场可有任意的形状;可以非周期性地传播一般可有全息性质.2.电磁场的传播速度可以小于、等于或大于光速.3.电磁场传播线可以是任意的曲线4.存在着共生的分蘖电磁场.可能存在着共生世界.对上述导出的奇异电磁场存在的实例,本文也作了推测及描述.大多涉及到现今各种物理模型难以解释的一些现象.     

Scheduling in Multiclass Networks with Deterministic Service Times

We consider general feed-forward networks of queues with deterministic service times and arbitrary arrival processes. There are holding costs at each queue, idling may or may not be permitted, and servers may fail. We partially characterize the optimal policy and give conditions under which lower priority should be given to jobs that would be delayed later in the network if they were processed now.     

On the foundations of game theory: The case of non-Archimedean utilities

Contrary to what appears to have become an accepted part of the folklore of game theory, a finite two-person zero-sum game with non-Archimedean utilities may have no equilibrium-point solution, and either one or both players may have no “minimax” strategy. Even when both players have “minimax” strategies, such a game may lack an equilibrium point.     

具有止步和中途退出的两不同服务台的可修排队

研究了等待空间有限的两服务台可修排队系统,其中一个服务台可能故障.到达的顾客可能进入系统也可能不进入系统(止步),进入系统的顾客可能因等待的不耐烦而中途退出.利用马尔可夫过程的方法建立了系统稳态概率满足的方程组,通过分块矩阵推导出了系统稳态概率向量的迭代计算公式,由此得到了系统各项性能指标的计算公式.最后,给出了一些数值结果.     

A prey-predator model with Holling II functional response and the carrying capacity of predator depending on its prey

One prey-predator model is formulated and the global behavior of its solution is analyzed. In this model, the carrying capacity of predator depends on the amount of its prey, and the Holling II functional response is involved. This model may have four classes of positive equilibriums and limit cycle. The positive equilibriums may be stable, or a saddle-node, or a saddle, or a degenerate singular point. In alpine meadow ecosystem, the dynamics of vegetation and plateau pika can be described by this model. Through simulating with virtual parameters, the cause of alpine meadow degradation and effective recovery strategy is investigated. Increasing grazing rate or decreasing plateau pika mortality may cause alpine meadow degradation. Correspondingly, reducing grazing rate and increasing plateau pika mortality may recover the degraded alpine meadow effectively.     

Families of functions and functions of proof

This article describes an activity for secondary school students that may constitute an appropriate opportunity to discuss with them the idea of proof, particularly in an algebraic context. During the activity the students may experience and understand some of the roles played by proof in mathematics in addition to verification of truth: explanation, discovery, intellectual challenge and self-fulfilment. They may learn that proof is not always a necessary condition for conviction since the work with several examples may provide confidence in the truth of a conjecture. The activity promotes the investigation of several families of quadratic functions and several families of cubic functions. The most important results are discussed and proven in the paper.     

Inhibitory control and mathematics learning: definitional and operational considerations

The topic of inhibition in mathematics education is both well timed and important. In this commentary, we reflect on the role of inhibition in mathematics learning through four themes that relate to how inhibition is defined, measured, developed, and applied. First, we consider different characterizations of inhibition and how they may shape the ways that inhibition is conceptualized and studied in mathematics contexts. Second, we discuss methods that researchers use to study inhibition and how differences across these methods may constrain researchers’ conclusions or what these differences may imply for students’ use of inhibition when solving authentic mathematics problems. Third, we consider the relationship between intuition and mathematics content knowledge, including how this relationship may vary for students with different levels of knowledge. We end with a discussion of inhibition’s practical educational relevance, in which we offer a set of questions that may inform future conversations or research in the field.     

Conducting secret ballot elections in computer networks: Problems and solutions

We discuss problems related to devising a secret balloting system with the following properties: (1) all eligible voters and they only may vote, (2) all ballots are secret, i.e. do not reveal the identity of the voter, (3) all voters may check whether their ballots have been correctly assigned, (4) the voters may revise their ballots within a predetermined time, and (5) errors in ballot assignment can be corrected within a predetermined time.     

Research problem the matrix numerical range

Every active mathematician has a storehouse of unresolved questions that he/she hopes someday to settle, but may never owing to changing interests, greener pastures elsewhere, or simply lack of a good idea. Since one mathematician's abandoned turf may be another's greener pasture, why not pose that unresolved question as a research problem? If it cannot be solved by anybody, the resulting publicity may confer luster on the proposer. and if it solved by somebody, the original proposer may be able to use the new ideas in further work. It's a winning stretegy to pose research problems, and a losing one not to since mathematics is a cooperative effort to reveal nature's truths     

Design of Compound Solenoids to Produce Highly Homogeneous Magnetic Fields

Solenoid systems comprising three or four coils may be designedto produce magnetic fields of extremely high homogeneity, byeliminating the leading perturbation terms in the field seriesformula. Alternatively, by minimizing the field deviation overa specified region, a three-coil design may be produced to providemore economically a similar degree of homogeneity. Residual field irregularities may be eliminated by means ofnon-solenoidal windings which generate individually the leadingterms in the spherical harmonic solution of Laplace's equation.     

可交易的水权安排对农户灌溉用水行为的影响——基于农户行为模型的理论分析

水资源用水总量控制与定额管理相结合的制度已成为我国水法的重要制度.但目前我国用水定额管理工作仅强调了通过用水定额管理并结合价格机制实行超定额累进加价征收水资源费和水费的办法来激励人们节约用水,没有明确界定这些用水定额的产权归属问题及用水定额的可交易性问题.将通过建立农户灌溉用水行为模型,利用边际分析方法分析可交易的农业用水定额对农户行为的影响.分析表明,当水权可交易时,水价政策与水市场的存在将激励农户节约用水,减少灌溉用水量.农户将通过采用灌溉效率更高的灌溉技术来节约单位面积的灌溉用水量或通过改变种植面积或种植结构的方式来节约总的灌溉用水量,而种植面积或种植结构的变化将进一步促进农地流转市场的发展.但水权交易成本的增加可能削弱出售水权农户的节水积极性并影响农户参与水市场的积极性从而影响水市场的形成与发展.