A Model of the Dynamics of the Third World War — An Exercise in Technology Transfer

The paper discusses two scenarios for a Third World War in Europe, and argues that it is often convenient to supplement a scenario by a formal model. The problems of creating such a model are examined, and a model is formulated for land, air, and sea combat in Europe and the Atlantic, using the System Dynamics approach, which has not hitherto been widely employed for military analysis.The model confirms the results of the two scenarios, and its use for the analysis of alternative force configurations is illustrated. Some implications in the interpretation of Soviet military literature are discussed, and the paper ends with speculations on the role and value of such models.     

战争地区邮递员问题

本文首次提出了赋权有向图上中国邮递员问题的一个推广－战争地区邮递员问题，并对解的存在性给出了若干充分条件和必要条件，得到了求解该问题的一个多项式算法。     

War and peace in veto voting

Let I={_i1,…,_in}$I=\{i_1\text{,}\dots \text{,}{i}_n\}$ be a set of voters (players) and A={_a1,…,_ap}$A=\{a_1\text{,}\dots \text{,}{a}_p\}$ be a set of candidates (outcomes). Each voter i∈I$i\in I$ has a preference P_i over the candidates. We assume that P_i is a complete order on A  . The preference profile P={_Pi,i∈I}$P=\{P_i\text{,}i\in I\}$ is called a situation. A situation is called war if the set of all voters I is partitioned in two coalitions K₁ and K₂ such that all voters of K_i have the same preference, i=1,2,$i=1\text{,}2\text{,}$ and these two preferences are opposite. For a simple class of veto voting schemes we prove that the results of elections in all war situations uniquely define the results for all other (peace) situations. In other words, the results depend only on the veto (or effectivity) function. We give several other examples from game (and from graph) theory with the same property.     

System Dynamics in Shipping

A system which exhibits time-varying fluctuations in measures which describe its state and which comprises inter-dependent feedback loops is likely to be amenable to the modelling methods of system dynamics. The shipping industry is analysed from this point of view with the aim of identifying its dynamic characteristics and their causal mechanisms. Examples are given of observed dynamic behaviour within and between trade sectors.     

A non-zero-zum War of Attrition

The division of a cake by two players is modelled by means of a game of timing in which the players have a probability of learning when their opponent acts. It is shown that the game has a unique Nash equilibrium when both players are non-noisy but that there are many Nash equilibria including pure ones when at least one of the players is noisy. Explicit expressions for the strategies used in these Nash equilibria are obtained.This work was carried out while Dr. Garnaev was visiting the University of Southampton on a Postdoctoral Fellowship of The Royal Society of London.     

Dynamics of hierarchical models in discrete-time

We derive and analyze a general class of difference equation models for the dynamics of hierarchically organized populations. Different forms of intra-specific competition give rise to different types of nonlinearities. For our models, we prove that contest competition results asymptotically in only equilibrium dynamics. Scramble competition, on the other hand, can result in more complex asymptotic dynamics. We study both the case when the limiting resource is a constant and when it is dynamically modeled. We prove, in all cases, that the population persists if the inherent net reproductive number of the population is greater than one.     

Dynamics of transitions in population interactions

A two-species model with transitions between population interactions is studied. Rich dynamics is observed as the number and quality of equilibria change when model parameters and functional responses vary. Existence and stability of equilibria and nonexistence of periodic solutions are established, existence of some bifurcation phenomena are analytically and numerically studied, explicit threshold values are computed to determine the kind of interaction (mutualism, competition, host-parasite) between the species, and several numerical examples are provided to illustrate the main results in this work.     

上海银行间同业拆放利率动态性研究

本文分析了2006年至2014年间上海银行间同业拆放利率市场隔夜、一周和一月利率品种的动态性。结论显示,短期利率存在显著的漂移项非线性,且随着期限延长而减弱;扩散项的非对称自相关性以及跳跃项的非连续性特征也显著地存在。比较而言,信息冲击非对称性比漂移项非线性的影响要大,而跳跃的影响最大。跳跃设定允许利率遵循混合正态过程,允许利率在两个不同状态之间转换。跳跃对利率水平值的贡献都很小,但对方差的贡献占比很高,且存在随期限延长而降低的趋势。     

Newton—Riemann时空中的动力学（Ⅳ）

讨论了Newton-Riemann时空中的Lagrange力学及其与N－R时空中的Newton力学及Hamilton力学的关系。     

拓扑动力系统研究的图像方法(英文)

This paper considers the graph sequence graph （f^n ）={x×f^n ： x ∈X} of the iterates f^n of a continuous map f ： X →X on a compact metric space （X, d）. The main aim is to introduce serval limit sets by using different recurrent time sets, and discuss the relation between dynamics of the underlying compact system （X, f） and the structure of these limit sets, from a topological or fractal viewpoint.     

The Art of Rearranging

Equimeasurable rearrangements of real-valued functions of one or more real variables are surveyed. We outline the development of a relevant theory over the years and some applications to mathematical analysis, calculus of variations and partial differential equations.