Running Uphill: An Experimental Result and its Applications

An experimentally derived formula has implications for (i) the measurement of a runner's workrate; (ii) choice of gradient in running uphill; and (iii) the use of Naismith's rule in deriving schedules for fell runners.     

Running waves and dynamical chaos in active media: A numerical study

In the framework of a self-similar problem, we numerically analyze the onset of solutions in the form of running waves in excitable and oscillating active media. We show that the passage to the solution in the form of a running wave occurs through cascades of bifurcations responsible for the development of chaotic dynamics in nonlinear dissipative systems of differential equations.     

Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.     

Fermi Rule and Scattering Amplitude Resonances

The behavior of the scattering amplitude near a resonance with a small imaginary part is investigated. We prove that the scattering amplitude as an energy function suffers a jump near the real part of the resonance and the jump is independent of the interaction details. In terms of the problem data, we derive an estimate for the imaginary part of the resonance.     

OR and energy: Problems of modelling

Attention is focused on three problem areas in energy modelling: (1) identifying the essential elements of the system, (2) coping with multiple criteria, (3) incorporating learning in the system. These aspects are illustrated through examples in current energy systems research, involving the oil market, power systems planning, and the role of nuclear energy.In modelling the word oil market, too heavy emphasis is placed on economic forces, but practically non on the political forces. However, certain economics-oriented studies indicate that financial gains of OPEC may actually be intensitive to the oil pricing policy followed. If that is indeed the case, the significant (political) elements and their motives have to be captured in the model in order to arrive at consistent results.Modelling the different objectives in power systems planning is an area where advances are urgently needed. A method is proposed, where decision alternatives are generated a posteriori, in contrast to recent approaches involving a priori articulation of preferences, or interactive methods. A multicriterion dynamic linear programming model and a fast algorithm are used in generating efficient solutions, which are then grouped, based on the clustering in objective values.The problem associated with changing system objectives is discussed and the nuclear programme is given as an example of how the system objectives move from costs to perceived risks. In line with the real system that ‘learns’ from its experience, we need models that change their objective functions as a result of their own outputs at prior times.     

几种电梯运行模式的比较及应用

通过对上班高峰时段的电梯运行情况进行分析,以"最后被运送的乘客的等待时间最短"的"最大最小"原则作为其评价指标,以"电梯运行周期与运行总时间之比等于电梯在一个周期内运送的乘客数与乘客总数之比"的"比例"原则为依据,对高层楼宇中人员流动高峰时段的几种电梯运行方案建立了数学模型进行描述与比较,找到了电梯停靠楼层的最佳方案,并对北京大学第三医院外科楼的运行方案做出定量的数学证明.     

ryabha a's Rule and Table for Sine-Differences

This paper gives both a new interpretation of ryabha a's rule for sine-differences prescribed in the second chapter of his ryabha ya(A.D. 499/510), one of the oldest astronomical texts in India, and a hypothesis about the origin of his table of sine-differences given in the first chapter of the same work.Copyright 1997 Academic Press.[FORMULA]Copyright 1997 Academic Press.[FORMULA]     

Square root 3 -Subdivision Schemes: Maximal Sum Rule Orders

Abstract. Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called $\sqrt 3$ -subdivision , has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix 2I , $\sqrt 3$ -subdivision is based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points. This paper concerns the problem of achieving maximal sum rule orders for stationary $\sqrt 3$ -subdivision schemes with given mask support, which is important because the sum rule order characterizes the order of the polynomial reproduction, and provides an upper bound on the Sobolev smoothness of the surface. We study both interpolating and approximating schemes for a natural family of symmetric mask support sets related to squares of sidelength 2n in Z ² , and obtain exact formulas for the maximal sum rule order for arbitrary n . For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit family of schemes based on repeated averaging [15]. In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in size by using symmetries. From this, we construct some new examples of smooth (C ² ,C ³ ) interpolating $\sqrt 3$ -subdivision schemes with maximal sum rule order and symmetric masks. The construction of associated dual schemes is also discussed.     

Complex random energy model: zeros and fluctuations

The partition function of the random energy model at inverse temperature $\beta $ is a sum of random exponentials $ \mathcal{Z }_N(\beta )=\sum _{k=1}^N \exp (\beta \sqrt{n} X_k)$ , where $X_1,X_2,\ldots $ are independent real standard normal random variables (=random energies), and $n=\log N$ . We study the large N limit of the partition function viewed as an analytic function of the complex variable $\beta $ . We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the random partition function at complex $\beta $ , both on the logarithmic scale and on the level of limiting distributions. Our results cover also the case of the sums of independent identically distributed random exponentials with any given correlations between the real and imaginary parts of the random exponent.     

Strategy in Fell Running: An Analysis of the Bob Graham Round

The ‘Bob Graham Round’ is an arduous route in the English Lake District which fell-runners attempt to complete in under 24 hours. Runners who complete the round and wish to have their achievement recognized must submit a detailed timetable of their progress. From an analysis of these submissions we have:(a) tested an elaboration to the well-known Naismith Rule for predicting progress in mountainous country;(b) tested the conjecture that successful athletes in stamina events apply a constant work rate;(c) estimated the effect of such additional factors as darkness or fatigue.The objective of our work is threefold. First, to help runners planning an attempt on the round. Secondly, (as the Lake District mountains are so well known and accessible) to provide any readers who are mountain walkers with an opportunity to check our estimates against their own experience and judgement. This can of course be done for any section of the route, and does not require the whole round to be tackled. Thirdly, to make our findings applicable for mountainous areas other than the Lake District.     

Superposition and Chain Rule for Bounded Hessian Functions

We study the properties of superposition of Bounded Hessian functions, establishing the validity of a second-order chain rule. We prove rectifiability properties of all noncritical level sets ofBH-functions by showing a geometric measure theory analogous of Dini's Theorem.     

对复合函数求导定理证明的评论与研究

本文指出了一些广泛使用的教科书对复合函数求导定理的证明是不严格,并创造性地举例阐明存在这样的复合函数f(u),它对自变量u可导,而对中间变量u=g(x)不可导。本文也给出了该定理的一个严格证明,同时揭示了复合函数求导法则的表达形式与其内容并不完全一致。     

决策信息系统的变换及其变换规则形式化

传统的粗糙集分类、约简、规则挖掘方法处理的对象是某个时间点上的静态信息系统,因而获得的知识也是静态的.实际上信息系统通常表现为易变性和过程性,为了挖掘决策信息系统动态变换的趋势和规则,本文扩展了粗糙集中传统的分类、约简、规则挖掘的应用模式,提出决策信息系统基于时间序列单步和过程变换模型, 建立面向决策信息系统变化趋势的类划分机制和相应的语义,对条件属性变迁与决策属性变迁的相关性进行研究,并给出变换规则的形式化表示.     

改进的L’Hospital法则的证明及其应用

对改进的L’Hospital法则提供了一个证明,所用的知识主要是函数极限的定义和柯西中值定理,而后又提供四个例子,作为改进的L’Hospital法则的应用.     

The Navier-Stokes equations: Existence theorems and energy equalities

Doklady Mathematics -