On uniqueness of an initial-value problem for ODE with hysteresis

An initial-value problem for a scalar differential equation with a scalar hysteresis nonlinearity (play and stop) is studied. As the main result a careful analysis of uniqueness problem posed in [1] is presented. Received January 23, 1996     

停止损失限额变换与保险风险比较(英文)

本文讨论了停止损失限额次序、凸次序、随机控制之间的关系,建立了风险集合与停止损失限额变换集合之间的一一对应．应用停止损失限额变换的性质证明了停止损失限额分离定理,并修正了ＡｌｆｒｅｄＭｕｌｌｅｒ在此定理证明中的一个错误．     

Acoustic band gaps in arrays of neutral inclusions

We analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform [H. Chen, C.T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Appl. Phys. Lett. 91 (2007) 183518]. We find that whereas a single coated inclusion is acoustically neutral at any frequency, an array of them might display some stop bands. More precisely, an array of freely vibrating coated voids is always neutral, whereas an array of clamped coated inclusions might display a zero frequency stop band. Interestingly, an array of radially symmetric coated inclusions behaves as local Helmholtz resonators, for which the eigenfield within each cloak is obtained in closed form, leading to a frequency estimate associated with the lower edge of the low frequency stop band. A finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source.     

含多抽水蓄能电站的电网多目标运行优化研究

广州抽水蓄能电站和惠州抽水蓄能电站开停机计划不够合理,导致两个蓄能电站不能实现均衡使用。针对此问题,提出在参照预测的日负荷曲线的基础上,利用加速变步长算法确定两个电站的调度方案,并运用回归分析预测法对每个电站的日抽水量进行预测。据此,可以合理安排两个蓄能电站的工作位置,避免机组的频繁启停,使其能够更好地发挥调峰填谷、调频、调压、提供备用等作用。     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.     

Creep and stress relaxation in the material of a cylindrical layer in its linear motion

Within the framework of the theory of large deformations, we consider deformation of some material with nonlinear elastic and viscous properties that is located in the gap between two rigid coaxial cylindrical surfaces when the inner surface moves rectilinearly. We study the uniformly acceleratedmotion of the inner cylinder, its subsequentmotion with a constant speed, and further deceleration till the full stop. We calculate stresses, reversible and irreversible deformations, displacements and study the stress relaxation after the full stop of the cylinder.     

Reliability of nonbranching programs in an arbitrary complete finite basis

We consider the realization of Boolean functions by nonbranching programs with conditional stop operators in an arbitrary complete finite basis. We assume that conditional stop operators are absolutely reliable, while all functional operators are prone to output inverse failures independently of each other with probability ɛ in the interval (0, 1/2). We prove that any Boolean function is realizable by a program with unreliability ɛ + 81ɛ ₂ for all ɛ ∈ (0, 1/960].     

On stabilization of Ek chains

We study special subgroups of infinite groups that generalize double centralizers. We analyze sufficient conditions for descending chains of such subgroups to stop after finitely many steps. We discuss whether this phenomenon can happen in the class of groups satisfying chain condition on centralizers.     

3/2 firefighters are not enough

The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning vertices to their unprotected neighbors. In every round, a small amount of unburnt vertices can be protected by firefighters. How many firefighters per turn, on average, are needed to stop the fire from advancing?We prove tight lower and upper bounds on the amount of firefighters needed to control a fire in the Cartesian planar grid and in the strong planar grid, resolving two conjectures of Ng and Raff.     

Study of wave dispersion in periodic composites by higher-order asymptotic homogenization method

We present [1] an application of the higher-order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable to the size of heterogeneities, successive reflections and refractions of the waves at the components interfaces lead to the formation of a complicated sequence of pass and stop frequency bands. The AHM provides a long-wave approximation valid in the low frequency range. Solution for the high frequencies is obtained on the basis of the Floquet–Bloch theorem by the plane-wave (PW) expansions method. Anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical fibres are considered. The dispersion curves are obtained, the pass and stop bands are identified. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal stopping and stochastic control differential games for jump diffusions

We study stochastic differential games of jump diffusions driven by Brownian motions and compensated Poisson random measures, where one of the players can choose the stochastic control and the other player can decide when to stop the system. We prove a verification theorem for such games in terms of a Hamilton–Jacobi–Bellman variational inequality. The results are applied to study some specific examples, including optimal resource extraction in a worst-case scenario, and risk minimizing optimal portfolio and stopping.     

Mathematical analysis of codons that stop protein synthesis

A mathematical analysis was performed, which shows that the maximum length of DNA in which translation is possible for at least one of three reading frames for any DNA strand is 10 nucleotides. In the case of any nonstandard stop codon triplet, this number can only decrease. Moreover, for any DNA consisting of at most 11 nucleotides, two and more genes overlaps in plus and minus strands are possible. The probability that a stop codon triplet chosen at random belongs to the group of stop codon triplets with these properties is less than 0.06.     

Plane harmonic wave propagation in three-dimensional composite media

An important characteristic of waves propagating through periodic materials is the existence of stop bands. A stop band implies the range of frequencies over which a medium completely reflects all incident waves and there is no transmission. Predicting stop band phenomena in periodic materials is regarded as the first step toward designing composite microstructures capable of propagating energy in a predetermined manner. In this paper a global–local modeling methodology previously proposed by the authors is used to successively predict stop bands in three-dimensional composite media. Numerical results reveal that the first stop band of the considered microstructures occurs where an acoustic shear mode veers with the lowest optical branch of the same symmetry class.     

State-dependent importance sampling schemes via minimum cross-entropy

We present a method to obtain state- and time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a state- and time-dependent estimator for the one-tailed probability of a light-tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two-tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature.     

Interconnected networks of queues with randomized arrival and departure blocking

In this paper, we study two interconnected multiclass non-exponential queueing networks. Jobs can jump from one cluster to another, but subject to randomized blocking depending on the class occupancies. Such systems naturally arise in communication networks, like Metropolitan Area Networks. We present sufficient conditions for the existence of a product form equilibrium distribution under both the recirculate and the stop blocking protocol. A number of examples are given.     

Continuous-time zero-sum stochastic game with stopping and control

We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also allowed to stop the process. Under suitable hypothesis we show that the game has a value and it is the unique solution of certain dynamic programming inequalities with bilateral constraints. In the process we also prescribe a saddle point equilibrium.     

Risk-sensitive stopping problems for continuous-time Markov chains

In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty equivalent of the stopping reward minus cost over the time horizon. We derive optimality equations for the value functions and prove the existence of optimal stopping times. The exponential utility is treated as a special case. In contrast to risk-neutral stopping problems it may be optimal to stop between jumps of the Markov chain. We briefly discuss the influence of the risk sensitivity on the optimal stopping time and consider a special house selling problem as an example.     

Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza

The basic reproduction number and the point of endemic equilibrium are two very important factors in any deterministic compartmental epidemic model as the basic reproduction number and the point of endemic equilibrium represent the nature of disease transmission and disease prevalence respectively. In this article the sensitivity analysis based on mathematical as well as statistical techniques has been performed to determine the importance of the epidemic model parameters. It is observed that 6 out of the 11 input parameters play a prominent role in determining the magnitude of the basic reproduction number. It is shown that the basic reproduction number is the most sensitive to the transmission rate of disease. It is also shown that control of transmission rate and recovery rate of the clinically ill are crucial to stop the spreading of influenza epidemics.