积累检测在光电设备中的应用分析

有些光电检测设备要求高的探测概率和低的虚警概率,使用单次检测不能达到要求。若采用积累榆测法则能满足系统要求。通过对积累检测在不同类型光电设备中的应用分析,建立了不同的数学模型,推导出各模型的探测概率和虚警概率的计算公式,并给出了相应的计算结果。计算结果表明：积累检测在主动探测设备中使用不连续的“K out of N”模型,能够有效提高探测概率,降低虚警概率。但在被动探测设备中,探测概率有所卜降,虚警概率会大大降低。     

温度为T时量子谐振子系统处在第n态的概率

研讨了温度为T时量子谐振子系统处在第n态的概率,并讨论了结果的物理意义．     

Jack polynomials and free cumulants

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group.     

A practical approach for reliability prediction of pipeline systems

Pipelines play an important role in the modern society. Failures of pipelines can have great impacts on economy, environment and community. Preventive maintenance (PM) is often conducted to improve the reliability of pipelines. Modern asset management practice requires accurate predictability of the reliability of pipelines with multiple PM actions, especially when these PM actions involve imperfect repairs. To address this issue, a split system approach (SSA) based model is developed in this paper through an industrial case study. This new model enables maintenance personnel to predict the reliability of pipelines with different PM strategies and hence effectively assists them in making optimal PM decisions.     

Optimal risk probability for first passage models in semi-Markov decision processes

This paper studies the risk minimization problem in semi-Markov decision processes with denumerable states. The criterion to be optimized is the risk probability (or risk function) that a first passage time to some target set doesn't exceed a threshold value. We first characterize such risk functions and the corresponding optimal value function, and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique. Then, we present some properties of optimal policies, and further give conditions for the existence of optimal policies. In addition, a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed. Finally, two examples are given to illustrate the value iteration procedure and essential characterization of the risk function.     

A disaster queue with Markovian arrivals and impatient customers

We consider a single server queueing system in which arrivals occur according to a Markovian arrival process. The system is subject to disastrous failures at which times all customers in the system are lost. Arrivals occurring during the time the system undergoes repair are stored in a buffer of finite capacity. These customers can become impatient after waiting a random amount of time and leave the system. However, these customers do not become impatient once the system becomes operable. When the system is operable, there is no limit on the number of customers who can be admitted. The structure of this queueing model is of GI/M/1-type that has been extensively studied by Neuts and others. The model is analyzed in steady state by exploiting the special nature of this type queueing model. A number of useful performance measures along with some illustrative examples are reported.     

Insurance claims modulated by a hidden Brownian marked point process

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.     

Asymptotic optimality of the static frequency caching in the presence of correlated requests

It is well known that the static caching algorithm that keeps the most frequently requested documents in the cache is optimal in case when documents are of the same size and requests are independent and identically distributed. However, it is hard to develop explicit and provably optimal caching algorithms when requests are statistically correlated. In this paper, we show that keeping the most frequently requested documents in the cache is still optimal for large cache sizes even if the requests are strongly correlated.     

The minimum speed for a blocking problem on the half plane

We consider a blocking problem: fire propagates on a half plane with unit speed in all directions. To block it, a barrier can be constructed in real time, at speed σ. We prove that the fire can be entirely blocked by the wall, in finite time, if and only if σ>1. The proof relies on a geometric lemma of independent interest. Namely, let K⊂R² be a compact, simply connected set with smooth boundary. We define dK(x,y) as the minimum length among all paths connecting x with y and remaining inside K. Then dK attains its maximum at a pair of points both on the boundary of K.     

The tax identity in risk theory — a simple proof and an extension

By linking queueing concepts with risk theory, we give a simple and insightful proof of the tax identity in the Cramér-Lundberg model that was recently derived in Albrecher & Hipp [Albrecher, H., Hipp, C., 2007. Lundberg’s risk process with tax. Blätter der DGVFM 28 (1), 13-28], and extend the identity to arbitrary surplus-dependent tax rates.