A fluctuation theory for Markov chains

A fluctuation theory for Markov chains on an ordered countable state space is developed, using ladder processes. These are shown to be Markov renewal processes. Results are given for the joint distribution of the extremum (maximum or minimum) and the first time the extremum is achieved. Also a new classification of the states of a Markov chain is suggested. Two examples are given.     

Spontaneous emission in Ĉerenkov FEL devices: a preliminary theoretical analysis

Summary The main features of the spectral characteristics of the spontaneously emitted Ĉerenkov light in circular and rectangular wave guides filled with dielectric are discussed. The characteristics of the radiation emitted by an electron beam moving near and parallel to the surface of a dielectric slab are also analysed. Finally, the relevance of these results to a possible FEL-Ĉerenkov operation is briefly discussed.

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Riassunto In questo lavoro si discutono le caratteristiche dello spettro della radiazione Ĉerenkov, emessa in guide d'onde circolari e rettangolari riempite con dielettrico. Si analizzano inoltre le proprietà della radiazione emessa da un fascio di elettroni in moto in prossimità e parallelamente alla superficie di una ?slab? di dielettrico. Si discute, infine, brevemente, l'importanza di questi risultati per la realizzazione di un possibile FEL-Ĉerenkov.

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Резюме Обсуждаются основиые особенности спектральных характеристик спонтанного черенковского излучения в круговых и прямоугольных волноводах, заполненных диэлектриком. Также анализируются характеристики излучения, испущенного электронным пучком, движущимся вблизи и пораллелйно поверхности диэлектрической пластинки. В заключение, вкратце обсуждется применимость полученных результатов в возможных FEL-черенковских приборах.

     

现代地貌过程中的人类作用

人为的风化、侵蚀、搬运、堆积、造貌等作用，是现代地貌过程中一种新的营力。这种作用的强度主要取决于人口、社会经济发展水平、科学技术水平等因素。而人为地貌作用导致的地貌环境变化又会对人类社会发展产生正负两方面的影响，尤其是其负面影响常常会产生与人们的主观愿望相反的效果。因此，必须根据可持续发展战略来处理人类与地貌环境的关系。     

Interaction of multi-raman-processes in miniature optically pumped NH3 fir laser

The principle of Raman gain superposition was introduced to the theory of multi-Raman- processes interaction. Spectral characteristics of Raman lines from miniature NH₃-optically pumped FiR lasers were studied and measured.supported by the National Nature Science Foundation of P.R.C. and the Special Research Foundation of Doctorate Stations of P.R.C.     

Application of B-splines finite basis sets to relativistic two-photon decay rates of level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies. Received: 6 January 1998 / Accepted: 31 March 1998     

Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems

A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily. Received: 5 September 1997 / Revised: 13 May 1998 / Accepted: 18 May 1998     

Periodic maintenance and repair rate control in stochastic manufacturing systems

In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.Research of this author was supported in part by the University of Georgia.Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.     

The inspection paradox in renewal-reward processes

To explore the inspection paradox in the context of a renewal-reward process, we obtain asymptotic expressions for the mean and distribution function of the reward associated with the spread (total life) of the process. These results also yield a simplified demonstration of the elementary renewal-reward theorem.     

Inventory control using a service constraint on the expected customer order waiting time

In this paper an analytical model is presented which permits the determination of the minimal inventory reorder point subject to (a) a maximum specified expected customer order waiting time or (b) a maximum specified probability of a customer order waiting more than a predetermined time span. The probability distribution of the customer order waiting time is determined for an arbitrary demand distribution (e.g. normal, gamma or exponential) and under stochastic replenishment lead time conditions by use of arguments from renewal theory. The results established can be used for the customer-oriented control of inventory policy as well as for the analysis of multi-echelon inventory systems.     

Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries

The general study of random walks on a lattice is developed further with emphasis on continuous-time walks with an asymmetric bias. Continuous time walks are characterized by random pauses between jumps, with a common pausing time distribution(t). An analytic solution in the form of an inverse Laplace transform for P(l, t), the probability of a walker being atl at timet if it started atl _o att=0, is obtained in the presence of completely absorbing boundaries. Numerical results for P(l, t) are presented for characteristically different (t), including one which leads to a non-Gaussian behavior for P(l, t) even for larget. Asymptotic results are obtained for the number of surviving walkers and the mean l showing the effect of the absorption at the boundary.This study was partially supported by ARPA and monitored by ONR(N00014-17-0308).