Optimal Linear Filtration of a Doubly Stochastic Process

An algorithm of optimal linear filtration of the volatility coefficient in the model of changing prices of financial assets is constructed.     

Doubly Stochastic Stream of Events with Independent Intensities

The main characteristics of a doubly stochastic Poisson stream of events with independent intensities that form a purely discontinuous Markovian process are determined.     

Mean Busy Period of Infinite Multilinear Queues with a Doubly Stochastic Input Flow

The mean busy period of an infinite multilinear queue with a doubly stochastic flow of incoming queries having two intensities and exponential server is calculated.     

Estimation of the Poisson Stream Intensity in a Multilinear Queue with an Exponential Job Queue Decay

Times the busy queue periods start are found for a multilinear queue with an exponential job queue decay and uniform resource allocation to individual servers. The stream intensity and the average job are estimated from observations of the times the queue busy periods start.     

Estimation of the Characteristics of a Poisson Stream of Queries From Observations of the Occupation Period for an M / G /∞ System with an Exponential Job Queue Decay

Allocations of the occupation period are found for an infinite linear queue with a recurrent service. Explicit expressions for the characteristic function of duration of the occupation period and for the first four moments are derived. The incoming stream intensity and the average service time are estimated, and their statistical characteristics are investigated.     

Resistance Calculation for an Infinite Simple Cubic Lattice Application of Green's Function

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) lattice is expressible rationally in terms of the known value of G ₀ (0,0,0). The resistance between arbitrary sites in an infinite SC lattice is also studied and calculated when one of the resistors is removed from the perfect lattice. The asymptotic behavior of the resistance for both the infinite perfect and perturbed SC lattice is also investigated. Finally, experimental results are obtained for a finite SC network consisting of 8×8×8 identical resistors, and a comparison with those obtained theoretically is presented.     

Calculation of the Probability of Survival of an Insurance Company with Allowance for the Rate of Return for a Poisson Stream of Premiums

The probability of survival of an insurance company with the working capital is calculated for a Poisson stream of premiums.     

Calculation of Conversion Efficiency of a Doubly Resonant Optical Parametric Oscillator

The problem of calculating the conversion efficiency for a doubly resonant optical parametric oscillator with a Fabry-Perot type resonator configuration is reinvestigated, extending the usual theoretical treatment, which is restricted to highly reflecting resonator mirrors, to the case of arbitrary reflectivity R of the output mirror. For decreasing R both the signal and the idler wave acquire growing portions of travelling waves, and it is shown by numerical analysis that this effect leads to a remarkable enhancement of the conversion efficiency (as a function of the relative excitation). In particular, the maximum efficiency may considerably exceed the value 50% to be attained by means of high quality resonators (1 — R < 1).     

Multiplicative Stochastic Resonance for a Linear System Driven by O-U Noise

In the paper, we study a linear system driven by O-U noise and give a method which is different from the one stated in Europhys. Lett. 40 （1997） 117. We find the same phenomenon of multiplicative stochastic resonance for the response of the system to the signal as the one found in Europhys. Left. 40 （1997） 117. The merit of our method is that it prevents the complex formulas when making sum from n = 0 to n →∞ as in Europhys. Lett. 40 （1997） 117, which leads to the approximate results of the figures.     

Phase Transitions for the Growth Rate of Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on d-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the “total number of particles” in this framework. The main results are roughly as follows: If d≥3 and the system is “not too random”, then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is “random enough”, then the growth rate is slower than its expectation. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization. Supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban (C) 17540112.     

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag–Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude(SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.     

Stochastic Huge-Resonance Caused by Coupling for a Globally Coupled Linear System

In the paper, we investigate a globally coupled linear system with finite subunits subject to temporal periodic force and with multiplicative dichotomous noise. It is shown that, the global coupling among the subunits can hugely enhance the phenomenon of SR for the amplitude of the average mean field as the functions of the transition rate of the noise and that as the function of the frequency of the signal respectively.     

直线感应加速器束心偏移轨迹的计算

给出了直线感应加速器在磁体失准情况下电子束质心运动轨迹的计算机模型.利用坐标变换求磁体失准后的三维磁场分布,并采用束包络方程和束心偏移方程耦合求解的方法计算束心的运动轨迹.磁体失准度与束流质心偏移的定量关系的计算研究对磁体安装定位及校正线圈使用是有意义的.     

An Averaging Principle for the Time-Dependent Abstract Stochastic Evolution Equations with Infinite Delay and Wiener Process

Journal of Statistical Physics - In this paper, averaging principle for the time-dependent stochastic evolution equations (TDSEEs) with infinite delay is investigated. In proper non-Lipschitz...     

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When , spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.     

Spline Approximations of the Correlation Function and Probability Density of the Doubly Stochastic Poisson Flow Intensity

Spline approximations of the correlation function and probability density of the doubly stochastic Poisson flow intensity are constructed from observations of the times of occurrence of events of the flow on a fixed time interval.     

Gauge Transformations for a Driven Quantum Particle in an Infinite Square Well

Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator, which is symmetric but not self-adjoint when defined on a finite interval. In spite of this symmetric part, the Hamiltonian operator is shown to be self-adjoint. This follows from a theorem by Kato and Rellich which guarantees the stability of a self-adjoint operator under certain symmetric perturbations. The result, which has been assumed tacitly by other authors, is important in order to establish the equivalence of different Hamiltonian operators related to each other by quantum gauge transformations.     

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

A linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system were derived. By means of numerical calculations, we found that: (i) At some fixed multiplicative noise intensities, the output signal amplitude with frequency exhibits the structure of a weak peak, even no peak as the dichotomous noise is asymmetric; (ii) In the case of asymmetric dichotomous noise, the signal frequency can cause non-monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity; (iii) The curve of SNR with frequency has a weak peak and a trough in the case of symmetric dichotomous noise, but no peak with asymmetric; (iv) Whether the multiplicative noise is symmetric or asymmetric, the noise can enhance response of the system; (v) The SNR increases with the correlation strength between the two noises decreasing. In addition, the plane of multiplicative noise intensity versus noise symmetric parameter was plotted.