The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/∞ system revisited: finiteness,summability, long range dependence,and reverse engineering

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads. AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10     

Regularity and long time behavior of the Boltzmann equation for granular gases

This paper investigates regularity of solutions of the Boltzmann equation with dissipative collisions in a thermal bath. In the case of pseudo-Maxwellian approximation, we prove that for any initial datum f₀(ξ) in the set of probability density with zero bulk velocity and finite temperature, the unique solution of the equation satisfies f(ξ,t)∈H^∞(R³) for all t>0. Furthermore, for any t₀>0 and s?0 the Hs norm of f(ξ,t) is bounded for t?t₀. As a consequence, the exponential convergence to the unique steady state is also established under the same initial condition.     

色散长波方程簇的Hamilton结构

本文导出了色散长波方程簇,并利用屠规彰迹恒等式方法,讨论它们的Hamil-ton结构。     

Calculation of cladding modes using both two layer and three layer geometry in LPFG

In this paper we have calculated cladding modes of long period fiber grating. We have calculated cladding modes using both two layer (Graphical solution method) geometry and three layer geometry proposed by Erdogan. We have compared both these techniques, discussed the limitations of Graphical solution method and benefits of three layer geometry.     

Comparison study of the luminescent properties of the white-light long afterglow phosphors: CaxMgSi2O5+x:Dy(x=1, 2, 3)

A series of Dy³⁺-doped calcium magnesium silicate phosphors: CaMgSi₂O₆:Dy³⁺, Ca₂MgSi₂O₇:Dy³⁺, and Ca₃MgSi₂O₈:Dy³⁺ with white long-lasting afterglow were prepared and investigated. The characteristic intra-configurational 4f emissions of Dy³⁺ were observed in the emission spectra as well as the afterglow spectra under ultraviolet excitation. The combination of the 480 nm blue emission corresponding to the ⁴F_9/2→⁶H_15/2 transition and the 575 nm yellow emission corresponding to the ⁴F_9/2→⁶H_13/2 transition yielded white-light emission. The white-coloured afterglow emission can last more than 1 h for most of the samples under study. The concentration dependence of the ratio of the yellow emission intensity with blue emission intensity was also examined and found to be varied for the different hosts. The thermoluminescence spectra above room temperature are employed for the discussion of the origin of the traps and the mechanism of the persistent luminescence.     

Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes

While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a Lévy-driven spatio-temporal Ornstein–Uhlenbeck process by randomly varying its rate parameter to model both short-range and long-range dependence. This particular set-up allows for non-separable spatio-temporal correlations which are desirable for real applications, as well as flexible spatial covariances which arise from the shapes of influence regions. Theoretical properties such as spatio-temporal stationarity and second-order moments are established. An isotropic g-class is also used to illustrate how the memory of the process is related to the probability distribution of the rate parameter. We develop a simulation algorithm for the compound Poisson case which can be used to approximate other Lévy bases. The generalized method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.