Exact and approximate numerical solutions of steady-state distributions arising in the queueGI/G/1

In this paper we first obtain, in a unified way, closed-form analytic expressions in terms of roots of the so-called characteristic equation (c.e.), and then discuss the exact numerical solutions of steady-state distributions of (i) actual queueing time, (ii) virtual queueing time, (iii) actual idle time, and (iv) interdeparture time for the queueGI/R/1, whereR denotes the class of distributions whose Laplace-Stieltjes transforms (LSTs) are rational functions (ratios of a polynomial of degree at mostn to a polynomial of degreen). For the purpose of numerical discussions of idle- and interdeparture-time distributions, the interarrival-time distribution is also taken to belong to the classR. It is also shown that numerical computations of the idle-time distribution ofR/G/1 queues can be done even ifG is not taken asR. Throughout the discussions it is assumed that the queue discipline is first-come-first-served (FCFS). For the tail of the actual queueing-time distribution ofGI/R/1, approximations in terms of one or more roots of the c.e. are also discussed. If more than one root is used, they are taken in ascending order of magnitude. Numerical aspects have been tested for a variety of complex interarrival- and service-time distributions. The analysis is not restricted to generalized distributions with phases such as Coxian-n (C _n ), but also covers nonphase type distributions such as uniform (U) and deterministic (D). Some numerical results are also presented in the form of tables and figures. It is expected that the results obtained from the present study should prove to be useful not only to practitioners, but also to queueing theorists who would like to test the accuracies of inequalities, bounds or approximations.     

Optical properties of silver colloidal centers in KCl crystals

The Ag colloidal centers in additively colored KCl: Ag crystals have been studied by optical and electron microscope methods. The transmission electron microscope studies reveal that the colloidal particles are spherical in shape and have a size distribution which can be described by the skewed zeroth order logarithmic distribution (ZOLD) function. The band shape of the experimental absorption spectra of colloidal particles agrees well with that calculated on the basis of Mie theory, if the optical constants are suitably modified and if the particle size distribution is taken into account. If the particle size is so small that the size distribution cannot be measured by electron microscope the optical absorption bands can be used to determine the size distribution parameters provided the distribution is well described by ZOLD, which in turn is used to calculate theoretical extinction bands.     

Study of Raman spectrum of uranium using a surface‐enhanced Raman scattering technique

Raman spectroscopic investigation on weak scatterers such as metals is a challenging scientific problem. Technologically important actinide metals such as uranium and plutonium have not been investigated using Raman spectroscopy possibly due to poor signal intensities. We report the first Raman spectrum of uranium metal using a surface‐enhanced Raman scattering‐like geometry where a thin gold overlayer is deposited on uranium. Raman spectra are detected from the pits and scratches on the sample and not from the smooth polished surface. The 514.5‐ and 785‐nm laser excitations resulted in the Raman spectra of uranium metal whereas 325‐nm excitation did not give rise to such spectra. Temperature dependence of the B_3g mode at 126 cm⁻¹ is also investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Defect characterization of mixed SrCa tartrates

A few defect characteristics which are typical of gel-grown mixed single crystals of SrCa tartrates (Sr_1−XCa_xC₄H₄O₆ · 4H₂O) having different concentration, x, of the cations have been described. The temperature of decomposition has been found to be related, to some extent, to dislocation concentration. The magnitude of configurational entropy, which is a manifestation of lattice disorder, has been computed. The Vickers microhardness and dislocation density of crystals have been found to bear good correlation. An empirical formula has been suggested to explain the observed variation in microhardness with the concentration of ions in the mixed lattice.     

Growth and characterization of mixed Sr: Ca tartrates

Single crystals of Sr_1−xCa_xC₄H₄O₆ · 4 H₂O of different compositions and forms were grown by controlled diffusion of ions through suitable silica gels and characterized. Pycnometer density, lattice parameter, dislocation density, dissolution, cleavage, etc. are some of the interesting features which distinguish mixed crystals from the pure ones.