Numerical analysis for bulk-arrival queueing systems: Root-finding and steady-state probabilities inGI r /M/1 queues

Queueing theorists have presented, as solutions to many queueing models, probability generating functions in which state probabilities are expressed as functions of the roots of characteristic equations, evaluation of the roots in particular cases being left to the reader. Many users have complained that such solutions are inadequate. Some queueing theorists, in particular Neuts [6], rather than use Rouché's theorem to count roots and an equation-solver to find them, have developed new algorithms to solve queueing problems numerically, without explicit calculation of roots. Powell [7] has shown that in many bulk service queues arising in transportation models, characteristic equations can be solved and state probabilities can be found without serious difficulty, even when the number of roots to be found is large. We have slightly modified Powell's method, and have extended his work to cover a number of bulk-service queues discussed by Chaudhry et al. [1] and a number of bulk-arrival queues discussed in the present paper.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Evolution of Orbits and Quantum Correlation Functions by Quadratic Hamiltonians

Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa     

Quantum Groups and Double Quiver Algebras

For a finite dimensional semisimple Lie algebra and a root q of unity in a field k, we associate to these data a double quiver . It is shown that a restricted version of the quantized enveloping algebras is a quotient of the double quiver algebra .*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001)     

The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field

In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity. It is shown that the conserved quantity is the same as the constant of motion in essence.     

Test of the intercombination rules on the two excited states (0 and 1) potential parameters of the second group metal atoms perturbed by inert gases

A set of intercombination rules has been used to calculate the two excited (³0 and ³1) state potential parameters ε₁₂ and R₁₂ of Hg, Cd and Zn interacting with inert gases (Xe, Kr, Ar and Ne). The results obtained with these rules are compared with various experimental and theoretical results for these molecules. The rules can be very well used for determination of the position of the potential minimum for the two states of all molecules. Concerning the well depths of the two states (³0 and ³1) of these molecules, it is observed that for the more bounded excited state ³0 some of these rules give results that are in close agreement with experimental data especially for molecules consisting of heavy atoms but for the shallow excited state ³1 these rules cannot be used.     

Painlev Analysis,Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin-Bona-Mahony-Burger (BBMB) Equation

In this paper,a variable-coefficient Benjamin-Bona-Mahony-Burger (BBMB) equation arising as a mathematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated.The integrability of such an equation is studied with Painlev analysis.The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method.Furthermore different types of solitary,periodic and kink waves can be seen with the change of variable coefficients.     

On the quantum Lorentz group

The quantum analog of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indices we construct a quantum Minkowski metric. In this framework we show explicitly the correspondence between the SL(2,C) and Lorentz quantum groups. Five matrices of the quantum Lorentz group are constructed in terms of the R matrix of SL(2,C) group. These matrices satisfy Yang–Baxter equations and two of which have adequate properties tied to the quantum Minkowski space structure as the reality conditions of the coordinates and the symmetrization of the metric. It is also shown that the Minkowski metric leads to invariant and central lengths of four-vectors.     

Radical grafting from carbon fiber surface: graft polymerization of vinyl monomers initiated by azo groups introduced onto the surface

This paper describes the radical graft polymerizations of vinyl monomers from carbon fiber surface initiated by azo groups introduced onto the fiber surface. The carbon fiber used in this experiment was the polyacrylonitrile type. The introduction of azo groups onto the carbon fiber surface was achieved by the reaction of 4,4'-azobis (4-cyanopentanoic acid) with isocyanate groups which were previously attached onto the surface by the treatment of the fiber with tolylene 2,4-diisocyanate. The amount of surface azo groups introduced onto nitric acid-treated carbon fiber was determined to be 0.60 x 10^-5 mol 9^-1 by nitrogen analysis. The radical graft polymerization of methyl methacrylate (MMA) was tried. Though the thermal polymerization of MMA proceeded slightly in the absence or in the presence of untreated carbon fiber, the rate of the polymerization was considerably low. In contrast, the graft polymerization of MMA was initiated in the presence of the carbon fiber having surface azo groups, and part of resultant poly(MMA) grafted onto the surface. The percentage of grafting increased with an increase in polymerization time and reached 42.8% after 24 h. The graft polymerizations of other monomers, such as styrene, vinyl acetate, and acrylic acid, were also initiated by the surface azo groups attached onto the carbon fiber, and the corresponding polymer effectively grafted onto the surface.