Skew-Hermitian Triangular Splitting Iteration Methods for Non-Hermitian Positive Definite Linear Systems of Strong Skew-Hermitian Parts

By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts.     

Equilibrium in Queueing Systems with Complementary Products

We study a model of a queueing system with two complementary products/services. In our model, there is one M/M/1 system and another facility that provides instantaneous service. The two services are complementary and the customer has no benefit from obtaining just one of them. We investigate the model under various price structures and ownership assumptions.AMS subject classification: 90B22, 91A10The authors are equal in their contribution to this paper. This paper is submitted by the first author to the Tokyo Institute of Technology as partial fulfillment of the requirements for the Ph.D. program in the Department of Value and Decision Sciences, and the order of names was chosen in compliance with program conditions. This research was supported by the Israel Science Foundation (grant No. 237/02).     

T 1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝ ^d , which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C₀rⁿ, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

Electrical properties of neodymium doped CaBi4Ti4O15 ceramics

Neodymium doped bismuth layer structure ferroelectrics (BLSFs) ceramics CaBi_4−xNd_xTi₄O₁₅ (x=0, 0.25, 0.50, 0.75) were prepared by solid-state reaction method. X-ray diffraction pattern showed that single phase was formed when x=0-0.75. The refined lattice parameters showed that a (b) axes decrease at x=0.25 and increase with more Nd³⁺ dopant. The effects of Nd³⁺ doping on the dielectric and ferroelectric properties of CaBi₄Ti₄O₁₅ ceramics are studied. Nd³⁺ dopant decreased the Curie temperature linearly, and the dielectric loss, tan δ, as well. The remnant polarization of Nd³⁺ doped CaBi₄Ti₄O₁₅ ceramics was increased by 80% at x=0.25, while more Nd³⁺ dopant decreased the remnant polarization. CaBi_3.75Nd_0.25Ti₄O₁₅ ceramics had the largest piezoelectric constant d₃₃. The structure and properties of CaBi_4−xNd_xTi₄O₁₅ ceramics showed that Nd³⁺ may occupy different crystal locations when Nd³⁺ content x is less than 0.25 and more than 0.50.     

A Triangle Inequality for Measurement

We introduce the triangle inequality for measurement. This is a property that when satisfied by a measurement enables one to construct a metric on the set of elements with measure zero that yields the relative Scott topology. The naturality of this construction permits a categorical solution to the model problem in domain theory for locally compact metric spaces. The first time such a solution has been achieved.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

164Lu的三轴超形变核态的理论计算

用三维TRS(totalrouthiansurface)自洽理论对奇奇核164Lu的位能面进行了计算,计算结果与实验上得到的ε2=0.38基本一致,从而从理论上确认了164Lu是三轴超形变核,并且指出了存在三轴超形变带的两个组态. Total routhian surface in~(164)Lu nuclei is calculated according to the three dimensional Total Routhian Surface (TRS) theory. The result of the calculation is in agreement with the experiment. At the same time, two TSD bands could be assigned to the configuration(π\(1/2), α=1/2)(ν\(5/2), α=1/2), (π\(1/2), α=1/2)(ν\(3/2), α=-1/2).     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.