Iterative methods for overflow queueing models I

Summary Markovian queueing networks having overflow capacity are discussed. The Kolmogorov balance equations result in a linear homogeneous system, where the right null-vector is the steady-state probability distribution for the network. Preconditioned conjugate gradient methods are employed to find the null-vector. The preconditioner is a singular matrix which can be handled by separation of variables. The resulting preconditioned system is nonsingular. Numerical results show that the number of iterations required for convergence is roughly constant independent of the queue sizes. Analytic results are given to explain this fast convergence.     

An upper bound for the speedup of parallel best-bound branch-and-bound algorithms

This paper derives an upper bound for the speedup obtainable by any parallel branch-and-bound algorithm using the best-bound search strategy. We confirm that parallel branch-and-bound can achieve nearly linear, or even super-linear, speedup under the appropriate conditions.This work was supported by U.S. Army Research Office grant DAAG29-82-K-0107.     

On the eigenvalue distribution of a class of preconditioning methods

Summary A class of preconditioning methods depending on a relaxation parameter is presented for the solution of large linear systems of equationAx=b, whereA is a symmetric positive definite matrix. The methods are based on an incomplete factorization of the matrixA and include both pointwise and blockwise factorization. We study the dependence of the rate of convergence of the preconditioned conjugate gradient method on the distribution of eigenvalues ofC ^–1 A, whereC is the preconditioning matrix. We also show graphic representations of the eigenvalues and present numerical tests of the methods.     

Non-Traditional Squares of Predication and Quantification

Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here.      

Crystallization kinetics of linear polyethylene: The maximum in crystal growth rate-temperature dependence

This rapid communication reports a summary of the key findings of crystallization kinetics studies of unfractionated high density (linear) polyethylene at extremely large supercoolings. We report, for the first time, the maximum in crystal growth rate-crystallization temperature data for linear polyethylene, which has been sought by many researchers since the 1950s. The maximum growth rate was found to occur in the range of 70-75 °C with two separate methods. The kinetics studies were performed using a newly developed quench-crystallization technique based on depolarized reflection light microscopy that is capable of achieving enormously higher quench rates than existing methods. Typical onset crystallization temperatures accessed with this technique range from 40 to 90 °C. Bulk growth rates of crystals were obtained as the reciprocal of crystallization half times measured from the change in the depolarized light intensity upon direct crystallization from the melt. Separately, radial growth rates of spherulites were measured over a wide range of supercoolings. Secondary nucleation analysis of the crystal growth rates resulted in single linear fits extending into deep regime III, suggesting no change in mechanism of formation of the crystals at the largest supercoolings. The deeply quenched films, crystallized at temperatures below the maximum, contain non-impinged spherulites, capable of further crystallization.     

Sampling measures for Bergman spaces on the unit disk

We provide a characterization of the sampling measures for the Bergman spaces. These are the positive measures on the unit disk for which there exists a constant such that These are the continuous analogues of the sets of sampling characterized by K. Seip [13,14] and A. Schuster [12]. Our characterization is in terms of weak* limits of the Moebius transformations of the measure , and mimics the notion for sequences that sampling means being uniformly far from zero sets. Received: 26 October 1998 / in revised form: 25 Juni 1999     

拟似然非线性模型的某些渐近推断:几何方法

Abstract. A modified Bates and Watts geometric framework is proposed for quasi-likelihoodnonlinear models in Euclidean inner product space. Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi-likelihood nonlinear models is stud-ied. Several previous results for nonlinear regression models and exponential family nonlinearmodels etc. are extended to quasi-likelihood nonlinear models.