A unifying approach to abstract matrix algebra preconditioning

In earlier papers Tyrtyshnikov [42] and the first author [14] considered the analysis of clustering properties of the spectra of specific Toeplitz preconditioned matrices obtained by means of the best known matrix algebras. Here we generalize this technique to a generic Banach algebra of matrices by devising general preconditioners related to “convergent” approximation processes [36]. Finally, as case study, we focus our attention on the Tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric Toeplitz systems can be constructed in this class. Received April 25, 1997 / Revised version received March 13, 1998     

Construction of infinite unimodular sequences with zero autocorrelation

Unimodular waveforms x are constructed on the integers with the property that the autocorrelation of x is one at the origin and zero elsewhere. There are three different constructions: exponentials of the form e^{2 pi na q},e^{2 pi i n^alpha theta}, sequences taken from roots of unity, and sequences constructed from the elements of real Hadamard matrices. The first is expected and elementary and the second is based on the construction of Wiener. The third is the most intricate and is really one of a family of distinct but structurally similar waveforms. A natural error estimate problem is posed for the last construction. The analytic solution is not as useful as the simulations because of the inherent counting problems in the construction.     

煤粉燃烧中NOx和SOx生成的详细反应机理模拟

采用详细化学反应机理与CFD方法耦合的煤粉燃烧数值模拟程序,计算了煤粉燃烧过 程中CO, NOx和SOx等的浓度分布特性. 通过与实验对照,验证了数值模拟方法的 可靠性,并分析了燃烧温度和煤粉细度等因素对于NO生成的影响. 结果表明温度对于NO的 生成影响较大,随着温度的增加,NO的生成浓度明显增加;对于不同煤种,可能存在一个温 度点,这时NO的生成速率将非常快;在计算范围内,温度对SO2的最终生成浓度没有 明显影响,而只影响SO2的释放过程. 煤粉细度对于NO生成有较小的影响.     

RELATIVELY WEAKLY COMPACT SETS IN THE DEN JOY SPACE

Some topological Properties of the completion H of the Denjoy space are studied. In particular sufficient conditions for a subsets of H be relatively compact and characterizations for a subsets of H be restively weakly compact are given.     

Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.     

A one dimensional Boltzmann equation with inelastic collisions

We consider the Boltzmann equation for inelastic particles on the line and prove some preliminary results on existence and uniqueness of the solutions. We also discuss some connections with another kinetic equation investigated by the same authors. Conferenza tenuta il 3 novembre 1997     

Ri?ausbreitung in amorphen Polymeren und deren Verbundstoffen

Ohne Zusammenfassung     

An Investigation of Coupled D. C.-Induction Arc Discharges

The object of this study is to analytically determine the properties of an arc discharge generated by a combination of induction and d. c. electromagnetic fields. Induction power is supplied to the discharge by a solenoidal coil whose axis of symmetry is aligned with the applied d. c. electric field. A numerical technique is used to simultaneously solve a set of linear differential equations which include Maxwell's field equations, the single fluid energy equation, the momentum balance equation, Ohm's law, and the radiation diffusion equation. It is necessary to make a number of reasonable assumptions to obtain the final set of equations for programming. These assumptions restrict the calculations to azimuthally symmetric plasmas with axial gradients only in static pressure. In addition, the radiant energy flux is assumed to be isotropic within the plasma.