On pairs of permutable Hermitian surfaces

We investigate the intersection R of two permutable Hermitian surfaces of PG(3,q²), q odd. We show that R is a determinantal variety. From the combinatorial point of view R comprises a complete (q²+1)-span of the two corresponding Hermitian surfaces.     

Domains of infinitesimal generators of automorphism flows

We present a systematic characterization of the domain of a generator of a one parameter group on certain C∗-subalgebras of via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of whose domain is not closed with respect to the C¹-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C₀-semigroups.     

Decision support for the career field selection process at the US Air Force Academy

Each year, the US Air Force Academy graduates nearly 1000 young men and women. To support the decision of which cadets will be classified into which career fields, we describe a linear programming formulation with appealing computational properties that enable it as the core of a decision support tool. We explore methods for measuring and balancing cadets' class standing, Air Force career field requirements, and cadets' career field preferences in the context of this model. Our computational experiments demonstrate the improvement of this method over previous classification approaches, yielding more than 10% increase in the number of cadets assigned to their top career field choice and yielding nearly a 100% reduction in the number of cadets not receiving any of their career field choices. We also explore alternative methods for measuring cadets' career field preferences and demonstrate the positive effect of the new measurement scheme on the overall classification. Because of the short running time of this model, it will serve as a flexible, real-time component of the Academy's classification process.     

Numerical solutions of incompressible Euler and Navier-Stokes equations by efficient discrete singular convolution method

An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional Navier-Stokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has the potential of being extended to numerically solve much broader problems in fluid dynamics. The project supported by the National Natural Science Foundation of China (No.19902010).     

Polydomain model predictions of liquid crystalline polymer orientation in mixed shear/extensional channel flows

 The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations, subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic LCPs. In slit-expansion flows, the simulations predict a 90^∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials are systematically more susceptible to the effects of extension. Received: 22 October 1999/Accepted: 13 January 2000     

Electromagnetic tomography (EMT): Theoretical analysis of the forward problem

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一个具有随机丢弃分组机制且分组成批到达的GI~X/M/1/N排队系统

利用排队论中输入流稀疏化的方法,在标准的GIX/M/1/N排队系统中嵌入网络交换设备随机丢弃分组的机制,建立了一个具有随机丢弃分组机制的扩充的GIX/M/1/N排队系统,并讨论了该排队系统的分组丢失率、系统利用率、队列长度的均值/方差、平均等待时间等性能评价指标.     

On upper bounds for the growth rate in the extended Taylor-Goldstein problem of hydrodynamic stability

For the extended Taylor-Goldstein problem of hydrodynamic stability governing the stability of shear flows of an inviscid, incompressible but density stratified fluid in sea straits of arbitrary cross-section a new estimate for the growth rate of an arbitrary unstable normal mode is given for a class of basic flows. Furthermore the Howard’s conjecture, namely, the growth rate kc _i → 0 as the wave number k → ∞ is proved for two classes of basic flows.     

Capabilities of a quasi-gasdynamic algorithm as applied to inviscid gas flow simulation

Ten well-known one-dimensional test problems reflecting the characteristic features of unsteady inviscid gas flows are successfully solved by a unified numerical algorithm based on the quasigasdynamic system of equations. In all the cases, the numerical solution converges to a self-similar one as the spatial grid is refined.     

A note on the paper “characterization of all optimal solutions and parametric maximal flows in networks” of G. Ruhe (optimization 16 (1985) 1, 51-61)

First it is shown that the implementation of the algorithm proposed in the considered paper may cause some problems if no further specification is made as to one of its steps. Secondly, such a specification is suggested.