Determination of the number and locations of time points in transit schedule design — Case of a single run

An analytical model for the determination of the number and locations of time points as well as the amount of slack times in transit schedule design is developed. The model considers a bus route with a special passenger demand pattern in which all boarding passengers coordinate their arrivals at each stop in such a way that they never miss their intended bus, and therefore designing the schedule separately a single run at a time, becomes possible. The model employs the dynamic programming method to deal with the trade-offs among various cost components associated with the schedule quantitatively, and yet is flexible enough to incorporate the existing rules of thumb as well as transit operators' policies. Numerical examples that illustrate the applications of the model are given. The model, although not quite applicable to bus routes with general passenger demand patterns, is useful in the analysis of the contributing factors to the design of an economical, reliable, and operational transit schedule, and is likely to be adaptable for more realistic cases.     

A Note on Boundary Unique Contination for Harmonic Functions in Non-Smooth Domains

In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain     

Eigenvalue density of cross-correlations in Sri Lankan financial market

We apply the universal properties with Gaussian orthogonal ensemble (GOE) of random matrices namely spectral properties, distribution of eigenvalues, eigenvalue spacing predicted by random matrix theory (RMT) to compare cross-correlation matrix estimators from emerging market data. The daily stock prices of the Sri Lankan All share price index and Milanka price index from August 2004 to March 2005 were analyzed. Most eigenvalues in the spectrum of the cross-correlation matrix of stock price changes agree with the universal predictions of RMT. We find that the cross-correlation matrix satisfies the universal properties of the GOE of real symmetric random matrices. The eigen distribution follows the RMT predictions in the bulk but there are some deviations at the large eigenvalues. The nearest-neighbor spacing and the next nearest-neighbor spacing of the eigenvalues were examined and found that they follow the universality of GOE. RMT with deterministic correlations found that each eigenvalue from deterministic correlations is observed at values, which are repelled from the bulk distribution.     

Isomorphisms of adjoint Chevalley groups over integral domains

It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.

     

Why Restricted Additive Schwarz Converges Faster than Additive Schwarz

Recently a variant of the additive Schwarz (AS) preconditioner, the restricted additive Schwarz (RAS) preconditioner has been introduced, and numerical experiments showed that RAS converges faster and requires less communication than AS. We show in this paper how RAS, which is defined at the matrix level, can be interpreted as an iteration at the continuous level of the underlying problem. This interpretation reveals why RAS converges faster than classical AS.This revised version was published online in October 2005 with corrections to the Cover Date.     

An implicit pseudo‐spectral multi‐domain method for the simulation of incompressible flows

A pseudo‐spectral method for the solution of incompressible flow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method allows the treatment of moderately complex geometries by means of a multi‐domain approach and it is able to cope with non‐constant fluid properties and non‐orthogonal problem domains. In addition, the fully implicit scheme yields improved stability properties as opposed to semi‐implicit schemes commonly employed. Key components of the method are a Chebyshev collocation discretization, a special pressure–correction scheme, and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the proposed method is investigated by considering several numerical examples of different complexity, and also includes comparisons to alternative solution approaches based on finite‐volume discretizations. Copyright © 2003 John Wiley & Sons, Ltd.     

On stability crossing curves for general systems with two delays

For the general linear scalar time-delay systems of arbitrary order with two delays, this article provides a detailed study on the stability crossing curves consisting of all the delays such that the characteristic quasipolynomial has at least one imaginary zero. The crossing set, consisting of all the frequencies corresponding to all the points in the stability crossing curves, are expressed in terms of simple inequality constraints and can be easily identified from the gain response curves of the coefficient transfer functions of the delay terms. This crossing set forms a finite number of intervals of finite length. The corresponding stability crossing curves form a series of smooth curves except at the points corresponding to multiple zeros and a number of other degenerate cases. These curves may be closed curves, open ended curves, and spiral-like curves oriented horizontally, vertically, or diagonally. The category of curves are determined by which constraints are violated at the two ends of the corresponding intervals of the crossing set. The directions in which the zeros cross the imaginary axis are explicitly expressed. An algorithm may be devised to calculate the maximum delay deviation without changing the number of right half plane zeros of the characteristic quasipolynomial (and preservation of stability as a special case).     

All-optical image switch based on bacteriorhodopsin film

While two waves are coupled in bacteriorhodopsin (bR) film, a beam of incident light carrying the image is transferred to two diffraction beams whose intensities can increase from zero to a maximum and then decrease to a stable value with the increase of the writing time. Based on the relation among the polarization states of image in a recording beam and diffraction beams, we have proposed and demonstrated the all-optical image transfer switch which depends on the effective time and has the function that within the effective time, a polarization state image is automatically transferred to two images whose polarization states are perpendicular, and the transfer stops automatically beyond the effective time. A time-dependent all-optical image switch with muti-outputs is implemented.