Conjugacy classes in maximal parabolic subgroups of general linear groups

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a ``matrix problem''. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a perfect field when one of the two blocks has dimension less than 6. In particular, this includes every maximal parabolic subgroup of GL_n(k) for n < 12 and k a perfect field. If our field is finite of size q, we also show that the number of conjugacy classes, and so the number of characters, of these groups is a polynomial in $q$ with integral coefficients.Comment: 23 pages, 6 figures. See also http://zaphod.uchicago.edu/~murray/research/index.html . Submitted to Journal of Algebr

Carter-Payne homomorphisms and branching rules for endomorphism rings of Specht modules

Let n be a positive integer and let p be a prime. Suppose that we take a partition of n, and obtain another partition by moving a node from one row to a shorther row. Carter and Payne showed that if the p-residue of the removed and added positions is the same, then there is a non-zero homomorphism between the corresponding Specht modules for the symmetric group of degree n, defined over a field of characteristic p. In this paper we give a very simple description of such a homomorphism, as a map between polytabloids, using the action of a Murphy-Jucys element. We also present a proof that in this context the homomorphism space is 1-dimensional. S. Lyle has already proved the more general result for Iwahori-Hecke algebras. In the process we give a formula for the Carter-Payne homomorphism as a linear combination of semi-standard homomorphisms. Our methods allow us to compute a lower bound for where the image of this homomorphism lies in the Jantzen filtration of the codomain Specht module. As an application, we show that the endomorphism ring of the restriction of a Specht module to the symmetric group of degree n-1 is an explicit direct product of truncated polynomial rings. A. Kleshchev proved the analogous result for the restriction of irreducible modules.Comment: 19 pages, submitte

Modelling rail track deterioration and maintenance: current practices and future needs

As commercialisation and privatisation of railway systems reach the political agendas in a number of countries, including Australia, the separation of infrastructure from operating business dictates that track costs need to be shared on an equitable basis. There is also a world-wide trend towards increased pressures on rail track infrastructure through increases in axle loads and train speeds. Such productivity and customer service driven pressures inevitably lead to reductions in the life of track components and increases in track maintenance costs. This paper provides a state-of-the-art review of track degradation modeling, as well as an overview of track maintenance decision support systems currently in use in North America and Europe. The essential elements of a maintenance optimisation model currently under development are also highlighted

Finite element analysis of a composite material interface

A finite element model of a composite material interface is developed to study the influence of the interface on the thermal strain in the composite. A plane stress model is used with an axisymmetric model as a check. The interface thickness, thermal coefficient, modulus, Poisson's ratio and the percent of mineral in the composite are variables in the study. The results confirmed the usability of the finite element model in studying the polymer-mineral interface

SIR epidemics in monogamous populations with recombination

We study the propagation of an SIR (susceptible-infectious-recovered) disease over an agent population which, at any instant, is fully divided into couples of agents. Couples are occasionally allowed to exchange their members. This process of couple recombination can compensate the instantaneous disconnection of the interaction pattern and thus allow for the propagation of the infection. We study the incidence of the disease as a function of its infectivity and of the recombination rate of couples, thus characterizing the interplay between the epidemic dynamics and the evolution of the population's interaction pattern.Comment: 7 pages, 3 figure

A mathematical model of the human respiratory system during exercise

This paper describes a respiratory control system model and the associated computer simulations for human subjects during incremental exercise, involving work rates from zero up to the highest level in the heavy exercise domain. Modelling the respiratory control system for conditions above lactate threshold has rarely been attempted because many subsystems begin to lose proportionality in their responses. Our model is built on the basis of putative mechanisms and is based on information identified from a large body of published work. Simulation results are presented and validated using experimental results from published sources. The model confirms that the human body employs an open-loop control strategy for ventilation during exercise, which contrasts with the negative feedback control mode employed for the rest condition. It is suggested that control of ventilation simultaneously involves at least two variables, one being proportional to the pulmonary CO2 output and another being proportional to blood acidity

Water supply and demand forecasting in the Zayandeh Rud Basin, Iran

Water demandWater supplyForecastingWater useRiver basinsReservoirsIranZayandeh Rud BasinChadegan Reservoir

Kaon Phase Space Density in Heavy Ion Collisions

The first measurement of kaon phase space densities are presented as a function of transverse mass, center of mass energy and the number of participants. The kaon phase space density increases with the number of participants from e+e- to Pb+Pb collisions. However the ratio of the kaon and pion phase space densities at low transverse momentum is independent of the number of participants for sqrt{s}=17GeV/nucleon This paper is dedicated to Francis Riccardelli, engineer for the Port Authority, who died on September 11th 2001 while evacuating others.Comment: 4 pages, 2 eps figures, proceedings of Strange Quarks in Matter, Frankfurt 2001, submitted to J. Phys. G In response to referees comments I derived an expresion for the ratio of kaon and pion phase space densites and made several clarifications in the tex

Constructive homomorphisms for classical groups

Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the projection from Delta to Delta/Omega and provide fast, polynomial-time algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent Delta/Omega as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of Omega. A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with forms. Our results are useful for the matrix group recognition project, can be used to solve element conjugacy problems, and can improve algorithms to construct maximal subgroups