Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

On the construction of nearest neighbour balanced row-column designs

Nearest–neighbour balance is considered a desirable property for an experiment to possess in situations where experimental units are influenced by their neighbours. This paper introduces a measure of the degree of nearest–neighbour balance of a design. The measure is used in an algorithm which generates nearest–neighbour balanced designs and is readily modified to obtain designs with various types of nearest–neighbour balance. Nearest–neighbour balanced designs are produced for a wide class of parameter settings, and in particular for those settings for which such designs cannot be found by existing direct combinatorial methods. In addition, designs with unequal row and column sizes, and designs with border plots are constructed using the approach presented here.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Twisted parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2)((2)) is given.

Capillary network models for transport in packed beds: Considerations of pore aspect ratio

The conventional analysis for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed for unconsolidated and grainy media.

A framework for selecting appropriate remotely sensed data dimensions for environmental monitoring and management

Two major factors are likely to impact the utilisation of remotely sensed data in the near future: (1)an increase in the number and availability of commercial and non-commercial image data sets with a range of spatial, spectral and temporal dimensions, and (2) increased access to image display and analysis software through GIS. A framework was developed to provide an objective approach to selecting remotely sensed data sets for specific environmental monitoring problems. Preliminary applications of the framework have provided successful approaches for monitoring disturbed and restored wetlands in southern California.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

An investigation of localised soil heterogeneities on solute transport using a multisegment percolation system

A multisegment percolation system (MSPS) consisting of 25 individual collection wells was constructed to study the effects of localised soil heterogeneities on the transport of solutes in the vadose zone. In particular, this paper discusses the transport of water and nutrients (NO3-, Cl-, PO43-) through structurally stable, free-draining agricultural soil from Victoria, Australia. A solution of nutrients was irrigated onto the surface of a large undisturbed soil core over a 12-h period. This was followed by a continuous irrigation of distilled water at a fate which did not cause pending for a further 18 days. During this time, the volume of leachate and the concentration of nutrients in the leachate of each well were measured. Very significant variation in drainage patterns across a small spatial scale was observed. Leaching of nitrate-nitrogen and chloride from the core occurred two days after initial application. However, less than 1% of the total applied phosphate-phosphorus leached from the soil during the 18-day experiment, indicating strong adsorption. Our experiments indicate considerable heterogeneity in water flow patterns and solute leaching on a small spatial scale. These results have significant ramifications for modelling solute transport and predicting nutrient loadings on a larger scale.

Sequence analysis of rabbit haemorrhagic disease virus (RHDV) in Australia: alterations after its release

Liver samples from rabbits killed by RHDV, collected from five States in Australia in 1996 and 1997 were analysed by RT-PCR. A 398 bp fragment of the capsid protein (VP60) gene was amplified by PCR and directly sequenced. The alignment of the nucleotide and amino acid sequences and their comparison with the original strain of the virus released in Australia indicated genetic changes after two years have been small with 98.2% to 100% identity. The constructed phylogenetic tree suggests slight differences in nucleotide substitutions in various States but there is no clear evidence of clustering of sequences according to their geographic origin. In practical terms, sequencing of viral RNA provides a means of testing the efficacy of further releases and subsequent spread of the virus if such a strategy is employed as a means of enhancing RHD as a biological control of the wild rabbit in Australia.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Binary vectors for sense and antisense expression of arabidopsis ESTs

Our laboratory is interested in devising methods to identify functions for the vast numbers of arabidopsis genes now available. For this purpose, we have constructed a set of binary vectors that will allow the quick production of transgenic arabidopsis plants containing either sense or antisense copies of EST clones obtained from the PRL2 library. These vectors are based on the pSLJ series containing the bialophos resistance (BAR) gene that confers resistance to the herbicide BASTA. Tn addition, our vectors contain a 35S CaMV promoter-polylinker-nos terminator cassette that allows the direct cloning of arabidopsis ESTs in either antisense (pAOV and pAOV2) or sense (pSOV and pSOV2) orientation. We also describe the construction of two additional vectors conferring BASTA resistance and containing the pBluescript polylinker in both orientations inserted between the 35S CaMV promoter and nos terminator (pKMB and pSMB).

An "openable," high-strength gradient set for orthopedic MRI

A novel three-axis gradient set and RF resonator for orthopedic MRT has been designed and constructed. The set is openable and may be wrapped around injured joints. The design methodology used was the minimization of magnetic field spherical harmonics by simulated annealing. Splitting of the longitudinal coil presents the major design challenge to a fully openable gradient set and in order to efficiently design such coils, we have developed a new fast algorithm for determining the magnetic field spherical harmonics generated by an are of multiturn wire. The algorithm allows a realistic impression of the effect of split longitudinal designs. A prototype set was constructed based on the new designs and tested in a 2-T clinical research system. The set generated 12 mT/m/A with a linear region of 12 cm and a switching time of 100 mu s, conforming closely with theoretical predictions. Preliminary images from the set are presented. (C) 1999 Academic Press.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

The crack tip strain field of AISI 4340 - Part I - Measurement technique

This is the first paper in a study on the influence of the environment on the crack tip strain field for AISI 4340. A stressing stage for the environmental scanning electron microscope (ESEM) was constructed which was capable of applying loads up to 60 kN to fracture-mechanics samples. The measurement of the crack tip strain field required preparation (by electron lithography or chemical etching) of a system of reference points spaced at similar to 5 mu m intervals on the sample surface, loading the sample inside an electron microscope, image processing procedures to measure the displacement at each reference point and calculation of the strain field. Two algorithms to calculate strain were evaluated. Possible sources of errors were calculation errors due to the algorithm, errors inherent in the image processing procedure and errors due to the limited precision of the displacement measurements. Estimation of the contribution of each source of error was performed. The technique allows measurement of the crack tip strain field over an area of 50 x 40 mu m with a strain precision better than +/- 0.02 at distances larger than 5 mu m from the crack tip. (C) 1999 Kluwer Academic Publishers.

Bird responses at inherent and induced edges in the Murray Mallee, South Australia. 2. Nest predation as an edge effect

We assayed nest predation as an edge effect, using artificial ground nests, at inherent (naturally occurring) and induced (human-created) edges, in the Murray Mallee, South Australia. Nests were constructed at distances between 0-120 m away from habitat edges. The relative predation rate on nests generally increased close to induced edges with a significant difference (P < 0.05) recorded for two out of five experiments. Predation rate at inherent edges was similar from the edge to the interior, and was lower than that recorded at induced edges. Our results suggest that increased predator numbers, activity or efficiency at locating nests occurred close to the induced edges at our study sites.