Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Nine classes of integrable boundary conditions for the eight-state supersymmetric fermion model

Nine classes of integrable boundary conditions for the eight-state supersymmetric model of strongly correlated fermions are presented. The boundary systems are solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations for all nine cases are given.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

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.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.

X-ray computed tomography to quantify tree rooting spatial distributions

Poor root development due to constraining soil conditions could be an important factor influencing health of urban trees. Therefore, there is a need for efficient techniques to analyze the spatial distribution of tree roots. An analytical procedure for describing tree rooting patterns from X-ray computed tomography (CT) data is described and illustrated. Large irregularly shaped specimens of undisturbed sandy soil were sampled from Various positions around the base of trees using field impregnation with epoxy resin, to stabilize the cohesionless soil. Cores approximately 200 mm in diameter by 500 mm in height were extracted from these specimens. These large core samples were scanned with a medical X-ray CT device, and contiguous images of soil slices (2 mm thick) were thus produced. X-ray CT images are regarded as regularly-spaced sections through the soil although they are not actual 2D sections but matrices of voxels similar to 0.5 mm x 0.5 mm x 2 mm. The images were used to generate the equivalent of horizontal root contact maps from which three-dimensional objects, assumed to be roots, were reconstructed. The resulting connected objects were used to derive indices of the spatial organization of roots, namely: root length distribution, root length density, root growth angle distribution, root spatial distribution, and branching intensity. The successive steps of the method, from sampling to generation of indices of tree root organization, are illustrated through a case study examining rooting patterns of valuable urban trees. (C) 1999 Elsevier Science B.V. All rights reserved.

Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

Integrable Kondo impurities in one-dimensional extended Hubbard models

Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

An extragalactic HI cloud with no optical counterpart?

We report the discovery, from the H I Parkes All-Sky Survey (HIPASS), of an isolated cloud of neutral hydrogen, which we believe to be extragalactic. The H I mass of the cloud (HIPASS J1712-64) is very low, 1.7 x 10(7) M-circle dot, using an estimated distance of similar to 3.2 Mpc. Most significantly, we have found no optical companion to this object to very faint limits [mu(B) similar to 27 mag arcsec(-2)]. HIPASS J1712-64 appears to be a binary system similar to, but much less massive than, H I 1225 + 01 (the Virgo H. I cloud) and has a size of at least 15 kpc. The mean velocity dispersion measured with the Australia Telescope Compact Array (ATCA) is only 4 km s(-1) for the main component and, because of the weak or nonexistent star formation, possibly reflects the thermal line width (T < 2000 K) rather than bulk motion or turbulence. The peak column density for HIPASS J1712-64, from the combined Parkes and ATCA data, is only 3.5 x 1019 cm(-2), which is estimated to be a factor of 2 below the critical threshold for star formation. Apart from its significantly higher velocity, the properties of HIPASS J1712-64 are similar to the recently recognized class of compact high-velocity clouds. We therefore consider the evidence for a Local Group or Galactic origin, although a more plausible alternative is that HIPASS J1712-64 was ejected from the interacting Magellanic Cloud-Galaxy system at perigalacticon similar to 2 x 10(8) yr ago.

Characterization of pore size distributions of mesoporous materials from adsorption isotherms

In this article, a new hybrid model for estimating the pore size distribution of micro- and mesoporous materials is developed, and tested with the adsorption data of nitrogen, oxygen, and argon on ordered mesoporous materials reported in the literature. For the micropore region, the model uses the Dubinin-Rudushkevich (DR) isotherm with the Chen-Yang modification. A recent isotherm model of the authors for nonporous materials, which uses a continuum-mechanical model for the multilayer region and the Unilan model for the submonolayer region, has been extended for adsorption in mesopores. The experimental data is inverted using regularization to obtain the pore size distribution. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41 synthesized with different templates, with results in agreement with those from the XRD method and nonlocal density functional theory. It was found that various other recent methods, as well as the classical Broekhoff and de Beer method, underpredict the pore diameter of MCM-41. The present model has been successfully applied to MCM-48, SBA's, CMK, KIT, HMS, FSM, MTS, mesoporous fly ash, and a large number of other regular mesoporous materials.

Experimental study of phase equilibria in the PbO-MgO-SiO2 system

Equilibrium phase relations in the PbO-Al2O3-SiO2 system have been investigated experimentally by means of high-temperature equilibration, quenching, and electron probe X-ray microanalysis (EPMA). The system has 21 primary phase fields including three monoxides (PbO, Al2O3, and SiO2), seven binary compounds (Al6Si2O13, PbAl2O4, PbAl12O19, Pb2Al2O5, PbSiO3, Pb2SiO4, and Pb4SiO6), and eleven ternary compounds (PbAl2Si2O8, Pb3Al10SiO20, Pb4Al2Si2O11, Pb4Al4SiO12, Pb4Al4Si3O16, Pb4Al4Si5O20, Pb5Al2Si10O28, Pb6Al2Si6O21, Pb8Al2Si4O19, Pb12Al2Si17O49, and Pb12Al2Si20O55). Three new ternary compounds, Pb4Al4SiO12, Pb4Al4Si5O20, and Pb12Al2Si17O49, were observed and characterized by EPMA. No extensive solid solution in any of the compounds was found in the present study. The liquidus isotherms were experimentally determined in most of the primary phase fields in the temperature range from 923 to 1873 K, and the ternary phase diagram of the PbO-Al2O3-SiO2 System has been constructed.

Initial results of ultrasound screening for aneurysm of the abdominal aorta in Western Australia: relevance for endoluminal treatment of aneurysm disease

Background. Increased life expectancy in men during the last thirty years is largely due to the decrease in mortality from cardiovascular disease in the age group 29-69 yr. This change has resulted in a change in the disease profile of the population with conditions such as aneurysm of the abdominal aorta (AAA) becoming more prevalent. The advent of endoluminal treatment for AAA has encouraged prophylactic intervention and fuelled the argument to screen for the disease. The feasibility of inserting an endoluminal graft is dependent on the morphology and growth characteristics of the aneurysm. This study used data from a randomized controlled trial of ultrasound screening for AAA in men aged 65-83 yr in Western Australia for the purpose of determining the norms of the living anatomy in the pressurized infrarenal aorta. Aims. To examine (1) the diameters of the infra-renal aorta in aneurysmal and non-aneurysmal cases, (2) the implications for treatment modalities, with particular reference to endoluminal grafting, which is most dependent on normal and aneurysmal morphology, and (3) any evidence to support the notion that northern Europeans are predisposed to aneurysmal disease. Methods. Using ultrasound, a randomized control trial was established in Western Australia to assess the value of a screening program in males aged 65-83 yr, The infra-renal aorta was defined as aneurysmal if the maximum diameter was 30 mm or more. Aortic diameter was modelled both as a continuous tin mm) and as a binary outcome variable, for those men who had an infra-renal diameter of 30 mm or more. ANOVA and linear regression were used for modelling aortic diameter as a continuum, while chi-square analysis and logistic regression were used in comparing men with and without the diagnosis of AAA. Findings. By December 1998, of 19.583 men had been invited to undergo ultrasound screening for AAA, 12.203 accepted the invitation (corrected response fraction 70.8%). The prevalence of AAA increased with age from 4.8% at 65 yr to 10.8% at 80 yr (chi (2) = 77.9, df = 3, P<0.001). The median (IQR) diameter for the non-aneurysmal group was 21.4 mm (3.3 mm) and there was an increase (<chi>(2) = 76.0, df = 1, P<0.001) in the diameter of the infra-renal aorta with age. Since 27 mm is the 95th centile for the non-aneurysmal infra-renal aorta, a diameter of 30 mm or more is justified as defining an aneurysm. The risk of AAA was higher in men of Australian (OR = 1.0) and northern European origin (OR = 1.0, 95%CL: 0.9. 1.2) compared with those of Mediterranean origin (OR = 0.5, 99%CL: 0.4, 0.7). Conclusion. Although screening has not yet been shown to reduce mortality from AAA. these population-based data assist the understanding of aneurysmal disease and the further development and use of endoluminal grafts for this condition. (C) 2001 Published by Elsevier Science Ltd on behalf of The International Society for Cardiovascular Surgery.