Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

N-Benzoyl-N ',N '-dimethylthiourea

In the title compound, C(10)H(12)N(2)OS, the amide NCO group is twisted relative to the thioureido SCN(2) group, forming a dihedral angle of 55.3 (2)degrees. The crystal packing shows intermolecular N-H center dot center dot center dot S and weak C-H center dot center dot center dot O interactions, the former giving rise to the formation of centrosymmetric R(2)(2)(8) dimers.

DJKM ALGEBRAS I: THEIR UNIVERSAL CENTRAL EXTENSION

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g circle times C[t, t(-1), u vertical bar u(2) = (t(2) - b(2))(t(2) - c(2))], appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from the Landau-Lifshitz differential equation.

Induced Modules for Affine Lie Algebras

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P(ps), P subset of P(ps). The structure of P-induced modules in this case is fully determined by the structure of P(ps)-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].

AUSLANDER GENERATORS OF ITERATED TILTED ALGEBRAS

Let A be an iterated tilted algebra. We will construct an Auslander generator M in order to show that the representation dimension of A is three in case A is representation infinite.

4-Methyl-3-(2-phenoxyacetyl)-5-phenyl-1,3,4-oxadiazinan-2-one

The 1,3,4-oxadiazinane ring in the title compound, C(18)H(18)N(2)O(4), is in a twisted boat conformation. The two carbonyl groups are orientated towards the same side of the molecule. The dihedral angle between the planes of the benzene rings is 76.6 (3)degrees. Molecules are sustained in the three-dimensional structure by a combination of C-H center dot center dot center dot O, C-H center dot center dot center dot pi and pi-pi [shortest centroid-centroid distance = 3.672 (6) angstrom] interactions.

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

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.

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Derivatives of 1,3,5-triamino-1,3,5-trideoxy-cis-inositas versatile pentadentate ligands for protein labeling with Re-186/188. Prelabeling, biodistribution, and X-ray structural studies

The pentadentate H(3)bhci [1,3,5-trideoxy-1,3-bis((2-hydroxybenzyl)amino)-cis-inistol] and its bifunctionalized analogue H(3)bhci-glu-H [1,3,5-trideoxy-1,3-bis((2-hydroxybenzyl)amino)-5-glutaramido-cis-inositol] were synthesized, and their coordination chemistry was investigated with inactive rhenium, with no carrier added Re-188 and with carrier added Re-186. The neutral Re(V) complexes [ReO-(bhci)] and [ReO(bhci-glu-H)] are formed in good yields starting from [ReOCl3(P(C6H5)(3))(2)] or in quantitative yield directly from [(ReO4)-Re-186/188](-) in aqueous solution by reduction with Sn(II) or Sn(0). The X-ray structures of [ReO(bhci)] and [ReO(bhci-glu-H)] were elucidated revealing pentadentate side on coordination of the ligands to the Re=O core. The basic cyclohexane frame adopts a chair form in the case of [ReO(bhci)] and a twisted boat form in the case of [ReO(bhci-glu-H)]. [ReO(bhci)] crystallizes in the monoclinic space group C2/c with a = 27.425(3), b = 14.185(1), c = 19.047(2) Angstrom, and beta = 103.64(2)degrees and [ReO(bhci-glu-H)] in the monoclinic space group P2(1)/c with a = 13.056(3), b = 10.180(1), c = 22.378(5) Angstrom and beta = 98.205(9)degrees Both Re-188 complexes are stable in human serum for at least 3 days without decomposition. After injection into mice, [ReO(bhci-glu)](-) is readily excreted through the intestines, while [ReO(bhci)] is excreted by intestines, liver, and the kidneys. TLC investigations of the urine showed exclusively the complexes [ReO(bhci-glu-H)] and [ReO(bhci)], respectively, and no decomposition products. For derivatization of antibodies, the carboxylic group of [ReO(bhci-glu-H)] was activated with N-hydroxysuccinimide, which required unusually vigorous reaction conditions (heating). The anti colon cancer antibody mAb-35 [IgG and F(ab')(2) fragment] was labeled with [(ReO)-Re-186/188(bhci-glu)] to a specific activity of up to 1.5 mCi/mg (55 MBq/mg) with full retention of immunoreactivity. Labeling yields followed pseudo-first-order kinetics in antibody concentration with the ratio of rates between aminolysis and hydrolysis being about 2. Biodistributions of Re-186-labeled intact mAb-35 as well as of its F(ab')(2) fragment in tumor-bearing nude mice revealed good uptake by the tumor with only low accumulation of radioactivity in normal tissue.