13,403 research outputs found
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
Planar lattice gases with nearest-neighbour exclusion
We discuss the hard-hexagon and hard-square problems, as well as the
corresponding problem on the honeycomb lattice. The case when the activity is
unity is of interest to combinatorialists, being the problem of counting binary
matrices with no two adjacent 1's. For this case we use the powerful corner
transfer matrix method to numerically evaluate the partition function per site,
density and some near-neighbour correlations to high accuracy. In particular
for the square lattice we obtain the partition function per site to 43 decimal
places.Comment: 16 pages, 2 built-in Latex figures, 4 table
Biomass-supported catalysts on Desulfovibrio desulfuricans and Rhodobacter sphaeroides
A Rhodobacter sphaeroides-supported dried, ground palladium catalyst (ââRs-Pd(0)ââ) was compared with a Desulfovibrio desulfuricans-supported catalyst (ââDd-Pd(0)ââ)and with unsupported palladium metal particles made by reduction under H2 (ââChem-Pd(0)ââ). Cell surface-located clusters of Pd(0) nanoparticles were detected on both D. desulfuricans and R. sphaeroides but the size and location of deposits differed among comparably loaded preparations.\ud
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These differences may underlie the observation of different activities of Dd-Pd(0) and Rs-Pd(0) when compared with respect to their ability to promote hydrogen release from hypophosphite and to catalyze chloride release from chlorinated aromatic compounds. Dd-Pd(0) was more effective in the reductive dehalogenation of polychlorinated biphenyls (PCBs), whereas Rs-Pd(0) was more effective in the initial dehalogenation of pentachlorophenol (PCP) although the rate of chloride release from PCP was comparable with both preparations after 2 h
Numerical Renormalization Group at Criticality
We apply a recently developed numerical renormalization group, the
corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice
models at their critical temperatures. It is shown that the combination of
CTMRG and the finite-size scaling analysis gives two independent critical
exponents.Comment: 5 pages, LaTeX, 5 figures available upon reques
On kernel engineering via PaleyâWiener
A radial basis function approximation takes the form
where the coefficients a 1,âŠ,a n are real numbers, the centres b 1,âŠ,b n are distinct points in â d , and the function Ï:â d ââ is radially symmetric. Such functions are highly useful in practice and enjoy many beautiful theoretical properties. In particular, much work has been devoted to the polyharmonic radial basis functions, for which Ï is the fundamental solution of some iterate of the Laplacian. In this note, we consider the construction of a rotation-invariant signed (Borel) measure ÎŒ for which the convolution Ï=ÎŒ Ï is a function of compact support, and when Ï is polyharmonic. The novelty of this construction is its use of the PaleyâWiener theorem to identify compact support via analysis of the Fourier transform of the new kernel Ï, so providing a new form of kernel engineering
Analysis of Three-Dimensional Protein Images
A fundamental goal of research in molecular biology is to understand protein
structure. Protein crystallography is currently the most successful method for
determining the three-dimensional (3D) conformation of a protein, yet it
remains labor intensive and relies on an expert's ability to derive and
evaluate a protein scene model. In this paper, the problem of protein structure
determination is formulated as an exercise in scene analysis. A computational
methodology is presented in which a 3D image of a protein is segmented into a
graph of critical points. Bayesian and certainty factor approaches are
described and used to analyze critical point graphs and identify meaningful
substructures, such as alpha-helices and beta-sheets. Results of applying the
methodologies to protein images at low and medium resolution are reported. The
research is related to approaches to representation, segmentation and
classification in vision, as well as to top-down approaches to protein
structure prediction.Comment: See http://www.jair.org/ for any accompanying file
The existence of matrices with prescribed characteristic and permanental polynomials
AbstractLet d(λ) and p(λ) be monic polynomials of degree nâ©Ÿ2 with coefficients in F, an algebraically closed field or the field of all real numbers. Necessary and sufficient conditions for the existence of an n-square matrix A over F such that det(λIâA)=d(λ) and per(λIâA=p(λ) are given in terms of the coefficients of d(λ) and p(λ)
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