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

A conjecture for the superintegrable chiral Potts model

We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-\alpha H}, where H is the associated hamiltonian. The spontaneous magnetization M_r can be expressed in terms of particular matrix elements of e^{-\alpha H} S^r_1 \e^{-\beta H}, where S_1 is a diagonal matrix.We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.Comment: 19 pages, one figure; Corrections made between 28 March 2008 and 28 April 2008: (1) 2.10: q to p; (2) 3.1: epsilon to 0 (not infinity); (3) 5.29: p to q; (4) p14: sub-head: p, q to q,p; (5) p15: sub-head: p, q to q,p; (6) 7.5 second theta to -theta ; (7) before 7.6: make more explicit definition of lambda_j. Several other typos fixed late

Some remarks on a generalization of the superintegrable chiral Potts model

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced hamiltonians H and a central spin operator S. We conjectured in a previous paper that W can be written as a determinant, similar to that of the Ising model. Here we generalize this conjecture to any Hamiltonians that satisfy a more general Onsager algebra, and give a conjecture for the elements of S.Comment: 18 pages, one figur

Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model

We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the Wu-Kadanoff duality between the cube and vertex type tetrahedron equations is obtained explicitly for the Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by considering the symmetry property of the weight function, which is corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube. And we write down the symmetry relations of the weight functions under the actions of the symmetry group $G$ of the cube. The six angles with a constrained condition, appeared in the tetrahedron equation, can be regarded as the six spectrums connected with the six spaces in which the vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29

A novel biomarker for beryllium sensitization in humans. 1997 annual progress report

'Overall, this project is designed to identify the beryllium reactive T-cell clones that are proliferating in vivo in individuals sensitized to beryllium. The basic method for identifying such clones is the hprt T-cell mutation assay. The rationale is that in vivo proliferating T-lymphocytes are more likely to undergo hprt mutations and/or be included in hprt mutant fractions of T-cells isolated from peripheral blood. T-lymphocytes isolated as hprt mutants from beryllium sensitized individuals are propagated in vitro and characterized for T-cell receptor (TCR)/3 gene usage patterns and antigen reactivity. Results will be compared with similar characteristics determined for T-cell clones from the same individuals that were developed in vitro from peripheral blood lymphocytes by beryllium stimulation. This research project has several specific aims. Progress for the year 10/1/96 to 9/30/97 is given.

A novel biomarker for beryllium sensitization in humans. 1998 annual progress report

'Beryllium reactive T-lymphocytes can be used as an indicator of sensitization. Traditionally, their presence is detected by an in vitro proliferation assay. However, this test is capricious (results varying from day to day in the same laboratory) and insensitive (rarely positive before clinical symptoms ). The objective of this project is to obtain and characterize beryllium reactive T-cells from peripheral blood using the hprt T-cell mutation assay. T-cells are selected on the basis of their mutation of the hprt gene which renders them insensitive to 6-thioguanine in culture. Such mutant populations are expected to be enriched for cells which are proliferating in vivo as a result of the sensitizing process. This hypothesis has been verified in a number of studies. The seven specific aims of this study will: (i) identify the in vivo proliferating T-cell clones in sensitized individuals by selecting for hprt mutants, (ii) determine T-cell receptor (TCR) gene usages and commonalities among these clones, (iii) demonstrate reactivity to beryllium of these clones, (iv) generate beryllium sensitized T-cells in vitro from peripheral blood of the same individual, (v) determine TCR gene usages and commonalities for these in vitro derived cells, (vi) compare TCR gene patterns between the in vivo and in vitro derived clones, and (vii) develop a quantitative PCR (qPCR) method for amplifying the common (and therefore relevant) TCR genes directly from peripheral blood. The last of these is the novel biomarker of early beryllium sensitization. This report summarizes studies of the first 20 months of this project.