Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq7), triangular lattice (q11), hexagonal lattice (q4), and Kagomé lattice (q6). The proofs are based on the Dobrushin uniqueness theorem.     

On formal integration in composition rings of polynomials

This author wants to express his thanks to the School of Information Engineering at Teesside Polytechnic, Middlesbrough, England, for its support and hospitality during a visiting appointment of 3 months in 1989, when this paper was written.     

A characterization of special laguerre planes and extended dual affine planes

A special Laguerre plane is a nondegenerate transversal 3-design such that the residue of each point is a dual affine plane. A special Laguerre plane is equivalent to an optimal code with three information digits and maximal length. An extended dual affine plane is an incidence structure (whose objects will be called points and blocks) such that the residue of each point is a dual affine plane, and each pair of points is in at least one block. Finite extended dual affine planes exist only of order 2, 4, and (dubiously) 10. We show that any finite incidence structure having the residue of each point a dual affine plane either is a transversal 3-design or has a block through each pair of points. Hence theorem: If a finite nondegenerate connected incidence structure has the residue of each point a dual affine plane, then is either an extended dual affine plane or a special Laguerre plane. This research was partially supported by NSF Grant MCS-8102361.     

On a class of operators on Hilbert space with applications to factorization and systems theory

A class of operators is defined in a Hilbert resolution space setting that offers a new perspective on problems of causal invertibility, special factorization, and the theory of quadratic cost optimization problems for dynamical systems. The major results include an extension of the special factorization to a class of noncompact operators and the definition of an abstract state space. These results are then used to obtain an optimal feedback solution to an abstract linear regular-quadratic cost problem.     

Perfect matchings in random s-uniform hypergraphs

Let E = {X₁, X₂…, X_m} where the X_i ? V for 1 ≤ i ≤ m are distinct. The hypergraph G = (V, E) is said to be s-uniform if |X₁| = s for 1 ≤ i ≤ m. A set of edges M = {X_i : i ? I } is a perfect matching if (i) i ≠ j ? I implies X_i ∩ X_i = 0, and (ii) ∪_i?I X_i = V. In this article we consider the question of whether a random s-uniform hypergraph contains a perfect matching. Let s ≥ 3 be fixed and m/n^4/3 → ∞. We show that an s-uniform hypergraph with m edges chosen uniformly from [74] contains a perfect matching with high probability. This improves an earlier result of Schmidt and Shamir who showed that m/n^3/2 → ∞ suffices. © 1995 John Wiley & Sons, Inc.     

Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective.     

Correction of finite element estimates for Sturm-Liouville eigenvalues

Summary It is shown that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k ⁴ h ²) toO(k h ²). The result still holds when the matrix elements are evaluated by Simpson's rule, but if the trapezoidal rule is used the error isO(k ² h ²). Numerical results demonstrate the usefulness of the correction even for low values ofk.     

A thioester substrate binds to the enzyme Arthrobacter thioesterase in two ionization states: evidence from Raman difference spectroscopy

4‐Hydroxybenzoyl‐CoA (4‐HB‐CoA) thioesterase from Arthrobacter is the final enzyme catalyzing the hydrolysis of 4‐HB‐CoA to produce coenzyme A and 4‐hydroxybenzoic acid in the bacterial 4‐chlorobenzoate dehalogenation pathway. Using a mutation E73A that blocks catalysis, stable complexes of the enzyme and its substrate can be analyzed by Raman difference spectroscopy. Here we have used Raman difference spectroscopy, in the non‐resonance regime, to characterize 4‐HB‐CoA bound in the active site of the E73A thioesterase. In addition, we have characterized complexes of the wild‐type enzyme complexed with the unreactive substrate analog 4‐hydroxyphenacyl‐CoA (4‐HP‐CoA). Both sets of complexes show evidence for two forms of the ligand in the active site: one population has the 4‐hydroxy group protonated, 4‐OH; while the second has the group as the hydroxide, 4‐O⁻. For bound 4‐HP‐CoA, X‐ray data show that glutamate 78 is close to the 4‐OH in the complex and it is likely that this is the proton acceptor for the 4‐OH proton. Although the pK_a of the 4‐OH group on the free substrate in aqueous solution is 8.6, the relative populations of ionized and neutral 4‐HB‐CoA bound to E73A remain invariant between pH 7.3 and 9.8. The invariance with pH suggests that the 4‐OH and the ‐COO⁻ of E78 constitute a tightly coupled pair where their separate pK_a ‘s lose their individual qualities. Narrow band profiles are seen in the CO double bond and C‐S regions, suggesting that the hydrolyzable thioester group is rigidly bound in the active site in a syn gauche conformation. Copyright © 2011 John Wiley & Sons, Ltd.