A de bruijn-type formula for enumerating patterns of partitions

We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.This work was supported in part by NSF Contract GP-43010.     

Characteristic functional equations of polynomials and the morera-carleman theorem

Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.     

A survey of pseudo (v,k, λ)-designs

This work is an attempt to give a complete survey of all known results about pseudo (v, k, )-designs. In doing this, the author hopes to bring more attention to his conjecture given in Section 6; an affirmative answer to this conjecture would settle completely the existence and construction problem for a pseudo (v, k, )-design in terms of the existence of an appropriate (v, k, )-design.     

Riesz decompositions and subtractivity for excessive measures

The convex cone of excessive measures of a right Markov process is an example of a superharmonic semigroup in the abstract potential theory developed by Arsove and Leutwiler. We show that their theory of Riesz decompositions can be sharpened in the case of excessive measures. In particular there is always a Riesz decomposition relative to a given potential cone (resp. harmonic cone). An element of an ordered convex cone is subtractive if each majorant is a specific majorant. This notion of subtractivity features prominently in the theory of harmonic cones. We give a complete characterization of the subtractive elements in the cone of excessive measures.The research of both authors was supported in part by NSF Grant DMS 87-21347.     

Lee–Yang Problems and the Geometry of Multivariate Polynomials

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.     

An integrative in silico approach to the structure of Omp33-36 in Acinetobacter baumannii

Omp33-36 in A. baumannii, a bacterium causing serious nosocomial infections, is a virulence factor associated with the pathogen metabolic fitness as well as its adherence and invasion to human epithelial cells. This protein is also involved in interaction of the bacteria with host cells by binding to fibronectin. Moreover, Omp33-36 renders cytotoxicity to A. baumannii in addition to inducing apoptosis and modulation of autophagy. In the present study, an integrated strategy is launched to pierce into the 3D structure of Omp33-36 protein. The signal peptide within the sequence was determined, then, topology as well as secondary and tertiary structures of the protein were predicted. The mature protein assigned as a 14-stranded barrel in which residues 1–19 is removed as signal peptide. The obtained 3D models were evaluated in terms of quality; and then, served as queries to find similar protein structures. The hits were analyzed regarding topology among which 14-stranded were considered. The most qualified model was refined and then its sequence aligned to its counterpart similar structure protein (CymA from Klebsiella oxytoca). The determined structure of Omp33-36 could justify its porin function and carbapenem-resistance associated with the loss of this protein.     

Existence and regularity for generalised harmonic maps associated to a nonlocal polyconvex energy of Skyrme type

We prove existence and regularity of critical points of arbitrary degree for a generalised harmonic map problem, in which there is an additional nonlocal polyconvex term in the energy, heuristically of the same order as the Dirichlet term. The proof of regularity hinges upon a special nonlinear structure in the Euler–Lagrange equation similar to that possessed by the harmonic map equation. The functional is of a type appearing in certain models of the quantum Hall effect describing nonlocal Skyrmions.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups

We determine the L ²-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L ²-cohomology of left-orderable groups, and deduce the non-L ² result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613.