Ground states in non-relativistic quantum electrodynamics

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state – one that minimizes the energy and satisfies the Schr?dinger equation. We prove quite generally that this state exists for all values of the fine-structure constant and the ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions. Oblatum 21-IX-2000 & 8-IV-2001?Published online: 18 June 2001     

Tables of curves with many points

These tables record results on curves with many points over finite fields. For relatively small genus () and a small power of or we give in two tables the best presently known bounds for , the maximum number of rational points on a smooth absolutely irreducible projective curve of genus over a field of cardinality . In additional tables we list for a given pair the type of construction of the best curve so far, and we give a reference to the literature where such a curve can be found.

     

Experimental and numerical study on the propagation of impulsive sound around buildings

Propagation of impulsive sound around buildings and induced structural loading are investigated experimentally and numerically. Experiments were conducted on a rectangular building at Virginia Tech using sonic booms generated by shaped charges with an explosive weight of 0.78 kg, constructed from detonation cord. These experiments were simulated with a three-dimensional numerical model, in the context of geometrical acoustics (GA), by combining the image source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. In this model, it is assumed that the acoustic propagation is linear and that all surfaces are acoustically rigid. This numerical model is validated against a boundary element (BE) solution and experimental data, showing a good overall agreement. The key advantages of this GA modeling approach for this application include the ability to model large three-dimensional domains over a wide frequency range and also to decompose the sound field into direct, reflected, and diffracted components, thus providing a better understanding of the sound-propagation mechanisms. Finally, this validated numerical model is used to investigate sound propagation around a cluster of six rectangular buildings, for a range of elevated source positions simulating sonic booms from aircraft.     

Covering the alternating groups by products of cycle classes

Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99].     

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α^3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α^3/2 and it is twice continuously differentiable with respect to the nuclear coordinates. Submitted: November 24, 2008. Accepted: March 4, 2009.     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.