The Translation Invariant Massive Nelson Model: I. The Bottom of the Spectrum

In this paper we analyze the bottom of the energy-momentum spectrum of the translation invariant Nelson model, describing one electron linearly coupled to a second quantized massive scalar field. Our results are valid for all values of the coupling constant and include an HVZ theorem, non-degeneracy of ground states, existence of isolated groundstates in dimensions 1 and 2, non-existence of ground states embedded in the bottom of the essential spectrum in dimensions 3 and 4, (i.e., at total momenta where no isolated groundstate eigenvalue exists), and we study regularity and monotonicity properties of the bottom of the essential spectrum, as a function of total momentum. Communicated by Joel Feldman submitted 04/11/04, accepted 17/02/05     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Graded parafermions: standard and quasiparticle bases

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset . The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural exclusion principle.     

On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

Three chiral vinyldioxaza­borocanes

The structures of three chiral vinyldioxaza­borocanes are reported, namely (2E)‐ and (2Z)‐6‐benzyl‐2‐buten‐2‐yl‐1,3,6,2‐dioxaza­borocane, C₂₇H₃₀BNO₂, (II) and (III), respectively, and (2Z)‐2‐buten‐2‐yl‐6‐isobutyl‐1,3,6,2‐dioxaza­boro­cane, C₂₄H₃₂BNO₂, (IV). These compounds may be useful in asymmetric reactions. In the structures reported here, the N—B donor–acceptor bond is longer than in any previously reported analogous compounds.     

Light Modulates Electric Phenomena in Hornet Cuticle¶

In the cuticle of live social hornets, such as Vespa orientalis (Hymenoptera, Vespinae), endogenous electric effects are encountered, i.e. voltages of 100–200 mV under illumination and currents amounting to several microamperes on its subjection to darkness—clearly a process of charging and discharging. Of the various wavelengths of sunlight, UV was found to be the most contributory to the active cuticular voltage generation. Throughout the warm season of the yearthe–the active period in colonies of social hornets and wasps—colony members exit from the dark nest during the daytime and fly to the field under the hot sun for various foraging purposes, ultimately returning to the nest. Thus, each hornet, be it queen, worker or drone, probably undergoes daily cyclical process of electric charge and discharge in the exterior part of their integument, cuticle, which lasts up to 30–40 min. Such photoelectric phenomenon was detected in both live, ether‐anaesthetized hornets and dead hornets, albeit in the latter the electric values recorded were lower. The present study addresses the possible impact of the phenomenon on vespan daily life and also compares it with a parallel occurrence in electric fish.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Thermal characterization of social vespid silk

In this paper we try to establish a link between the microclimate in the wasp nest and the structure and thermal stability of vespid silk. We suggest that there are at least two types of water that is absorbed by the silk of Oriental hornets, namely, surface water and intrinsic structural water. The release of both types of water was found to be reversible. The enthalpy values of the endothermic peaks associated with the release of water from different silk samples do not differ substantially and are in the range of 106 to 130 J g^-1 for the Vespa orientalis male larvae silk (sample #1), Paravespula germanica (yellowjacket) worker larvae silk (#3) and Vespa orientalis nest envelope(#4). For the Vespa orientalis worker larvae silk (sample #2), however, it is twice as large (228 J g^-1). This is in agreement with the increased total amount of absorbed water. The silk studied has a fibrilar structure with interconnecting surfaces overlying entire regions. It is assumed that the initial water loss stems from water evaporation from the coat of the fibers - a daily occurrence in the hornets' nest. Heating to above 70°C may result in structural changes in the silk core. This revised version was published online in July 2006 with corrections to the Cover Date.