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.     

The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

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.     

The asymptotic behaviour of certain entire functions of order zero

Summary A certain class of entire functionsF(s) of order zero which are asymptotically equal to the sum of just two neighbouring terms of their power series when |s| with |args| < – for any fixed > 0, is investigated. Which two terms one has to take, depends upons. It is shown that these functions have infinitely many negative zeros, and the asymptotic behaviour of the zeros is also determined.     

Photodynamic Therapy of 9L Gliosarcoma with Liposome-Delivered Photofrin

Abstract— The effect of Photofrin encapsulated in a liposome delivery vehicle for photodynamic therapy (PDT) of the 9L gliosarcoma and normal rat brain was tested. We hypothesized that the liposome vehicle enhances therapeutic efficacy, possibly by increasing tumor tissue concentration of Photofrin. Male Fisher rats bearing a 9L gliosarcoma were treated 16 days after intracerebral tumor implantation with either Photofrin in dextrose (n = 5) or Photofrin in liposome (n = 6). Nontumor-bearing animals were treated with Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle. Tissue concentrations of Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle were measured in tumor, brain adjacent to tumor and in normal brain tissue. Photofrin was administered (intraperitoneally) at a dose of 12.5 mg/kg and PDT (17 J/cm₂ of 632 nm light at 100 mW/cm₂) was performed 24 h after Photofrin administration. Brains were removed 24 h after PDT and stained with hematoxylin and eosin for analysis of cellular damage. The PDT using Photofrin in the liposome vehicle caused significantly more damage to the tumor ( P < 0.001) than did PDT with Photofrin in dextrose. The PDT of tumor with Photofrin delivered in liposomes caused a 22% volume of cellular necrosis, while PDT of tumor with Photofrin delivered in dextrose caused only scattered cellular damage. Photofrin concentration in tumors was significantly higher ( P = 0.021) using liposome (33.8 ± 18.9 μg/g) compared to dextrose delivery (5.5 ± 1.5 μg/g). Normal brain was affected similarly in both groups, with only scattered cellular necrosis. Our data suggest that the liposome vehicle enhances the therapeutic efficacy of PDT treatment of 9L tumors.