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.     

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

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.     

Structural and magnetic investigations of the mixed-valence Fe(II,III) two-dimensional layer complex, [Fe2(II) Fe2(III)(HCOO)10(C6H7N)6]n.

The structure of the complex, [Fe2(II)Fe2(III)(HCOO)10(C6H7N6)n, (1) exhibits a neutral two-dimensional layer network of alternating iron(II) and iron(III) ions, bridged equatorially by formate groups. All iron atoms are octahedrally coordinated, with iron(III) coordinating axially to one gamma-picoline and one formate group, while the iron(II) centers interact axially with two gamma-picoline groups, above and below the layer plane. The complex crystallizes in the triclinic space group P1 at all studied temperatures [at 120 K, the cell dimensions are: a = 10.228(1), b = 12.071(1), c = 12.072(1) A, alpha = 89.801(2), beta = 71.149(2), gamma = 73.371(2) degrees]. An intralayer antiferromagnetic exchange interaction of J = -2.8 cm(-1) between iron(II) and iron(III) was observed in the magnetic studies. Decreasing the temperature to close to 20 K causes a magnetic-ordering phenomenon to occur and a low-temperature phase with a long-range antiferromagnetic spin orientation appears. The magnetic phase transition was confirmed by M?ssbauer spectroscopic studies at temperatures above and below the critical temperature. Structural information of 1 from synchrotron X-ray diffraction data collected at room temperature and 16 K suggests that the antiferromagnetic ordering is caused by an enhanced pi-pi interaction between chi-picoline groups from adjacent layers.     

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.