A functional model for polynomially posinormal operators

In this paper we introduce a class of operators naturally extending the classes of hyponormal and posinormal operators. For this class we construct a generating family of eigendistributions, unitary invariants and a functional model.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

Jordan Superalgebras Defined by Brackets

Jordan superalgebras defined by brackets on associative commutativesuperalgebras are studied. It is proved that any such superalgebrais imbedded into a superalgebra defined by Poisson brackets.In particular, all Jordan superalgebras of brackets are i-special.The speciality of these superalgebras is also examined, andit is proved, in particular, that the Cheng–Kac superalgebrais special.     

On the structure of weight modules

Given any simple Lie superalgebra , we investigate the structure of an arbitrary simple weight -module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W. Most of them are simply Levi subalgebras of , in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.

     

Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka–Volterra type interactions defined on a d-dimensional lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous active-to-absorbing state phase transition. Field-theoretic arguments, supported by Monte Carlo simulation results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by essentially stationary localized clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka–Volterra system displays complex, correlated spatio-temporal patterns of competing activity fronts. Correspondingly, the population densities in our numerical simulations turn out to oscillate irregularly in time, with amplitudes that tend to zero in the thermodynamic limit. Yet in finite systems these oscillatory fluctuations are quite persistent, and their features are determined by the intrinsic interaction rates rather than the initial conditions. We emphasize the robustness of this scenario with respect to various model perturbations.     

Invariance of the non-vanishing specializations of polynomials

This paper resolves a recent conjecture of I. Kaplansky concerning the nonsingularity of linear maps that preserve the set of nonzero specializations of polynomials.     

Low‐bandgap donor–acceptor copolymers with 4,6‐bis(3′‐(2‐ethylhexyl)thien‐2′‐yl)thieno[3,4‐c][1,2,5]thiadiazole: synthesis,optical, electrochemical,and photovoltaic properties

Two new low‐bandgap alternating copolymers (CEHTF and CEHTP) consisting of 4,6‐bis(3′‐(2‐ethylhexyl)thien‐2′‐yl)thieno[3,4‐c][1,2,5] thiadiazole and 9,9‐bis(2‐ethylhexyl)fluorene or 2,5‐bis(isopentyloxy)benzene were synthesized by Suzuki coupling reaction of corresponding comonomers. Their optical, electrochemical, and photovoltaic (PV) properties were studied and are reported. Both the copolymers exhibited long‐wavelength absorption covering the whole visible spectral region, which is in CEHTP thin films extended up to near infrared region, ambipolar redox properties, and electrochromism. High‐electron affinities and low‐optical bandgap values, 1.37 and 1.15 eV, were determined for CEHTF and CEHTP, respectively. PV devices with bulk heterojunction made of blends of copolymers and fullerene derivative [6,6]‐phenyl‐C⁶¹‐butyric acid methyl ester ([60]PCBM) were prepared and characterized. Effects of intramolecular charge transfer strength and side‐chain nature and length on photophysical properties are discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.