The null energy condition and cosmology

Field theories that violate the null energy condition (NEC) are of interest both for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter w < −1. We consider two recently proposed models that violate the NEC. The ghost condensate model requires higher-derivative terms in the action, and this leads to a heavy ghost field and energy unbounded from below. We estimate the rates of particle decay and discuss possible mass limitations to protect the stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to energy unbounded from below. In this case, the energy spectrum is continuous, and there are no particle-like excitations. This model admits a natural UV completion because it comes from superstring theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 3–12, April, 2008.     

Heterocyclo-Substituted Sulfa Drugs: Part XII. Mercapto-S-Azo-Benzothiazol Dyes and Their Metal Complexes

New azo sulfadrugs of 2-mercapto-S-azo ( p '-heterocyclo-substituted benzene-sulfonyl) benzothiazole derivatives (L 1 and L 2 ) were synthesized by coupling of p '-heterocyclo-substituted-benzene-sulphonyl diazonium salts with 2-mercapto-benzothiazole in acid medium. The corresponding iron(III), cobalt(II), nickel(II), copper(II), and mercury(II) chelates were prepared in a 1:1 metal to ligand molar ratio. The ligands and their chelates were characterized on the basis of microanalysis, UV, IR, and H 1 -NMR spectrometry. Thermal decomposition of the complexes was studied in static air. On the basis of the thermogravimetric curves some decomposition steps could be correlated with the proper decomposition products. The photochemical behavior of the ligands and their complexes were investigated. The photosensitivity shown by the complexes was attributed to the photoreactivity of their free ligands. The ligands and their chelates were screened in vitro for their antimicrobial activities (antibacterial and antifungal). The complexes induce a remarkable increase in the antimicrobial activity compared to the corresponding ligands.     

On a model of quantum field theory

A model of quantum field theory in an accelerated frame of reference is considered. It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal Gibbsian distribution. However, in justifying the assertion a singular transformation was implicitly performed, and doubts were expressed by some researches. We discuss a model of quantum field theory in an accelerated frame of reference in the two-dimensional spacetime for the wave equation. By using the Mellin transform, we obtain a representation of solutions of the wave equation. The representation includes a dependence on a parameter. The Unruh field corresponds to a singular limit of the representation.     

Integrable and chaotic motions of four vortices

Conclusive numerical evidence of chaos in the four-vortex problem is presented using the method of Poincaré sections. The problem is formally reduced to a two degrees of freedom hamiltonian. The advection of a passive marker by three vortices displays chaos.     

Nonlinear excursions of particles in ideal 2D flows

A number of problems related to particle trajectories in ideal 2D flows are discussed. Both regular particle paths, corresponding to integrable dynamics, and irregular or chaotic paths may arise. Examples of both types are shown. Sometimes, in the same flow, certain particles will follow regular paths while others follow irregular paths. Even in the chaotic region the amount of regularity or irregularity of a path depends on initial conditions and system parameters. The notion of a transported fluid region or “atmosphere” is mentioned. Various conclusions, ideas and queries are formulated based on the examples given. The intimate mix of regular and chaotic trajectories complicates a purely Lagrangian approach to fluid flow problems.     

Gustafson,weidmann, kato,wolf, schechter and browder essential spectra of some matrix operator and application to two‐group transport equation

In this paper, we investigate the Gustafson, Weidmann, Kato, Wolf, Schechter and Browder essential spectra of a 2 × 2 block matrix operator defined on a Banach space where entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components under some properties. Furthermore, we give an application to two‐group transport equation. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Time asymptotic behaviour for unbounded linear operator arising in growing cell populations

This paper is concerned with the spectral analysis of a class of unbounded, linear operators, originally proposed by M. Rotenberg (J. Theor. Biol. 96 (1982) 495; J. Theor. Biol. 103 (1983) 181). After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C⁰-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible if the boundary operator is strictly positive. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

Existence of Solutions of a Nonlinear Hammerstein Integral Equation

In this article, we are concerned with existence results for a nonlinear Hammerstein integral equation in L ¹ spaces. Making use of the De Blasi measure of weak noncompactness, we establish variants of some Krasnosel'skii type theorem involving the weak topology of Banach spaces.     

On a characterization of the essential spectra of some matrix operators and application to two-group transport operators

In this paper, we investigate the essential approximate point spectrum and the essential defect spectrum of a 2 × 2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to two-group transport operators in the Banach space L _p ([−a, a] × [−1, 1]) × L _p ([−a, a] × [−1, 1]), a > 0, p ≥ 1.