Vacuum expectation values of quantum fields

We propose a new system of vacuum expectation values for quantum fields. For finite series, these distributions satisfy the linear Wightman axioms. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 41–63, October, 2008.     

Modelling of multi-line Brillouin/erbium fibre lasers

Laser sources with unique properties can be produced using a combination of nonlinear Brillouin gain in single-mode optical fibre (SMOF) and gain in erbium-doped fibre (EDF). Narrow bandwidth nonlinear gain from stimulated Brillouin scattering in SMOF determines the wavelength of operation, and gain in EDF allows efficient operation and large power extraction. Various cascading schemes based on the Brillouin/erbium fibre laser (BEFL) as well as distinctive multi-wavelength versions of the BEFL were proposed, being able to produce 10GHz combs of over 30 lines at 1550 nm. These multi-wavelength sources may be of use in future dense wavelength-division multiplexing systems. We explore fundamental aspects of BEFLs configured to generate multiple wavelengths with particular focus on the effects of the Brillouin and EDF pumps on the number of lines and the relationship between the intensities of the individual lines in the comb.     

Macrocycles from pentafluoropyridine and tetrafluoropyrimidine

Macrocycles were synthesised by sequential nucleophilic aromatic substitution processes involving pentafluoropyridine and tetrafluoropyrimidine and various diamines as the structural components.     

Algorithms for solving multiobjective discrete control problems and dynamic c-games on networks

In this paper we study a special class of multiobjective discrete control problems on dynamic networks. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost by a certain trajectory. Applying Nash and Pareto optimality principles we study multiobjective control problems on dynamic networks where the dynamics is described by a directed graph.Polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph. Properties of time-expanded networks are characterized. A constructive scheme which consists of several algorithms is presented.     

Synthesis,Characterization, and Reaction Studies of Pd(II) Tripeptide Complexes

The aqueous synthesis of Pd(II) complexes with alkylated tripeptides led to the hydrolysis of the peptides at low pH values and mixtures of complexed peptides were formed. A non-aqueous synthetic route allowed the formation and isolation of single products and their characterization. Pd(II) complexes with α-Asp(OR)AlaGly(OR), β-Asp(OR)AlaGly(OR), and TrpAlaGly(OR) (R = H or alkyl) as tri and tetradentate chelates were characterized. The tridentate coordination mode was accompanied by a fourth monodentate ligand that was shown to participate in both ligand exchange reactions and a direct removal to form the tetradentate coordination mode. The tetradentate coordination revealed a rare a hemi labile carbonyl goup coordination mode to Pd(II). Reactivity with small molecules such as ethylene, acids, formate, and episulfide was investigated. Under acidic conditions and in the presence of ethylene; acetaldehyde was formed. The Pd(II) is a soft Lewis acid and thiophilic and the complexes abstract sulfur from episulfide at apparent modest catalytic rates. The complexes adopt a square planar geometry according to a spectroscopic analysis and DFT calculations that were employed to evaluate the most energetically favorable coordination geometry and compared with the observed infrared and NMR data.     

The Extensions of the Generalized Quadrangle of Order (3, 9)

It is shown that there is only one extension of GQ(3, 9) namely the one admitting the sporadic simple groupMcLas a flag-transitive automorphism group. The proof depends on a computer calculation.     

Open bosonic string amplitudes

The theory of the partially U (1) compactified scalar massless field on the domain on the compact Riemann surface with Nambu-Goto action is defined. The partition function is determined completely by a choice of the finite-dimensional approximations. The correlation functions are the correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. The Nielsen's conjecture for the scattering amplitudes is correctly proved.In Memory of Mikhail Constantinovich PolivanovV. A. Steklov Mathematical Institute, Russian Academy of Sciences. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 3, pp. 498–506, September, 1992.