Frobenius-Perron operators and approximation of invariant measures for set-valued dynamical systems

A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of .     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

q-transformation theory

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU _q (2) algebra. To obtain transition probabilities, one must take the Woronowicz square.     

The influence of cyclodextrin complexation on proton transfer in piperidinomethyl-2-naphthol

Summary Piperidinomethyl-2-naphthol forms inclusion complexes with -cyclodextrin with an equilibrium constant of 265M ^–1 in aqueous solution. The proton transfer equilibrium between the neutral and the zwitterionic form is strongly influenced by the association.

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Der Einfluß der Komplexierung mit -Cyclodextrin auf das Protontransfer-Gleichgewicht in Piperidino-2-naphthol (Kurze Mitt.)

Zusammenfassung Piperidinomethyl-2-naphthol bildet Einschlußkomplexe mit -Cyclodextrin mit einer Gleichgewichtskonstante von 265M ^–1. Das Protontransfer-Gleichgewicht zwischen neutraler Form und zwitterionischer Struktur wird durch diese Assoziation stark beeinflußt.

     

Base-catalyzed cyclization of β-(2-arylaminoethoxy)styrenes

-(2-Arylaminoethoxy)styrenes undergo cyclization in the presence of KOH to giveN-aryl-2-benzyloxazolidines inca. 90 % yield. The structures of the products were confirmed by IR and NMR spectroscopy.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 340–341, February, 1994.     

On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

Preparation and characterization of a viscosity index improver for naphthenic and paraffinic base oils

Copolymers of -methyl styrene and 2-ethylhexyl acrylate were prepared in a benzene solution. The presence of the copolymers were confirmed by solubility, IR and NMR tests. The molecular weight and the polydispersity of the polymers were estimated by GPC. The copolymers obtained were blended with paraffinic and naphthenic base oils. The viscosity, the viscosity index (VI) the Q value as well as the stability to shear and oxidation were obtained for these blends. The results are compared with the results obtained with an oil blend containing a commonly used high temperature additive. Two of the copolymers obtained have shown to be good alternatives for specific applications.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Interactions between octyl-β-D-glucoside and α-amino acids or small peptides

The interactions between octyl--D-glucoside and glycine in water have been investigated by surface tension, viscosity, and density measurements. The results show that the -amino acid causes an unexpected lowering of the critical micellar concentration of octyl--D-glucoside. Such a finding has been interpreted in temss of dipole-dipole interactions between the hydrophilic site of the surfactant and the peptidic cosluttes. From three to seven amino acid molecules have been estimated to be coordinated with each glucoside unity in the micellar state. The research has been extended to glycine oligopeptides and L-lysine. The latter compound has effects similar to those observed with glycine whereas diglycine and triglycine show weaker effects on the micellization process.     

Polynitro-substitutedN-alkylalkaneimidoyl chlorides

The reaction of -fluorosubstituted polynitroalkylaldimines with HCl results in replacement of the fluorine atom by a chlorine atom. The hitherto unknown -chlorosubstituted polynitroalkylaldimines have been obtained, and their X-ray structural investigation has been performed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 440–443, March, 1994.     

Stable σ-adducts of 4,6-dinitrotetrazolo[1,5-a]pyridine with alkoxide anions

The reaction of 2-chloro-3,5-dinitropyridine with two equivalents of KN₃ in the presence of ROH results in stable Meisenheimer-type -adducts of 4,6-dinitrotetra-zolo[1,5-a]pyridine with RO^– anions (R = H, Alk, Ph). The mechanism of -complex formation was suggested. The structure of the -adduct with R = Me was established by IR and NMR spectroscopy and by X-ray diffraction analysis.For the preliminary communication, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1278–1283, July, 1994.This work was supported by the Russian Foundation for Basic Research (project code 93-03-5329).