Relaxation Time of Quantized Toral Maps

We introduce the notion of relaxation time for noisy quantum maps on the 2d-dimensional torus – generalization of previously studied dissipation time. We show that the relaxation time is sensitive to the chaotic behavior of the corresponding classical system if one simultaneously considers the semiclassical limit together with the limit of small noise strength (ε → 0). Focusing on quantized smooth Anosov maps, we exhibit a semiclassical régime (where E > 1) in which classical and quantum relaxation times share the same asymptotics: in this régime, a quantized Anosov map relaxes to equilibrium fast, as the classical map does. As an intermediate result, we obtain rigorous estimates of the quantum-classical correspondence for noisy maps on the torus, up to times logarithmic in On the other hand, we show that in the “quantum régime” quantum and classical relaxation times behave very differently. In the special case of ergodic toral symplectomorphisms (generalized “Arnold’s cat” maps), we obtain the exact asymptotics of the quantum relaxation time and precise the régime of correspondence between quantum and classical relaxations. Communicated by Jens Marklof submitted 4/01/05, accepted 2/02/05     

TGA/DTG/DSC investigation of thermal ageing effects on polyamide–imide enamel

Thermoanalytical investigations TGA/DTG/DSC of polyamide–imide enamel after thermal ageing have been presented. The lifetimes at 260, 270, 280, 290, 300 °C were determined. The thermograms of the enamels after attaining of their lifetimes much depend on the ageing temperature. The temperatures of 5% loss of mass that much increase after thermal ageing appear the most sensitive indicator of ageing rate. The residue of mass at 800 °C increases after ageing, even to 27%, due to diffusion of copper ions from the conductor into enamel during annealing. The copper contents in aged coatings could be also an indicator of ageing rate.     

Experimental and quantum-chemical studies of 1H, 13C and 15N NMR coordination shifts in Pd(II) and Pt(II) chloride complexes with quinoline, isoquinoline, and 2,2'-biquinoline

1H, 13C, and 15N NMR studies of platinide(II) (M=Pd, Pt) chloride complexes with quinolines (L=quinoline-quin, or isoquinoline-isoquin; LL=2,2'-biquinoline-bquin), having the general formulae trans-/cis-[ML2Cl2] and [M(LL)Cl2], were performed and the respective chemical shifts (delta1H, delta13C, delta15N) reported. 1H coordination shifts of various signs and magnitudes (Delta1Hcoord=delta1Hcomplex-delta1Hligand) are discussed in relation to the changes of diamagnetic contribution to the relevant 1H shielding constants. The comparison to the literature data for similar complexes containing auxiliary ligands other than chlorides exhibited a large dependence of delta1H parameters on electron density variations and ring-current effects (inductive and anisotropic phenomena). The influence of deviations from planarity, concerning either MN2Cl2 chromophores or azine ring systems, revealed by the known X-ray structures of [Pd(bquin)Cl2] and [Pt(bquin)Cl2], is discussed in respect to 1H NMR spectra. 15N coordination shifts (Delta15Ncoord=delta15Ncomplex-delta15Nligand) of ca. 78-100 ppm (to lower frequency) are attributed mainly to the decrease of the absolute value of paramagnetic contribution in the relevant 15N shielding constants, this phenomenon being noticeably dependent on the type of a platinide metal and coordination sphere geometry. The absolute magnitude of Delta15Ncoord parameter increased by ca 15 ppm upon Pd(II)-->Pt(II) replacement but decreased by ca. 15 ppm following trans-->cis transition. Experimental 1H, 13C, 15N NMR chemical shifts are compared to those quantum-chemically calculated by B3LYP/LanL2DZ+6-31G**//B3LYP/LanL2DZ+6-31G*, both in vacuo and in CHCl3 or DMF solution.     

Enantioselective epoxidation of electrophilic olefins by using glycosyl hydroperoxides

Anomeric hydroperoxides derived from 3,4,6-tri-O-benzyl-galactose and glucose were used for enantioselective epoxidation of naphthoquinone (12), chalcone (13), (E)-1,2-dibenzoyl ethylene (14) and (E)-iso-butyryl-phenyl ethylene (15). In the presence of sodium hydroxide, the epoxidations showed exceptional high asymmetric induction. The exchange of sodium by a potassium ion resulted in a low asymmetric induction. These results pointed to the crucial role of the counterion and strongly suggested that coordination of the alkaline ion occurs in the transition state of the epoxidation process by both reagents, hydroperoxide and the olefin. Theoretical studies of the reaction mechanism at the DFT B3LYP/6-31G* level fitted very well with experimental results.     

REACTION OF BIS-[DIALKOXYPHOSPHORYL]- AND BIS-[DIALKOXYTHIOPHOSPHORYL]- DISULFIDES WITH TRIALKYLSILYLCYANIDES NEW ROUTE TO DIALKYLPHOSPHORO- AND DIALKYLTHIOPHOSPHORO THIOCYANIDATES AND O,O,O,O-TETRAALKYLPYROPHOS- PHOROTRITHIOATES

Abstract

The reaction of organophosphorus disulfides with trialkylsilylcyanide has been investigated. It provided direct evidence for the intermediacy of thiocyanidate >P(X)SCN, X=O, S in this type of reaction. The disulfides studied involved phosphoryl, phosphonyl and/or phosphinyl disulfides. They have been shown to follow the common mechanism. The studied reaction of thiophosphoryl disulfides with trimethylsilylcyanide represents a new and highly efficient route to tetraalkylpyrophosphoro-trithioates.     

Surface relief grating formation in luminescent dye doped photochromic polymer containing azobenzene side groups

We study the formation of a surface relief grating and photoluminescence in a thin layers of a photochromic polymer doped with the luminescent dyes 3-(1,1-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole and Rhodamine 6G. Surface topography measurements via Atomic Force Microscopy confirmed the existence of a surface relief grating with amplitudes as high as 650 nm both for doped and undoped photochromic polymers. Spectroscopic measurements carried out for polymers containing luminescent dyes have shown efficient photoluminescence and amplified spontaneous emission which is characteristic for gain media.     

Basicity comparison for di-substituted 4-nitropyridine derivatives in polar non-aqueous media

Acid dissociation, as well as cationic homoconjugation equilibria have been studied potentiometrically in systems involving four di-substituted 4-nitropyridines and conjugate cationic acids in the polar non-aqueous solvents - aprotic protophobic acetonitrile (AN) and propylene carbonate (PC), the amphiprotic methanol (MeOH), and in the aprotic protophilic dimethyl sulfoxide (DMSO). The influence of solvent effect on the obtained acidity constants has been discussed. The acidity constants (expressed as pK_a values) were compared with those previously determined in another polar protophobic aprotic solvent - acetone (AC), and obtained for the unsubstituted pyridine (Py). A comparison of the acid dissociation constants determined in all media studied has proved that the strength of the cationic acids increases on going from acetonitrile through propylene carbonate, acetone, and methanol to dimethyl sulfoxide. Furthermore, the values of acidity constants in the non-aqueous media have shown that in all the solvents studied they change according to the substituent effects. It has been also found that substituted 4-nitropyridine derivatives studied exhibit no tendency towards cationic homoconjugation in acetonitrile, propylene carbonate, and methanol and dimethyl sulfoxide. Moreover, it has been demonstrated that the acid dissociation constants determined by potentiometric titration method in all the solutions investigated correlate well with the calculated energy parameters of the protonation reactions in the gaseous phase.     

Spontaneous emission and quantum discord: Comparison of Hilbert–Schmidt and trace distance discord

Hilbert–Schmidt and trace norm geometric quantum discord are compared with regard to their behavior during local time evolution. We consider the system of independent two-level atoms with time evolution given by the dissipative process of spontaneous emission. It is explicitly shown that the Hilbert–Schmidt norm discord has nonphysical properties with respect to such local evolution and cannot serve as a reasonable measure of quantum correlations and the better choice is to use trace norm discord as such a measure.     

Pointwise products of some Banach function spaces and factorization

The well-known factorization theorem of Lozanovski? may be written in the form L¹≡E⊙E^′$L^1\equiv E\odot E^{\prime }$, where ⊙ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize F through E  , i.e., when F≡E⊙M(E,F)$F\equiv E\odot M(E,F)$, where M(E,F)$M(E,F)$ is the space of pointwise multipliers from E to F  . Properties of M(E,F)$M(E,F)$ were investigated in our earlier paper [41] and here we collect and prove some properties of the construction E⊙F$E\odot F$. The formulas for pointwise product of Calderón–Lozanovski? _Eφ$E_{\phi }$-spaces, Lorentz spaces and Marcinkiewicz spaces are proved. These results are then used to prove factorization theorems for such spaces. Finally, it is proved in Theorem 11 that under some natural assumptions, a rearrangement invariant Banach function space may be factorized through a Marcinkiewicz space.