Canonical commutation relations of quantum mechanics and stochastic regularity

In a previous publication (Boletin de la Sociedad Matematica Mexicana 1975) it was established that any weakly stationary linearly regular stochastic process is unitarily equivalent to a quantum mechanical momentum evolution. The object of the present note is, as promised in the previous publication, to amplify some of the details concerning the just mentioned interesting connection, giving in particular a direct proof of the Szego-Kolmolgorov-Krein characterization of regular stationary processes. We also show that although the so-called decaying states without regeneration do not exist for unstable quantum systems, they are natural for regular stationary processes.     

Hawking-Unruh effect on thermal equilibrium state

It is pointed out that the usual (Gibbs) thermal equilibrium state in Minkowski spacetime is no longer a thermal equilibrium state for a uniformly accelerated observer. Similarly, the thermal equilibrium state in Kruskal spacetime is not a thermal state for a Schwarzschild observer.     

Electro-optical properties of doped anthracene films

Electroluminescence in anthracene doped with anthraquinone (10^?3 mole%) films are presented. Films are deposited at room temperature in a vacuum of 10^?5 torr. It is observed that at constant frequency the brightness/voltage relationship follows the relation $\text{B = B}{}_0\text{exp}\text{(?b/V}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. The results show that electroluminescent brightness increases linearly with frequency. At lower frequencies green electroluminescent (EL) emission and at higher frequencies blue EL emission is observed. Similar nature for I–V and brightness/voltage relationship are found in anthracene doped with 10^?4 mole% anthraquinone.     

Synthesis, spectroscopic, and structural aspects of two trinuclear cyano-bridged heterometallic complexes

Two new cyano-bridged trinuclear heterometallic complexes [Sr₂(Phen)₄(CF₃CO₂)(H₂O)₃Fe(CN)₆]·2H₂O (1) [Ca₂(Phen)₄(CF₃CO₂)(H₂O)Co(CN)₆]·2H₂O (2) (where Phen=1,10-phenanthroline) have been synthesized and their crystal structures have been determined. The structure of complex (1) features a central [Fe(CN)₆]³⁻ unit that links a monocation, [Sr(Phen)₂(OH₂)(OOCCF₃)]⁺ and a dication, [Sr(Phen)₂(OH₂)₂]²⁺ via two trans cyanide bridges. The complex (2) features a central [Co(CN)₆]³⁻ unit that links two monocations of [Ca(Phen)₂(OH₂)(OOCCF₃)]⁺ (the positions of the trifluoro acetate and water molecules are disordered over two positions) via two trans cyanide bridges. Each metal atom is seven coordinated and achieves pentagonal bipyramidal geometry. Two cocrystallized water molecules are present in both the complexes. The presence of an extensive network of hydrogen bonding imparts the overall stability to both the systems.     

Aqueous polymerization of acrylamide initiated by acidic potassium permanganate–ascorbic acid redox system

The polymerization of acrylamide initiated by the acidic permanganate–ascorbic acid redox pair has been studied in aqueous media at 30 ± 0.2°C in nitrogen atmosphere. The initial rate of polymerization has been found to be proportional to nearly the first power of the catalyst KMnO₄ concentration within the range 6.0 × 10^?3–14.0 × 10^?3 mole/l. The rate is proportional to the first power of the monomer concentration within the range 4.00 × 10^?2–12.0 × 10^?2 mole/l. However, the rate of polymerization is independent of ascorbic acid concentration within the range 3.0 × 10^?3–6.0 × 10^?3 mole/l., but the further increase of the concentration depresses the rate of polymerization as well as maximum conversion. The initial rate increases but the maximum conversion decreases as the temperature is increased within the range 20–35°C. The overall energy of activation has been found to be 9.8 kcal/mole. The optimum amount of sulfuric acid is essential to initiate the polymerization but its presence in excess produces no effect either on the rate of reaction or the maximum conversion. Water-miscible organic solvents and salts, e.g., CH₃OH, C₂H₅OH, (CH₃)₂CHOH, KCl, and Na₂SO₄, depress the rate. Slight amounts of MnSO₄ · H₂O and a complexing agent NaF increase the rate of polymerization. Cationic and anionic detergents have been found to decrease and increase the rate, respectively, while nonionic surfactants have no effect on the rate of polymerization.     

Surface-Enhanced Raman Scattering of Rhodamine 123 in Silver Hydrosols and in Langmuir-Blodgett Films on Silver Islands

Surface-enhanced Raman scattering(SERS) of the Rhodamine 123 (Rh 123) molecule on ion-induced silver colloids has been studied. A time-dependent study of the SER spectra at a particular pH confirms charge transfer interaction between the probe molecule and the metal. The SER spectra of Rh 123 in Ag sol is compared with that of the molecules organized in a monolayer on silver island films by the Langmuir-Blodgett (LB) technique. The origin of high SERS activity of Rh 123 molecules in a monolayer on a silver island film is shown to be due to physisorption whereas in the ion-induced colloidal SERS both physisorption and chemisorption machanisms are involved. From these results, the contribution of charge transfer interaction to SERS in Ag sol has been estimated. In monolayer SERS, all the in-plane and out-of-plane (of xanthene ring) modes are more or less equally enhanced. This indicates that the xanthene plane of Rh 123 molecule organized in a LB film is oriented neither flat nor perpendicular to the silver island surface but is tilted. Copyright 2001 Academic Press.     

Grafting onto cellulose. VIII. Graft copolymerization of poly(ethylacrylate) onto cellulose by use of redox initiators. Comparison of initiator reactivities

In an attempt to compare the relative reactivities of different redox systems in graft copolymerization of vinyl monomers onto cellulose, we studied grafting of ethylacrylate (EA) in aqueous medium by using the well-known redox intiator, ferrous ammonium sulfate–potassium persulfate (FAS–KPS) system, and its reactivity was compared with that of Fenton's reagent (Fe²⁺ ?H₂O₂) towards grafting of EA onto cellulose. Optimum conditions for affording maximum grafting were evaluated and percent grafting is expressed as functions of different reaction variables. Evidence of grafting was obtained from IR spectroscopic measurements, SEM, and TGA studies of the grafted and ungrafted cellulose. A plausible explanation for the observed reactivity pattern shown by (FAS–KPS) and (FAS–H₂O₂) redox systems is offered. Fenton's reagent (Fe²⁺ ?H₂O₂) was found to be several times more reactive than (FAS–KPS) redox system.     

Higher isoprenoids—VIII: Diterpenoids from the oleoresin of hardwickia pinnata part 1: hardwickiic acid

The oleoresin from Hardwickia pinnata Roxb. is shown to be a complex blend of sesquiterpenes and diterpenes. (?)-Copaene, (?)-caryophyllene and humulene account for over 90% of the sesquiterpenes present. The diterpenes, which constitute some 60% of the oleoresin, have been found to consist of a series of closely related new diterpenoids of ent-clerodane type. Evidence leading to the elucidation of the absolute stereostructure of the main diterpenoid-hardwickiic acid—is presented.     

Aqueous polymerization of methacrylic acid initiated by Ce4+ -glycolic acid redox pair

The aqueous polymerization of methacrylic acid (MAA) initiated by a Ce⁴⁺ -glycolic acid (GA) system was observed in a sulfuric acid medium at 35 ± 0.2°C in a nitrogen atmosphere. The rate of monomer disappearance was proportional to [MAA]¹ and the rate of ceric ion disappearance was proportional to [GA][Ce⁴⁺]. An increase in the reaction temperature from 30 to 45°C raised the rate and the overall activation energy was 63 kJ/mol. The molecular weight increased with a rise in [MAA] and a reduction in [Ce⁴⁺]. The effect of varying [H₂SO₄] was also studied.