Stop times in fock space stochastic calculus

Summary A stop time S in the boson Fock space over L ₂()₊ is a spectral measure in [0,] such that {S([0,t])} is an adapted process. Following the ideas of Hudson [6], to each stop time S a canonical shift operator U ^Sis constructed in . When S({}) has the vacuum as a null vector U ^Sbecomes an isometry. When S({})=0 it is shown that admits a factorisation _S]{S where _{S is the range of U ^Sand _S] is a suitable subspace of called the Fock space upto time S. This, in particular, implies the strong Markov property of quantum Brownian motion in the boson as well as fermion sense and the Dynkin-Hunt property that the classical Brownian motion begins afresh at each stop time. The stopped Weyl and fermion processes are defined and their properties studied. A composition operation is introduced in the space of stop time to make it a semigroup. Stop time integrals are introduced and their properties constitute the basic tools for the subject.     

EXAFS studies of cobalt oxides and oxide glasses

The exafs of Co²⁺ has been studied in rare earth cobaltites and in sulphate and borate glasses. It has been found that the environment of Co²⁺ ions is very similar in these cases. It appears feasible to study local structures in glasses using probe ion exafs. Communication No. 151 from the Solid State and Structural Chemistry Unit.     

Synthetic analogues of wedelolactone

The syntheses of 7′-methoxy- and 5′,7′,6-trimethoxy-coumarino(3′,4′:3,2)coumarones (IIa and IIb) are described.     

Topochemical anion metathesis routes to the Zr2N2S phases and the Na2S and ACl derivatives (A = Na,K, Rb)

Anion metathesis reactions between ZrNCl and A(2)S (A = Na, K, Rb) in the solid state follow three different pathways depending on reaction temperature and reactant stoichiometry: (1) the reaction of ZrNCl with A(2)S in the 2:1 stoichiometry at 800 degrees C/72 h/in vacuo yields alpha-Zr(2)N(2)S with the expected layered structure of La(2)O(2)S. Above 850 degrees C, alpha-Zr(2)N(2)S (P3 macro m1; a = 3.605(1) A, c = 6.421(3) A) neatly transforms to beta-Zr(2)N(2)S (P6(3)/mmc: a = 3.602(1) A, c = 12.817(1) A). The structures of the alpha- and beta-forms are related by an a/2 shift of successive Zr(2)N(2) layers. (2) The same reaction at low temperatures (300-400 degrees C) yields ACl intercalated phases of the formula A(x)Zr(2)N(2)SCl(x) (0 < x < approximately 0.15), where alkali ions are inserted between the S/Cl.S/Cl van der Waals gap of a ZrNCl-type structure. The S and Cl ions are disordered and the c lattice parameters are alkali dependent (R3 macro m, a approximately 3.6 A, c approximately 28.4 (Na), 28.9 (K), and 30.5 A (Rb). A(x)Zr(2)N(2)SCl(x) phases are hygroscopic and reversibly absorb water to give monohydrates. (3) Reaction of ZrNCl with excess A(2)S at 400-1000 degrees C gives A(2)S intercalated phases of the formula A(2)(x)Zr(2)N(2)S(1+)(x) (0 < x < 0.5), where the alkali ions reside between the S.S van der Waals gap of a ZrNCl type structure (R3 macro m, a approximately 3.64 A, c approximately 29.48 A). Structural characterization of the new phases and implications of the results are described.     

Dispersed fluorescence spectroscopy of primary and secondary alkoxy radicals

Dispersed fluorescence (DF) spectra of 1-propoxy, 1-butoxy, 2-propoxy, and 2-butoxy radicals have been observed under supersonic jet cooling conditions by pumping different vibronic bands of the B-X laser induced fluorescence excitation spectrum. The DF spectra were recorded for both conformers of 1-propoxy, three conformers of the possible five of 1-butoxy, the one possible conformer of 2-propoxy, and two conformers of the possible three of 2-butoxy. Analysis of the spectra yields the energy separations of the vibrationless levels of the ground X and low-lying A electronic state as well as their vibrational frequencies. In all cases, the vibrational structure of the DF spectra is dominated by a CO stretch progression yielding the nuCO stretching frequency for the X state and in most cases for the A state. In addition to the experimental work, quantum chemical calculations were carried out to aid the assignment of the vibrational levels of the X state and for some conformers the A state as well. Geometry optimizations of the different conformers of the isomers were performed and their energy differences in the ground states were determined. The results of the calculation of the energy separations of the close-lying X and A states of the different conformations are provided for comparison with the experimental observations.     

Synthesis,characterization and electrochemical studies of ruthenium(III) heterocyclic Schiff bases

A series of hexacoordinated Ru^III–PPh₃ complexes of general formula [RuCl(PPh₃)L] (L = tetradentate Schiff bases derived from the condensation of 2-furaldehyde or thiophene-2-carboxyaldehyde with alkyl and aryl diamines have been synthesized. The complexes were characterized by elemental analyses, spectroscopic and cyclic voltammetric studies. All of the complexes were paramagnetic. Coordination of the Schiff base appears to occur through the two nitrogen and two heterocyclic oxygen/sulphur atoms.     

Permeation liquid membrane for trace metal speciation in natural waters. Transport of liposoluble Cu(II) complexes

In this paper, the transport of Cu(II) in the presence of lipophilic Cu(II) organic complexes through permeation liquid membranes (PLMs) have been investigated. In natural waters, small organic compounds, which form liposoluble neutral complexes with Cu(II), are potentially toxic and bioavailable. Hence, to understand the role of liposoluble Cu(II) complexes in natural waters, four organic ligands: phthalic acid, bipyridyl, pyrocatechol and hydroxyquinoline, which form uncharged or lipophilic Cu(II) complexes, were tested. The results showed that the transport of lipophilic Cu(II) complexes through PLM depends on the lipophilicity of the complex. Applications of PLMs in natural waters are presented.