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.     

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.     

Rare earth impurities in high purity lanthanum oxide determined by neutron activation analysis

Individual rare earth impurities in high purity La₂O₃ (99.9%) have been determined by NAA after pre-separation of the matrix (La). The separation is carried out on an anion exchanger (Dowex 1×8) using different mixtures of methanol/nitric acid as eluants. The rare earth elements from Dy to Lu are eluted quantitatively using a 10% 1M HNO₃-90% methanol mixture, while the light rare earths from Ce to Gd are eluted quantitatively using a 10% 0.05M HNO₃-90% methanol mixture. La, which is retained on the column, is eluted using 0.1M HNO₃. The recoveries of the various rare earth elements have been checked using radiotracers and also by spiking the sample with known amount of elements, and the recoveries are found to be quantitative. Results obtained on a typical high purity lanthanum oxide are reported here.     

STEREOCHEMISTRY OF INCIPIENT ELECTROPHILIC AND NUCLEOPHILIC REACTIONS AT DIVALENT SELENIUM CENTER: ELECTROPHILIC-NUCLEOPHILIC PAIRING AND ANISOTROPIC SHAPE OF Se IN Se…Se INTERACTIONS

Abstract

Using the Cambridge Crystallographic Data Base and computer retrieval methods, we have studied the preferred directions of approach of nucleophiles and electrophiles at divalent selenium centers. We find that electrophiles approach Se in a direction nearly normal to the selenide plane Y-Se-Z while nucleophiles approach Se nearly in the selenide plane and along the back side of Y-Se or Z-Se bonds. We also found evidence for the incipient formation of attractive electrophile-nucleophile pairing in Se…Se interactions. Other Se…Se contacts which did not fit the above pattern showed non-spherical effective shape for Se atoms. The preferred directions of approach of electrophiles and nucleophiles for Se and S are very similar and may be understood in terms of frontier orbitals. Such similarity in the shape and orbital environment of S and Se indicate to some extent how Se can play the role of S in some enzymes.     

Towards a black‐box for biological EXAFS data analysis. II. Automatic BioXAS Refinement and Analysis (ABRA)

In biological systems, X‐ray absorption spectroscopy (XAS) can determine structural details of metal binding sites with high resolution. Here a method enabling an automated analysis of the corresponding EXAFS data is presented, utilizing in addition to least‐squares refinement the prior knowledge about structural details and important fit parameters. A metal binding motif is characterized by the type of donor atoms and their bond lengths. These fit results are compared by bond valance sum analysis and target distances with established structures of metal binding sites. Other parameters such as the Debye–Waller factor and shift of the Fermi energy provide further insights into the quality of a fit. The introduction of mathematical criteria, their combination and calibration allows an automated analysis of XAS data as demonstrated for a number of examples. This presents a starting point for future applications to all kinds of systems studied by XAS and allows the algorithm to be transferred to data analysis in other fields.