Random rotations of the Wiener path

Summary Let (W, H, ) be an abstract Wiener space and letR(w) be a strongly measurable random variable with values in the set of isometries onH. Suppose that Rh is smooth in the Sobolev sense and that it is a quasi-nilpotent operator onH for everyhH. It is shown that (R(w)h) is again a Gaussian (0, |h| _H ² )-random variable. Consequently, if (e _i ,i)W ^* is a complete, orthonormal basis ofH, then defines a measure preserving transformation, a rotation, onW. It is also shown that if for some strongly measurable, operator valued (onH) random variableR, (R(w+k)h) is (0, |h| _H ² )-Gaussian for allk, hH, thenR is an isometry and Rh is quasi-nilpotent for allHH. The relation between the stochastic calculi for these Wiener pathsw and , as well as the conditions of the inverbibility of the map are discussed and the problem of the absolute continuity of the image of the Wiener measure under Euclidean motion on the Wiener space (i.e. composed with a shift) is studied.The research of the second author was supported by the Fund for the Promotion of Research at the TechnionDedicated to the memory of Albert Badrikian     

Symmetric orbits of orthogonal veronese actions and their second order envelopes

The orbits of Lie groups acting in Euclidean spaces by isometries are extrinsically symmetric iff they are parallel, i.e. satisfy ${\overline \nabla} h =0 $ Submanifolds characterized by the integrability condition $ {\overline R}\o\ h =0 $ of this system ${\overline \nabla} h =0$ are called semi-parallel (or semi-symmetric, extrinsically); they are the 2nd order envelopes of the symmetric orbits. For the orthogonal Veronese action, corresponding to the map well-known from the algebraic geometry, all symmetric orbits will be determined, as well as their 2nd order envelopes. The results are essential for the classification of the semi-parallel submanifolds.     

Some results about the spectrum of commutative Banach algebras under the weak topology and applications

LetA be a commutative Banach algebra with a nonempty spectrum A. By weak we denote the relative weak topology induced on A by (A ^*,A ^**). In this note we study some properties of the topological space (A, weak) and present some applications of the results obtained and tools used to amenability, weakly compact homomorphisms, weakly compact subsets of the spectrum of the uniform algebras and to a characterization of the synthesizable ideals of the algebraA.     

Isolation of xylose reductase gene ofPichia stipitis and its expression inSaccharomyces cerevisiae

Applied Biochemistry and Biotechnology - A NADPH/NADH-dependent xylose reductase gene was isolated from the xylose-assimilating yeast,Pichia stipitis. DNA sequence analysis showed that the gene...     

Determination of iodide in drinking water by isotope dilution analysis

The most suitable way of determination iodine-deficiency is to measure iodine concentrations in water and urine. For this reason, a method that can determine iodide concentrations in drinking water and suitable for routine analysis, is developed. Water samples have been collected from four Aegean localities: Izmir, Salihli, Ödemis and Tire situated in the western Turkey. The method is based on substochiometric isotope dilution analysis. Iodile concentrations vary within 9.86–85.14 μg/l ranges in the analyzed samples. Mean value is 44.92±22.07 μg/l.     

Study on labeling conditions of125I-synkavit by the iodogen method

Labeling conditions of synkavit (2-methyl-1,4-naphthoquinol disodium phosphate) with iodine-125 have been studied. In this study, labeling temperature, reaction time, successive using of iodogen coated tubes, iodogen amount and synkavit concentrations have been determined to get optimum conditions for maximum labeling. Final results showed that when the labeling temperature, reaction time, synkavit concentration, and iodogen amount were, at room temperature, 15 min (in the case of successive using of three iodogen coated tubes), 2 mg ml^–1 and 5 mg, respectively; labeling yield was 90% and specific activities of the order of 555 GBq mmol^–1 (15 Ci mmol^–1) have been obtained.     

Vibrational Spectroscopic Studies on the Hofmann-dabn-Type Benzene Clathrates: M(1,4-diaminobutane)Ni(CN)4° 1.5C6H6 (M = Mn, Fe, Co, Ni or Cd)

IR spectra of M(1,4-diaminobutane)Ni(CN)4° 1.5C6H6 (M = Mn, Fe, or Co), and IR and Raman spectra of M(1,4-diaminobutane)Ni(CN)4° 1.5C6H6 (M = Ni or Cd) clathrates are reported. The spectral features suggest that the compounds are similar in structure to the Hofmann-dabn-type clathrates.     

Stereochemical Analysis of an Aromatic Triplet Di-π-methane Rearrangement

It is shown that (−)-(S)-N,N-dimethyl-2-(1′-methylallyl)aniline ((−)-(S)- 4 ), on direct irradiation in MeCN at 20°, undergoes in its lowest-lying triplet state an aromatic di-π-methane (ADPM) rearrangement to yield (−)-(1′R,2′R)- and (+)-(1′R,2′S)-N,N-dimethyl-2-(2-methylcyclopropyl)aniline ((−)-trans- and (+)-cis- 7 ) in an initial trans/cis ratio of 4.71 ± 0.14 and in optical yields of 28.8 ± 5.2% and 15 ± 5%, respectively. The ADPM rearrangement of (−)-(S)- 4 to the trans- and cis-configurated products occurs with a preponderance of the path leading to retention of configuration at the pivot atom (C(1′) in the reactant and C(2′) in the products) for (−)-trans- 7 and to inversion of configuration for (+)-cis- 7 , respectively. The results can be rationalized by assuming reaction paths which involve the occurrence of discrete 1,4- and 1,3-diradicals (cf. Schemes 10, 12, and 13). A general analysis of such ADPM rearrangements which allows the classification of these photochemical reactions in terms of borderline cases is presented (Scheme 14). It is found that the optical yields in these ‘step-by-step’ rearrangements are determined by the first step, i.e. by the disrotatory bond formation between C(2) of the aromatic moiety and C(2′) of the allylic side chain leading to the generation of the 1,4-diradicals. Moderation of the optical yields can occur in the ring closure of the 1,3-diradicals to the final products, which may take place with different trans/cis-ratios for the individual 1,3-diradicals. Compounds (−)-trans- 7 as well as (+)-cis- 7 easily undergo the well-known photochemical trans/cis-isomerization. It mainly leads to racemization. However, a small part of the molecules shows trans/cis-isomerization with inversion of configuration at C(1′), which is best explained by a photochemical cleavage of the C(1′)–C(3′) bond.     

Immobilization of Mercuric reductase from aPseudomonas putida strain on different activated carriers

Mercuric reductase was isolated fromPseudomonas putida KT2442::mer-73 and immobilized on Chromatographic carriers activated by various methods. The immobilization methods for covalent coupling were compared with regard to preservation of enzymatic activity and coupling yields. Highest yields were obtained with carriers bearing the most reactive functional groups. Best results were achieved with tresyl chloride-activated carriers. The optimum binding conditions were found at pH 8. Application of the immobilized mercuric reductase for continuous treatment of Hg(II)-containing water was examined in a fixed bed reactor. Space-time yields up to 510 nmol/min-mL were attained. The kinetics of immobilized enzyme systems were not diffusion-controlled.