Symmetries of Itô and Stratonovich Dynamical Systems and Their Conserved Quantities

A new definition for the symmetries of Itô and Stratonovich dynamicalsystem is given. Determining systems of symmetries for Itô andStratonovich systems have been obtained, and their relation has beendiscussed. It has been shown that some of the Lie point symmetries ofthe Fokker–Planck equation can be constructed using the symmetries ofItô dynamical systems. Conserved quantities can be found from thesymmetries of stochastic dynamical systems which do not arise from aHamiltonian. The results have been applied to an example.     

Non-gravitating scalars and spacetime compactification

We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincaré invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.     

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Novel Enantioselective Synthesis of Both Enantiomers of Furan‐2‐yl Amines and Amino Acids

A new enantioselective synthesis of furan‐2‐yl amines and amino acids is described, in which the key step is the oxazaborolidine‐catalyzed enantioselective reduction of O‐benzyl (E)‐ and (Z)‐furan‐2‐yl ketone oximes to the corresponding chiral amines. The chirality of the furan‐2‐yl amines is fully controlled by the appropriate choice of the geometrical isomer of the O‐benzyl oxime. Oxidation of the furan ring furnished amino acids in high yields.     

An oestrogen-derivative labeled with 99mTc and its radiopharmaceutical potential

An oestrogen derivative 3,17-a-oestradiolyl propyl 1,4,8,11-tetraazacyclotetradecanyl-1-(4-methylbenzoic acid)ester (ESTCPTA) that is 3,17-a-oestradiolyl propinol coupled to 1-(4-methylbenzoic acid)1,4,8,11-tetraazacyclotetradecane (CPTA) was synthesized in five steps. The product was purified by recrystallization in ethyl alcohol, and analysed by NMR and IR spectroscopy. ESTCPTA was labeled with ^99mTc and radio thin layer chromatography (RTLC) and radio-paper electrophoresis were used to determine the radiochemical yields. Specific activity was approximately 23.7 GBq/mmol and the labeling yield was over 95%. The biodistribution studies were performed on female Albino Wistar rats. The rats were sacricified by ether narcotization at certain time intervals and the activity of the organs was counted by a gamma counter. The activity per gram tissue was calculated and time activity curves were generated.     

Determination of the stability constants of uranyl complex with 8-hydroxyquinolinium sulfate

8-Hydroxyquinoline (8-HOQ) is known as an important chelating agent for several metal ions. This compound is practically insoluble in water. For this reason, in this study its water soluble sulfate salt has been used for complexing uranyl ions and the stability constants of the complex have been determined. The Irving-Rosotti method computing the Calvin-Bjerrum pH-titration data, was applied. Finally, the stability constants of the complex formed between (8-HOQN-H)₂SO₄ and uranyl ions were found to be lgK₁=8.25 and lgK₂=4.15, the overall stability constant being {ie55-1}.     

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.     

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.