The Jacobian and the Ginzburg-Landau energy

We study the Ginzburg-Landau functional for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional. Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001     

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.     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.     

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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}.     

Sodium p‐nitro­benzoxasulfamate monohydrate

The title compound, alternatively named sodium 6‐nitro‐3H‐1,2,3‐benzoxa­thia­zole 2,2‐dioxide monohydrate, Na⁺·C₆H₃­N₂O₅S^?·H₂O, consists of chains of NaO₇ units, with the seven donor‐O atoms coming from two water mol­ecules and five p‐­nitro­benzoxasulfamate anions. The seven‐coordinate geometry around the Na⁺ ion is described as monocapped trigonal prismatic, but with a large distortion from ideal geometry. Each triangular face is defined by one O atom each from a water mol­ecule, a nitro group and a sulfonyl group. An O atom from a sulfonyl group caps one of the square faces of the trigonal prism in an unsymmetrical fashion. The water mol­ecules and one sulfonyl O atom are involved in bridging adjacent units, as is the nitro group of the anion. The sulfamate ions adopt an antiparallel alignment between the NaO₇ units and are connected to each other by C—H?O and π–π interactions. The three‐dimensional crystal structure is stabilized by a network of strong O—H?N hydrogen bonds.     

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.