Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

Buchbesprechungen

Ohne Zusammenfassung     

Levels of natural and artifical radioactivity in sediments in the Eastern Black Sea of Turkey

Sediment samples collected from the Eastern Black Sea in 1993 from 15 sampling stations of different depths have been analyzed. Natural and artifical radionuclide activity levels in offshore sediment samples from the Eastern Black Sea in Turkey are reported about seven years after the Chernobyl accident. The purpose of this paper is to follow up the earlier study and present results for the distributions of radionuclides in sediments of the Black Sea.     

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.