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.     

The assignment of credit limits with a behaviour-scoring system

Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the riskof a customer defaulting to be quantified. These risks mustbe incorporated into a credit strategy which assigns creditlimits and makes authorization decisions in the most effectivemanner. This paper introduces the concept of marginal risk whichhas proved a useful tool in defining credit limit strategiesfor a mail-order company. Behaviour scores for authorizations are similar to credit applicationscores in that they predict the overall risk of a customer defaulting.If a cut-off risk can be established, then the optimal strategywould appear to be to withhold credit for customers exceedingthis risk and to grant unlimited credit for the remainder (thisis analogous to application strategies). The notion of grantingunlimited credit is often commercially unacceptable (particularlyif customers are to be informed of their credit limits!) andso strategies which give all or nothing are of limited valueand need further refinement. In order to overcome this problem, the concept of marginal riskhas been devised. The marginal risk is the risk of the ‘last£’ of an account being defaulted. This reflectsthe fact that small-balance customers may well pay off theircurrent balance only to default on larger subsequent purchases.Although the overall risk of customers with a given behaviourscore defaulting is relatively constant, their marginal riskwill vary according to their outstanding balance. This paperexplores the relationships between marginal risk and overallrisk and between marginal risk and outstanding balance. A modelwhich summarizes these relationships is proposed, and contoursof equal marginal risk are built on the basis of this model.These contours provide strategies for allocating credit limitswhich are both practical and optimal for a well formulated cut-offrisk and which suggest that the probability of defaulting isnot the best criterion for allocating credit limits. The results of the application of this approach will be demonstrated.Some of the problems that have been overcome are discussed,as are some of the outstanding problems.     

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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}.     

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.