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.     

射频磁控溅射法制备薄膜电池电极的计算机模拟初步

计算机模拟仿真射频磁控溅射实验制备薄膜及离于电池电极,研究了在特定实验条件下薄膜的生长过程,并分析了影响薄膜生长的部分因素。     

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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.     

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.     

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.     

Security analysis of a spatiotemporal-chaos-based cryptosystem

An S-box modified one-way coupled map lattice is applied as a chaotic cryptograph. The security of the system is evaluated from various attacks currently used, including those based on error function analysis, statistical property analysis, and known-plaintext and chosen-ciphertext analytical computations. It is found that none of the above attacks can be better than the brute force attack of which the cost is exhaustively quantitated by the key number in the key space. Also, the system has fairly fast encryption (decryption) speed, and has extremely long period for finite-precision computer realization of chaos. It is thus argued that this chaotic cryptosystem can be a hopeful candidate for realistic service of secure communications.