Die Zerlegung von Zahlen mit Hilfe periodischer Kettenbrüche

Ohne Zusammenfassung     

Thermal analysis of glasses for proecological applications

Thermal behaviour and biochemical activity of potassium-silicate-phosphate glasses modified by addition of Ca, Mg, acting as ecological fertilisers of controlled release rate of the nutrients for plants were studied. It has been found that the biochemical activity of silicate-phosphate glasses depends on the nature and the number of components forming the glassy framework and is related to the thermal stability of glass demonstrated by the formation of new compounds during the process of crystallisation. It is proved that these seemingly different properties are determined by the same parameters which are the strengths bonds of glass network-formers and modifiers as well as their chemical affinity. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

A representation of the Belavkin equation via Feynman path integrals

 The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the complex Cameron-Martin space is given. Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002 Mathematics Subject Classification (2000): 81, 81S40, 60H15 Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals     

Approximate Solution of the de la Vallée Poussin Problem for a Differential Equation of Neutral Type by the Projection-Iterative Method

We solve the de la Vallée Poussin problem for a functional-differential equation by the projection-iterative method. We construct an algorithm, establish conditions sufficient for the convergence of the method, and present a computational scheme.     

Structure and properties of the mesophase of syndiotactic polystyrene. II. Effect of stepwise extraction on the preparation of the mesophase

In this study, a novel stepwise extraction method has been examined. The guest molecules housed between the helices of the clathrate δ form of syndiotactic polystyrene can be removed completely with this method. A systematic study of the preparation of a solvent‐free mesophase (emptied clathrate) membrane, its helical and residual solvent contents, and its structural transformations has been performed. In this first attempt, an enhancement in the TTGG helical content has been observed in the extracted membrane, and a conceptual mechanism is proposed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 269–273, 2003     

Highlights and Prospects of Hyperspherical Approach in Few-Body Quantum-Mechanical Systems

The binding energy of excitonium negative ion for ground ¹S-state in bulk conductors: Ge, Si, CdSe and for green and yellow lines of Cu₂O in hyperspherical coordinate method are found. Angular and radial correlations between electrons are taken into account by the channel functions, which are the eigen-functions of operator on the surface of sphere in six-dimensional sphere. The calculation of energies have been done using the adiabatic and Born-Oppenheimer approximations. In Born-Oppenheimer approximation is enough to give a binding energy with only 1.2% error, in adiabatic approximation this error drops to 0.7 %.     

Necessary stationary condition for polarized radiation in scattering media

The stationary condition is derived taking into account the polarization of radiation in the general case of a scattering inhomogeneous medium in an arbitrary-shape emitter. The necessary stationary condition for an emitter in which radiation is emitted and extinguished simultaneously is complete extinction of the entire emitted radiation. Radiation extinction as a result of absorption by the medium and the emergence of radiation from the emitter is analyzed. The stationary condition is an analytical form of writing that extinction of radiation is a sure event whose probability is equal to unity. The passage of radiation through the medium is described on the basis of the linear transport theory with the help of the matrices of the Green functions. The stationary condition includes the characteristics of polarized radiation extinction of which is analyzed, the absorption coefficients of the medium, and the elements of the matrices of the Green functions, which are determined by optical and geometrical parameters of the emitter. The stationary condition obtained is used for deriving the relations between the components of scalar intensity observed in an arbitrary region of the emitter. These relations include, in addition to the absorption coefficients and the matrix elements of the Green functions, the powers of the primary radiation. Possible applications of the stationary condition and the relations between intensity components in computations and experimental studies are considered.