Reliability of Deterioration System

Mathematical models of the reliability assessment of a structure treated as the time to the first passage of the capacity which is degrading in the time are presented. Two stochastic models of the structure degradation caused by different factors and two stochastic models of loading are considered. The relationships for calculating the probability of failure for presented models of the structure load and the capacity degradation, are given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Injective Tensor Product of Distinguished Frechet Spaces

An example of two distinguished Fréchet spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E?F is not distinguished. On the other hand, it is proved that for arbitrary reflexive Fréchet space E and arbitrary compact set K the space of E - valued continuous functions C(K, E) is distinguished and its strong dual is naturally isomorphic to ? where L¹(μ) = C(K)¹.     

Helical conformations of isotactic polyacetaldehyde and other isotactic polytrihaloacetaldehydes

Minimum potential energy helical conformations for a family of four isotactic polyacetaldehydes have been determined. Our results indicate that all of the polymers form irrational helices. Comparisons have been made with the reported structures for two of these stereoregular polymers based on earlier X-ray diffraction data. c-Axis values associated with the pitch of the helix for polyacetaldehyde and for polytrichloroacetaldehyde (polychloral) were experimentally measured to be 0.48 and 0.51 nm, respectively. Our calculated conformations afforded values for a helix pitch of 0.47 and 0.52 nm, respectively, which derive from a 3.9/1 helix for polyacetaldehyde and a 3.7/1 helix for polychloral. The structure for polytribromoacetaldehyde (polybromal) was predicted to be similar to that for polychloral. For polytrifluoroacetaldehyde (polyfluoral) and polyacetaldehyde, a number of helical conformations with similar energies were found. All of these conformations could be related to the polychloral helical structure. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1855–1860, 1998     

On no-wait and no-idle flow shops with makespan criterion

The paper deals with the NP-hard problems of minimizing the makespan in m-machine no-wait and no-idle permutation flow shops. We identify networks whose longest path lengths represent the makespans. These networks reveal the duality between the two problems, and show graphical explanations of the fact that under no-wait and no-idle conditions the makespan can be a decreasing function of some job processing times. Moreover, they also lead to a natural reduction of the no-wait flow shop problem to the traveling salesman problem, some lower bounds on the shortest makespan, and new efficiently solvable special cases.     

Solid-state electrochemistry of silicotungstic acid immobilized by sol-gel chemistry

Voltammetry of silicotungstic acid (STA), H₄SiW₁₂O₄₀, that was encapsulated in silica was performed in the absence of a contacting liquid phase. Two one-electron reductions that are separated by 200?mV were observed, which is the same behavior as in aqueous solution. At scan rates, v, below 10?mV s^?1 with a 10?μm dia. carbon fiber indicator electrode, plateaus with limiting currents which are independent of v were observed, which is indicative of spherical diffusion from a field that is much larger than the electrode area. At v?>?20?V?s^?1, peaks were observed with currents directly proportional to v ^½. For a gel aged for 2 days, an effective diffusion coefficient, D _eff, of 3?×?10^?7?cm² s^?1 was estimated by voltammetry and chronoamperometry; the concentration of the redox sites thereby determined was about 0.5?M. The D _eff values that were obtained in this study were larger than expected for a solid electrolyte, which suggests an important role of residual water. In support of this model, gels that were aged in a humidistat at 33% humidity at room temperature for 2 and 5 days lost 16% and 13%, respectively, of their mass when dried at 120°.     

多元正态的两个均匀性检验

本文提出两个均匀性统计量用于检验多元正态性．该检验建立在多元正态分布的一个特征性质基础上，模拟研究和实例分析显示该均匀性统计量可以帮助解释来自已有正态性检验统计量的结论．     

Measurements of sensitivity to hydrostatic pressure and temperature in highly birefringent photonic crystal fibers

We report on experimental studies of polarimetric sensitivity to hydrostatic pressure and temperature in two highly birefringent index guided photonic crystal fibers, in which birefringence is induced by one row of the cladding holes with diameters smaller than the other cladding holes. The sensitivity measurements were carried out in the spectral range from 0.6 μm to 1.6 μm. Our results show that absolute value of the polarimetric sensitivity to hydrostatic pressure can reach 23 rad/MPa × m, which is almost one order of magnitude higher than in conventional fibers with elliptical core. Simultaneously, polarimetric sensitivity to temperature is at least two orders of magnitude lower than in conventional highly birefringent fibers. Moreover, we proved experimentally that one of the investigated fibers is completely insensitive to temperature at certain wavelength.     

Conway Polynomial and Oriented Rotant Links

We prove that the Conway polynomial of oriented links is not changed by the rotation operation of Anstee, Przytycki and Rolfsen.Mathematics Subject Classifications (2000). 57M25, 57M27Supported by KBN grant No 2P03A00218