Representations of ordered random variables in the terms of the sums or products of independent variables

This is a survey of the available representations capable of expressing dependent ordered variables like order statistics and records as sums of independent summands or as products of independent random multipliers. Some new similar representations are obtained that in a similar manner express the common distributions of representatives of these two types of ordered random variables.     

Structure determination of aligned samples of membrane proteins by NMR spectroscopy

The paper briefly reviews the process of determining the structures of membrane proteins by NMR spectroscopy of aligned samples, describes the integration of recent developments in the interpretation of spectra of aligned proteins and illustrates the application of these methods to the trans-membrane helical domain of a protein. The emerging methods of interpreting the spectral parameters from aligned samples of isotopically labeled proteins provide opportunities for simultaneously assigning the spectra and determining the structures of the proteins, and also for comparing the results from solid-state NMR experiments on completely aligned samples with those of solution NMR experiments on weakly aligned samples.     

On upper records in sequences of non-identically distributed random variables

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 124–133, 1992.     

On the average number of records for sequences of not identically distributed random variables

The scheme of n series of independent random variables X ₁₁, X ₂₁, …, X _k1, X ₁₂, X ₂₂, …, X _k2, …, X _1n , X _2n , …, X _kn is considered. Each of these successive series X _1m , X _2m , …, X _km , m = 1, 2, …, n consists of k variables with continuous distribution functions F ₁, F ₂, …, F _k , which are the same for all series. Let N(nk) be the number of upper records of the given nk random variables, and EN(nk) be the corresponding expected value. For EN(nk) exact upper and lower estimates are obtained. Examples are given of the sets of distribution functions for which these estimates are attained.     

Representations of order statistics,based on exponential variables with different scaling parameters

One presents a representation for order statistics, encountered frequently in the theory of queuing systems.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 136, pp. 162–164, 1984.     

Inhibition of Acinetobacter baumannii biofilm formation on a methacrylate polymer containing a 2-aminoimidazole subunit

A polymeric composite containing a 2-aminoimidazole derivative was synthesized. It was found that this polymer was resistant to biofilm colonization by Acinetobacter baumannii, no leaching of the 2-aminoimidazole derivative was observed after 2 weeks of treatment with deionized water, and the resulting polymer was not hemolytic.     

k-th record times and their generalizations

A series of asymptotic results are given for the k-th record times and for their generalizations, the so-called k_n-record times. All possible limiting distributions are obtained for some generalizations of the k-th record variables. These distributions are closely related with the corresponding limit distributions of the extremal order statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 115–121, 1986.