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

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

Conditional distributions of record values and characterizations of distributions

We consider some regression relations for record values X(n), n > 0, generated by a sequence of independent random variables X₁, X₂, X₃,... with a common continuous cumulative distribution function F(x). New characterizations of distributions based on regression properties of record values are obtained. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 5–14.     

Records in the Fα-scheme. II. Limit laws

Limit theorems for the number of records in a sequence of independent nonidentically distributed random variables are obtained. A generalization of the so-called F^α-scheme is given. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 42–51. Translated by A. Sudakov.     

High-resolution NMR spectroscopy of membrane proteins in aligned bicelles

High-resolution solid-state NMR spectra can be obtained from uniformly (15)N-labeled membrane proteins in magnetically aligned bicelles. Fast uniaxial diffusion about the axis of the bilayer normal results in single-line spectra that contain the orientational information necessary for protein structure determination.     

A class of limit distributions for maximum cumulative sum

Let X₁, X₂, ... be a sequence of independent identically distributed random variables with zero mathematical expectation and finite variances. S_o=0 and S_n=∑ _i=1 ⁿ X_i. It is proved that is the limit distribution function of the normalized random variable a(k, n)} for some sequence of centering constants a (k,n).     

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.     

End-to-end correlation for a C-12 hydrocarbon chain

The 19F nuclear spin-lattice relaxation rate constants were measured as a function of magnetic field strength for 1,12-diaminododecane labeled at one end with a nitroxide radical and at the other with a trifluoromethyl group. The magnetic relaxation dispersion profile (MRD) reports the spectral density function appropriate to the end-to-end correlation function for the doubly labeled molecule. After extrapolation to zero concentration to eliminate the intermolecular relaxation contribution to relaxation, the resulting intramolecular MRD profile was compared with several model approaches. The rotational model for the spectral density functions as included in the Solomon-Bloembergen-Morgan equations does not describe the data well. The earlier model of Freed for nuclear spin relaxation induced by a freely diffusing paramagnetic co-solute is not rigorous for this case because the paramagnet is tethered to the observed nuclear spin and only a restricted space in the immediate vicinity of the nuclear spin is accessible for pseudo-translational diffusion of one end of the molecule with respect to the other. A generalization of the Torrey model for magnetic relaxation by translational diffusion developed by Nevzorov and Freed, which includes the effect of restrictions imposed by the finite length of the chain, describes the experiment within experimental errors. A simple modification of the Hwang-Freed model that does not specifically include the dynamical effects of the finite tether also provides a good approximation to the data when the tether chain is sufficiently long.     

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.