Rotational diffusion of membrane proteins in aligned phospholipid bilayers by solid-state NMR spectroscopy

Solid-state NMR experiments on mechanically aligned bilayer and magnetically aligned bicelle samples demonstrate that membrane proteins undergo rapid rotational diffusion about the normal in phospholipid bilayers. Narrow single-line resonances are observed from 15N labeled sites in the trans-membrane helix of the channel-forming domain of the protein Vpu from HIV-1 in phospholipid bilayers with their normals at angles of 0 degrees, 20 degrees, 40 degrees, and 90 degrees, and bicelles with their normals at angles of 0 degrees and 90 degrees with respect to the direction of the applied magnetic field. This could only occur if the entire polypeptide undergoes rotational diffusion about the bilayer normal. Comparisons between experimental and simulated spectra are consistent with a rotational diffusion coefficient (DR) of approximately 10(5)s-1.     

On the maximal value of the expectation of record numbers

There are n independent identically distributed random variables with a continuous distribution function. The problem considered is, getting sequentially the values of these variables and selecting one of them as an initial point, how we can maximize the expected number of records among the rest of this sequence of random variables (without knowledge of the future values).     

Joint distribution of order statistics generated by records

Probability distributions of some order statistics connected with the k th records values are discussed. Some useful representations for the exponential records and the corresponding order statistics are given. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarrow POMI, Vol. 228, 1996, pp. 24–30.     

Quasifixed-point scenario in a modified nonminimal supersymmetric standard model

The modified next-to-minimal supersymmetric standard model is the simplest model that is obtained as an extension of the minimal supersymmetric standard model and which is compatible with the LEP II experimental constraint on the mass of the lightest Higgs boson at tan β～1. The renormalization of Yukawa coupling constants and of the parameters of a soft breakdown of supersymmetry is investigated within this model. The possibility of unifying the Yukawa coupling constants for the b quark and the τ lepton at the Grand Unification scale M _X is studied. The spectrum of particles is analyzed in the vicinity of a quasifixed point where solutions to the renormalization-group equations are concentrated at the electroweak scale.     

On some regression relationships relating sample means and successive maxima

In recent years, a number of papers have appeared in which characterizations of a series of distributions in terms of regression properties of order statistics were obtained. In particular, characterizations of the Student’s t ₂-distribution in terms of linear regression relation-ships, including the sample median X _{2, 3} and the sample mean T ₃, were obtained in 2002. Later, similar results were also established for samples of larger sizes, and characterizations of families of distributions containing the t ₂-distribution were put forward. These characterizations are based, in particular, on linear regression relationships relating sample means T _{2k + 1} and sample medians X _{k + 1, 2k + 1}, k = 1, 2, ...     

Record values in sequences of sample ranges

The classical representation of record values in sequences of independent random variables with the standard exponential distribution E(1) as sums of exponentially distributed random summands plays an important role in the mathematical theory of records. A generalization of this representation is proposed. A new similar result that makes it possible to express the record values of sample ranges as sums of independent exponentially distributed random variables is obtained.