Bootstrap for Maxima and Records

The asymptotic properties and structure of bootstrapping maxima and record values are investigated. Bibliography: 19 titles.     

Gauge coupling unification in the exceptional supersymmetric Standard Model

We consider the renormalisation group flow of gauge couplings within the so-called exceptional supersymmetric Standard Model (E₆SSM) based on the low-energy matter content of 27-dimensional representations of the gauge group E₆$E_6$, together with two additional non-Higgs doublets. The two-loop beta functions are computed, and the threshold corrections are studied in the E₆SSM. Our results show that gauge coupling unification in the E₆SSM can be achieved for phenomenologically acceptable values of α₃(MZ)${\alpha }_3(M_Z)$, consistent with the central measured low-energy value, unlike in the minimal supersymmetric Standard Model (MSSM) which, ignoring the effects of high energy threshold corrections, requires significantly higher values of α₃(MZ)${\alpha }_3(M_Z)$, well above the experimentally measured central value.     

Cosmological constant in SUGRA models and the multiple-point principle

Physics of Atomic Nuclei - An attempt is made to explain the tiny order of magnitude of the cosmological constant in a model involvingt he following ingredients: supersymmetry breaking in N = 1...     

Rate of convergence to the normal law of order statistics for nonidentically distributed random variables

One obtains estimates for the rate of convergence to the normal law as n of order statistics X_k,n in the case of nonidentically distributed random variables.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 137–146, 1983.     

On the possibility of studying the electronic factor in catalysts using the method of space charge limited currents

A possibility is proposed for studying changes in the electronic characteristics of surface defects in adsorption and catalysis, using conductivity measurements in the region of injection currents. The change in the spectrum of electron traps is interpreted by a coordinative mechanism of adsorption.

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One property of student’s distribution with two degrees of freedom

Characterizations of Students t₂-distribution and some related distributions based on regressional properties of order statistics are obtained. Bibliography: 8 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 148–157.This research was supported by the Russian Foundation for Basic Research, grants 00-15-96019, 01-01-00031, and 02-01-00779.Translated by A. V. Sudakov.