Large deviations for sample quantities

One obtains certain theorems for the probabilities of large deviations of uniform order statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 144–150, 1980.     

Friction properties of physically modified polymers

The effectiveness of using physical methods of modifying the surface layers of polymers in order to improve their friction properties is demonstrated.Institute of Mechanics of Metal—Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. L. Ya.Karpov Scientific-Research Physicochemical Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 839–842, September–October, 1974.     

Particle spectrum in the modified nonminimal supersymmetric standard model in the strong Yukawa coupling regime

A theoretical analysis of solutions of renormalization group equations in the minimal supersymmetric standard model, which lead to a quasi-fixed point has shown that the mass of the lightest Higgs boson in these models does not exceed 94 ± 5 GeV. This implies that a considerable part of the parameter space in the minimal supersymmetric model is in fact eliminated by existing LEPII experimental data. In the nonminimal supersymmetric standard model the upper bound on the mass of the lightest Higgs boson reaches its maximum in the strong Yukawa coupling regime when the Yukawa constants are substantially greater than the gauge constants on the grand unification scale. In the present paper the particle spectrum is studied using the simplest modification of the nonminimal supersymmetric standard model which gives a self-consistent solution in this region of parameter space. This model can give m _h ～ 125 GeV even for comparatively low values of β ≥ 1.9. The spectrum of Higgs bosons and neutralinos is analyzed using the method of diagonalizing mass matrices proposed earlier. In this model the mass of the lightest Higgs boson does not exceed 130.5 ± 3.5 GeV.     

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...     

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.     

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.     

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.