Replica Symmetry Breaking in an Axial Model of Quadrupolar Glass

We investigate the replica symmetry breaking (RSB) in a neighborhood of the instability point of the replica-symmetric solution in the axial quadrupolar glass model. We show that the solution with the first-stage RSB is stable against the subsequent RSB. Although there is no reflection symmetry, the first-stage RSB solution continuously bifurcates from the replica-symmetric one. This implies that our model does not belong to either of the two classes into which spin glasses are usually divided.     

Stress–Strain Analysis of Rectangular Plates with a Variable Thickness and Constant Weight

The stress–strain state of rectangular plates with a variable thickness and constant weight is analyzed. The laws of variation in the thickness are specified to depend on parameters so that the plate weight remains constant for any of their values. To solve the problem, discrete Fourier series are used, which makes it possible to reduce a two-dimensional problem to one-dimensional. Calculation results are presented.     

Forecasting call frequency at a financial services call centre

A forecasting model is developed for the number of daily applications for loans at a financial services telephone call centre. The purpose of the forecasts and the associated prediction intervals is to provide effective staffing policies within the call centre. The model building process is constrained by the availability of only 2 years and 7 months of data. The distinctive feature of the data is that demand is driven in the main by advertising. The analysis given focuses on applications stimulated by press advertising. Unlike previous analyses of broadly similar data, where ARIMA models were used, a model with a dynamic level, multiplicative calendar effects and a multiplicative advertising response is developed and shown to be effective.     

A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

Electric generators of singlet delta oxygen for an oxygen-iodine laser

Experimental and theoretical research into electric generators of singlet delta oxygen (SDO) for an oxygen-iodine laser made at the Lebedev Physics Institute and TRINITI is discussed. Breakdown and current-voltage characteristics of self-sustained electric discharge in SDO were studied both experimentally and theoretically, indicating that SDO and pure oxygen have quite different electric features. The electric properties and spectroscopy of an e-beam sustained discharge (EBSD) in oxygen and oxygen gas mixtures were experimentally studied. A comprehensive numerical model describing SDO kinetics in different kinds of discharge was developed. The pulsed EBSD in pure oxygen and its mixtures with noble gases was shown to be very unstable and characterized by low input energy. When adding small amounts of carbon monoxide or hydrogen, the electric stability of the EBSD increases, the specific input energy (SIE) per molecular component being more than order of magnitude higher and coming to 6.5 kJ/(l atm(O₂ + CO)) for the gas mixture O₂: Ar: CO = 1: 1: 0.1. Theoretical calculations demonstrated that, for an SIE of 6.5 kJ/(l atm), the SDO yield may reach ∼20%, exceeding its threshold value needed for oxygen-iodine laser operation at room temperature. The calibration of the optical scheme for measuring the SDO absolute concentration and yield using the detection of luminescence of the SDO going from a chemical SDO generator was performed. The measurement of the SDO yield demonstrated that it was ∼10.5% for an SIE of ∼3.0 kJ/(l atm(O2 + CO)), which is about 1.5 times less than the results of theoretical calculations for such an SIE. SDO production in RF slab discharge ignited in oxygen gas mixtures was experimentally studied, experimental SDO yield being about 10%. The choice of electrode material was demonstrated to be very important. Original Text ? Astro, Ltd., 2006.     

On the distribution of the number of real zeros of a random polynomial

In this note, we find the distibution of the number of real zeros of a random polynomial. We also derive a formula for the expected number of complex zeros lying in a given domain of the complex plane. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 69–79.     

The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.