Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

玻璃陶瓷材料中Tm3+离子红外到蓝色上转换发光

系统研究了PbF2+GeO2+WO3ⅩⅣTmF3玻璃陶瓷材料中,在近红外光(1.06μm)激发下,Tm3+离子的发光特性.实验中观测到Tm3+离子的两组峰值位置分别在20920cm-1和22173cm-1的蓝色上转换发光,并证实这两组上转换发光分别与吸收三个和四个光子有关,同时建立了上转换发光的模型.为了选择最佳掺杂浓度,详细地测量了Tm3+离子峰值为20920cm-1的蓝色上转换发光强度与TmF3浓度的关系.     

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.     

Estimation of multivariate binary density using orthogonal functions

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.     

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.     

Definition and properties of characteristic frequencies of a linear equation

The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of nonstability is given. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005.     

Holomorphic map with unipotent jacobian matrices in C 3

We prove that the holomorphic unipotent Jacobian conjecture is valid when n = 3.