Components of plants of the family Empetraceae. II. Flavonoids of Empetrum nigrum

Tomsk Medical Institute. Translated from Khimiya Prirodynkh Soedinenii, No. 6, pp. 875–876, November–December, 1988.     

Estimates for Solutions to Neutral Differential Equations with Periodic Coefficients of Linear Terms

Siberian Mathematical Journal - Under study are the systems of nonlinear delay differential equations of neutral type with periodic coefficients of linear terms. We establish sufficient conditions...     

Magnetic and electrical properties of cation-substituted sulfides MexMn1 ? xS (Me = Co, Gd)

The temperature dependences of the specific magnetization σ and the electrical resistivity ρ of Me _x Mn_{1 − x} S single crystals (Me= Co, Gd; x= 0.05) have been studied in the temperature range 80 K < T < 1000 K. The samples under study have revealed the presence of a spontaneous magnetic moment below the Néel temperature (T _N) and ferromagnetic clusters in Gd_0.05Mn_0.95S in the temperature range 146 K < T < 680 K. Substitution of gadolinium for manganese initiates a transition from p-type to n-type conduction. The change in the conduction type is accompanied by an increase in the electrical resistivity at 300 K by approximately one order of magnitude and, accordingly, by a decrease in the activation energy. The magnetic and electrical properties of the crystals under study have been interpreted in terms of the cluster model with temperature-dependent ferromagnetic exchange and an electron localized in this cluster. Original Russian Text ? S.S. Aplesnin, L.I. Ryabinkina, O.B. Romanova, V.V. Sokolov, A.Yu. Pichugin, A.I. Galyas, O.F. Demidenko, G.I. Makovetskiĭ, K.I. Yanushkevich, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 4, pp. 661–664.     

Radiation dose reconstruction from L-band in vivo EPR spectroscopy of intact teeth: Comparison of methods

In vivo EPR tooth dosimetry is a more challenging problem than in vitro EPR dosimetry because of several potential additional sources of variation associated with measurements that are made in the mouth of a living subject. For in vivo measurement a lower RF frequency is used and, unlike in the in vitro studies, the tooth cannot be processed to optimize the amount and configuration of the enamel that is measured. Additional factors involved with in vivo measurements include the reproducibility of positioning the resonator on the surface of the tooth in the mouth, irregular tooth geometry, and the possible influence of environmental noise. Consequently, in addition to using the theoretical and empirical models developed for analyzing data from measurements of teeth in vitro, other unconventional and more robust methods of dose reconstruction may be needed. The experimental parameter of interest is the peak-to-peak amplitude of the spectrum, which is correlated to the radiation dose through a calibration curve to derive the reconstructed dose. In this study we describe and compare the results from seven types of computations to measure the peak-to-peak amplitude for estimation of the radiation induced signal. The data utilized were from three sets of in vivo measurements of irradiated teeth. Six different teeth with different doses were placed in the mouth of a volunteer in situ and measurements of each tooth were carried out on three different days. The standard error of dose prediction (SEP) is used as a figure of merit for quantifying precision of the reconstruction. We found that many of the methods gave fairly similar results, with the best error of prediction resulting from a computation based on a Lorentzian line model whose center field corresponds to the known parameter of the radiation-induced EPR spectra of teeth, with corrections from a standard sample that was measured as part of the data acquisition scheme. When the results from the three days of measurement were pooled, the SEP decreased dramatically, which suggests that one of the principal sources of variation in the data is the ability to precisely standardize the measurements conditions within the mouth. There are very plausible ways to accomplish improvements in the existing procedures.     

Systems of differential equations of higher dimension and delay equations

We establish connections between the solutions to a class of systems of ordinary differential equations of higher dimension and delay equations.     

Criteria for Unconstrained Global Optimization

We develop criteria for the existence and uniqueness of the global minima of a continuous bounded function on a noncompact set. Special attention is given to the problem of parameter estimation via minimization of the sum of squares in nonlinear regression and maximum likelihood. Definitions of local convexity and unimodality are given using the level set. A fundamental theorem of nonconvex optimization is formulated: If a function approaches the minimal limiting value at the boundary of the optimization domain from below and its Hessian matrix is positive definite at the point where the gradient vanishes, then the function has a unique minimum. It is shown that the local convexity level of the sum of squares is equal to the minimal squared radius of the regression curvature. A new multimodal function is introduced, the decomposition function, which can be represented as the composition of a convex function and a nonlinear function from the argument space to a space of larger dimension. Several general global criteria based on majorization and minorization functions are formulated.     

Integral operators determined by quasielliptic equations. II

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 35, No. 1, pp. 41–65, January–February, 1994.     

A Model of Regular Nanostructure

Using the methods of statistical physics, the properties of nanostructured elements produced by breaking a large system of internal interfaces are investigated. Taking into account the resulting dependences, a quantum model of nanostructured state is formulated in approximations of Kroning–Penney, and electronic properties are calculated as a function of grain size.