Reliability Estimation of Classification Algorithms. I. Introduction to the Problem. Point Frequency Estimates

The study deals with estimating the reliability of classification algorithms. The present article (the first of three) examines the statistical methods used for point estimation of the reliability of classifiers in the frequency approach. The estimation results are applicable to the small-sample case, which is of considerable importance in practice.     

Optimal Control of Distributions

The article develops the principles of optimal control theory for probability distributions on the configuration space of a controlled dynamical system. Necessary conditions of optimality are derived in the form of the Pontryagin principle for various classes of problems. Analytical representations in the space of distributions and observables are considered. Special modes are examined. The relationship between distribution control theory and nonlocal optimization problems is demonstrated.     

Simulation of Convective Flow of an Electrically Conducting Fluid in a Cavity

A new quasi-hydrodynamic algorithm is proposed for numerical analysis of convective flows in the presence of a homogeneous external magnetic field. The Marangoni convection problem in a square cross-section cavity is solved.     

Embedding of Nonprimary Subgroups in the Symmetric Group S 9

The nonprimary subgroups of the symmetric group S ₉ are investigated. Embedding properties of these subgroups are listed in a table. Properties such as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research leans upon the technique of Burnside marks, as well as upon pertinent information on the table of marks of S ₉ from the computer algebra package GAP. The subgroups were investigated up to conjugacy; the total number of conjugacy classes of nonprimary subgroups of S ₉ is 432. Some subgroups were additionally checked by other programs based on the double coset method. Bibliography: 24 titles.     

An Integral Formula for the Complex Intersection Number of Real Cycles in a Real Algebraic Variety with Topologically Rational Singularities

A formula of type indicated in the title is presented and discussed. Bibliography: 7 titles.     

Thermal expansion and thermal conductivity of CuGa<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te<Subscript>2</Subscript> solid solutions

The thermal expansion coefficients and the thermal conductivity of Bridgman-grown crystals of CuGa_1−x In_xTe₂ solid solutions are investigated. It is found that the thermal expansion coefficient varies with x linearly, while the thermal conductivity is minimal when x=0.5. The Debye temperature and the rms dynamic atomic displacements are calculated from experimental data. It is shown that the Debye temperature decreases and the rms displacements in the crystal lattice sharply increase as the In content in the solid solutions grows.     

Recyclization of 2,3-Disubstituted 5-Arylamino-2,5-dihydro-1,2,4-thiadiazoles and Related Salts into Benzothiazole Derivatives

Russian Journal of General Chemistry -     

Norm Series in High-Dimensional Local Fields

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.