Convergence of genetic algorithms

The mean convergence of various versions of a genetic algorithm are considered. A number of convergence statements are formulated and relevant estimates are obtained. A hypothesis concerning the form of these estimates under variation of the structure of a genetic algorithm is put forward. Roman Riviyanovich Sharapov. Born 1981. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: genetic algorithms, neural networks, and financial mathematics. Aleksandr Vyacheslavovich Lapshin. Born 1980. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: financial mathematics, genetic algorithms, and neural networks.     

Tritium Labeling of Androst-4-ene-3,17-dione by Liquid-Phase Selective Hydrogenation and Factors Affecting the Process

Androstenedione labeled with tritium at positions 1 and 2 was prepared. The molar radioactivity of the sample prepared using homogeneous catalysts was as high as 1.4-1.5 PBq mol^{- 1}. [1,2-³H]Androst-4-ene-3,17-dione can be converted into the [1-³H]steroid with the molar radioactivity of 0.9 PBq mol^{- 1}.     

The Onsager relations analyzed using an ellipsoidal statistical equation

Validity on the well-known Onsager reciprocal relations L ₁₂=L ₂₁ is verified in the kinetic theory of gases taking into account mass and heat transfer near the surface. Using an analytical solution to the ellipsoidal statistical equation (providing for the true Prandtl number), it is demonstrated that the Onsager relations are obeyed, at least to within exponential corrections of the type exp(−1/Kn) in the Knudsen number.     

Acoustic emission method for research and control of friction pairs

One of the new physical methods that provides much information about the processes going on in a friction contact zone in real time is acoustic emission (AE). Basic experimental results of AE in friction are presented and analysed. Using AE signals we can get an indication about the state of the friction processes, about the quality of solid and liquid layers on the contacting surfaces in real time, sometimes about intensity of wear, changing of wear and friction regimes and so on. The influence of sliding velocity, load, roughness and some physical and mechanical properties of the body on the parameters of AE are also given. Some attention to the practical implementation of these techniques for control of capability for work of friction pairs in real conditions are given. Modern methods and devices enable condition monitoring of sliding and rolling bearings.     

On the nonuniformity of a capillary flow

It is established that the capillary rise of a liquid has an oscillatory character, in contrast to the commonly accepted opinion that a vertical capillary is filled at a monotonically varying velocity. The value of the tangential shear stress arising in an ascending liquid is evaluated for ethyl alcohol and distilled water.