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The article discusses the mathematical model on the estimation of the distance between a finite set of standard images under a translation plane. It determines the translation of a template image which ensures the best coincidence of the image being tested. It examines the effect of the template image on a qualitative level. The model considers a pair considering of the colored part of an image and the density of coloring. It indicates that if a random superposition is good, the translation maximizing the coincidence of images being tested is a small part of the diameter of the template image. Several formulas for solving mathematical problems are also provided.

Results of experiments on the kinetics of hydrogen generation by electrochemical dispersion of an aluminum alloy D16 in an aqueous solution of sodium hydroxide under alternating (AC) electric current are provided. It was found that the rate of hydrogen evolution under alternating electric current is significantly greater than the rate of hydrogen evolution in a reaction without the application of an electric current. The use of an alternating current produces Al(OH) powders with more highly disperse particles. [ABSTRACT FROM AUTHOR]

An X-ray tomographic system has been developed to measure the intensity of soft X rays and construct a two-dimensional profile of the electron temperature in plasma generated by the TOKAMAK T-11M facility. The system is based on cooled semiconductor CdTe detectors and is designed to operate in the energy range of 3–8 keV. [ABSTRACT FROM AUTHOR]

The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding system of Newton polytopes. In Pukhlikov and Khovanskiĭ (Algebra i Analiz 4(4):188-216, 1992), Pukhlikov and the second author noticed that the cohomology ring of smooth projective toric varieties over C can be computed via the BKK Theorem. This complemented the known descriptions of the cohomology ring of toric varieties, like the one in terms of Stanley-Reisner algebras. In Sankaran and Uma (Comment Math Helv 78(3):540-554, 2003), Sankaran and Uma generalized the "Stanley-Reisner description" to the case of toric bundles, i.e., equivariant compactifications of (not necessarily algebraic) torus principal bundles. We provide a description of the cohomology ring of toric bundles which is based on a generalization of the BKK Theorem, and thus extends the approach by Pukhlikov and the second author. Indeed, for every cohomology class of the base of the toric bundle, we obtain a BKK-type theorem. Furthermore, our proof relies on a description of graded-commutative algebras which satisfy Poincaré duality. From this computation of the cohomology ring of toric bundles, we obtain a description of the ring of conditions of horospherical homogeneous spaces as well as a version of Brion-Kazarnovskii theorem for them. We conclude the manuscript with a number of examples. In particular, we apply our results to toric bundles over a full flag variety G / B . The description that we get generalizes the corresponding description of the cohomology ring of toric varieties as well as the one of full flag varieties G / B previously obtained by Kaveh (J Lie Theory 21(2):263-283, 2011)., (© The Author(s) 2023.)