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Search Results: 1 - 10 of 2509 matches for " Andrey Trepalin "
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Quotients of conic bundles
Andrey Trepalin
Mathematics , 2013,
Abstract: Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is birationally equivalent to a quotient of other k-rational conic bundle cyclic group of order $2^k$, dihedral group of order $2^k$, alternating group of degree $4$, symmetric group of degree $4$ or alternating group of degree $5$ effectively acting on the base of conic bundle. Also we construct infinitely many examples of such quotients which are not k-birationally equivalent to each other.
Quotients of del Pezzo surfaces of high degree
Andrey Trepalin
Mathematics , 2013,
Abstract: In this paper we study quotients of del Pezzo surfaces of degree four and more over arbitrary field $\Bbbk$ of characteristic zero by finite groups of automorphisms. We show that if a del Pezzo surface $X$ contains a point defined over the ground field and the degree of $X$ is at least five then the quotient is always $\Bbbk$-rational. If the degree of $X$ is equal to four then the quotient can be non-$\Bbbk$-rational only if the order of the group is $1$, $2$ or $4$. For these groups we construct examples of non-$\Bbbk$-rational quotients.
Quotients of cubic surfaces
Andrey Trepalin
Mathematics , 2015,
Abstract: Let $\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\mathbb{P}^3_{\Bbbk}$ and $G$ be a group acting on $X$. We show that if $X(\Bbbk) \ne \varnothing$ and $G$ is not trivial and not a group of order $3$ acting in a special way then the quotient surface $X / G$ is rational over $\Bbbk$. For the group $G$ of order $3$ we construct examples of both rational and nonrational quotients of both rational and nonrational $G$-minimal cubic surfaces over $\Bbbk$.
Rationality of the quotient of $\mathbb{P}^2$ by finite group of automorphisms over arbitrary field of characteristic zero
Andrey S. Trepalin
Mathematics , 2011,
Abstract: Let $\Bbbk$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\Bbbk$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\Bbbk$ is algebraically closed. In this paper we prove that $\mathbb{P}^2_{\Bbbk} / G$ is rational for an arbitrary field $\Bbbk$ of characteristic zero.
Hierarchical Clustering of Large Databases and Classification of Antibiotics at High Noise Levels
Sergei V. Trepalin,Alexander V. Yarkov
Algorithms , 2008, DOI: 10.3390/a1020183
Abstract: A new algorithm for divisive hierarchical clustering of chemical compounds based on 2D structural fragments is suggested. The algorithm is deterministic, and given a random ordering of the input, will always give the same clustering and can process a database up to 2 million records on a standard PC. The algorithm was used for classification of 1,183 antibiotics mixed with 999,994 random chemical structures. Similarity threshold, at which best separation of active and non active compounds took place, was estimated as 0.6. 85.7% of the antibiotics were successfully classified at this threshold with 0.4% of inaccurate compounds. A .sdf file was created with the probe molecules for clustering of external databases.
An Electrostatic Catastrophe Machine as an Attosecond Pulse Generator  [PDF]
Andrey Gitin
Optics and Photonics Journal (OPJ) , 2014, DOI: 10.4236/opj.2014.412034
Abstract: The generation of an attosecond pulse in the ultraviolet range is described in the terms of the catastrophe theory. A simple criterion of tunneling is proposed. The criterion allows constructing the quasiclassical model of the generator of attosecond laser pulses based on the interaction of an electric field of extremely powerful femtosecond pulse with the valence electron in the potential well of the gas atom.
Unified Theory of Force Fields (Electromagnetic and Gravitational)  [PDF]
Chaykin Andrey
World Journal of Condensed Matter Physics (WJCMP) , 2017, DOI: 10.4236/wjcmp.2017.71003
Abstract: In this paper, the superfluid substance is described by the same equations of the electromagnetic field and the gravitational field. The gravitational mass is sufficiently considered as the gravitational charge, having the same dimensions as electric charge.
The Influence of Leadership Art on Modern Enterprise Management  [PDF]
Dryamin Andrey
Open Journal of Business and Management (OJBM) , 2019, DOI: 10.4236/ojbm.2019.72067
Abstract: In today’s society, the rapid development of the knowledge-based economy puts forward new requirements for the leadership of enterprises: improving the ideas of employees and enterprises, improving leadership art has become extremely important content for the leadership management model in this new era. Leadership art is the content and performance of the leadership style. The correct use of leadership art is very important for the whole enterprise. It can not only effectively improve the efficiency of the enterprise, but also promote the common development of the company and employees. However, how to make the successful use of leadership art in enterprises has become an urgent problem to be solved. In this article, two or more existing situations are studied to determine their similarities and differences, the background, development, current conditions and environmental interactions of one or more individuals, groups, communities, businesses or institutions is observed, recorded and analyzed for stages of patterns in relation to internal and external influences. This article will briefly discuss the influence of leadership art on modern enterprise management.
Local Search Heuristics for NFA State Minimization Problem  [PDF]
Andrey V. Tsyganov
Int'l J. of Communications, Network and System Sciences (IJCNS) , 2012, DOI: 10.4236/ijcns.2012.529074
Abstract: In the present paper we introduce new heuristic methods for the state minimization of nondeterministic finite automata. These methods are based on the classical Kameda-Weiner algorithm joined with local search heuristics, such as stochastic hill climbing and simulated annealing. The description of the proposed methods is given and the results of the numerical experiments are provided.
Multi-Parameter Analysis of Optimal Transitions from Chaotic to Stable Regions for Two Classes of Systems  [PDF]
Yury Talagaev, Andrey Tarakanov
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.31A030

The study of the parameter space of chaotic systems is complicated by its high dimensionality (multi-parametricability). Two approaches to the study of chaotic systems are presented: multi-parameter analysis and optimal suppression of chaotic dynamics. For non-autonomous chaotic systems, this is the way to compare the effectiveness of various correction parameters that provide optimal removal of irregular dynamics. For the class of autonomous chaotic systems, this is the way to investigate the optimal conditions of super-stable behavior for the chaotic system.

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