Efficient verification of polynomial completeness of quasigroups
Polynomial completeness of an operation guarantees that deciding solvability of equations over this operation is an NP-complete problem. Thus this property is beneficial from the viewpoint of cryptographic applications. We propose an algorithm for verification of polynomial completeness of quasigroups and analyse efficiency of its serial and parallel implementations.
The Russian Princes of the pre-Mongolian time quite sequentially followed the prohibitions not only on the marriages of the close relatives, but also on the matromonies related by marriage.A unique case of the violation of the Canon prohibition on so called Crisscross Matrymonies when a sister and the brother from one family get into marital union with a brother and a sister from another family is studied in this paper. Also the authors consider the matrimonial strategy of Rurikids dynaty. and showed the extraordinary importance of the affinity in the organization of the military and political unions and coalitions in the 12th century
The complexity of decision of the polynomial (functional) completeness of a finite quasigroup is investigated. It is shown that the polynomial conpleteness of a finite quasigroup can be decided in polynomial time with respect to the order of the quasigroup.
This book constitutes the refereed proceedings of the 12th International Conference on Parallel Computational Technologies, PCT 2018, held in Rostov-on-Don, Russia, in April 2018.
The 24 revised full papers presented were carefully reviewed and selected from 167 submissions. The papers are organized in topical sections on high performance architectures, tools and technologies; parallel numerical algorithms; supercomputer simulation.
We propose a construction that allows generating large families of Latin squares, i.e., Cayley tables of finite quasigroups. This construction generalizes proper families of functions over Abelian groups introduced by Nosov and Pankratiev. We also show that all quasigroups generated by the original construction contain at least one subquasigroup, while the generalized construction generates quasigroups free of subquasigroups.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.