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The Voronoi conjecture for parallelohedra with simply connected δ-surfaces
Discrete and Computational Geometry. 2015. Vol. 53. No. 2. P. 245-260.
We show that the Voronoi conjecture is true for parallelohedra with simply connected δ-surfaces. That is, we show that if the boundary of parallelohedron P remains simply connected after removing closed nonprimitive faces of codimension 2, then P is affinely equivalent to a Dirichlet–Voronoi domain of some lattice. Also, we construct the π-surface associated with a parallelohedron and give another condition in terms of a homology group of the constructed surface. Every parallelohedron with a simply connected δ-surface also satisfies the condition on the homology group of the π-surface.
Gavrilyuk A. A., Труды Математического института им. В.А. Стеклова РАН 2015 Т. 288 С. 49-66
The method of canonical scalings is substantiated for lifts of tilings of Euclidean space. A new combinatorial-geometric approach to the construction of a generatrix of a tiling is proposed. The construction is based on a simple and geometrically transparent operation of lifting a face to an earlier lifted neighbor. The approach is applied to the ...
Added: November 5, 2015
Yakovlev E., Епифанов В. Ю., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2018 № 2(46) С. 47-55
The objects of research are two-dimensional compact polyhedra with an Euclidean cell decomposition, which are pseudomanifolds with boundary. The goal is to create new effective algorithms for computing the bases of absolute and relative homology groups modulo 2. Proposed a reduction procedure to a similar problem for polyhedra of lesser dimensionality, containing fewer number of cells. We ...
Added: October 4, 2018
Dutour Sikirić M., Grishukhin V., Magazinov A., European Journal of Combinatorics 2014 Vol. 42 P. 49-73
A parallelotope P is a polytope that admits a facet-to-facet tiling of space by translation copies of P along a lattice. The Voronoi cell P_V(L) of a lattice L is an example of a parallelotope. A parallelotope can be uniquely decomposed as the Minkowski sum of a zone closed parallelotope P and a zonotope Z(U), where Uis the set of vectors used to generate the zonotope. In this ...
Added: October 4, 2018
E. I. Yakovlev, Chekmaryov D. T., Russian Mathematics (USA) 2018 Vol. 62 No. 9 P. 72-85
We discuss numerical schemes of finite element method for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this paper we show that the obstacle to the construction of this design may be ...
Added: October 14, 2018
Rybnikov G., / Cornell University. Series math "arxiv.org". 2014.
We study a special type of $E_\infty$-operads that govern strictly unital $E_\infty$-coalgebras (and algebras) over the ring of integers. Morphisms of coalgebras over such an operad are defined by using universal $E_\infty$-bimodules. Thus we obtain a category of $E_\infty$-coalgebras. It turns out that if the homology of an $E_\infty$-coalgebra have no torsion, then there is ...
Added: February 26, 2014
Magazinov A., Moscow Journal of Combinatorics and Number Theory 2015 Vol. 5 No. 3 P. 86-131
In 1908 Voronoi conjectured that every parallelohedron is a Voronoi parallelohedron for some Euclidean metric in E^d . Although the conjecture is still neither proved, nor disproved, there are several positive results for some special classes of parallelohedra. In this paper we extend the list of such classes by one new case. Let I be ...
Added: October 4, 2018
Magazinov A., Моделирование и анализ информационных систем 2013 Т. 20 № 4 С. 71-80
В 1929 году Б. Н. Делоне привел полную классификацию комбинаторных типов схождений параллелоэдров в гранях коразмерности 3. Оказалось, что любое схождение дуально одному из следующих пяти трехмерных многогранников: тетраэдру, четырехугольной пирамиде, октаэдру, треугольной призме или параллелепипеду. В статье приводится новое доказательство этого результата, основанное на формуле Эйлера. С использованием этой классификации получены некоторые дальнейшие свойства граней коразмерности 3 разбиений ...
Added: October 4, 2018
Magazinov A., European Journal of Combinatorics 2013 Vol. 34 No. 7 P. 1108-1113
Consider a face-to-face parallelohedral tiling of R^d and a (d−k)-dimensional face F of the tiling. We prove that the valence of F (i.e. the number of tiles containing F as a face) is not greater than 2^k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices ...
Added: October 4, 2018
Magazinov A., Advances in Geometry 2018
In this short note we prove a sharp lower bound for the second moment of a lattice Voronoi cell in terms of the respective covering radius. This gives an affirmative answer to a conjecture by Haviv, Lyubashevsky and Regev. We also characterize those lattice Voronoi cells for which this lower bound is attained. ...
Added: October 4, 2018
Yakovlev E., Epifanov V., Lobachevskii Journal of Mathematics 2019 Vol. 40 No. 5 P. 690-698
We solve some computational problems for triangulated closed three-dimensional manifolds
using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms
for computing intersection numbers of 1- and 2-dimensional cycles are developed. Using these
algorithms it is possible to construct a basis of the cohomology group from a given basis of the
homology group of complementary dimension. ...
Added: October 8, 2019
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357
Added: July 8, 2014