Karpenkov O., Ustinov A., Journal of Number Theory 2017 Vol. 176 P. 375–419
In this paper we investigate the combinatorial structure of 3-dimensional Minkowski–Voronoi continued fractions. Our main goal is to prove the asymptotic stability of Minkowski–Voronoi complexes in special two-parametric families of rank-1 lattices. In addition we construct explicitly the complexes for the case of White's rank-1 lattices and provide with a hypothetic description in a more ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Квант 2006 № 6 С. 10–14
The article is devoted to problems related to possible arrangements of circles on plane lattices. ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Математическое образование 2006 № 4 С. 47–67
We continue publishing educational materials from the Specialized Educational and Scientific Center of Moscow State University (formerly Physics and Mathematics School No. 18). We offer three chapters from the brochure "Problems on Gridded Paper" by Specialized Educational and Scientific Center instructors V. V. Vavilov and A. V. Ustinov. The rest of the manual will be ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Математическое образование 2007 № 2 С. 33–57
We are completing the publication of the textbook "Problems on Gridded Paper" by V. V. Vavilov and A. V. Ustinov, instructors at the Moscow State University Specialized Educational and Scientific Center. The beginning of the textbook was published in issue 4(39), 2006. Similar issues are discussed in the book "Polygons on Lattice" by the same ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Квант 2007 № 6 С. 13–15
The article is devoted to semiregular polygons on lattices. ...
Added: October 12, 2025
Ustinov A., Дальневосточный математический журнал 2011 Т. 11 № 2 С. 213–221
Voronoi's algorithm for computing a system of fundamental units of a complex number field is based on a geometric properties of 3-dimensional lattices. This algorithm is based on Voronoi's theorem about cylindric minima for a lattice in general position. In the original proof and it's refinement published by Delone and Faddeev some significant cases were ...
Added: October 9, 2025
Ustinov A., Современные проблемы математики 2012 № 16 С. 103–128
The article is devoted to the development of the theory of three-dimensional continued fractions. ...
Added: October 9, 2025
Ustinov A., Математический сборник 2015 Т. 206 № 7 С. 103–134
In 1964, Linnik and Skubenko established the equidistribution of the integral points on the determinantal surface detX=P, where X is a (3×3) matrix with independent entries and P is an increasing parameter. Their method involved reducing the problem by one dimension (that is, to the determinantal equations with a (2×2) matrix). In this paper a more precise version of the Linnik-Skubenko reduction is proposed. It ...
Added: October 9, 2025
Ustinov A., Успехи математических наук 2015 Т. 70 № 3 С. 107–180
This survey is devoted to results related to metric properties of classical continued fractions and Voronoi–Minkowski three-dimensional continued fractions. The main focus is on applications of analytic methods based on estimates of Kloosterman sums. An apparatus is developed for solving problems about three-dimensional lattices. The approach is based on reduction to the preceding dimension, an ...
Added: October 9, 2025
Spiridonov I., Mathematical notes 2019 Vol. 106 No. 1-2 P. 146 – 150
Added: April 27, 2025
Нурлигареев Х. Д., Ярославский педагогический вестник 2011 Т. 3 № 3 С. 15–18
В настоящей статье дано описание полуправильных (равносторонних и равноугольных) многоугольников, которые могут быть расположены на каждом из 11 правильных паркетов. Приведены основные идеи и ключевые моменты доказательств, также статья снабжена большим количеством иллюстраций. ...
Added: October 4, 2022
Нурлигареев Х. Д., Ярославский педагогический вестник 2010 Т. 3 № 4 С. 12–17
Данная статья посвящена вопросам дискретной геометрии, которые традиционно излагаются в курсе математики школы имени А.Н. Колмогорова СУНЦ МГУ. Рассматривается понятие решетки и основные ее свойства, исследуется вопрос о правильных многоугольниках, вершины которых имеют целочисленные координаты, разбирается формула Пика. Теоретическую часть сопровождают задачи, предлагаемые школьникам на практических занятиях. ...
Added: October 4, 2022
Rumynin D., Hristova K., Capdeboscq I., Sbornik Mathematics 2020 Vol. 211 No. 8 P. 1065–1079
We initiate an investigation of lattices in a new class of locally compact groups: so-called locally pro-p-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild assumptions, a cocompact lattice in this completion contains no elements of order p. This statement is still an open question for the Caprace-Rémy-Ronan completion. Using this, ...
Added: September 7, 2021
Springer, 2021.
This book constitutes the proceedings of the 16th International Conference on Formal Concept Analysis, ICFCA 2021, held in Strasbourg, France, in June/July 2021.
The 14 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 32 submissions. The book also contains four invited contributions in full paper length.
The research part ...
Added: July 10, 2021
Zhuk D., Journal of Multiple-Valued Logic and Soft Computing 2015 Vol. 24 No. 1-4 P. 251–316
The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, ...
Added: June 15, 2020
Popov V. L., Zarhin Y. G., / Series math "arxiv.org". 2020.
We explore whether a root lattice may be similar to the lattice $\mathscr O$ of integers of a number field $K$ endowed with the inner product $(x, y):={\rm Trace}_{K/\mathbb Q}(x\cdot\theta(y))$, where $\theta$ is an involution of $K$. We classify all pairs $K$, $\theta$ such that $\mathscr O$ is similar to either an even root lattice ...
Added: February 14, 2020
Rybakin A. S., Кулонен Г. А., СПб.: ВКАС им. Буденного, 1999.
Added: February 10, 2013