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September 22, 2026
Personal Interest in Doctoral Thesis Topic Most Important for Confidence in Successful Defence
A researcher at HSE University analysed data on 1,539 doctoral students from 161 Russian universities to identify which features of a thesis topic are associated with academic success and engagement. The most important factor was found to be personal interest in the research topic, which was associated with almost all key aspects of doctoral programme experience—from engaging with the academic supervisor to research activity and confidence about successfully defending the thesis. The findings have been published in Higher Education.
September 21, 2026
Researchers Develop Methodology to Assess the Quality of Legal Representation in Criminal Proceedings
Having a good defence attorney in criminal proceedings can largely determine whether a defendant retains their freedom, health and good name. Researchers at HSE University propose a method for predicting an attorney’s performance based on the outcomes of their previous cases. The methodology takes into account the severity of the charges, the complexity of the cases, and the most likely outcome, drawing on judicial statistics.
September 21, 2026
Algebra, Geometry, and AI: Russian and Vietnamese Mathematicians Discuss Current Research
A delegation of scientists from Hanoi visited the HSE Faculty of Computer Science and then took part in a Russian-Vietnamese conference in St Petersburg. The events were part of the three-year project ‘Flexibility and Computational Methods.’ Over the course of the project, the researchers have prepared joint publications and obtained new mathematical results.

 

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Задачи на клетчатой бумаге

Математическое образование. 2006. № 4. С. 47–67.
Вавилов В. В., Ustinov A.

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 published in future issues of the journal.

Language: Russian
Text on another site
Keywords: решеткиlattice
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Целые точки в областях
Ustinov A., Потенциал 2008 № 9 С. 53–53
Added: October 12, 2025
Geometry and combinatoric of Minkowski–Voronoi 3-dimensional continued fractions
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
Окружности на решетках
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
Задачи на клетчатой бумаге (окончание)
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
Полуправильные многоугольники на решетках
Вавилов В. В., Ustinov A., Квант 2007 № 6 С. 13–15
The article is devoted to semiregular polygons on lattices. ...
Added: October 12, 2025
К теореме Вороного о цилиндрических минимумах трехмерных решеток
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
Минимальные системы векторов в трехмерных решетках и аналог теоремы Валена для трехмерных цепных дробей Минковского
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The article is devoted to the development of the theory of three-dimensional continued fractions. ...
Added: October 9, 2025
О распределении решений детерминантного уравнения
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
Трехмерные цепные дроби и суммы Клостермана
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
Action of a Graph Automorphism on the Space of Flows
Spiridonov I., Mathematical notes 2019 Vol. 106 No. 1-2 P. 146 – 150
Added: April 27, 2025
Полуправильные многоугольники на правильных паркетах
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
Избранные главы дискретной геометрии в курсе математики специализированных школ
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
Cocompact lattices in locally pro-p-complete rank-2 Kac-Moody groups
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
Formal Concept Analysis: 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021, Proceedings
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
The lattice of all clones of self-dual functions in three-valued logic
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
Root lattices in number fields
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
Алгебраические системы
Rybakin A. S., Кулонен Г. А., СПб.: ВКАС им. Буденного, 1999.
Added: February 10, 2013
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