Batle, J.; Shutov, A. V.; Maleev, A. V. Dipole-dipole minimum energy configuration for platonic, Archimedean and Catalan solid structures. (English) Zbl 1448.78019 Phys. Lett., A 384, No. 36, Article ID 126916, 32 p. (2020). MSC: 78A30 74F15 52B10 PDF BibTeX XML Cite \textit{J. Batle} et al., Phys. Lett., A 384, No. 36, Article ID 126916, 32 p. (2020; Zbl 1448.78019) Full Text: DOI
Shutov, Anton Vladimirovich Generalized Rauzy tilings and bounded remainder sets. (Russian. English summary) Zbl 1439.52020 Chebyshevskiĭ Sb. 20, No. 3(71), 372-389 (2019). MSC: 52C20 05B45 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 20, No. 3(71), 372--389 (2019; Zbl 1439.52020) Full Text: DOI MNR
Zhukova, Alla Adol’fovna; Shutov, Anton Vladimirovich \(n\)-crowns in toric tilings into bounded remander sets. (Russian. English summary) Zbl 1441.37022 Chebyshevskiĭ Sb. 20, No. 3(71), 246-260 (2019). MSC: 37B52 37B10 PDF BibTeX XML Cite \textit{A. A. Zhukova} and \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 20, No. 3(71), 246--260 (2019; Zbl 1441.37022) Full Text: DOI MNR
Shutov, Anton; Maleev, Andrey Coordination numbers of the vertex graph of a Penrose tiling. (English) Zbl 1444.82038 Acta Crystallogr., Sect. A 74, No. 2, 112-122 (2018). MSC: 82D25 52C22 PDF BibTeX XML Cite \textit{A. Shutov} and \textit{A. Maleev}, Acta Crystallogr., Sect. A 74, No. 2, 112--122 (2018; Zbl 1444.82038) Full Text: DOI
Shutov, Anton Vladimirovich Substitutions and bounded remainder sets. (Russian. English summary) Zbl 1445.11076 Chebyshevskiĭ Sb. 19, No. 2(66), 501-522 (2018). Reviewer: Symon Serbenyuk (Kyiv) MSC: 11K06 11K38 11K55 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 19, No. 2(66), 501--522 (2018; Zbl 1445.11076) Full Text: DOI MNR
Shutov, A. V. Nonautonomous bounded remainder sets. (English. Russian original) Zbl 07043869 Russ. Math. 62, No. 12, 81-87 (2018); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 12, 94-101 (2018). MSC: 11K06 11K38 11K55 PDF BibTeX XML Cite \textit{A. V. Shutov}, Russ. Math. 62, No. 12, 81--87 (2018; Zbl 07043869); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 12, 94--101 (2018) Full Text: DOI
Zhukova, A. A.; Shutov, A. V. Geometrization of numeration systems. (Russian. English summary) Zbl 07197290 Chebyshevskiĭ Sb. 18, No. 4(64), 222-245 (2017). MSC: 11B PDF BibTeX XML Cite \textit{A. A. Zhukova} and \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 18, No. 4(64), 222--245 (2017; Zbl 07197290) Full Text: DOI MNR
Shutov, A. V.; Zhuravlev, V. G.; Balci, A. S.; Khripunova, M. B. Boris Veniaminovich Levin. On his 90th anniversary. (Russian. English summary) Zbl 1437.01037 Chebyshevskiĭ Sb. 18, No. 2(62), 315-330 (2017). MSC: 01A70 PDF BibTeX XML Cite \textit{A. V. Shutov} et al., Chebyshevskiĭ Sb. 18, No. 2(62), 315--330 (2017; Zbl 1437.01037) Full Text: DOI MNR
Shutov, A. V.; Kolomeikina, E. V. On a number of polyhex plane tilings. (Russian. English summary) Zbl 1395.52024 Dal’nevost. Mat. Zh. 17, No. 2, 257-265 (2017). Reviewer: Elizaveta Zamorzaeva (Chişinău) MSC: 52C20 52C05 PDF BibTeX XML Cite \textit{A. V. Shutov} and \textit{E. V. Kolomeikina}, Dal'nevost. Mat. Zh. 17, No. 2, 257--265 (2017; Zbl 1395.52024) Full Text: MNR
Shutov, A. V. Local discrepancies in the problem of fractional parts distribution of a linear function. (English. Russian original) Zbl 1418.11113 Russ. Math. 61, No. 2, 74-82 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2017, No. 2, 88-97 (2017). MSC: 11K38 11K06 11K31 PDF BibTeX XML Cite \textit{A. V. Shutov}, Russ. Math. 61, No. 2, 74--82 (2017; Zbl 1418.11113); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2017, No. 2, 88--97 (2017) Full Text: DOI
Shutov, A. V. Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split. (English) Zbl 1436.74074 Comput. Methods Appl. Mech. Eng. 306, 151-174 (2016). MSC: 74S05 74C20 65M60 PDF BibTeX XML Cite \textit{A. V. Shutov}, Comput. Methods Appl. Mech. Eng. 306, 151--174 (2016; Zbl 1436.74074) Full Text: DOI
Zhukova, A. A.; Shutov, A. V. On the distribution function of the remainder term on bounded remainder sets. (Russian. English summary) Zbl 1440.11128 Chebyshevskiĭ Sb. 17, No. 1(57), 90-107 (2016). MSC: 11J71 37A44 PDF BibTeX XML Cite \textit{A. A. Zhukova} and \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 17, No. 1(57), 90--107 (2016; Zbl 1440.11128) Full Text: MNR
Shutov, A. V.; Kolomeĭkina, E. V. The estimation of the number of \(p2\)-tilings of a plane on a polyomino of given area. (Russian. English summary) Zbl 1436.52019 Chebyshevskiĭ Sb. 17, No. 3(59), 204-214 (2016). MSC: 52C20 PDF BibTeX XML Cite \textit{A. V. Shutov} and \textit{E. V. Kolomeĭkina}, Chebyshevskiĭ Sb. 17, No. 3(59), 204--214 (2016; Zbl 1436.52019) Full Text: MNR
Davlet’yarova, E. P.; Zhukova, A. A.; Shutov, A. V. Geometrization of the generalized Fibonacci numeration system with applications to number theory. (Russian. English summary) Zbl 1428.11022 Chebyshevskiĭ Sb. 17, No. 2(58), 88-112 (2016). MSC: 11A67 11B39 PDF BibTeX XML Cite \textit{E. P. Davlet'yarova} et al., Chebyshevskiĭ Sb. 17, No. 2(58), 88--112 (2016; Zbl 1428.11022) Full Text: DOI MNR
Shutov, A. V. Trigonometric integrals over one-dimensional quasilattices of arbitrary codimension. (English. Russian original) Zbl 1359.11071 Math. Notes 99, No. 4, 590-597 (2016); translation from Mat. Zametki 99, No. 4, 603-612 (2016). Reviewer: Tonko Tonkov (Sofia) MSC: 11L03 11H31 PDF BibTeX XML Cite \textit{A. V. Shutov}, Math. Notes 99, No. 4, 590--597 (2016; Zbl 1359.11071); translation from Mat. Zametki 99, No. 4, 603--612 (2016) Full Text: DOI
Zhukova, A. A.; Shutov, A. V. Binary additive problem with numbers of special type. (Russian. English summary) Zbl 1437.11027 Chebyshevskiĭ Sb. 16, No. 3(55), 246-275 (2015). MSC: 11B39 11H06 11P32 11K38 PDF BibTeX XML Cite \textit{A. A. Zhukova} and \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 16, No. 3(55), 246--275 (2015; Zbl 1437.11027) Full Text: MNR
Kuznetsova, D. V.; Shutov, A. V. Exchanged toric tilings, Rauzy substitution, and bounded remainder sets. (English. Russian original) Zbl 1387.11052 Math. Notes 98, No. 6, 932-948 (2015); translation from Mat. Zametki 98, No. 6, 878-897 (2015). MSC: 11J71 11H06 37B10 37B50 PDF BibTeX XML Cite \textit{D. V. Kuznetsova} and \textit{A. V. Shutov}, Math. Notes 98, No. 6, 932--948 (2015; Zbl 1387.11052); translation from Mat. Zametki 98, No. 6, 878--897 (2015) Full Text: DOI
Shutov, A. V. Trigonometric sums over one-dimensional quasilattices of arbitrary codimension. (English. Russian original) Zbl 1331.11062 Math. Notes 97, No. 5, 791-802 (2015); translation from Mat. Zametki 97, No. 5, 781-793 (2015). Reviewer: Tonko Tonkov (Sofia) MSC: 11L03 PDF BibTeX XML Cite \textit{A. V. Shutov}, Math. Notes 97, No. 5, 791--802 (2015; Zbl 1331.11062); translation from Mat. Zametki 97, No. 5, 781--793 (2015) Full Text: DOI
Shutov, A. V. Farey fractions and permutations generated by fractional parts \(\{i\alpha\}\). (English) Zbl 1434.11050 Chebyshevskiĭ Sb. 15, No. 1(49), 195-203 (2014). MSC: 11B57 05A05 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 15, No. 1(49), 195--203 (2014; Zbl 1434.11050) Full Text: MNR
Davlet’yarova, E. P.; Zhukova, A. A.; Shutov, A. V. Geometrization of the Fibonacci numeration system, with applications to number theory. (English. Russian original) Zbl 1369.11013 St. Petersbg. Math. J. 25, No. 6, 893-907 (2014); translation from Algebra Anal. 25, No. 6, 1-23 (2013). MSC: 11B39 11A67 PDF BibTeX XML Cite \textit{E. P. Davlet'yarova} et al., St. Petersbg. Math. J. 25, No. 6, 893--907 (2014; Zbl 1369.11013); translation from Algebra Anal. 25, No. 6, 1--23 (2013) Full Text: DOI
Kuznetsova, D. V.; Shutov, A. V. On the first return times for toric rotations. (Russian. English summary) Zbl 1425.37008 Chebyshevskiĭ Sb. 14, No. 4(48), 127-130 (2013). MSC: 37A50 PDF BibTeX XML Cite \textit{D. V. Kuznetsova} and \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 14, No. 4(48), 127--130 (2013; Zbl 1425.37008) Full Text: DOI MNR
Shutov, A. V. On the speed of attainment of the remainder term exact boundaries in the Hecke-Kesten problem. (Russian. English summary) Zbl 1430.11095 Chebyshevskiĭ Sb. 14, No. 2(46), 173-179 (2013). MSC: 11J71 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 14, No. 2(46), 173--179 (2013; Zbl 1430.11095) Full Text: MNR
Shutov, A. V. Multidimensional generalization of sums of fractional parts and their number-theoretic applications. (Russian. English summary) Zbl 1434.11148 Chebyshevskiĭ Sb. 14, No. 1(45), 104-118 (2013). MSC: 11K31 11K38 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 14, No. 1(45), 104--118 (2013; Zbl 1434.11148) Full Text: DOI MNR
Shutov, A. V. Trigonometric sums over one-dimensional quasilattices. (Russian) Zbl 1311.11077 Chebyshevskiĭ Sb. 13, No. 2(42), 136-148 (2012). MSC: 11L03 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 13, No. 2(42), 136--148 (2012; Zbl 1311.11077) Full Text: MNR
Shutov, A. V. Inhomogeneous diophantine approximations and distribution of fractional parts. (English. Russian original) Zbl 1296.11094 J. Math. Sci., New York 182, No. 4, 576-585 (2012); translation from Fundam. Prikl. Mat. 16, No. 6, 189-202 (2010). Reviewer: Oto Strauch (Bratislava) MSC: 11K38 11K31 PDF BibTeX XML Cite \textit{A. V. Shutov}, J. Math. Sci., New York 182, No. 4, 576--585 (2012; Zbl 1296.11094); translation from Fundam. Prikl. Mat. 16, No. 6, 189--202 (2010) Full Text: DOI
Krasil’shchikov, V. V.; Shutov, A. V. Distribution of points of one-dimensional quasilattices with respect to a variable module. (English. Russian original) Zbl 1347.11017 Russ. Math. 56, No. 3, 14-19 (2012); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 3, 17-23 (2012). MSC: 11B39 11B83 05B45 PDF BibTeX XML Cite \textit{V. V. Krasil'shchikov} and \textit{A. V. Shutov}, Russ. Math. 56, No. 3, 14--19 (2012; Zbl 1347.11017); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 3, 17--23 (2012) Full Text: DOI
Shutov, A. V. On a family of two-dimensional bounded remainder sets. (Russian) Zbl 1302.11048 Chebyshevskiĭ Sb. 12, No. 4(40), 264-271 (2011). Reviewer: Dmitriy Frolenkov (Moscow) MSC: 11J71 11H06 11K06 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 12, No. 4(40), 264--271 (2011; Zbl 1302.11048) Full Text: MNR
Shutov, A. V. The two-dimensional Hecke-Kesten problem. (Russian) Zbl 1306.11055 Chebyshevskiĭ Sb. 12, No. 2(38), 151-162 (2011). Reviewer: Dmitriy Frolenkov (Moscow) MSC: 11J71 11H06 11K06 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 12, No. 2(38), 151--162 (2011; Zbl 1306.11055) Full Text: MNR
Shutov, A. V. The Hecke-Kesten problem for some integrals. (Russian) Zbl 1302.11047 Chebyshevskiĭ Sb. 12, No. 1(37), 172-177 (2011). Reviewer: Dmitriy Frolenkov (Moscow) MSC: 11J71 11K38 11K31 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 12, No. 1(37), 172--177 (2011; Zbl 1302.11047) Full Text: MNR
Krasil’shchikov, V. V.; Shutov, A. V. Description and exact maximum and minimum values of the remainder in the problem of the distribution of fractional parts. (English. Russian original) Zbl 1303.11078 Math. Notes 89, No. 1, 59-67 (2011); translation from Mat. Zametki 89, No. 1, 43-52 (2011). Reviewer: Dmitriy Frolenkov (Moscow) MSC: 11J71 11K38 11K31 PDF BibTeX XML Cite \textit{V. V. Krasil'shchikov} and \textit{A. V. Shutov}, Math. Notes 89, No. 1, 59--67 (2011; Zbl 1303.11078); translation from Mat. Zametki 89, No. 1, 43--52 (2011) Full Text: DOI
Shutov, A. V. On the sum of the fractional parts \(\sum_{n\leq x}\{ne\}\). (Russian. English summary) Zbl 1295.11079 Chebyshevskiĭ Sb. 11, No. 1(33), 263-265 (2010). Reviewer: Artūras Dubickas (Vilnius) MSC: 11J54 11K31 11K38 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 11, No. 1(33), 263--265 (2010; Zbl 1295.11079) Full Text: MNR
Shutov, A. V. The arithmetic and geometry of one-dimensional quasilattices. (Russian. English summary) Zbl 1290.11103 Chebyshevskiĭ Sb. 11, No. 1(33), 255-262 (2010). MSC: 11H06 11D04 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 11, No. 1(33), 255--262 (2010; Zbl 1290.11103) Full Text: MNR
Krasil’shchikov, V. V.; Shutov, A. V.; Zhuravlev, V. G. One-dimensional quasiperiodic tilings admitting progressions enclosure. (English. Russian original) Zbl 1195.11084 Russ. Math. 53, No. 7, 1-6 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 7, 3-9 (2009). Reviewer: Michael Baake (Bielefeld) MSC: 11H06 PDF BibTeX XML Cite \textit{V. V. Krasil'shchikov} et al., Russ. Math. 53, No. 7, 1--6 (2009; Zbl 1195.11084); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 7, 3--9 (2009) Full Text: DOI
Shutov, A. V.; Maleev, A. V. Quasiperiodic plane tilings based on stepped surfaces. (English) Zbl 1370.52066 Acta Crystallogr., Sect. A 64, No. 3, 376-382 (2008). MSC: 52C23 PDF BibTeX XML Cite \textit{A. V. Shutov} and \textit{A. V. Maleev}, Acta Crystallogr., Sect. A 64, No. 3, 376--382 (2008; Zbl 1370.52066) Full Text: DOI
Shutov, A. V. Sturm sequences: Rauzy graphs and forcing. (Russian) Zbl 1236.11028 Chebyshevskiĭ Sb. 8, No. 2(22), 128-139 (2007). Reviewer: Alexander Zvonkin (MR 2641009) MSC: 11B85 37B10 05A05 11A55 05C70 68R10 68R15 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 8, No. 2(22), 128--139 (2007; Zbl 1236.11028)
Shutov, A. V. New estimates in the Hecke-Kesten problem. (English) Zbl 1165.11062 Laurinčikas, A. (ed.) et al., Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25–29, 2006. Vilnius: TEV (ISBN 978-9955-680-81-9/hbk). 190-203 (2007). Reviewer: Zhu Yaochen (Beijing) MSC: 11K38 11K31 37B50 PDF BibTeX XML Cite \textit{A. V. Shutov}, in: Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25--29, 2006. Vilnius: TEV. 190--203 (2007; Zbl 1165.11062)
Shutov, A. V. Number systems and bounded remainder sets. (Russian) Zbl 1241.11091 Chebyshevskiĭ Sb. 7, No. 3(19), 110-128 (2006). Reviewer: Olaf Ninnemann (Berlin) MSC: 11K38 11K31 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 7, No. 3(19), 110--128 (2006; Zbl 1241.11091)
Shutov, A. V. On sums of fractional parts. (Russian) Zbl 1241.11073 Chebyshevskiĭ Sb. 7, No. 1(17), 278-285 (2006). MSC: 11J54 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 7, No. 1(17), 278--285 (2006; Zbl 1241.11073)
Budarina, N. V.; Manuĭlov, N. N.; Shutov, A. V. N. M. Korobov and the theory of the distribution of fractional parts. (Russian) Zbl 1142.11300 Chebyshevskiĭ Sb. 6, No. 1(13), 82-83 (2005). MSC: 11-03 01A70 11J71 PDF BibTeX XML Cite \textit{N. V. Budarina} et al., Chebyshevskiĭ Sb. 6, No. 1(13), 82--83 (2005; Zbl 1142.11300)
Shutov, A. V. On the distribution of fractional parts. (Russian. English summary) Zbl 1144.11060 Chebyshevskiĭ Sb. 5, No. 3(11), 112-121 (2004). Reviewer: Zhu Yaochen (Beijing) MSC: 11K06 11J71 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 5, No. 3(11), 112--121 (2004; Zbl 1144.11060)
Shutov, A. V. The growth of 1-periodic graphs. (Russian) Zbl 1106.05089 Chebyshevskiĭ Sb. 4, No. 2(6), 109-121 (2003). Reviewer: Ljuben Mutafchiev (Sofia) MSC: 05C80 05C12 PDF BibTeX XML Cite \textit{A. V. Shutov}, Chebyshevskiĭ Sb. 4, No. 2(6), 109--121 (2003; Zbl 1106.05089)
Shutov, A. V. Growth of 1-periodic graphs. (English. Russian original) Zbl 1063.05116 J. Math. Sci., New York 122, No. 6, 3709-3714 (2004); translation from Zap. Nauchn. Semin. POMI 286, 215-226 (2002). MSC: 05C75 PDF BibTeX XML Cite \textit{A. V. Shutov}, J. Math. Sci., New York 122, No. 6, 3709--3714 (2002; Zbl 1063.05116); translation from Zap. Nauchn. Semin. POMI 286, 215--226 (2002) Full Text: DOI