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| ====Tentative list of publications: | ====Tentative list of publications: | ||
| - | - Characteristic sequences of non-associative algebras (with D.K. Kudryavtsev) | + | The most recent list of publications is available at [[http:// |
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| + | - Non-surjective linear transformations of tropical matrices preserving the cyclicity index (with E. Kreines, A. Vlasov) Kybernetika, | ||
| + | - Pairs of maps preserving singularity on subsets of matrix algebras (with | ||
| + | - On the lengths of group algebras of finite abelian groups in the semi-simple case (with M.~Khrystik, | ||
| + | - On the lengths of group algebras of finite abelian groups in the modular case (with M.A.~Khrystik, | ||
| + | - On the lengths of standard composition algebras (with S.A. Zhilina) | ||
| + | - Linear functions preserving Green' | ||
| + | - Transformations of assembly number for 4-regular graphs (with E.M. Kreines, N.V. Ostroukhova) | ||
| + | - Linear converters of weak, directional and strong majorizations (with P. Shteyner) | ||
| + | - Length function and characteristic sequences of quadratic algebras (with D.K. Kudryavtsev) | ||
| + | - Integrability of diagonalizable matrices and a dual Schoenberg type inequality (with S. Danielyan, | ||
| + | - Converting immanants on skew-symmetric matrices (with M.A. Duffner, | ||
| + | - Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces (with L. Arambašić, | ||
| + | - Operators preserving mutual strong Birkhoff-James orthogonality on B(H) (with L. Arambašić, | ||
| + | - Upper bounds on scrambling index for non-primitive digraphs (with A.M. Maksaev) | ||
| + | - Linear transformations of tropical matrices preserving the cyclicity index (with E. Kreines, | ||
| + | - Linear immanant converters on skew-symmetric matrices of order 4 (with M.A. Duffner, I.A. Spiridonov) Journal of Mathematical Sciences, 2021, 255:3, 242–253 | ||
| + | - Relation graphs of the sedenion algebra (with S.A. Zhilina) Journal of Mathematical Sciences, 2021, 255:3, 254–270 | ||
| + | - Orthograph related to mutual strong Birkhof-James orthogonality in $C^*$-algebras (with L. Arambašić, | ||
| + | - The length of the group algebra of the group $Q_8$ (with O.V. Markova) New Trends in Algebras and Combinatorics. World Scientific Publ, 2020, 105-133, doi: 10.1142/ | ||
| + | - Higher-distance commuting varieties (with M. Elyze, R. Morrison, K. \v{S}ivic) Linear and Multilinear Algebra, 2020, doi: 10.1080/ | ||
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| - Majorization for (0, | - Majorization for (0, | ||
| - Orthogonality for (0,-1) tropical normal matrices (with B. Bakhadly and M. J. de la Puente) | - Orthogonality for (0,-1) tropical normal matrices (with B. Bakhadly and M. J. de la Puente) | ||
| - Permanent Polya problem for additive surjective maps (with I.A. Spiridonov) Linear Algebra and Its Applications, | - Permanent Polya problem for additive surjective maps (with I.A. Spiridonov) Linear Algebra and Its Applications, | ||
| - Upper bounds for the length of non-associative algebras (with D.K. Kudryavtsev) Journal of Algebra, 544, 2020, 483-497 | - Upper bounds for the length of non-associative algebras (with D.K. Kudryavtsev) Journal of Algebra, 544, 2020, 483-497 | ||
| - | - Linear transformtions preserving majorizations for matrix tuples (with P. Shteyner) Vestnik St.Petersburg University, Mathematics, | + | - Linear transformtions preserving majorizations for matrix tuples (with P. Shteyner) Vestnik St.Petersburg University, Mathematics, |
| - 2-words, their graphs and matrices (with E.M. Kreines and N.V. Ostroukhova) Zapiski Nauch. Sem. POMI, 482, 2019, 45-72 | - 2-words, their graphs and matrices (with E.M. Kreines and N.V. Ostroukhova) Zapiski Nauch. Sem. POMI, 482, 2019, 45-72 | ||
| - Graph characterization of fully indecomposable nonconvertible (0, | - Graph characterization of fully indecomposable nonconvertible (0, | ||
| - Krauter conjecture on permanents is true (with M.V. Budrevich) Journal of Combinatorial Theory - Series A, 162, 2019, 306-343 | - Krauter conjecture on permanents is true (with M.V. Budrevich) Journal of Combinatorial Theory - Series A, 162, 2019, 306-343 | ||
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| - | | + | - More on geometry of Krein space C-numerical range (with R. Lemos and G. Soares) Applied Mathematics and Computation, |
| - | + | - Double centralizing theorem with respect to q-commutativity relation (with Gregor Dolinar, Bojan Kuzma, Olga Markova) Journal of Algebra and its Applications, | |
| - | - More on geometry of Krein space C-numerical range (with R. Lemos and G. Soares) | + | - Additive maps preserving scrambling index are bijective (with A.M. Maksaev) Acta Mathematica Hungarica, 84(1-2), 2018, 19-38 |
| - | + | - Majorization for matrix classes (with Geir Dahl and Pavel Shteyner) Linear Algebra and Its Applications, | |
| - | | + | - Extremal generalized centralizers in matrix algebras (with G. Dolinar, B. Kuzma, O. Markova) Communications in Algebra, 46(7), 2018, 3147-3154 |
| - | | + | - A resolution of Paz’s conjecture in the presence of a nonderogatory matrix (with T. Laffey, O. Markova, H. Smigoc) |
| - | | + | - On Hartwig–Nambooripad orders (with X. Mary, P. Shteyner) Semigroup Forum (2018). doi.org/ |
| - | | + | - Linear isomorphisms preserving Green’s relations for matrices over anti-negative semifields (with Marianne Johnson, Mark Kambites) Linear Algebra and Its Applications, |
| - | | + | - Monotone linear maps of matrices over semirings (with E.M. Kreines, Q.-W. Wang) Journal of Mathematical Sciences (New York), 233(5), 2018, 675-686 |
| - | | + | - Maps preserving scrambling index (with Maksaev A.M.) Linear and Multilinear Algebra, 69(4), 2018, 840-851 |
| - | | + | - Converting immanants on singular symmetric matrices (with Duffner A.) Lobachevskii Journal of Mathematics, |
| - | | + | - The lengths of the quaternion and octonion algebras (with Kudryavtsev D.K.) Journal of Mathematical Sciences (New York), 224(6), 2017, 826-833 |
| - | | + | - Preserving 0 and 1 values of the scrambling index (with Maksaev A.M.) Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics: |
| - | | + | - Lower bound for Polya problem on permanent (with Mikhail V. Budrevich, Gregor Dolinar, Bojan Kuzma) International Journal of Algebra and Computation, |
| - | | + | - Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, |
| - | | + | - Rank functions of tropical matrices (with Ya. Shitov) Linear Algebra and its Applications, |
| - | | + | - On the C-determinantal range for special classes of matrices (with R. Lemos and G. Soares) Applied Mathematics and Computation (New York), 275, 2016, 86-94. |
| - | | + | - The realizability problem for the values of the length function of quasi-commuting matrix pairs (with Markova O.V.) Journal of Mathematical Sciences (New York), 216(6), 2016, 761-769 |
| - | - 26. Rank functions of tropical matrices (with Ya. Shitov) | + | - Continuous monotone matrix maps for orders induced by the group inverse (with Efimov M.A.) Journal of Mathematical Inequalities, |
| - | | + | - Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, |
| - | | + | - New matrix partial order based on spectrally orthogonal matrix decomposition (with A. Herrero, N. Thome) Linear and Multilinear Algebra, 64(3), 2016, 362-374 |
| - | | + | - On the divisibility of permanents for (+/ |
| - | | + | - The arctic rank of a Boolean matrix (with Beasley L.B., Shitov Ya. N.) Journal of Algebra, 433, 2015, 168-182 |
| - | | + | - Maps on operators strongly preserving sharp order (with Efimov M.A.) Operators and Matrices, 9(3), 2015, 711-731 |
| - | | + | - Graphs Defined by Orthogonality (with B.R. Bakhadly, O.V. Markova) Journal of Mathematical Sciences (New York), 207(5), 2015, 698-717 |
| - | | + | - Characterizing monotone maps on matrices and operators, Classical and Functional |
| - | | + | - Immanant conversion on symmetric matrices (with C. Purificacao, A. Duffner) Special Matrices, 2(1), 2014, 1-10. |
| - | | + | - On the Polya conversion problem for permanents and determinants, Journal of Mathematical Sciences, 187(6), 2014, 782-786 |
| - | | + | - Monotone maps on diagonalizable matrices (with M.A. Efimov), Mathematical Inequalities and Applications, |
| - | | + | - Tropical Cramer determinants revisited (with M. Akian, S. Gaubert) American Mathematical Society, Contemporary Mathematics, |
| - | - - Guterman A. E., On the Polya conversion problem for permanents and determinants | + | - The algebra of semi-magic matrices and its length (with O.V. Markova, S.D. Sochnev) Zapiski POMI, 419, 2013, 52-77. |
| - | | + | - Commuting graphs and extremal centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Ars Mathematica Contemporanea, |
| - | | + | - Commutativity preservers via matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Publicationes Mathematicae Debrecen, 84(3-4) (2014), 439-450 |
| - | | + | - Extremal matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Linear Algebra and its Applications, |
| - | | + | - Extremal case in Marcus-Oliveira conjecture and beyond (with R. Lemos, and G. Soares) Linear and Multilinear Algebra, 61(9), 2013, 1206-1222 |
| - | | + | - Permanent versus determinant over a finite field (with G. Dolinar, B. Kuzma, M. Orel) Journal of Mathematical Sciences (New-York), 193(3), 2013, 404-412 |
| - | | + | - Monotone maps on index one matrices (with M.A. Efimov), Zapiski POMI, 405, 2012, 67-96. |
| - | | + | - On the Gibson bounds over finite fields (with M.V. Budrevich), Serdica Math. J. 2012, 38, 395-416 |
| - | | + | - Automorphisms of B(H) with respect to the left-star and the right-star partial order (with G. Dolinar and J. Marovt) Mathematical Inequalities and Applications, |
| - | | + | - Students Olympiads in Algebra at the Department of Mathematics and Mechanics, MSU (with I.V. Arzhantsev, V.V. Batyrev, E.I. Bunina, E.S. Golod, M.V. Zaicev, A.I. Zobnin, A.A. Klyachko, V.T. Markov, A.A. Nechaev, A.Yu. Olshanskii, E.A. Porshnev, Yu.G. Prokhorov), Moscow, MCCME, 2012, pp. 72. |
| - | | + | - Permanent has less zeros than determinant over finite fields (with M. Budrevich) American Mathematical Society, Contemporary Mathematics, |
| - | - 395-416 | + | - On the Polya permanent problem over finite fields (with G. Dolinar, B. Kuzma, M. Orel) European Journal of Combinatorics, |
| - | | + | - On Gibson barrier for Polya problem (with G. Dolinar, B. Kuzma), |
| - | - Dolinar and J. Marovt), Mathematical Inequalities and Applications, | + | - Operators preserving primitivity for matrix pairs (with L.B. Beasley), Matrix Methods: Theory, Algorithms, Applications, |
| - | | + | - Additive Frobenius endomorphisms for Sylvester and related bounds (with Graca Soares), Contributions to General Algebra, Verlag Johannes Heyn, 19, 2010, 91-102 |
| - | - (with I.V. Arzhantsev, V.V. Batyrev, E.I. Bunina, E.S. Golod, M.V. Zaicev, A.I. Zobnin, A.A. Klyachko, V.T. Markov, A.A. Nechaev, A.Yu. Olshanskii, E.A. Porshnev, Yu.G. | + | - The correspondence between tropical convexity and mean payoff games (with Marianne Akian, Stephane Gaubert), Mathematical Theory of Networks and Systems, 2010, 1295-1302 |
| - | - Prokhorov), Moscow, MCCME, 2012, pp. 72. | + | - On the independence numbers of distance graphs with vertices at $\{-1, |
| - | | + | - Frobenius endomorphisms of matrix spaces and their applications, |
| - | - Mathematical Society, Contemporary Mathematics, | + | - On the independence numbers of distance graphs with vertices at $\{-1, |
| - | | + | - Frobenius Endomorphisms on matrix spaces |
| - | | + | - Matrix ranks and linear independence over tropical semirings (with M. Akian, S. Gaubert), American Mathematical Society, Contemporary Mathematics, |
| - | | + | - Preserving zeros of a polynomial (with B. Kuzma), Communications in Algebra, 37(11), 2009, 3801-3827. |
| - | | + | - Matrix invariants over semirings, Handbook of Algebra, Elseiver, 6, 2009, 3-33. |
| - | | + | - The characterization of operators preserving primitivity for matrix k-tuples (with L. B. Beasley), Linear Algebra and its Applications, |
| - | | + | - Commutative matrix subalgebras and length function (with O. V. Markova), Linear Algebra and its Applications, |
| - | | + | - Maps preserving zeros of matrix polynomials (with B. Kuzma), Doklady of Russian Academy of Sciences, Mathematics, |
| - | | + | - Preserving regular tournaments and term rank-1 (with L.B. Beasley, D. Brown), Linear Algebra and its Applications, |
| - | | + | - Operators preserving primitivity for matrix pairs (with L. B. Beasley), Matrix Methods: Theory, Algorithms, Applications, |
| - | | + | - On linear operators preserving the set of positive polynomials (with B. Shapiro), Journal of Fixed Point Theory and Applications, |
| - | | + | - Characterization of transformations strongly preserving zeros of matrix polynomials (with B. Kuzma), Uspehi Mat. Nauk, 63(5), 2008, 184-185. [in |
| - | | + | - Rank and determinant functions for semirings, London Mathematical Society Lecture Notes, 347, 2007, 1-33. |
| - | | + | - Transformations preserving matrix invariants over semirings, Idempotent and tropical mathematics and problems of mathematical physics, Moscow, MCCME, 1, 2007, 84-90 |
| - | | + | - Monotone additive transformations on matrices, Mat. Zametki, 81(5), 2007, 681–692. |
| - | | + | - Monotone matrix mappings defined by the group inverse and simultaneous diagonalizability (with I. I. Bogdanov), Mat. Sbornik, 198(1), 2007, 3-20. |
| - | | + | - Idempotent matrices and majorisation (with L. B. Beasley, K.-T. Kang, S.-Z. Song), Fundamental and Applied Mathematics, |
| - | | + | - Frobenius and Dieudonne theorems over semirings (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear and Multilinear Algebra, 55(1), 2007, 19-34 |
| - | | + | - Linear preservers of extremes of rank inequalities over semirings: the row and column ranks (with L. B. Beasley, Y.-B. Jun, S.-Z. Song), Linear Algebra Appl., 413, 2006, 495-509 |
| - | | + | - Rank-permutable additive mappings (with A. A. Alieva, B. Kuzma), Linear Algebra Appl., 414, 2006, 607-616 |
| - | | + | - Linear preservers for Sylvester and Frobenius bounds on matrix rank (with L. B. Beasley, C. L. Neal), Rocky Mountain Journal of Mathematics, |
| - | | + | - Linear preservers of zeros of matrix polynomials (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear Algebra and its Applications, |
| - | | + | - Monotone linear transformations on matrices are invertible (with A. A. Alieva), Communications in Algebra, 33, 2005, 3335-3352 |
| - | | + | - Rank inequalities over semirings (with L. B. Beasley), Journal of Korean Math. Soc., 42(2), 2005, 223-241 |
| - | | + | - Factor rank for nonnegative matrices (with O. A. Vaysman), Chebyshevskii Sbornik, 6(4), 2005, 64-67 [in Russian] |
| - | | + | - Linear preservers of extremes of rank inequalities over semirings: term rank and zero-term rank (with L. B. Beasley and S.-C. Yi), Fundamental and Applied Mathematics, |
| - | | + | - Linear preservers of rank permutability (with A. A. Alieva), Linear Algebra and its Applications, |
| - | | + | - Linear Transformations Preserving the Grassmannian over M_n(Z+) (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear Algebra and its Applications, |
| - | | + | - Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Mathematics. Mechanics. Informatics. 10 years RFFI. Fizmatlit, 2004, 501(3), |
| - | | + | - LP-problems for rank inequalities over semirings: factorization rank (with L.B. Beasley), Sovrem. Mat. Prilozh. |
| - | | + | - Rank permutability and additive operators preserving some rank product conditions (with A. A. Alieva), Fundamental and Applied Mathematics, |
| - | | + | - Linear transformations preserving rank-commutativity (with A. A. Alieva), Bull. of the Moscow State University. Ser. 1. Mathematics. Mechanics, 6, 2003, 11-17 [in Russian] |
| - | | + | - Transformations of non-negative integer matrices preserving the determinant, |
| - | | + | - Monotone Matrix Maps Preserve Non-Maximal Rank, Lecture Notes in Pure and Applied Mathematics, |
| - | | + | - General Algebra and Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Fundamental and Applied Mathematics, |
| - | | + | - Linear transformations that preserve the Dieudonne determinant over an arbitrary division ring, Uspehi Mat. Nauk, 57(4), 2002, 171-172 [in Russian] |
| - | | + | - Identities of near-triangular matrices, Matem. Sbornik, 192(6), 2001, 3-15 |
| - | | + | - Linear preservers for matrix inequalities and partial orderings, Linear Algebra and its Applications, |
| - | | + | - Frobenius type theorems in the noncommutative case, Linear and Multilinear Algebra, 48(4), 2001, 293-312 |
| - | | + | - Linear preservers for Drazin star partial order, Communications in Algebra, 29(9), 2001, 3905-3917 |
| - | | + | - Linear transformations, |
| - | | + | - Graded local rings, Fundamental and Applied Mathematics, |
| - | | + | - Some general techniques on Linear Preserver Problems (with C.-K. Li, P. Semrl), Linear Algebra and Applications, |
| - | | + | - Singularity preservers over local domains, Journal of Mathematical Sciences, 102(6), 2000, 4591-4597. |
| - | | + | - On the Growth of Identities (with A.Regev), Algebra. Berlin, New York: Walter de Gruyter, 2000, 319-331 |
| - | | + | - On determinant preservers over noncommutative Principal Ideal Domains (with A. V. Mikhalev), Lie Algebras, Rings, and Related Topics, Hong Kong: Springer-Verlag, |
| - | | + | - Ph. Hall type theorems for modules (with E. Kreines), Universal Algebra and its Applications, |
| - | | + | - A note on linear preservers of a certain matrix partial order, Formal Power Series and Algebraic Combinatorics, |
| - | | + | - On the applications of Model Theory for the classifications of linear transformations preserving matrix invariants, Mathematical Methods and Applications, |
| - | | + | - P. Hall’s theorem on transversals for modules (with E. Kreines), Fundamental and Applied Mathematics, |
| - | | + | - Identities and codimensions of a certain subalgebra of triangular matrix algebra, Mathematical Methods and Applications, |
| - | | + | - Linear transformations preserving Adjamagbo determinant, |
| - | | + | - Frobenius type results for matrices over the skew-fields (with E. M. Kreines, A. V. Mikhalev), Mathematical Methods and Applications, |
| - | | + | - Frobenius type theorems (with A. V. Mikhalev), Proceedings of Workshop on General Algebra and Discrete Mathematics, |
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