Russian Academy of Sciences

Landau Institute for Theoretical Physics

Sergei V. Savchenko

Researcher

Ph. D.

Email:

Publications

    1. S.V. Savchenko, On the number of 8-cycles for two particular regular tournaments of order N with diametrically opposite local properties, arXiv:2403.07629, ADS: 2024arXiv240307629S, zbMath: arXiv:2403.07629.
    2. S.V. Savchenko, On 5-cycles and strong 5-subtournaments in a tournament of order n, Journal of Graph Theory (accepted); arXiv:2403.19555 , ADS: 2024arXiv240319555S, zbMath: arXiv:2403.19555.
    3. Sergey Savchenko, Moon-type theorems on circuits in strongly connected tournaments of order N and diameter D, arXiv:2311.13377, ADS: 2023arXiv231113377S, zbMath: arXiv:2311.13377.
    4. S.V. Savchenko, On (sub)stochastic and transient weightings of infinite strong digraphs, Linear Algebra and its Applications (accepted); arXiv:2311.13340, ADS: 2023arXiv231113340S, zbMath: arXiv:2311.13340.
    5. S.V. Savchenko, On the number of 7-cycles in regular n-tournaments, Discrete Mathematics, 340(2), 264-285 (2017), WoS: 000390076800032, Scopus: 2-s2.0-84993965581, ADS: -, RINTs: 28275455, MathSciNet: 3578823, zbMath: 1351.05098, EDN: XUTNYZ .
    6. S.V. Savchenko, On 5-cycles and 6-cycles in regular n-tournaments, J. Graph Theory, 83(1), 44-77 (2016), WoS: 000379955300004, Scopus: 2-s2.0-84978033473, RINTs: 27015515, MathSciNet: 3529947, zbMath: 1346.05098, EDN: WTERUR.
    7. S.V. Savchenko, Konechnye priblizheniya beskonechnykh neotritsatel’nykh matrits:termodinamicheskii formalizm, Seminar Ya. G. Sinaya, IPPI, Moskva, 10 sentyabrya 2013.
    8. S.V. Savchenko, Non-critical vertices and long circuits in strong tournaments of order n and diameter d, J. Graph Theory, 70(4), 361-383 (2012), WoS: 000306785700001, Scopus: 2-s2.0-84864474479, RINTs: 20483126, MathSciNet: 2957053, zbMath: 1247.05093, EDN: RGGAVJ.
    9. S.V. Savchenko, How the minimum number of cycles of length m in a strongly connected tournament of order n depends on the maximum distance between two vertices, Abstracts of Int. Conf. «Mathematics of Distances and Applications» (MDA 2012), July 02-05, 2012, Varna, Bulgaria. Ed. by M. Deza e.a. Sofia: ITHEA, 2012, p. 50.
    10. S.V. Savchenko, Dlinnye tsikly v sil’no svyaznykh turnirakh poryadka n i diametra d, Materialy XI Mezhdunarodnogo seminara «Diskretnaya matematika i ee prilozheniya», posvyashchennogo 80-letiyu so dnya rozhdeniya akademika O. B. Lupanova (Moskva, 18-23 iyunya 2012 g.). M.: MGU, s. 309-312 (2012).
    11. S. Savchenko, Strongly transient non-negative matrices, III Int. Conf. on Matrix Methods in Mathematics and Applications (MMMA-2011), Moscow, 22-25 June 2011. Book of Abstr., p. 16 (2011).
    12. S. Savchenko, The rate of convergence of the spectral radii of finite principal submatrices and the spectral properties of the original infinite irreducible matrix with non-negative entries, Pure and Applied Linear Algebra: The new Generation: 17th Conf. of the International Linear Algebra Society (ILAS2011), Braunschweig, Germany, August 22-26, 2011. Book of Abstr., p.167 (2011).
    13. S.V. Savchenko, On the number of non-critical vertices in strong tournaments of order N with minimum out-degree δ+ and in-degree δ−, Discrete Mathematics, 310(6-7), 1177-1183 (2010), WoS: 000274870500006, Scopus: 2-s2.0-73649110982, ADS: -, RINTs: 15320298, MathSciNet: 2579851, zbMath: 1236.05118.
    14. S.V. Savchenko, O chisle tsiklov dliny m, m, Materialy X Mezhdunarodnogo seminara «Diskretnaya matematika i ee prilozheniya» (Moskva, 1-6 fevralya 2010), M.: MGU, 2010, s. 328-330.
    15. D.S. Lyubshin, S.V. Savchenko, Cayley digraphs with normal adjacency matrices, Discrete Mathematics, 309(13), 4343-4348 (2009), WoS: 000266760400017, Scopus: 2-s2.0-67349166114, RINTs: 13608016, MathSciNet: 2519171, zbMath: 1179.05053, EDN: LLUKAH.
    16. S.V. Savchenko, Normal matrices and their principal submatrices of co-order one, Linear Algebra Appl., 419 (2-3), 556-568 (2006), WoS: 000242744000018, Scopus: 2-s2.0-33748907451, RINTs: 13512154, MathSciNet: 2277987, zbMath: 1115.15022, EDN: LJRVYH .
    17. S.V. Savchenko, O chisle nekriticheskikh vershin v sil’no svyaznykh orgrafakh, Matem. zametki, 79(5), 743-755 (2006) [S.V. Savchenko, On the number of noncritical vertices in strongly connected digraphs, Math. Notes, 79(5), 687-696 (2006)], WoS: 000238504700011, Scopus: 2-s2.0-33747846167, RINTs: 9198914, MathSciNet: 2249132, zbMath: 1133.05043, EDN: HTHUPV.
    18. S.V. Savchenko, On the change of the Jordan form under the transition from the adjacency matrix of a vertex-transitive digraph to its principal submatrix of co-order one, Linear Algebra Appl., 394, 225-235 (2005), WoS: 000225181600013, Scopus: 2-s2.0-7544246010, RINTs: 13486968, MathSciNet: 2100585, zbMath: 1066.15011, EDN: LJDNJJ.
    19. S.V. Savchenko, O razlozhenii v ryad Lorana determinanta matritsy skalyarnykh rezol’vent, Matem. sb., 196(5), 121-144 (2005) [S.V. Savchenko, Laurent expansion for the determinant of the matrix of scalar resolvents, Sb.: Math., 196(5), 743-764 (2005)], WoS: 000232539400005, Scopus: 2-s2.0-27444436580, ADS: 2005SbMat.196..743S, RINTs: 9135693, MathSciNet: 2154784, zbMath: 1087.15009, EDN: HRXVKB.
    20. S.V. Savchenko, Principal submatrices of co-order one with the biggest Perron root, Linear Algebra Appl., 389, 1-22 (2004), WoS: 000223567400001, Scopus: 2-s2.0-3943062885, RINTs: 13463079, MathSciNet: 2080391, zbMath: 1071.15010.
    21. S.V. Savchenko, Ob izmenenii spektral’nykh svoistv matritsy pri vozmushchenii dostatochno nizkogo ranga, Funkts. analiz i ego pril., 38(1), 85-88 (2004) [S.V. Savchenko, On the change in the spectral properties of a matrix under perturbations of sufficiently low rank, Funct. Anal. Appl., 38(1), 69-71 (2004)], WoS: 000221663700009, Scopus: 2-s2.0-3543118388, RINTs: 13446786, MathSciNet: 2061795, zbMath: 1092.15005, EDN: LIGQYT.
    22. S.V. Savchenko, On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices, Linear Algebra Appl., 361, 257-277 (2003), WoS: 000180417000022, Scopus: 2-s2.0-84867968295, RINTs: 20821722, MathSciNet: 1955565, zbMath: 1018.15019.
    23. S.V. Savchenko, O tipichnom izmenenii spektral’nykh svoistv pri vozmushchenii operatorom ranga odin, Matem. zametki, 74(4), 590-602 (2003) [S.V. Savchenko, Typical changes in spectral properties under perturbations by a rank-one operator, Math. Notes, 74(4), 557-568 (2003)], WoS: 000186455400030, Scopus: 2-s2.0-0346494622, RINTs: 13416967, MathSciNet: 2042972, zbMath: 1073.47021.
    24. N.Yu. Savchenko, S.V. Savchenko, A.V. Toporensky, Asymptotic states in brane cosmology with a nonlocal anisotropic stress, Class. Quantum Grav., 19(19), 4923-4931 (2002); gr-qc/0204071, WoS: 000178755400010, Scopus: 2-s2.0-0036387358, ADS: 2002CQGra..19.4923S, InSpire: 585674, RINTs: 13405010, MathSciNet: 1933312, zbMath: 1017.83040.
    25. S.V. Savchenko, O maksimal’nykh podorgrafakh s naibol’shim chislom Perrona, Uspekhi mat. nauk, 56:6(342), 165-166 (2001) [S.V. Savchenko, Maximal suborgraphs with the biggest Perron number, Russ. Math. Surv., 56(6), 1181-1182 (2001)], WoS: 000175108600017, Scopus: 2-s2.0-0035563474, ADS: 2001RuMaS..56.1181S, RINTs: -, MathSciNet: 1886736, zbMath: 1054.05069.
    26. S.V. Savchenko, O spektral’nykh svoistvakh nerazlozhimoi neotritsatel’noi matritsy i ee glavnykh podmatrits koporyadka odin, Uspekhi mat. nauk, 55:1(331), 191-192 (2000) [S.V. Savchenko, Spectral properties of an indecomposable non-negative matrix and its principal submatrices of co-order one, Russ. Math. Surv., 55(1), 184-185 (2000)], WoS: 000088114800013, Scopus: -, ADS: 2000RuMaS..55..184S, RINTs: -, MathSciNet: 1751830, zbMath: 0959.15021.
    27. A.Yu. Kamenshchik, I.M. Khalatnikov, S.V. Savchenko, A.V. Toporensky, Topological entropy for some isotropic cosmological models, Phys. Rev. D 59, 123516 (1999) [8 pages]; gr-qc/9809048, WoS: 000080779200025, Scopus: 2-s2.0-85037891249, ADS: 1999PhRvD..59l3516K, InSpire: 476385, RINTs: 41774506.
    28. S.V. Savchenko, O spektrakh svyaznykh grafov, Diskret. matem., 11(3), 29-47 (1999) [S.V. Savchenko, On the spectra of connected graphs, Discrete Math. Appl., 9(5), 503-522 (1999)], WoS: -, Scopus: 2-s2.0-29444457871, RINTs: -, MathSciNet: 1739067, zbMath: 0965.05070.
    29. S.V. Savchenko, Gomologicheskie neravenstva dlya konechnykh topologicheskikh tsepei Markova, Funkts. analiz i ego pril., 33(3), 91–93 (1999) [S.V. Savchenko, Cohomological inequalities for finite topological Markov chains, Funct. Anal. Appl., 33(3), 236-238 (1999)], WoS: 000084499000012, Scopus: 2-s2.0-22844456445, RINTs: 13305987, MathSciNet: 1724277, zbMath: 0995.37001.
    30. S.V. Savchenko, O veroyatnosti sushchestvovaniya lokalizovannogo osnovnogo sostoyaniya dlya diskretnogo uravneniya Shredingera so sluchainym potentsialom, vozmushchennogo kompaktnym operatorom, Teor. veroyatn. i ee prim., 43 (1), 166-171 (1998) [S.V. Savchenko, On the probability of the existence of a localized basic state for a discrete Schrödinger equation with random potential, perturbed by a compact operator, Theor. Prob. Appl., 43 (1), 158-162 (1999)], WoS: 000079809600016, Scopus: 2-s2.0-0040081266, RINTs: 13297459, MathSciNet: 1670012, zbMath: 0928.60055.
    31. S.V. Savchenko, Ob osnovnom sostoyanii svobodnogo i sluchainogo diskretnykh gamil’tonianov, vozmushchennykh operatorom ranga odin, pri kriticheskom znachenii konstanty svyazi, TMF, 114(1), 94-103 (1998) [S.V. Savchenko, On the ground state of free and random discrete Hamiltonians perturbed by an operator of rank one for a critical value of the coupling constant, Theor. Math. Phys., 114(1), 73-80 (1998)], WoS: 000073538400004, Scopus: 2-s2.0-0032385749, ADS: 1998TMP...114...73S, RINTs: 13277232, MathSciNet: 1756563, zbMath: 0960.82002.
    32. B.M. Gurevich, S.V. Savchenko, Termodinamicheskii formalizm dlya simvolicheskikh tsepei Markova so schetnym chislom sostoyanii, Uspekhi mat. nauk, 53:2(320), 3-106 (1998) [B.M. Gurevich, S.V. Savchenko, Thermodynamic formalism for countable symbolic Markov chains, Russ. Math. Surv., 53(2), 245-344 (1998)], WoS: 000075655600001, Scopus: 2-s2.0-0003228859, ADS: 1998RuMaS..53..245G, RINTs: 31251353, MathSciNet: 1639451, zbMath: 0926.37009, EDN: XRMQIA.
    33. S.V. Savchenko, Ob ustoichivosti verkhnei granitsy spektra otnositel’no vozmushchenii diagonal’nymi matritsami dlya nekotorogo klassa samosopryazhennykh operatorov, Uspekhi mat. nauk, 53:2(320), 163–164 (1998) [S.V. Savchenko, Stability of the upper bound of a spectrum under perturbations by diagonal matrices for a class of self-adjoint operators, Russ. Math. Surv., 53(2), 406-407 (1998)], WoS: 000075655600016, Scopus: 2-s2.0-0039982663, RINTs: -, MathSciNet: 1639436, zbMath: 0931.47012.
    34. S.V. Savchenko, Spetsial’nye potoki, postroennye po schetnym topologicheskim tsepyam Markova, Funkts. analiz i ego pril., 32(1), 40-53 (1998) [S.V. Savchenko, Special flows constructed from countable topological Markov chains, Funct. Anal. Appl., 32(1), 32-41 (1998)], WoS: 000075334000004, Scopus: 2-s2.0-0007210127, RINTs: 13276028, MathSciNet: 1627271, zbMath: 0919.58037, EDN: LENMYP .
    35. A.Yu. Kamenshchik, I.M. Khalatnikov, S.V. Savchenko, A.V. Toporensky, Cosmological dynamics for closed isotropic models with scalar field and hydrodynamical matter, Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J. Paul, T. Montmerle, and E. Aubourg (CEA Saclay), abstr. ID. 129 [Nucl. Phys. B Proc. Suppl., 80, CDROM contents, 12/15 (2000)], ADS: 1998tx19.confE.129K.
    36. S.V. Savchenko, O spektrakh konechnykh podmatrits beskonechnykh nerazlozhimykh matrits, Uspekhi mat. nauk, 52:3(315), 175-176 (1997) [S.V. Savchenko, On the spectra of finite submatrices of infinite irreducible matrices, Russ. Math. Surv., 52(3), 619-620 (1997)], WoS: A1997YA37800011, Scopus: 2-s2.0-0031515478, ADS: 1997RuMaS..52..619S, MathSciNet: 1479401, zbMath: 0913.15007.
    37. S.V. Savchenko, Ravnovesnye sostoyaniya s nepolnymi nositelyami i periodicheskie traektorii, Matem. zametki, 59(2), 230-253 (1996) [S.V. Savchenko, Equilibrium states with incomplete supports and periodic trajectories, Math. Notes, 59(2), 163-179 (1996)], WoS: A1996UP82900021, Scopus: 2-s2.0-27544436592, RINTs: 27981578, MathSciNet: 1391838, zbMath: 0880.58022.
    38. S.V. Savchenko, Periodicheskie tochki schetnykh topologicheskikh markovskikh tsepei, Matem. sb., 186(10), 103–140 (1995) [S.V. Savchenko, Periodic points of denumerable topological Markov chains, Sb.: Math., 186(10), 1493–1529 (1995)], WoS: A1995TX11300017, Scopus: 2-s2.0-27544471898, ADS: 1995SbMat.186.1493S, RINTs: 30889230, MathSciNet: 1361597, zbMath: 0865.58037.
    39. S.V. Savchenko, Dzeta-funktsiya i gibbsovskie mery, Uspekhi mat. nauk, 48:1(289), 181-182 (1993) [S.V. Savchenko, The zeta-function and Gibbs measures, Russ. Math. Surv., 48(1), 189-190 (1993)], WoS: A1993NF83400018, Scopus: 2-s2.0-27544437996, ADS: 1993RuMaS..48..189S, RINTs: 27834669, MathSciNet: 1227962, zbMath: 0808.60084.