cubature formulas; assimptotically optimal algorithms of computation; Banach spaces of real variables function; boundary problems of differential equations with partipal derivatives.
Subject:
The boundary problems for differential equations with singular perturbations was considered. Particularly it was one elliptic problem modeling an ideal liquid flow around the thin wing with the edge. At the Banach spaces theory it was established exactly embedding theorems about restrictions and prolongations for common less surfaces in $R^n$. the operator of best prolongation in common Banach Spaces was calculated. At the theory of cubature formulas the lattice formulas were investigated and the sufficient conditions for its asymptotical optimum about coefficients and lattices were established. The estimates were mode in scale of Winner spaces with the hypoelliptic symbols of less. The algorithms its formulas were constructed and the programs for integrations in two dimensions domain with arbitrarily boundary were created.
Biography
Graduated from Faculty of Mechanics and Mathematics of M. V. Lomonosov Moscow State University (MSU) in 1961 (department of differential equations) Ph.D. thesis was defended in 1965. D.Sci. thesis was defended in 1977. A list of my works containing more than 70 titles. I am one of leaders of the research seminar "Cubature formulas and its applications".
In 1983 I was awarded the title of honourable scientist of Bashkir Republic.
Main publications:
Ramazanov MD Optimal norms of the error functional of the lattice cubature formula in the scale of Wiener spaces // Report of the Russian Academy of Sciences, 1997, vol. 361, no. 6.
Ramzanov M. D. To the $ L_p $ theory of Sobolev // Advances in Mathematics, 1999, v. 9, No. 1, p. & Nbsp; 99 & 125.
Ramazanov, MD, Bessel Scales of Banach Spaces, Dokl. Akad. Nauk SSSR, 2001, vol. & Nbsp; 337, No. 2, pp. 158-160.
Ramazanov MD Theorems on traces and extensions // Doklady RAN, 2002, vol. & Nbsp; 382, № 6, с. & Nbsp; 1 & ndash; 3.
Ramazanov M.D. Multidimensional variational splines in general Banach spaces // Doklady RAS 2011, Volume 343, №5, p.603-605
M. D. Ramazanov, “A Criterion for a Normed Algebra in the Scale of Sobolev Spaces”, Math. Notes, 109:3 (2021), 496–499
2.
Ramazanov M. D., “Sovremennoe sostoyanie teorii i prilozhenii kubaturnykh formul S. L. Soboleva”, Problemy differentsialnykh uravnenii, analiza i algebry, Materialy 7-oi mezhdunarodnoi nauchnoi konferentsii, Aktyubinskii Gosudarstvennyi Universitet im. K. Zhubanova, 2015, 291–293
3.
Ramazanov M. D., Reshetchatye kubaturnye formuly na izotropnykh prostranstvakh, IMVTs UNTs RAN, Ufa, 2014 , 210 pp.
4.
M.D. Ramazanov, “Nenasyschaemyi algoritm asimptoticheski optimalnykh kubaturnykh formul”, Materialy XX Vserossiiskoi konferentsii “Teoreticheskie osnovy i konstruirovanie chislennykh algoritmov resheniya zadach matematicheskoi fiziki”, posvyaschennoi pamyati K. I. Babenko (Moskva), IPM im. M. V. Keldysha RAN, 2014, 89
5.
Ramazanov M. D., “Sobolevskaya teoriya reshetchatykh kubaturnykh formul. Problemy, algoritmy i primeneniya”, Mezhdunarodnaya konferentsiya “Differentsialnye uravneniya, funktsionalnye prostranstva, teoriya priblizhenii” (Novosibirsk, 18–24.08.2013 gg.), 2013, 355
6.
M. D. Ramazanov, D. Y. Rakhmatullin, “Applications of Sobolev lattice cubature formulas”, Eurasian Math. J., 4:3 (2013), 137–139
7.
M. D. Ramazanov, “Asymptotically optimal unsaturated lattice cubature formulae with bounded boundary layer”, Sb. Math., 204:7 (2013), 1003–1027
8.
Ramazanov M. D., “Nenasyschaemyi algoritm reshetchatykh kubaturnykh formul”, Mezhdunarodnaya konferentsiya “Funktsionalnyi analiz i ego prilozheniya” (Kazakhstan, Astana. 02–05.10.2012), 2012, 89
9.
Ramazanov M. D., “Teoremy vlozhenii i mnogomernye splainy”, Mezhdunarodnaya konferentsiya “Funktsionalnyi analiz i ego prilozheniya” (Kazakhstan, Astana. 02–05.10.2012), 2012, 89
10.
Ramazanov M. D., “Nenasyschaemyi algoritm reshetchatykh kubaturnykh formul”, Vserossiiskaya konferentsiya po vychislitelnoi matematike KVM-2011, Institut vychislitelnoi matematiki i matematicheskoi geofiziki SORAN, 2011 http://www.ict.nsc.ru/ws/show_abstract.dhtml?ru+220+16176
11.
M. D. Ramazanov, “Nenasyschaemyi algoritm reshetchatykh kubaturnykh formul”, Sbornik materialov mezhdunarodnoi konferentsii “Kubaturnye formuly, metody Monte-Karlo i ikh prilozheniya”, posvyaschennoi 90-letiyu so dnya rozhdeniya I. P. Mysovskikh (Krasnoyarsk, 4–7 iyulya 2011 goda), 2011, 97–99
12.
M .D. Ramazanov, “Multidimensional variational splines in general Banach spaces”, Dokl. Math., 83:2 (2011), 238–240 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
Ramazanov M. D., “Teoriya reshetchatykh kubaturnykh formul”, Teoriya priblizhenii, Mezhdunarodnaya konferentsiya (6-8 maya 2010 g., g. Sankt-Peterburg), SPb: VVM, 2010, 86–87
14.
Ramazanov M. D., “Vychislenie variatsionnykh splainov v negilbertovykh prostranstvakh”, Mezhdunarodnaya konferentsiya po prikladnoi matematike i informatike, posvyaschennaya 100-letiyu so dnya rozhdeniya akademika A. A. Dorodnitsyna (VTs RAN, Moskva, 7–11 dekabrya 2010 g.), VTs RAN, 2010, 137–138
15.
M. D. Ramazanov, D. Y. Rakhmatullin, E. L. Bannikova, “Cubature formulas of S. L. Sobolev: evolution of the theory and applications”, Eurasian Math. J., 1:1 (2010), 123–136
M. D. Ramazanov, “New algorithm of asymptotically optimal lattice cubature formulae”, Ufimsk. Mat. Zh., 2:3 (2010), 63–82
17.
Ramazanov M. D., Teoriya reshetchatykh kubaturnykh formul s ogranichennym pogranichnym sloem, DizainPoligrafServis, Ufa, 2009 , 178 pp.
18.
M. D. Ramazanov, D. Ya. Rakhmatullin, L. Z. Valeeva, E. L. Bannikova, “Reshenie integralnykh uravnenii na mnogoprotsessornykh vychislitelnykh sistemakh”, Zhurnal Sibirskogo Federalnogo Universiteta, seriya matematicheskaya, 2:1 (2009), 69–87 , SFU, Krasnoyarsk http://matem.anrb.ru/sites/default/files/publications/6_ramaz_1.pdf
19.
Marat D. Ramazanov, Dzhangir Y. Rakhmatullin, “Parallel algorithms of numeric integration using lattice cubature formulas”, Parallel Computing Technologies, 10th International Conference, PaCT 2009 (Novosibirsk, Russia. August 31 – September 4, 2009), Springer-Verlag, Berlin, 2009, 147–152http://dblp.uni-trier.de/db/conf/pact/pact2009.html#RamazanovR09
20.
M. D. Ramazanov, “Exact embedding theorems for traces and extensions”, Further Progress in Analysis, Proceedings of the 6Th International Isaac Congress (Ankara, Turkey, August 13–18, 2007), World Scientific, Hackensack, NJ, 2009, 734–739
21.
Ramazanov M. D., “Ob asimptotike koeffitsientov optimalnykh periodicheskikh vesovykh reshetchatykh kubaturnykh formul”, Sb. mezhdunarodnoi konferentsii “Matematicheskoe i kompyuternoe modelirovanie estestvennonauchnykh i sotsialnykh problem” (21–28 maya 2008 g. Penza), Penzenskii gosudarstvennyi universitet, 2008, 84–87 (to appear)
22.
Ramazanov M. D., “Optimalnye kubaturnye formuly”, Evraziiskii matematicheskii zhurnal, 2007, no. 2, Resp. Kazakhstan, Astana, Evraz. nats. univ. i MGU, 47–50
23.
Ramazanov M. D., “Kubaturnye formuly s ogranichennym pogranichnym sloem”, Trudy mezhdunarodnogo seminara-soveschaniya “Kubaturnye formuly i ikh prilozheniya”, Ufa: IMVTs UNTs RAN, 2007, 137–175
24.
Ramazanov M. D., “Reshetchatye kubaturnye formuly na prostranstvakh Vinera”, Trudy mezhdunarodnogo seminara-soveschaniya “Kubaturnye formuly i ikh prilozheniya”, IMVTs UNTs RAN, Ufa, 2007, 128–137
25.
M. D. Ramazanov, “Embedding theorems and multidimensional splines”, Dokl. Math., 75:2 (2007), 224–227 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
26.
Ramazanov M. D., “Asimptoticheski optimalnye posledovatelnosti kvadraturnykh formul s ogranichennym pogranichnym sloem i neotritsatelnymi koeffitsientami”, Vestnik BashGU, 1 (2006), 10–15
27.
Ramazanov M. D., Teoremy vlozheniya, BashGU, Ufa, 2006 , 68 pp., ISSN 5-86911-261-3
28.
L. M. Bakusov, B. G. Il'yasov, M. D. Ramazanov, Sh. M. Safin, “Biological calculations: general principles”, Probl. Upr., 1 (2006), 61–68
29.
M. D. Ramazanov, “Periodic optimal cubature formula in $\widetilde_p^{m*}$”, Vychisl. Tekhnol., 11 (2006), 90–96
30.
Ramazanov M. D., Rakhmatullin D. Ya., “Dostizhenie nailuchshego poryadka priblizheniya integralov funktsii iz W_2^m (R^2) na reshetchatykh kubaturnykh formulakh za schet povorota reshetki uzlov”, Kubaturnye formuly i ikh prilozheniya, Materialy VIII mezhdunarodnogo seminara-soveschaniya (15–22 avgusta 2005 g. – Ulan-Ude), Izdatelstvo VSGTU, 2005, 109–116
31.
V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S1–S7
32.
M. D. Ramazanov, “Trace and extension theorems”, Dokl. Math., 65:1 (2002), 108–110 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
33.
V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in”, Russ. J. Math. Phys., 9:1 (2002), 1–5 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
34.
M. D. Ramazanov, “Bessel scales of Banach spaces”, Dokl. Math., 63:2 (2001), 158–160 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
35.
M. D. Ramazanov, Kh. M. Shadimetov, “Weighted optimal cubature formulas in a periodic Sobolev space”, Dokl. Math., 60:2 (1999), 453–455 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
36.
M. D. Ramazanov, “To the $L_p$-theory of Sobolev formulas”, Sib. Adv. Math., 9:1 (1999), 99–125 , Springer Us, New York, NY; Pleiades Publishing (Allerton Press), New York, NY; Maik “Nauka/Interperiodica”, Moscow
37.
M. D. Ramazanov, “Optimization of the norm of the error functional for the lattice cubature formula in the scale of Wiener spaces”, Dokl. Math., 58:1 (1998), 743–745 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
38.
M. D. Ramazanov, “Grid cubature formulas”, Aktual'nye problemy sovremennoj matematiki, Sbornik nauchnykh trudov, v. 2, Nii Mioo Ngu, Novosibirsk, 1996, 132–139
39.
M. D. Ramazanov, “The asymptotic theorem of I. Babushka”, Dokl. Math., 54:2 (1996), 724–727 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
40.
M. D. Ramazanov, “The asymptotic theory of I. Babushka”, Dokl. Akad. Nauk, 350:4 (1996), 449–452
41.
M. D. Ramazanov, “Optimizing the arrangement of nodes in latticed cubature formulas”, Dokl. Math., 52:1 (1995), 64–65 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
42.
M. D. Ramazanov, “Optimization of the arrangement of nodes of lattice cubature
formulas”, Dokl. Akad. Nauk, 343:4 (1995), 456–457
43.
M. D. Ramazanov, “Boundary layer functions of asymptotically optimal lattice cubature formulas”, Russ. Acad. Sci., Dokl., Math., 49:2 (1994), 25–26 , American Mathematical Society (AMS), Providence, RI
44.
M. D. Ramazanov, “Functions of a boundary layer of asymptotically optimal lattice
cubature formulas”, Dokl. Math., 49:2 (1994), 240–243
45.
M. D. Ramazanov, “Universal optimality of lattice cubature formulas”, Russ. Acad. Sci., Dokl., Math., 45:3 (1992), 1 , American Mathematical Society (AMS), Providence, RI
46.
M. D. Ramazanov, “Universal optimality of lattice cubature formulas”, Dokl. Math., 45:3 (1992), 665–669
47.
M. D. Ramazanov, “Asymptotically optimal control in a problem with perturbation”, Asymptotic methods for solving problems of mathematical physics, Collect. Sci. Works, Ufa, 1989, 96–108
48.
Asymptotische Methoden in der Analysis, v. 46 (M 53), Wissenschaftliche Beiträge, eds. Roland Riedel and Marat D. Ramazanov, Martin–Luther–Universität Halle–Wittenberg, Halle (Saale), 1988 , 96 pp.
49.
M. D. Ramazanov, “On the degree of convergence of lattice cubature formulas in spaces with dominant derivative”, Sov. Math., Dokl., 30 (1984), 135–137 , American Mathematical Society, Providence, RI
50.
M. D. Ramazanov, “An elliptic problem with a small parameter”, Tr. Semin. S. L. Soboleva, no. 1, 1984, 110–131
51.
M. D. Ramazanov, “The order of convergence of lattice cubature formulas in spaces
with a dominant derivative”, Dokl. Akad. Nauk SSSR, 277:3 (1984), 551–553
52.
M. D. Ramazanov, I. Umarkhanov, “A quadrature formula with a simple weight function”, Dokl. Akad. Nauk UzSSR, 1982:5 (1983), 4–7 , Academy of Sciences of the Uzbek Soviet Socialist Republic – UzSSR (Akademiya Nauk UzSSR), Tashkent; “FAN”, Tashkent
53.
M. D. Ramazanov, N. I. Blinov, L. V. Vojtishek, Z. Zh. Zhamalov, F. Ya. Zagirova, V. I. Polovinkin, G. N. Salikhov, T. Kh. Sharipov, Ts. B. Shojnzhurov, “The development of the theory of Sobolev cubature formulas”, Theory of cubature formulas and numerical mathematics, Pap. Conf. Differential equations and numerical mathematics (Novosibirsk 1978), 1980, 118–125
54.
M. D. Ramazanov, “Finite-difference approximations of multipliers”, Siberian Math. J., 20:2 (1979), 316–318
55.
M. D. Ramazanov, “Differenzenapproximation von Multiplikatoren”, Sib. Mat. Zh., 20 (1979), 442–444 , Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk
56.
M. D. Ramazanov, “Cube formulas on spaces of continuously differentiable functions”, Sib. Math. J., 16 (1976), 969–985 , Springer Us, New York, NY; Pleiades Publishing, New York, NY; Maik “Nauka/Interperiodica”, Moscow
57.
M. D. Ramazanov, “An optimal lattice cubature formula in Banach spaces of periodic functions”, Math. Notes, 17:1 (1975), 39–40
58.
M. D. Ramazanov, “Cubature formulae on spaces of continuously differentiable functions”, Siberian Math. J., 16:6 (1975), 969–985
59.
M. D. Ramazanov, “Construction of cubature formulae for multidimensional domains with smooth boundaries”, Acta Univ. Carol., Math. Phys., 15:1–2 (1975), 137–140 , Charles University, Prague
60.
M. D. Ramazanov, “Asymptotic optimality of grid cubature formulas on spaces of continuously differentiable functions”, Sov. Math., Dokl., 15 (1974), 789–793 , American Mathematical Society, Providence, RI
61.
M. D. Ramazanov, “Asymptotic optimality of grid cubature formulas on Hilbert spaces”, Sov. Math., Dokl., 15 (1974), 755–757 , American Mathematical Society, Providence, RI
62.
M. D. Ramazanov, “Asymptotic optimality of grid cubature formulas on spaces of continuously differentiable functions”, Dokl. Akad. Nauk SSSR, 216:2 (1974), 270–273
63.
M. D. Ramazanov, “Asymptotic optimality of grid cubature formulas on Hilbert spaces”, Dokl. Akad. Nauk SSSR, 216:1 (1974), 44–45
64.
Ramazanov M. D., Lektsii po teorii kubaturnykh formul, Ufa: Izd-vo BashGU, 1973 , 177 pp.
65.
M. D. Ramazanov, “An optimal error functional on the periodic functions of the space $\tilde H^\mu_p$”, Siberian Math. J., 13:1 (1972), 162–164
66.
M. D. Ramazanov, “The optimal error functionals over periodic functions of Banach spaces”, Siberian Math. J., 13:2 (1972), 334–336
67.
M. D. Ramazanov, “Über optimale Fehlerfunktionale über periodischen Funktionen aus Banachräumen”, Sib. Mat. Zh., 13 (1972), 481–484 , Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk
M. D. Ramazanov, “Construction of an asymptotically optimal cubature formula in $\tilde W^m_2 (\Omega)$”, Sov. Math., Dokl., 13 (1972), 98–102 , American Mathematical Society, Providence, RI
69.
M. D. Ramazanov, “Construction of an asymptotically optimal cubature formula in $\widetilde{W}_2^m(\Omega)$”, Dokl. Akad. Nauk SSSR, 202:2 (1972), 290–293
70.
M. D. Ramazanov, “Theorems on traces und extensions of functions from surfaces”, Sov. Math., Dokl., 11 (1970), 210–214 , American Mathematical Society, Providence, RI
71.
M. D. Ramazanov, “Theorems on traces and extensions of functions from surfaces”, Dokl. Akad. Nauk SSSR, 190:4 (1970), 784–787
72.
M. D. Ramazanov, “Theorems on traces and continuations of functions from surfaces. I”, Sov. Math., Dokl., 10 (1969), 502–506 , American Mathematical Society, Providence, RI
73.
M. D. Ramazanov, “Theorems on traces and extensions of functions from surfaces”, Dokl. Akad. Nauk SSSR, 185:6 (1969), 1239–1242
74.
M. D. Ramazanov, “A priori estimates of solutions to the Dirichlet problem for certain hypoelliptic equations”, Sov. Math., Dokl., 9 (1968), 455–458 , American Mathematical Society, Providence, RI
75.
M. D. Ramazanov, “A priori estimates of solutions of the Dirichlet problem for certain hypoelliptic equations”, Dokl. Akad. Nauk SSSR, 179:4 (1968), 783–785
76.
M. D. Ramazanov, “Function spaces and the Fourier transform”, Proc. Steklov Inst. Math., 91 (1967), 153–178
77.
M. D. Ramazanov, Differ. Uravn., 2:1 (1966), 65–82
78.
M. D. Ramazanov, “A priori solutions of the $L\sp p$ type of solutions of parabolic equations”, Sov. Math., Dokl., 6 (1965), 470–473 , American Mathematical Society, Providence, RI
79.
M. D. Ramazanov, “A priori solutions of type $L^p$ of solutions of parabolic equations”, Dokl. Akad. Nauk SSSR, 161:3 (1965), 530–533
80.
M. D. Ramazanov, “A boundary-value problem for a class of differential equations”, Mat. Sb. (N.S.), 64(106):2 (1964), 234–261
81.
M. D. Ramazanov, “A boundary value problem”, Sov. Math., Dokl., 4 (1963), 1444–1447 , American Mathematical Society, Providence, RI
82.
M. D. Ramazanov, “On a boundary-value problem”, Dokl. Akad. Nauk SSSR, 152:4 (1963), 827–830
83.
V. M. Babich, R. R. Gadyl'shin, A. R. Danilin, S. Yu. Dobrokhotov, V. A. Il'in, L. A. Kalyakin, E. F. Mishchenko, V. Yu. Novokshenov, Yu. S. Osipov, M. D. Ramazanov, N. Kh. Rozov, V. A. Sadovnichii, “Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)”, Differ. Equ., 38:8 (2002), 1075–1080
Presentations in Math-Net.Ru
1.
О теории кубатурных формул С.Л.Соболева M. D. Ramazanov Seminar of Laboratory of Theory of Functions "Modern Problems of Complex Analysis" May 18, 2017 12:00
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