Saint Petersburg State University




НазваниеSaint Petersburg State University
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Free University of Berlin


Monograph

  1. “Self-organization of complex molecules. Properties of structures of different levels organization” Ed. V.I. Korotkov. St.Petersburg State University (2008) 242p,

  2. Grishchenko A.E., Kononov A.I., Michailova N.A., Naumova L.V. “Self-Organisation of polymer molecules in interfacial” St.Petersburg State University, (2010) 197p


Selected papers

  1. V.I. Korotkov Mathematical models in chemical physics and combustion theory. In Encyclopaedia of Life Support Systems (EOLSS), Developed under the auspices of the UNESCO, Eolss Publishers, Oxford, UK, (2006). [http://www.eolss.net ]

  2. Surface nanocrystal hydrogen-bonded complex for photochemical water splitting V.I. Korotkov, I.A. Akimov, S.O. Visotskaya, A.A. Evstrapov, .N. Jasnikov. Journal of Photochemistry and Photobiology, A: Chemistry V 196 (2008), 138-142.

  3. Investigation of adsorption of 2,2'-bipyridine on МСМ-41 silica matrix by NMR 15N spectroscopy. S.B. Lesnichin, N. Kamdem, D. Mauder, G. S. Denisov, I.G. Shenderovich. Russian J. Gen. Chem. (2010) 80, 1718-1722.

  4. ‘Counteranion-Dependent Mechanisms of Intramolecular Proton Transfer in Aprotic Solution. S.B. Lesnichin, P.M. Tolstoy, H.-H. Limbach, I.G. Shenderovich Phys. Chem. Chem. Phys. (2010) 12, 10373-10379.

  5. NMR Study of Proton Transfer to Strong Bases on Inner Surfaces of MCM-41 B.C.K. Ip, D.V. Andreeva, G. Buntkowsky, D. Akcakayiran, G.H. Findenegg, I.G. Shenderovich Micropor. Mesopor. Mater. (2010) 134, 22-28.

  6. Density Functional Study of the Proton Transfer Effect on Vibrations of Strong (Short) Intermolecular O-H· · N/O-· ·H-N+ Hydrogen Bonds in Aprotic Solvents S. Kong, I. G. Shenderovich, M. V. Vener J. Phys. Chem. A (2010) 114, 2393–2399.

  7. D. Mauder, D. Akcakayiran, S. B. Lesnichin, G. H. Findenegg, I. G. Shenderovich Acidity of Sulfonic and Phosphonic Acid Functionalized SBA-15 under Almost Water Free Conditions J. Phys. Chem. C (2009) 113, 19185-19192.

  8. I. Alkorta, J. Elguero, H.-H. Limbach, I.G. Shenderovich, T. Winkler A DFT and AIM analysis of the spin-spin couplings across the hydrogen bond in the 2-fluorobenzamide and related compounds Magn. Reson. Chem. (2009) 47, 585–592.

  9. N.S. Golubev, C. Detering, S.N. Smirnov, I.G. Shenderovich, G.S: Denisov, H.-H. Limbach, P.M. TolstoyH/D isotope effects on NMR chemical shifts of nuclei involved in a hydrogen bridge of hydrogen isocyanide complexes with fluoride anion Phys. Chem. Chem. Phys. (2009) 11, 5154-5159.

  10. N.S. Golubev, G.S. Denisov, S. Mcholl, S.N. Smirnov, I.G. Shenderovich, P.M. Tolstoy. NMR study of blue-shifting hydrogen bonds formed by fluoroform in solution Z. Phys. Chem. (2008) 222, 1225-1245.

  11. I.G. Shenderovich, D. Mauder, D. Akcakayiran, G. Buntkowsky, H.-H. Limbach, G.H. Findenegg. NMR provides checklist of generic properties for atomic-scale models of periodic mesoporous silicas J. Phys. Chem. B (2007) 111, 12088-12096.

  12. S. Sharif, I.G. Shenderovich, L. González, G.S. Denisov, D.N. Silverman; H.-H. Limbach. NMR and Ab initio Studies of Small Complexes Formed between Water and Pyridine Derivatives in Solid and Liquid Phase J. Phys. Chem. A (2007) 111, 6084-6093.

  13. I.G. Shenderovich Qualitative Analysis of the Geometry of the Hydrogen Bond in the Homoconjugated Pyridine Ion Russian J. Gen. Chem. (2007) 4, 620-625.

  14. A. Vyalikh, Th. Emmler, I. Shenderovich, Y. Zeng, G.H. Findenegg, G. Buntkowsky 2H-solid state NMR and DSC study of isobutyric acid in mesoporous silica materials Phys. Chem. Chem. Phys. (2007) 9, 2249–2257.

  15. D.V. Andreeva, B. Ip, A.A. Gurinov, P.M. Tolstoy, I.G. Shenderovich, H.-H. Limbach Geometrical features of hydrogen bonded complexes involving sterically hindered pyridines. J. Phys. Chem. A (2006) 110, 10872-10879.

  16. I.G. Shenderovich Maximum Value of the Chemical Shift in the 1H NMR Spectrum of a Hydrogen-Bonded Complex. Russian J. Gen. Chem. (2006) 76, 501-506.

  17. Grishchenko A.E., Michailova N.A.,Naumova L.V.,Gubarev A.S., Makarova N.N. Study of orientational in thin films of disklike heptameric polycyclosiloxane molecules by means of the oblique-polarised-ray method. J. of Optical Technology (2005) V.72 Issue 1, 15-19.

  18. Shtennikova I.N., Grishchenko A.E., Michailova N.A., Kolbina G.F., Khotimskii V.S. The studies of Molecular strucrure poly (1-trimethylsilyl-1-propyne) stereoisomers by the flow birefrengence method. European polymer J. (2006) V42, N6, 1325-1329.

  19. GrishchenkoA.E, Khudyakova O.V., Michailova N.A.,Gubarev C.A., Ionov A.N. Molecular characteristics and surface layer structure of poly (siloxane imides) Polymer Sci Ser A. (2007) V49, N5, 532-537.

  20. GrishchenkoA.E, Roizard D., Petrakov A.P., Mikhailova N.A., Molecular Structure and Morfology of memrane-Forming Copolymers of tolylene dinrea and poly(dimethylsiloxane) Polymer Sci Ser A. (2007) V49, N5, 571-577.

  21. GrishchenkoA.E., Kononov A.I., Michailova N.A., Makarova N.N., Сhizhova N.V., Zaitseva I.I. Self-Organisation and Self-Assocition of Pentameric Polyorganocyloxane Molecules at the Interface: a Study by the inclined Polarized Beam Method. Doklady Pysical Chemistry. (2008) V.241, Part 1, 179-181.

  22. V.M. Malkin, V.L. Rapoport. Photochemical detection of the stacking aggregation of thymine chromophores in aqueous solutions of polythymidylic acid. Biophysics, (2005) Vol. 50, No, 6 874-878.

  23. V.L. Rapoport, V.M. Malkin, S.V. Zorina, S.M. Komarov, and V.V. Goryuchko. Luminescence detection of tightly bound stacking aggregates of adenine and adenosine in aqueous solutions – the candidates for the role of the first genetic templates. Doklady Biochemistry and Biophysics. (2006) Vol. 406, 23-26.

  24. V.M. Malkin, V.L. Rapoport. A study of the spectral and luminescence manifestations of the aggregation of thymine chromophores in polythymidylic acid aqueous solutions at room temperature in the context of photochemical information recording using thymine, Biophysics (2008) Vol. 53 No. 5 336-340.


Selected Projects

  • Investigation of a role of physical and chemical factors in self-organizing of chain molecules on phase boundaries. Prof. A.E. Grischenko, Grant RNP № 2.1.1. 4139, 2006-2008

  • Investigation of long-living electron states and energy transfer in organic polycrystals. Prof. V.I. Korotkov, Contract, 2008-2009

  • Investigation of influence of electromagnetic fields of different frequency ranges on organic nanostructures and alive systems. Sen. Res. V.E. Stefanov, Grant RNP № 2.1.1.485 2009-2010.

  • Photonics and spintronics of low-dimensional condensed phases for informational technology. Prof. A.A. Tzyganenko, Grant NPK, 2009-2013.

  • Physical and chemical investigation of given polycrystalline structures. Prof. V.I. Korotkov, Contract, 2010-2012.

  • Photophysics of complex organic and biological molecules. Prof. V.I. Korotkov, Grant SpbSY № 26.11.2010, 2010-2014.

  • Characterization of the structure and dynamics of mesoporous host-guest materials using solid state NMR techniques. Principal Investigators: Prof. Dr. H.-H. Limbach and Dr. I. Shenderovich. Grant DFG (German Research Foundation) 2007-2009.

  • Solid state NMR studies of cofactor-protein systems with functional hydrogen bonds Principal Investigators: Prof. Dr. H.-H. Limbach, Dr. G. Buntkowsky and Dr. I. Shenderovich Grant DFG (German Research Foundation) 2006-2008.

  • Investigation of geometry of functional hydrogen bonds in solutions by NMR/IR/UF spectroscopy. Sen. Res. I.G. Shenderovich, Grant RFBR 09-03-91336, 2009-2011.

  • Luminescence and quantum chemical study of tightly bound stacking aggregates of adenine and uracil in connection with modelling of first stages of chemical evolution. Prof. V. L. Rapoport . State Contract with Institute of Cytology RAS. 2007.

  • Luminescence and quantum chemical modelling of first stages of chemical evolution in systems adenine+uracil and adenine+thymine. Prof. V. L. Rapoport . State Contract with Institute of Cytology RAS. 2008.

  • Luminescence and quantum chemical study of first stages of chemical evolution including tightly bound stacking aggregates of nucleic bases. Prof. V. L. Rapoport . State Contract with Institute of Cytology RAS. 2009.

  • Luminescence study of first stages of chemical evolution with participation of tightly bound stacking aggregates of adenine and uracil. Prof. V. L. Rapoport . State Contract with Institute of Cytology RAS. 2010.

Mathematics and Mathematical Physics





Professor Vladimir S. Buslaev, Head of the Department

M.Sc. (1959), Ph.D. (1962), D.Sc. (1973)


Selected staff members

Prof. Vladimir S. Buslaev, the Head of the Department; Prof. Ludvig D. Faddeev, fellow of the Russian Academy of Sciences. Full professors: Boris A. Plamenevsky, Natalia V. Smorodina, Tatiana A. Suslina, Mikhail A. Lyalinov, Mikhail I. Belishev, Alexei P. Kiselev, Mikhail V. Babich, Eugeny L. Korotyaev. Leading research fellow: Serguei N. Naboko. Associate Professors: Alexander S. Blagoveschensky, Alexander M. Budylin, Ludmila A. Dmitrieva, Maria V. Perel, Oleg V. Sarafanov, Vladimir V. Sukhanov, Mikhail M. Faddeev, Alexander A. Fedotov, Nikolai D. Filonov, Alexei L. Pirozersky, Vladimir A. Sloushch, Alexander V. Kiselev, Roman V. Romanov. Senior lecturers: Alexei N. Popov, Natalia G. Gelfreih, Alexei A. Pozharsky. Assistant Professor: Sergey A. Simonov.

Major teaching areas

Physics, radiophysics, applied mathematics and physics.


M.Sc. Programme profile

Theoretical and mathematical physics 010700/17 (programme No. 25 – problems of mathematical and computational physics)


Selected lecture courses

General courses

  1. Mathematical analysis.

  2. Algebra.

  3. Methods of mathematical physics.

  4. Probability theory.


Special courses.

  1. Function theory.

  2. Functional analysis.

  3. Manifold geometry.

  4. Spectral theory of linear operators.

  5. Asymptotic methods for ordinary differential equations.

  6. Lie groups and algebras.

  7. Sobolev spaces and their applications.

  8. Ray method in the wave propagation theory.

  9. Scattering theory.

  10. Spectral theory of partial differential operators.

  11. Markov processes and their applications.

  12. Spectral theory of ordinary differential operators.

  13. Pseudo-differential operators and boundary value problems.

  14. Canonical problems of wave propagation theory.

  15. Inverse problems in wave propagation theory.

  16. Non-linear integrable systems.


Main research areas


  • Spectral theory of differential operators: Maxwell operator, Schrodinger operator, operators with periodic coefficients, Weyl asymptotics, absolute continuity of the spectrum.

  • Homogenization of periodic differential operators. Operator estimates of the error. Homogenization in the scattering problems.

  • Few-body scattering. Coulomb potentials, singularities of the scattering matrix.

  • Spectral properties and the behavior of solutions of one-dimensional almost-periodic Schrodinger operators. Behavior at infinity of solutions to equations with analutic potentials of general form and with large coupling constant.

  • Behavior of exponential sums with large numbers of terms.

  • Mathematical problems of the wave propagation theory in non-homogeneous waveguides (electronic, electromagnetic, acoustical). Development of asymptotic and numeric methods. Applications to nano- and microelectronics.

  • The theory of hyperbolic initial-boundary value problems in domains with singularities, in particular, development of asymptotical methods. Applications to dynamical problems of elasticity theory and flaw theory. Pseudo-differential operators on manifolds with singularities.

  • Mathematical methods in scattering of acoustic and electromagnetic waves in domains with conic and wedge-like singularities of the boundary, asymptotic methods in the mathematical theory of diffraction, function-difference, integral equations and their applications in the wave propagation theory.

  • Investigations in the area of probability theory and stochastic analysis – theorems on the convergence of stochastic integral distributions, probabilistic representations of solutions to differential equations.

  • Inverse spectral problems for ordinary differential equations. Investigation of asymptotic behavior of solutions to non-linear integrable equations.

  • Spectral analysis of Hermitian Jacobi matrices.

  • Mathematical theory of elastic surface waves. The theory of optical beams and bundles.

  • Multidimensional dynamical and spectral inverse problems. Problems on manifolds. Inverse problems for multi-velocity systems. Problems on graphs. Connections between inverse problems and control theory, systems theory, operator theory and C*-algebras.


Permanent collaboration with foreign universities and institutes.

  • Paris 13 University, Laboratory of algebra, geometry, analysis and applications.

  • Bath University, UK.

  • University of Sannio in Benevento, Italy.

  • Institute of High Frequency Technique, Stuttgart University, Germany.

  • CEA (Commissariat Energy Atomique), France.

  • Bohn University, Germany.

  • UAB – University of Alabama at Birmingham.

  • University of Cardiff, UK.

  • Institute of Mathematics, Polish Academy of Sciences, Krakow.

  • Institute of Mathematics, National Academy of Sciences, Ukraine.

  • Bordeaux 1 University, France.

  • Valladolid University, Spain.

  • Department of applied analysis of the Higher School of Informatics, University of Kyoto, Japan.

  • Department of Mathematical Information technology, Jyväskylä University, Finland.

Monographs


  • M.Sh. Birman, M.Z. Solomyak. Spectral theory of self-adjoint operators in Hilbert spaces. 2nd edition. Lan', St.Pb., 2010.

  • M.Sh. Birman. Selected papers. Mathematical scattering theory. Spectral shift function. RHD, Moscow-Izhevsk, 2010.

  • L.D. Faddeev, O.A. Yakubovskii. Lectures on quantum mechanics for mathematics students. AMS, Providence, RI. 2009, 234.

  • L.D. Faddeev, L. Takhtajan, Hamiltonian methods in theory of solitons, Berlin: Springer, 2007.

  1. V.M. Babich, M.A Lyalinov, V.E. Grikurov: Diffraction Theory. The Sommerfeld-Malyuzhinets Technique, Alpha Science Ser. Wave Phenom. (Alpha Science, Oxford 2008).

  2. Pseudo-differential operators on piecewise-smooth manifolds. Tamara Rozhkovskaya publishers, Novosibirsk, 2010.

  3. A.A. Fedotov. Complex WKB method for adiabatic perturbations of periodic operators with applications towards the study of the spectrum of almost-periodic operators. To appear in: London Math Society Lecture Notes



Selected research papers

  1. L.D. Faddeev, A.J. Niemi, Spin-charge separation, conformal covariance and the SU(2) YangMills theory, Nuclear Physics B, v. 776, Issues 1-2, (2007), Pages 38-65.

  2. L.D . Faddeev, M.N. Chernodub A.J. Niemi Non-abelian supercurrents and de Sitter ground state in electroweak theory, J. High Energy Phys. (2008), 0812-014.

  3. L.D. Faddeev, Discrete series of representations for the modular double of the quantum group U_q(sl(2,R)), Functional Analysis and Its Applications, Volume 42, Number 4, 330-335.

  4. L.D. Faddeev, Volkov, A.Yu. Discrete evolution for the zero modes of the quantum Liouville model, Journal of Physics A Mathematical and Theoretical (2008),41 (19), art.no. 194008.

  5. L.D. Faddeev Notes on divergences and dimensional transmutation in Yang-Mills theory, Theor. Math. Phys.(2006)Vol. 148(1), pp. 986-994.

  6. M.Sh.Birman, T.A.Suslina, Operator error estimates in the homogenization problem for nonstationary periodic equations, Algebra i Analiz, vol. 20 (2008), no. 6, 30-107; English transl., St.Petersburg Math. J., vol. 20 (2009), no. 6, 873-928.

  7. T.A.Suslina, Homogenization in the Sobolev class H1(Rd) for second order periodic elliptic differential operators with the inclusion of first order terms, Algebra i Analiz, vol. 22 (2010), no. 1, 108-222; English transl., St.Petersburg Math. J., vol. 22 (2011), no. 1, 81-162.

  8. V.S.Buslaev and S.B.Levin, Asymptotic behavior of the eigenfunctions of many-particle Schr\"{o}dinger operator.~I. One-dimensional
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