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OLEKSIY ZHEDANOV
教授
主要研究方向：Exactly solvable models in theoretical and mathematical physics; Special functions
办公室：数学楼215
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教育经历
MsD: Donetsk University, Physics Department, 1980
PhD: Donetsk University, Physics Department, 1985 -
工作经历
Assistant and associated Prof., Donetsk University, 1986-1995;
Senior researcher, Donetsk Institute for Physics, 1995-2016
Professor, Renmin Univresity, Beijing, 2016- -
科研成果
Published papers:
1. Granovski_Ya. I.; Zhedanov, A. S. Periodic structures
on a quantum spin chain, Sov.Phys.JETP, 62 (1985), 1244{1248.
2. Granovski_Ya. I.; Zhedanov, A. S. Integrability of a
classical XY chain. JETP Lett. 44 (1986), 304-307.
3. Granovski_Ya. I.; Zhedanov, A. S. Domain-type solutions
in anisotropic magnetic chains. (Russian) Teoret.Mat. Fiz. 71 (1987), 143-153.
4. Granovski_Ya. A.; Zhedanov, A. S. Nature of the symmetry
group of the 6j-symbol. Soviet Phys. JETP 67 (1988), 1982-1985.
5. Zhedanov, A. S. Toda lattice: solutions with dynamical
symmetry and classical orthogonal polynomials. (Russian)
Teoret. Mat. Fiz. 82 (1990), 11-17.
6. Granovski_Ya. I.; Zhedanov, A. S.; Lutsenko, I. M.
Quadratic algebras and dynamical symmetry of the Schrdinger
equation. Soviet Phys. JETP 72 (1991), 205-209.
7. Zhedanov, A. S. Nonlinear shift of q-Bose operators and
q-coherent states. J. Phys. A:Math. and Gen. 24 (1991), L1129-L1132.
8. Zhedanov, A. S. The "Higgs algebra" as a "quantum"
deformation of SU(2). Modern Phys. Lett. A 7 (1992),
507-512.
9. Zhedanov, A. S. Bogoliubov q-transformation and Clebsch-
Gordan coe_cients for a q-oscillator. Phys. Lett. A, 165 (1992), 53-57.
10. Zhedanov, A. S. "Hidden symmetry" of the Askey-Wilson
polynomials. (Russian) Teoret. Mat. Fiz. 89 (1991),
190-204.
11. Granovski_Ya. I.; Lutzenko, I. M.; Zhedanov, A. S.
Mutual integrability, quadratic algebras, and dynamical
symmetry. Ann. Physics 217 (1992), 1-20.
12. Granovski Ya. I.; Zhedanov, A. S.; Lutsenko, I. M.
Quadratic algebras and dynamics in curved space. I. An
oscillator. (Russian) Teoret. Mat. Fiz. 91 (1992), 207-
216.
13. Zhedanov, A. S. On the realization of the Weyl commutation
relation HR = qRH. Phys. Lett. A 176 (1993),300-302.
14. Granovski_Ya. I.; Zhedanov, A. S. Linear covariance
algebra for SLq(2). J. Phys. A: Math. and Gen. 26(1993), L357-L359.
15. Granovski Ya. I.; Zhednov, A. S. New construction of
3nj-symbols. J. Phys. A:math. and Gen. 26 (1993),4339-4344.
16. Zhedanov, A. S. Hidden symmetry algebra and overlap
coe_cients for two ring-shaped potentials. J. Phys. A:Math.
and Gen. 26 (1993), 4633-4641.
17. Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei,
Di_erence Schrodinger operators with linear and exponential
discrete spectra. Lett. Math. Phys. 29 (1993), 63-73.
18. I.Lutzenko and A.Zhedanov, q bosons as quasifermions,
Phys.Rev. E, 50 (1994), 97-103.
19. I.Lutzenko and A.Zhedanov, Superuidity of repulsive
quasifermions, Phys.Rev.Lett. , 74 (1995), 3507-3510.
20. Spiridonov, Vyacheslav; Zhedanov, Alexei, Discrete re-
ectionless potentials, quantum algebras, and q-orthogonal
polynomials. Ann. Physics 237 (1995), no. 1, 126-146.
21. Spiridonov, Vyacheslav; Zhedanov, Alexei, Discrete Darboux
transformations, the discrete-time Toda lattice, and
the Askey-Wilson polynomials. Methods Appl. Anal. 2
(1995), 369-398.
22. A.S.Zhedanov, Gauss sums and orthogonal polynomials,
Internat. J. Mod. Phys. A, 12 (1997), 289 - 294.
23. S.Kharchev, A.Mironov and A.Zhedanov, Faces of relativistic
Toda chain, Intern.J.Mod.Phys. A., 12 (1997), 2675-2724.
24. V.Spiridonov and A.Zhedanov, Zeros and orthogonality
of the Askey-Wilson polynomials for q a root of unity,
Duke Mathem.J., 89 (1997), 283-305.
25. V.Spiridonov and A.Zhedanov, Discrete-time Volterra chain
and classical orthogonal polynomials, J.Phys. A: Math. Gen. 30 (1997) , 8727-8737.
26. A.Zhedanov, Rational Spectral Transformations and Orthogonal
Polynomials, J.Comput.Appl.Math., 85 (1997), 67-86.
27. A.Zhedanov, On some classes of polynomials orthogonal
on arcs of the unit circle connected with symmetric orthogonal
polynomials on an interval, J.Approx.Theory, 93 (1998), 73-106.
28. A.Zhedanov, The "classical" Laurent biorthogonal polynomials
J.Comput.Appl.Math., 98 (1998), 121-147.
29. O.Yermolayeva and A.Zhedanov, Spectral transformations
and generalized Pollaczek polynomials, Methods and Appl.Anal
6 (1999), 261-280.
30. A.Zhedanov, Biorthogonal rational functions and the generalized
eigenvalue problem, J.Approx.Theory, 101 (1999),
303-329.
31. A.Zhedanov and V.Spiridonov, Hypergeometric biorthogonal
rational functions, Uspekhi Matem.Nauk, 54, (1999),
No. 2, 173-174 (in Russian).
32. V. Spiridonov and A. Zhedanov, Spectral transformation
chains and some new biorthogonal rational functions,
Comm. Math. Phys. 210 (2000), 49-83.
33. V. Spiridonov and A. Zhedanov, Classical biorthogonal
rational functions on elliptic grids, C. R. Math. Acad.
Sci. Canada 22, no. 2 (2000), 70-76.
34. L.Vinet, O.Yermolayeva and A.Zhedanov, A new family
of Krall polynomials, Methods and Appl. of Analysis, 8
(2001), 1-14.
35. A. Zhedanov and A. Korovnichenko Leonard pairs in
classical mechanics, J.Phys. A: Math. & Gen. 35
(2002), 5767 - 5780.
36. L.Vinet and A.Zhedanov, Two-Dimensional Krall-She_er
polynomials and quantum systems on spaces with constant
curvature, Letters in Mathematical Physics 65 (2003), 83-94.
37. Y.Nakamura and A.Zhedanov, Special solutions of the
Toda chain and combinatorial numbers, J.Phys. A: Math.
Gen. 37 (2004), 5849-5862.
38. A.Zhedanov, Biorthogonality of the Lagrange interpolants,
J.Comput.Appl.Mathem., 172 (2004), 1-6.
39. V. P. Burskii and A. S. Zhedanov, On Dirichlet problem
for string equation, Poncelet problem, Pell-Abel equation,
and some other related problems, Ukrainian Math. J. 58,
No. 4 (2006), 487-504.
40. V.Spiridonov and A.Zhedanov, Elliptic grids, rational
functions, and Pade interpolation, Ramanujan J., 13,
No. 13 (2007), 285-310.
41. F.Peherstorfer, V.Spiridonov and A.Zhedanov, Toda chain,
Stieltjes function, and orthogonal polynomials, Theor.Mat.Phys.
Volume 151 (2007) Issue 1, 505-528 .
42. V.Spiridonov, S.Tujimoto and A.Zhedanov, Integrable
discrete time chains for the Frobenius-Stickelberger-Thiele
polynomials, Comm.Math.Phys. 272 (2007), 139-165.
43. M.Derevyagin and A.Zhedanov, An operator approach to
multipoint Pade approximations, J.Approx.Theor. 157
(2009), 70-88.
44. A.Zhedanov, Elliptic polynomials orthogonal on the unit
circle with a dense point spectrum, Ramanujan Journal,
19 (2009) 351-384.
45. L.Vinet and A.Zhedanov, The Poncelet problem and the
discrete-time pendulum, J. Phys. A: Math. Theor. 42
175206 (2009).
46. S.Tsujimoto and A.Zhedanov, Elliptic Hypergeometric
Laurent Biorthogonal Polynomials with a Dense Point
Spectrum on the Unit Circle, SIGMA 5 (2009), 033.
47. L.Vinet and A.Zhedanov, Elliptic solutions of the restricted
Toda chain, Lame polynomials and generalization
of the elliptic Stieltjes polynomials, J. Phys. A:
Math. Theor. 42 (2009) 454024.
48. L.Vinet and A.Zhedanov, A 'missing' family of classical
orthogonal polynomials, J. Phys.A: Math and Gen. 44
(2011), 085201.
49. L.Vinet and A.Zhedanov, A limit q = -
荣誉获奖
JSPS long-term fellowship 2009-2010, Kyoto University