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 About the Institute Departments · of General Mathematics · of Algebra · of Geometry · of Mathematical Analysis · of Differential Equations · of Theory of Functions and Approximations · of Theoretical Mechanics · of Aerohydromechanics Personal Pages · Prof. M.Arslanov · Prof. F.Avkhadiev · Asc.Prof. V.Fomin · Ass.Prof. K.Igudesman · Asc.Prof. S.Ilyin · Asc.Prof. I.Kayumov · Asc.Prof. M.Malakhaltsev · Prof. D.Mushtari · Ass.Prof. M.Nasrutdinov · Prof. Yu.Obnosov · Asc.Prof. A.Podkovyrin · Asc.Prof. E.Shirokova · Prof. V.Shurygin · Asc.Prof. S.Tronin

Department of Theory of Functions and Approximations
Rus

EDUCATIONAL BACKGROUND

 Doctor of Science (D. Sc., Habilitate) in Mathematics, Sobolev Institute of Math. in Siberian branch of Academy of Science, Novosibirsk, USSR (1990). D. Sc. Thesis: Geometric Properties of Conformal and Locally Quasiconformal Maps with given Boundary Behavior PhD in Mathematics, Kazan State University, USSR (1972). Advisor: Prof. L. A. Aksent'ev. PhD Thesis: Some Sufficient Conditions of Univalence and their Applications to Inverse Boundary-value Problems M. Sc. (cum laudi) in Mathematics, Kazan State University, USSR (1969) Undergraduate at the Kazan State University, Faculty of Mechanics and Mathematics, USSR (1964-1969)

PROFESSIONAL EMPLOYMENT

1969 - present: Chebotarev Inst. of Math. and Mech. of the Kazan State University:

Researcher (1969 - 1974),
Senior Researcher (1974 - 1990),
Principal Researcher (1999 - present),
Head of the Department of Mathematical Analysis (1993 - present),
Head of the Department of Mathematics (1999 - present)

September 1977 - June 1980: University of Annaba, Algeria, Associate Professor
1994 - present: Department of Mathematical Statistics of the Institute of Computer Science and Cybernetics of the Kazan Federal University, Professor
2008 - present: Department of Theory of Functions and Approximations of the Institute of Mechanics and Mathematics Kazan Federal University, Head of the Department

TEACHING EXPERIENCE

• at the Kazan State University: Mathematical Analysis, Geometric Function Theory-Selected Topics, Inverse Boundary-value Problems, Functional Analysis, Convex Analysis, Methods for the Dirichlet Boundary-value Problem, Isoperimetric Inequalities in Mathematical Physics, Complex Analysis
• at the University of Annaba, Algeria (1977 - 1980): Mathematics, Theory of Functions of a Complex Variable, Algebra
• at the Kazan State Pedagogic University (2 Semesters): Algebra
• at the Kazan State Academy of Architecture and Constructions (3 Semesters): Mathematics

Advisor for PhD Thesis of 4 Students: F. Kh. Arslanov(1991), I. R. Kayumov (1997), R. G. Salahudinov (1998), Mohamed Sabri Salem Ali (2000)

GRANTS and AWARDS

• Grants of the Russian Foundation of Basic Research: No 96 - 01 - 00110 (1996 - 1998), No 99 - 01 - 00366 (1999 - 2001), No 02 - 01 - 00168 (2002 - 2004), No 05 - 01 - 00523 (2005 - 2007)
• Grants of the Deutsche Forschungsgemeinschaft in 1998, 1999, 2001, 2002, 2004, 2005, 2007
• Mushtary Prize in the field of Mathematics, Mechanics and Technique (2004, Tatarstan Academy of Science competition)
• Internal Prizes of the Kazan State University for Best Research Paper of the Year (1979, 1983, 1993)

CONFERENCE PRESENTATIONS (incomplete list)

• Int. Conf. on Function Spaces, Approximation Theory, Nonlinear Analysis, dedicated to the centennial of S. M. Nikolskii, Moscow, Russia, May 23-29, 2005
• Int. Conf. on Algebra and Analysis, Kazan, Russia, July 2 - 9, 2004
• Int. Conf. on Geometric Analysis and Appl., Volgograd, Russia, May 24-30, 2004
• Int.Workshop on Potential Theory and Appl., Kiev, Ukraine, August, 2003
• Int. Conf. on Geometric Function Theory, dedicated to Herbert Groetzsch, Halle, Germany, May 27-30, 2002
• Int. Conf., dedicated to D. F. Egorov, Kazan, Russia, September 13-18, 1999
• Int. Conf., dedicated to P. L. Chebyshev, Moscow, Russia, May, 1996
• Int. Workshop on Planar Harmonic Mappings, Technion, Haifa, Israel, May 8-15, 1995
• IX Int. Conf. on Finite Elements in Fluids, Venice, Italy, October 15-21, 1995
• Int. Congress of Mathematics, Zurich, July 2-10, 1994
• Int. Conf. and the VII-th Romanian - Finnish Seminar on Complex Analysis, Timishoara, Rumania, August 23-27, 1993
• I European Congress of Mathematics, Paris, France, July 6 - 10, 1992

LIST of MAIN PUBLICATIONS

63. Avkhadiev, F.G.; Wirths, K.-J. Unified Poincar\'e and Hardy inequalities with sharp constants for convex domains. ZAMM, 14, No. 8-9, 532-632 (2007).

62. Avkhadiev, F.G.; Chuprunov, A.N. The probability of a successful allocation of ball groups by boxes. Lobachevskii J. Math., 25, 3-7 (2007).

61. Avkhadiev, F.G.; Wirths, K.-J. The punishing factors for convex pairs are 2^n-1. Revista Mat. Iberoamericana, 23, No. 3, 847-860 (2007).

60. Avkhadiev, F.G.; Wirths, K.-J. Punishing factors and Chua's conjecture. Bull. Belgian Math. Soc., Simon Stevin, 14, 333-340 (2007).

59. Avkhadiev, F.G.; Wirths, K.-J. Sharp Bounds for Sums of Coefficients of Inverses of Convex Functions. Comp. Methods and Function Theory, 7, No. 1, 105-109 (2007).

58. Avkhadiev, F.G.; Wirths, K.-J. A proof of the Livingston conjecture. Forum Mathematicum, 19, 149-157 (2007).

57. Avkhadiev, F.G.; Wirths, K.-J. Subordination under concave univalent functions. Complex Variables and Elliptic Equations, 52, No. 4, 299-305 (2007).

56. Avkhadiev, F.G. Hardy-Type Inequalities on Planar and Spatial Open Sets. (Russian, English) Proc. Steklov Inst. Math., 255, 1-11 (2006); translation from Trudy Mat. Inst. V. A. Steklova, 255, 8-18 (2006).

55. Avkhadiev, F.G.; Pommerenke, Ch.; Wirths, K.-J. Sharp inequalities for the coefficients of concave univalent functions. Commentarii Mathematicae Helvetici, 81, 801-807 (2006).

54. Avkhadiev, F.G. Hardy type inequalities in higher dimensions with explicit estimate of constants. Lobachevskii J. Math., 21, 3-31 (2006).

53. Avkhadiev, F.G.; Wirths, K.-J. Punishing Factors for Finitely Connected Domains. Monatshefte Math., 147, 103-115 (2005).

52. Avkhadiev, F.G. A Simple Proof of the Gauss-Winckler Inequality. Amer. Math. Monthly, 112, No.5, 459-462 (2005).

51. Avkhadiev, F.G.; Kacimov, A.R. Analytic solutions and estimations for microlevel flows in fracturs. J. Porous Media, 8, No.2, 125-148 (2005).

50. Avkhadiev, F.G.; Wirths, K.-J. The Conformal Radius as a Function and its Gradient Image. Israel J. Math., 149, 349-374 (2005).

49. Avkhadiev, F.G. New isoperimetric inequalities for moments of domains and torsional rigidity. (Russian, English) Russ. Math. 48, No.7, 1-9 (2004); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2004, 48 No.7, 3-11 (2004).

48. Avkhadiev, F.G. Conformally Invariant Inequalities in Mathematical Physics . (Russian) Naukoemkie Tekhnol., 5(4), 47-51 (2004).

47. Avkhadiev, F.G. Mobius transformations and multiplicative representations for spherical potentials. Publications de l'Institut Mathematique. Nouvelle serie (Beograd), Tome 75(89), 253-260 (2004).

46. Avkhadiev, F.G.; Kayumov, I.R. Comparison theorems of isoperimetric type for moments of compact sets. Collectanea Math. 55, no. 1, 1-9 (2004).

45. Avkhadiev, F.G.; Pommerenke, Ch.; Wirths, K.-J. On the coefficients of concave univalent functions. Math. Nachr. 271, 3-9 (2004).

44. Avkhadiev, F.G.; Wirths, K.-J. Schwarz-Pick Inequality for Hyperbolic Domains in the Extended Plane. Geometriae Dedicata, 106, 1-10 (2004).

43. Avkhadiev, F.G.; Wirths, K.-J. Poles Near the Origin Produce Lower Bounds for Coefficients of Meromorphic Univalent Functions. Michigan Math. J. 52(1), 119-130 (2004).

42. Avkhadiev, F.G.; Wirths, K.-J. On a conjecture of Livingston. Mathematika, 46(69), No.1, 19-23 (2004).

41. Avkhadiev, F.G.; Wirths, K.-J. Punishing Factors for Angles. Computational Methods and Function Theory, 3, No.1, 127-141 (2003).

40. Avkhadiev, F.G.; Wirths, K.-J. Schwarz-Pick Inequality for Derivatives of Arbitrary Order. Constr. Approx. 19, 265-277 (2003).

39. Avkhadiev, F.G.; Salahudinov, R.G. Isoperimetric inequalities for conformal moments of plane domains. J. Inequal. Appl. 7, No.4, 593-601 (2002).

38. Avkhadiev, F.G.; Wirths, K.-J. Convex holes produce lower bounds for coefficients. Complex Variables,Theory Appl. 47, No.7, 553-563 (2002).

37. Avkhadiev, F.G.; Maklakov, D.V. New equations of convolution type obtained by replacing the integral by the maximum. (Russian, English) Math. Notes 71, No.1, 17-24 (2002); translation from Mat. Zametki 71, No.1, 18-26 (2002).

36. Avkhadiev, F.G.; Wirths, K.-J. On the coefficient multipliers theorem of Hardy and Littlewood. Lobachevskii J. Math. 11, 7-12, electronic only (2002).

35. Avkhadiev, F.G.; Elizarov, A.M. Bilateral estimates of the critical Mach number for some classes of carrying wing profiles. ANZIAM J. 42, No.4, 494-503 (2001).

34. Avhadiev, F.G.; Salahutdinov, R.G. Bilateral isoperimetric inequalities for boundary moments of plane domains. Lobachevskii J. Math. 9, 3-5, electronic only (2001).

33. Avkhadiev, F.G.; Wirths, K.-J. Asymptotically sharp bounds in the Hardy-Littlewood inequalities on mean values of analytic functions. Bull. Lond. Math. Soc. 33, No.6, 695-700 (2001).

32. Avhadiev, F.G.; Schulte, N.; Wirths, K.-J. On the growth of nonvanishing analytic functions. Arch. Math. 74, No.5, 356-364 (2000).

31. Avhadiev, F.G.; Kayumov, I.R. Admissible functionals and infinite-valent functions. Complex Variables, Theory Appl. 38, No.1, 35-45 (1999).

30. Avhadiev, Farit; Wirths, Karl-Joachim Estimates of derivatives in an $\alpha$-invariant set of analytic functions. Analysis, 19, No.1, 19-27 (1999).

29. Avkhadiev, F.G. Variational conformally invariant inequalities and their applications. (Russian, English) Dokl. Math. 57, No.2, 278-281 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 359, No.6, 727-730 (1998).

28. Avkhadiev, F.G. Solution of the generalized Saint Venant problem. (Russian, English) Sb. Math. 189, No.12, 1739-1748 (1998); translation from Mat. Sb. 189, No.12, 3-12 (1998).

27. Avkhadiev, F.G.; Aksent'ev, L.A.; Bil'chenko, G.G. Classes of univalent and multivalent Schwarz-Christoffel integrals and their applications. (Russian, English) Russ. Math. 41, No.3, 63-66 (1997); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1997, No.3(418), 64-67 (1997).

26. Avkhadiev, F.G. Conformal maps and boundary-value problems. (Russian) Monograph, ISBN 5-9000975-03-7,Matematika Foundation in Kazan, Kazan, 216 pages (1996).

25. Avkhadiev, F.G.; Kayumov, I.R. Estimates in the Bloch class and their generalizations. (Russian, English) Dokl. Math. 54, No.1, 574-576 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 349, No.5, 583-585 (1996).

24. Avkhadiev, F.G. Conformal mappings that satisfy the boundary condition of equality of metrics. (Russian, English) Dokl. Math. 53, No.2, 194-196 (1996); translation from Dokl. Akad. Nauk 347, No.3, 295-297 (1996).

23. Avkhadiev, F.G.; Elizarov, A.M. Exact bounds of solution to a variation inverse boundary value problem in a countable-connected domain. (Russian, English) Russ. Math. 40, No.3, 1-11 (1996); translation from Isv. Vyssh. Zaved., Mat. 1996, No.3(406), 3-13 (1996).

22.Avhadiev, F.G.; Kayumov, I.R. Estimates for Bloch functions and their generalization. Complex Variables, Theory Appl. 29, No.3, 193-201 (1996).

21. Avkhadiev, F.G.; Maklakov, D.V. The analytic method for construction of the hydrodynamic profile according to a given cavitation diagram. (Russian, English) Phys.-Dokl. 40, No.7, 356-358 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 343, No.2, 195-197 (1995).

20. Avkhadiev, F.G.; Elizarov, A.M.; Fokin, D.A. Estimates for critical Mach number under isoperimetric constraints. Eur. J. Appl. Math. 6, No.5, 385-398 (1995).

19. Avkhadiev, F.G.; Shokleva, L.I. Generalizations of certain Beurling's theorem with applications for inverse boundary value problem. (Russian, English) Russ. Math. 38, No.5, 78 81 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No.5(384), 80-83 (1994).

18. Avkhadiev, F.G.; Shabalina, S.B. Zeros of coefficients of transforms and conditions for the solvability of inverse boundary value problems. (Russian, English) Russ. Math. 38, No.8, 1-9 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No.8(387), 3-10 (1994).

17. Avkhadiev, F.G.; Maklakov, D.V. A solvability criterion for a problem of design of profiles by cavitation diagram. (Russian, English) Russ. Math. 38, No.7, 1-10 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No.7(386), 3-12 (1994).

16. Avkhadiev, F.G.; Elizarov, A.M.; Fokin, D.A. Maximization of the critical Mach number for lifting airfoils. (Russian, English) Fluid Dyn. 27, No.3, 423-428 (1992); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 1992, No.3, 155-162 (1992).

15. Avkhadiev, F.G. Estimates in the Zygmund class and their application to boundary value problems. (Russian, English) Sov. Math., Dokl. 40, No.1, 217-220 (1990); translation from Dokl. Akad. Nauk SSSR 307, No.6, 1289-1292 (1989).

14. Avkhadiev, F.G. Admissible functionals under injectivity conditions for differentiable mappings of n-dimensional domains. (Russian, English) Sov. Math. 33, No.4, 1-12 (1989); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1989, No.4(323), 3-12 (1989).

13. Avkhadiev, F.G. On injectivity in the domain of open isolated mappings with given boundary properties. (Russian, English) Sov. Math., Dokl. 35, 117-120 (1987); translation from Dokl. Akad. Nauk SSSR 292, 780-783 (1987).

12. Avkhadiev, F.G.; Aksent'ev, L.A.; Elizarov, A.M. Sufficient conditions for the finite-valence of analytic functions and their applications. (Russian, English) J. Sov. Math. 49, No.1, 715-799 (1990); translation from Itogi Nauki Tekh., Ser. Mat. Anal. 25, 3-121 (1987).

11. Avkhadiev, F.G.; Aksent'ev, L.A. Progress and problems in sufficient conditions for finite-valence of analytic functions. (Russian, English) Sov. Math. 30, No.10, 1-20 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No.10(293), 3-16 (1986).

10. Avkhadiev, F.G.; Nasyrov, S.R. Construction of a Riemann surface with respect to its boundary. (Russian, English) Sov. Math. 30, No.5, 1-12 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No.5(288), 3-11 (1986).

9. Avkhadiev, F.G. Some geometric inequalities and sufficient conditions for p-valence. (Russian, English) Sov. Math. 27, No.10, 1-13 (1983); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1983, No.10(257), 3-12 (1983).

8. Avhadiev, F.G. Sufficient conditions for the univalence of quasiconformal mappings. (Russian, English) Math. Notes 18, 1063-1067 (1975); translation from Mat. Zametki 18, 793- 802 (1975).

7. Avhadiev, F.G.; Aksent'ev, L.A. The main results on sufficient conditions for an analytic function to be schlicht. (Russian, English) Russ. Math. Surv. 30, No.4, 1-63 (1975); translation from Usp. Mat. Nauk 30, No.4(184), 3-60 (1975).

6. Avkhadiev, F.G. Sufficient conditions for one-sheetedness in nonconvex domains. (Russian, English) Sib. Math. J. 15(1974), 679-685 (1975); translation from Sib. Mat. Zh. 15, 963-971 (1974).

5. Avhadiev, F.G.; Aksent'ev, L.A. Functions of the Bazilevic class in the disc and in an annulus. (Russian, English) Sov. Math., Dokl. 15, 78-82 (1974); translation from Dokl. Akad. Nauk SSSR 214, 241-244 (1974).

4. Avhadiev, F.G.; Aksent'ev, L.A. The subordination principle in sufficient conditions for univalence. (Russian, English) Sov. Math., Dokl. 14, 934-939 (1973); translation from Dokl. Akad. Nauk SSSR 211, 19-22 (1973).

3. Avkhadiev, F.G.; Aksent'ev, L.A. Sufficient conditions for univalence of analytic functions. (Russian, English) Sov. Math., Dokl. 12, 859-863 (1971); translation from Dokl. Akad. Nauk SSSR 198, 743-746 (1971).

2. Avkhadiev, F.G. Radii of convexity and close-to-convexity of certain integral representations. (Russian, English) Math. Notes 7, 350-357 (1970); translation from Mat. Zametki 7, 581-592 (1970).

1. Avkhadiev, F.G. On sufficient conditions for univalence of solutions of inverse boundary value problems. (Russian, English) Sov. Math., Dokl. 11, 109-112 (1970); translation from Dokl. Akad. Nauk SSSR 190, 495-498 (1970).

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