Complex Analysis and Potential Theory: Proceedings of the by Tahir Aliyev Azeroglu, Promarz M. Tamrazov

By Tahir Aliyev Azeroglu, Promarz M. Tamrazov

This quantity gathers the contributions from amazing mathematicians, reminiscent of Samuel Krushkal, Reiner Kühnau, Chung Chun Yang, Vladimir Miklyukov and others.It can assist researchers to resolve difficulties on advanced research and capability idea and speak about numerous purposes in engineering. The contributions additionally replace the reader on fresh advancements within the box. furthermore, a distinct a part of the quantity is totally dedicated to the formula of a few vital open difficulties and fascinating conjectures.

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LAVRENTIEV: S u r u n e classe de representations continue. - Math. , v. 42, n. 4, 1935, 407-424. On distortion under quasiconformal mappings. - DAN SSSR, v. 91, 26. P. BELINSKII: n. 5, 1953, 997-998. 27. P. BELINSKII: On measure area under quasiconformal mappings . - DAN SSSR, v. 121, n. 1, 1958, 16-17. Solution of extremal problems of the quasiconformal mappings theory 28. P . P . BELINSKII: with the variational method. - Sib. math. , v. 1, n. 3, 1960, 303-330. 29. L. KRUSHKAL’: O n mappings E-quasiconformal in ”means”.

Without loss of generality, we assume d l 5 d2. Therefore, k 5 2d2 1. Note that n > 3 and k / d a is an integer. We deduce that k = 2d2. And thus d2 = d l 1, which shows that d l and d2 are relatively prime. Note that d l can divide k . Thus, there + + 32 are two possibilities: dl = 1 or d l = 2. Therefore, k = 4 or k = 6, which contradicts the assumption. Hence F can not satisfy (iii) in Theorem A. A similar arguments shows that P ( f ) can not satisfy (ii) in Theorem A as well. By Theorem 2, we see that ( 3 ) holds for any positive number E .

9. A. BRAKALOVA Math. 76, 67-92, 1998. 0 . MARTIO,T. SUGAWA and M. VUORINEN: O n the Degenerate 10. V. GUTLYANSKII, Beltrami Equation. Trans. Amer. Math. ,v. 357, n. 3, 2005, 875-900. 11. 0. M. MIKLYUKOV: O n existence and uniqueness of degenerate Beltrami equation. - Complex Var. Theory Appl. 49, n. , 12. M. MIKLYUKOV: Isothermac coordinates o n singular surfaces. - Mat. Sb. 195,n. 1, 2004, 69-88. Conformal representation. mhridge at the University Press, 13. C . CARATH~ODORY: 1932. 44 14. J. EELLSand B.

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