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Growth properties of entire functions depending on a parameter

100%

Halvarsson S.

nr 1

71-96

We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.

On certain functions with positive real part

75%

Sendrutiu R.

tom Vol. 32

85-90

On factorization of polynomials with holomorphic coefficients

63%

Frontczak M. , Skibiński A. , Spodzieja S.

1998

tom Vol. 46, no 1

39-54

In the paper some equivalent conditions to pointwise reducibility of polynomials with holomorphic coefficients (in an arbitrary connected set) are given.

Fourth Hankel and Toeplitz determinants for a subclass of analytic functions subordinate to 1+sin(z)

51%

Ganesh K. , Rayaprolu B. S. , Saroja K. , Yakaiah K.

2023

tom Vol. 51, no. 2

321--338

The purpose of the present paper is to determine the coefficient bounds, fourth Hankel determinants, Toeplitz determinants for the function f in a subclass of analytic functions subordinate to 1+sin(z). We also study the Fekete-Szegö inequality and Zalcman conjecture for functions in this class.

Celem tego badania jest ustalenie oszacowań współczynników wyznaczników Hankela czwartego rzędu oraz wyznaczników Toeplitza dla funkcji należących do podklasy funkcji analitycznych podporządkowanych wyrażeniu 1 + sin z. Dodatkowo, analizujemy nierówność Fekete-Szegő-Szegő oraz hipotezę Zalcmana dla funkcji w tejże klasie.

The method of developing the complex stress tensor by basic states for the construction solutions of spatial boundary problems of the linear elasticity theory

51%

Pabyrivskyi V. , Pukach P. , Pabyrivskyi V.

Journal of Applied Mathematics and Computational Mechanics

2024

tom Vol. 23, nr 2

66--78

The apparatus of holomorphic functions of many complex variables is applied to solving spatial boundary value problems of the linear theory of elasticity. The construction of the solution of the boundary value problem is based on the representation of the displacement vector in the form of J. Dougall through spatial harmonic potentials. The transition from spatial harmonic potentials to holomorphic functions of two complex variables z1, z2 was carried out and a boundary value problem for the above functions was formulated. By presenting these holomorphic functions in the form of homogeneous polynomials of order k relative to complex variables z1 , z2 , solutions were constructed by the method of development of the complex tensor of stresses by basic states. The application of this technique is illustrated in the examples of marginal problems, the real components of solutions that correspond to the solutions of Grashof’s problem for an elastic beam. Imaginary components of exact analytical solutions are obtained and corresponding structures of external load vectors for elastic beams of complex cross-section are constructed.