scholarly journals ANALYTIC FUNCTIONS OF INFINITE ORDER ON THE HALF-PLANE WITH ZEROS ON IMAGINARY AXIS

2021 ◽  
pp. 287
Author(s):  
T. V. Shevtsova
Keyword(s):  
Half Plane ◽  
Analytic Functions ◽  
Imaginary Axis ◽  
Infinite Order

Analytic stress solution for a circular tunnel in half plane with a concentrated force

2019 ◽  
Vol 24 (12) ◽  
pp. 3862-3879
Author(s):  
Hui Cai ◽  
Ai-zhong Lu ◽  
Yao-cai Ma
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
Half Plane ◽  
Analytic Functions ◽  
Surrounding Rock ◽  
Circular Tunnel ◽  
Concentrated Force ◽  
Stress Solution ◽  
Stress Boundary Condition ◽  
Stress Boundary

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

scholarly journals Differential Subordination Results for Analytic Functions in the Upper Half-Plane

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huo Tang ◽  
M. K. Aouf ◽  
Guan-Tie Deng ◽  
Shu-Hai Li
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Upper Half Plane ◽  
Admissible Functions

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

scholarly journals Radius of starlikeness for some classes containing non-univalent functions

2021 ◽  
pp. 2250009
Author(s):  
Shalu Yadav ◽  
Kanika Sharma ◽  
V. Ravichandran
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Univalent Function ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
The Past ◽  
The Right ◽  
Starlike Univalent Function

A starlike univalent function [Formula: see text] is characterized by [Formula: see text]; several subclasses of starlike functions were studied in the past by restricting [Formula: see text] to take values in a region [Formula: see text] on the right-half plane, or, equivalently, by requiring [Formula: see text] to be subordinate to the corresponding mapping of the unit disk [Formula: see text] to the region [Formula: see text]. The mappings [Formula: see text], [Formula: see text], defined by [Formula: see text] and [Formula: see text] map the unit disk [Formula: see text] to certain nice regions in the right-half plane. For normalized analytic functions [Formula: see text] with [Formula: see text] and [Formula: see text] are subordinate to the function [Formula: see text] for some analytic functions [Formula: see text] and [Formula: see text], we determine the sharp radius for them to belong to various subclasses of starlike functions.

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