scholarly journals A Fundamental Inequality of Algebroidal Function

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yingying Huo ◽  
Daochun Sun
Keyword(s):  
Angular Domain ◽  
Algebroidal Function

By using a new mapping of Ahlfors covering surfaces, a fundamental inequality in the angular domain for the algebroidal function is obtained.

ON A HOMOGENEOUS PARABOLIC PROBLEM IN AN INFINITE ANGULAR DOMAIN

2019 ◽  
Vol 7 (1) ◽  
pp. 38-52
Author(s):  
Jenaliyev M.T. ◽  
◽  
Ramazanov M.I. ◽  
Iskakov S.A. ◽  
Keyword(s):  
Parabolic Problem ◽  
Angular Domain

Deep illumination angular domain spectroscopic imaging: tissue-mimicking phantom study

2011 ◽  
Author(s):  
Yan Zhang ◽  
Fartash Vasefi ◽  
Eldon Ng ◽  
Astrid Chamson-Reig ◽  
Bozena Kaminska ◽  
...  
Keyword(s):  
Spectroscopic Imaging ◽  
Phantom Study ◽  
Angular Domain

scholarly journals Borel Directions and Uniqueness of Meromorphic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
HongYan Xu ◽  
Hongxun Yi
Keyword(s):  
Meromorphic Functions ◽  
Angular Domain ◽  
Recent Theorem ◽  
The Relationship

We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line. Our result is an improvement of a recent theorem given by Long and Wu (2012).

scholarly journals Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain

2020 ◽  
Vol 27 (2) ◽  
pp. 211-231
Author(s):  
Roland Duduchava ◽  
Medea Tsaava
Keyword(s):  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Bessel Potential ◽  
Angular Domain ◽  
Mixed Boundary Value Problems ◽  
Classical Setting ◽  
Mellin Convolution ◽  
Bessel Potential Spaces

AbstractThe purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain {\Omega_{\alpha}\subset\mathbb{R}^{2}} of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces {\mathbb{H}^{s}_{p}(\Omega_{\alpha})}, {s>\frac{1}{p}}, {1<p<\infty}. The investigation is carried out using the potential method by reducing the problems to an equivalent boundary integral equation (BIE) in the Sobolev–Slobodečkii space on a semi-infinite axis {\mathbb{W}^{{s-1/p}}_{p}(\mathbb{R}^{+})}, which is of Mellin convolution type. Applying the recent results on Mellin convolution equations in the Bessel potential spaces obtained by V. Didenko and R. Duduchava [Mellin convolution operators in Bessel potential spaces, J. Math. Anal. Appl. 443 2016, 2, 707–731], explicit conditions of the unique solvability of this BIE in the Sobolev–Slobodečkii {\mathbb{W}^{r}_{p}(\mathbb{R}^{+})} and Bessel potential {\mathbb{H}^{r}_{p}(\mathbb{R}^{+})} spaces for arbitrary r are found and used to write explicit conditions for the Fredholm property and unique solvability of the initial model BVPs for the Helmholtz equation in the non-classical setting. The same problem was investigated in a previous paper [R. Duduchava and M. Tsaava, Mixed boundary value problems for the Helmholtz equation in arbitrary 2D-sectors, Georgian Math. J. 20 2013, 3, 439–467], but there were made fatal errors. In the present paper, we correct these results.

Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values

2021 ◽  
Vol 58 (1) ◽  
pp. 104-118
Author(s):  
Yang Tan ◽  
Qingcai Zhang
Keyword(s):  
Conformal Mapping ◽  
Meromorphic Functions ◽  
Angular Domain ◽  
Uniqueness Results ◽  
Algebroid Functions

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

Sign in / Sign up

Export Citation Format

Share Document