Growth theorem of convex mappings on bounded convex circular domains

1998 ◽  
Vol 41 (2) ◽  
pp. 123-130 ◽  
Author(s):  
Taishun Liu ◽  
Guangbin Ren
Keyword(s):  
Growth Theorem ◽  
Convex Mappings ◽  
Circular Domains ◽  
Bounded Convex

scholarly journals The Lindelöf principle and angular derivatives in convex domains of finite type

2002 ◽  
Vol 73 (2) ◽  
pp. 221-250 ◽  
Author(s):  
Marco Abate ◽  
Roberto Tauraso
Keyword(s):  
Finite Type ◽  
Boundary Behaviour ◽  
Convex Domains ◽  
Kobayashi Distance ◽  
Angular Derivatives ◽  
Circular Domains ◽  
Lindelöf Principle ◽  
Real Analytic ◽  
Bounded Convex ◽  
Carathéodory Theorem

AbstractWe describe a generalization of the classical Julia-Wolff-Carathéodory theorem to a large class of bounded convex domains of finite type, including convex circular domains and convex domains with real analytic boundary. The main tools used in the proofs are several explicit estimates on the boundary behaviour of Kobayashi distance and metric, and a new Lindelöf principle.

scholarly journals Kernel convergence and biholomorphic mappings in several complex variables

2003 ◽  
Vol 2003 (67) ◽  
pp. 4229-4239 ◽  
Author(s):  
Gabriela Kohr
Keyword(s):  
Unit Ball ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Compact Sets ◽  
Growth Theorem ◽  
Convex Mappings ◽  
Loewner Chains ◽  
Kernel Convergence

We deal with kernel convergence of domains inℂnwhich are biholomorphically equivalent to the unit ballB. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings onB, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings onB.

Convex mappings on some circular domains

2009 ◽  
Vol 53 (5) ◽  
pp. 1265-1274
Author(s):  
Yi Hong ◽  
WenGe Chen
Keyword(s):  
Convex Mappings ◽  
Circular Domains

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals Magnetic Configurations in Modulated Cylindrical Nanowires

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 600
Author(s):  
Cristina Bran ◽  
Jose Angel Fernandez-Roldan ◽  
Rafael P. del Real ◽  
Agustina Asenjo ◽  
Oksana Chubykalo-Fesenko ◽  
...  
Keyword(s):  
Domain Walls ◽  
Magnetocrystalline Anisotropy ◽  
Logic Gates ◽  
Local Domain ◽  
Magnetic Nanowires ◽  
Precise Control ◽  
Magnetic Layers ◽  
State Present ◽  
Circular Domains ◽  
3D Applications

Cylindrical magnetic nanowires show great potential for 3D applications such as magnetic recording, shift registers, and logic gates, as well as in sensing architectures or biomedicine. Their cylindrical geometry leads to interesting properties of the local domain structure, leading to multifunctional responses to magnetic fields and electric currents, mechanical stresses, or thermal gradients. This review article is summarizing the work carried out in our group on the fabrication and magnetic characterization of cylindrical magnetic nanowires with modulated geometry and anisotropy. The nanowires are prepared by electrochemical methods allowing the fabrication of magnetic nanowires with precise control over geometry, morphology, and composition. Different routes to control the magnetization configuration and its dynamics through the geometry and magnetocrystalline anisotropy are presented. The diameter modulations change the typical single domain state present in cubic nanowires, providing the possibility to confine or pin circular domains or domain walls in each segment. The control and stabilization of domains and domain walls in cylindrical wires have been achieved in multisegmented structures by alternating magnetic segments of different magnetic properties (producing alternative anisotropy) or with non-magnetic layers. The results point out the relevance of the geometry and magnetocrystalline anisotropy to promote the occurrence of stable magnetochiral structures and provide further information for the design of cylindrical nanowires for multiple applications.

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