Radial Growth of a Univalent Function and its Derivatives Off Sets of Measure Zero

1985 ◽  
pp. 69-76
Author(s):  
T. MacGregor
Keyword(s):  
Univalent Function ◽  
Radial Growth ◽  
Measure Zero

scholarly journals Radial growth of harmonic functions in the unit ball

2012 ◽  
Vol 110 (2) ◽  
pp. 273 ◽  
Author(s):  
Kjersti Solberg Eikrem ◽  
Eugenia Malinnikova
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Harmonic Functions ◽  
Radial Growth ◽  
Measure Zero ◽  
Hausdorff Measures ◽  
Doubling Condition ◽  
Exceptional Sets

Let $\Psi_v$ be the class of harmonic functions in the unit disk or unit ball in ${\mathsf R}^m$ which admit a radial majorant $v(r)$. We prove that a function in $\Psi_v$ may grow or decay as fast as $v$ only along a set of radii of measure zero. For the case when $v$ fulfills a doubling condition, we give precise estimates of these exceptional sets in terms of Hausdorff measures.

scholarly journals RADIAL AND TANGENTIAL GROWTH OF CLOSE-TO-CONVEX FUNCTIONS

2005 ◽  
Vol 48 (1) ◽  
pp. 231-240 ◽  
Author(s):  
J. B. Twomey
Keyword(s):  
Univalent Function ◽  
Convex Functions ◽  
Unit Disc ◽  
Radial Growth ◽  
Subject Classification ◽  
Primary 30C55 ◽  
Boundary Points

AbstractSome results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescribed radial growth.AMS 2000 Mathematics subject classification: Primary 30C55

Microsized Structures Fabricated with Nanoparticles as Building Blocks

1998 ◽  
Vol 536 ◽  
Author(s):  
Yongchi Tian ◽  
A. D. Dinsmore ◽  
S. B. Qadri ◽  
B. R. Ratna
Keyword(s):  
Radial Growth ◽  
Building Blocks ◽  
Higher Order ◽  
Surfactant Templating ◽  
Order Structures

AbstractHere we report a nanoparticulate route to Y2O3 nanofibers (~50 nm in diameter and a few micrometers in length) and for the radial growth of ZnS spheres (200-800 nm diameter). Well-defined higher order structures are developed upon thermostatically aging the dispersions of monomeric nanocrystals. The shapes of the “macromolecules„ are correlated to primary monomeric nanocrystallites, the growing time and temperature, and surfactant templating agents. It is anticipated that this approach should inspire fabrication of nanoparticulate structures by using primary nanoparticles as monomers.

DENDROCHRONOLOGICAL RESEARCHES IN ARTIFICIAL PLANTINGS OF NUR-SULTAN CITY

2020 ◽  
Author(s):  
A N. Kabanov ◽  
◽  
S.A. Kabanova ◽  
Keyword(s):  
Pinus Sylvestris ◽  
Radial Growth ◽  
Climatic Conditions ◽  
Solar Insolation ◽  
Dendrochronological Analysis ◽  
Different Ages ◽  
Green Zone

Dendrochronological analysis was carried out in forest cultures of Pinus sylvestris of different ages growing in the green zone of Nur-Sultan city. It was found that the value of the annual radial growth is subject to a cycle with a period of 10-11 years. This is due to climatic conditions, in particular, with periods of solar insolation, which is confirmed by researches of other authors.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

Dynamics of stem radial growth of Picea meyeri during the growing season at the treeline of Luya Mountain, China

2013 ◽  
Vol 36 (9) ◽  
pp. 956-964 ◽  
Author(s):  
Man-Yu DONG ◽  
Yuan JIANG ◽  
Hao-Chun YANG ◽  
Ming-Chang WANG ◽  
Wen-Tao ZHANG ◽  
...  
Keyword(s):  
Radial Growth ◽  
Growing Season

Inhibition of Fungal Growth by Macerated Plant Tissues in a Closed Environment

HortScience ◽  
1998 ◽  
Vol 33 (3) ◽  
pp. 476e-476
Author(s):  
Craig S. Charron ◽  
Catherine O. Chardonnet ◽  
Carl E. Sams
Keyword(s):  
Radial Growth ◽  
Fungal Pathogens ◽  
Solid Phase ◽  
Indian Mustard ◽  
Fungal Growth ◽  
Allyl Isothiocyanate ◽  
Pythium Ultimum ◽  
Alternative Methods ◽  
Gas Chromatography Mass Spectrometry ◽  
Clean Air

The U.S. Clean Air Act bans the use of methyl bromide after 2001. Consequently, the development of alternative methods for control of soilborne pathogens is imperative. One alternative is to exploit the pesticidal properties of macerated tissues of Brassica spp. This study tested the potential of several Brassica spp. for control of fungal pathogens. Pythium ultimum Trow or Rhizoctonia solani Kühn plugs on potato-dextrose agar on petri dishes were sealed in 500-ml glass jars (at 22 °C) containing macerated leaves (10 g) from one of six Brassica spp. Radial growth was measured 24, 48, and 72 h after inoculation. Indian mustard (B. juncea) was the most suppressive, followed by `Florida Broadleaf' mustard (B. juncea). Volatile compounds in the jars were sampled with a solid-phase microextraction device (SPME) and identified by gas chromatography-mass spectrometry (GC-MS). Allyl isothiocyanate (AITC) comprised over 90% of the total volatiles measured from Indian mustard and `Florida Broadleaf' mustard. Isothiocyanates were detected in jars with all plants except broccoli. (Z)-3-hexenyl acetate was emitted by all plants and was the predominant volatile of `Premium Crop' broccoli (B. oleracea L. var. italica), `Michihili Jade Pagoda' Chinese cabbage (B. pekinensis), `Charmant' cabbage (B. oleracea L. var. capitata), and `Blue Scotch Curled' kale (B. oleracea L. var. viridis). To assess the influence of AITC on radial growth of P. ultimum and R. solani, AITC was added to jars to give headspace concentrations of 0.10, 0.20, and 0.30 mg·L–1 (mass of AITC per volume of headspace). Growth of both fungi was inhibited by 0.10 mg·L–1 AITC. 0.20 mg·L–1 AITC was fungicidal to P. ultimum although the highest AITC level tested (0.30 mg·L–1) did not terminate R. solani growth. These results indicate that residues from some Brassica spp. may be a viable part of a soilborne pest control strategy.

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