A short note on harmonic functions and zero divisors on the Sierpinski fractal

2015 ◽  
Vol 106 (2) ◽  
pp. 183-188 ◽  
Author(s):  
Brigitte E. Breckner
Keyword(s):  
Harmonic Functions ◽  
Short Note ◽  
Zero Divisors

scholarly journals A short note on harmonic functions on self-similar structures

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 160-166
Author(s):  
Brigitte E. Breckner
Keyword(s):  
Harmonic Functions ◽  
Short Note ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Harmonic Structure ◽  
Zero Divisors ◽  
Self Similar

A sufficient condition is given concerning the harmonic structure on a post critically finite self-similar structure K that ensures that harmonic functions are not zero divisors in the algebra of real-valued continuous functions on K.

Harmonic Spinors on Hyperbolic Space

1993 ◽  
Vol 36 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Pierre-Yves Gaillard
Keyword(s):  
Differential Equations ◽  
Symmetric Space ◽  
Representation Theory ◽  
Hyperbolic Space ◽  
Harmonic Functions ◽  
Short Note ◽  
Harmonic Forms ◽  
Semisimple Symmetric Space ◽  
Invariant Differential ◽  
Harmonic Spinors

AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere considered. The connection between invariant differential equations on a Riemannian semisimple symmetric spaceG/Kand homological aspects of the representation theory ofG, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.

scholarly journals Groebner Basis and its Applications

2019 ◽  
Vol 9 (1) ◽  
pp. 1092-1097
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Science And Technology ◽  
Short Note ◽  
Reaction Network ◽  
Groebner Basis ◽  
Zero Divisors ◽  
Pure Mathematics ◽  
State Detection ◽  
Vast Area

This paper is a survey on Groebner basis and its applications on some areas of Science and Technology. Here we have presented some of the applications of concepts and techniques from Groebner basis to broader area of science and technology such as applications in steady state detection of chemical reaction network (CRN) by determining kinematics equations in the investigation and design of robots. Groebner basis applications could be found in vast area in circuits and systems. In pure mathematics, we can encounter many problems using Groebner basis to determine that a polynomial is invertible about an ideal, to determine radical membership, zero divisors, hence so forth. A short note is being presented on Groebner basis and its applications.

Introduction

2018 ◽  
Author(s):  
Peter Hopkins
Keyword(s):  
Final Section ◽  
Short Note ◽  
Current Situation ◽  
Research Projects ◽  
Everyday Lives ◽  
Early Settlement ◽  
The Everyday ◽  
Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

Short Note: A Record of Twin Fetuses in a Harbor Porpoise (Phocoena phocoena) Stranded on the Dutch Coast

2014 ◽  
Vol 40 (4) ◽  
pp. 394-397 ◽  
Author(s):  
Lonneke L. IJsseldijk ◽  
Andrea Gröne ◽  
Sjoukje Hiemstra ◽  
Jeroen Hoekendijk ◽  
Lineke Begeman
Keyword(s):  
Short Note ◽  
Phocoena Phocoena ◽  
Harbor Porpoise ◽  
Dutch Coast

Short Note: Habitat Characteristics of the Critically Endangered Taiwanese Humpback Dolphins (Sousa chinensis) of the Eastern Taiwan Strait

2014 ◽  
Vol 40 (4) ◽  
pp. 368-374 ◽  
Author(s):  
Lauren E. Dares ◽  
Jordan M. Hoffman ◽  
Shih Chu Yang ◽  
John Y. Wang
Keyword(s):  
Short Note ◽  
Taiwan Strait ◽  
Habitat Characteristics ◽  
Critically Endangered ◽  
Sousa Chinensis

Short Note: Predation of Harbour Porpoises (Phocoena phocoena) by Grey Seals (Halichoerus grypus) in Wales

2015 ◽  
Vol 41 (2) ◽  
pp. 188-191 ◽  
Author(s):  
Thomas Stringell ◽  
Dave Hill ◽  
Dafydd Rees ◽  
Ffion Rees ◽  
Padrig Rees ◽  
...  
Keyword(s):  
Short Note ◽  
Halichoerus Grypus ◽  
Phocoena Phocoena

Impact of Optimal Cropping Patterns on Incomes in a Punjab District

1976 ◽  
Vol 15 (2) ◽  
pp. 218-221
Author(s):  
M. Arshad Chaudhry
Keyword(s):  
Developing Countries ◽  
Linear Programming ◽  
Short Note ◽  
Cropping Pattern ◽  
Small Farms ◽  
Cropping Patterns ◽  
Punjab Province ◽  
Optimal Cropping

To improve farm incomes in developing countries, the foremost question that the farmer must address himself to is: what cropping pattern best uses the fixed resources in order to get the highest returns? During the last decade, the agricultural economists have shown great interest in applying the tools of linear programming to individual farms. Most of the studies conducted elsewhere have shown that, under existing cropping pattern, farm resources were not being utilized optimally on the small farms.[l, 4]. We conducted a survey in the canal-irrigated areas of the Punjab province of Pakistan1 to investigate into the same problem. This short note aims at identifying the opti¬mal cropping pattern and to estimate the increase in farm incomes as a result of a switch towards it on the sampled farms.

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry
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