The Sign of a Harmonic Function Near a Zero

2001 ◽  
pp. 31-32
Author(s):  
David H. Armitage ◽  
Stephen J. Gardiner
Keyword(s):  
Harmonic Function

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals A note on n-harmonic majorants

1986 ◽  
Vol 34 (3) ◽  
pp. 461-472
Author(s):  
Hong Oh Kim ◽  
Chang Ock Lee
Keyword(s):  
Harmonic Function ◽  
Complex Plane ◽  
Unit Disc ◽  
Dirichlet Integral ◽  
Harmonic Majorant ◽  
Harmonic Majorants

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

On the fatou theorem for p-harmonic function

1988 ◽  
Vol 13 (6) ◽  
pp. 651-668 ◽  
Author(s):  
Juan J. Manfredi ◽  
Allen Weitsman
Keyword(s):  
Harmonic Function ◽  
Fatou Theorem

A noise reduction method for semi-supervised community detection based on harmonic function

2018 ◽  
Vol 32 (14) ◽  
pp. 1850166 ◽  
Author(s):  
Lilin Fan ◽  
Kaiyuan Song ◽  
Dong Liu
Keyword(s):  
Harmonic Function ◽  
Prior Knowledge ◽  
Community Detection ◽  
Detection Methods ◽  
Detection Process ◽  
Knowledge Based ◽  
Detection Approach ◽  
Series Of Experiments ◽  
Novel Strategy ◽  
The Impact

Semi-supervised community detection is an important research topic in the field of complex network, which incorporates prior knowledge and topology to guide the community detection process. However, most of the previous work ignores the impact of the noise from prior knowledge during the community detection process. This paper proposes a novel strategy to identify and remove the noise from prior knowledge based on harmonic function, so as to make use of prior knowledge more efficiently. Finally, this strategy is applied to three state-of-the-art semi-supervised community detection methods. A series of experiments on both real and artificial networks demonstrate that the accuracy of semi-supervised community detection approach can be further improved.

Cancelling of Self-Excited Vibrations by Means of Parametric Excitation

1999 ◽  
Author(s):  
Aleš Tondl ◽  
Horst Ecker
Keyword(s):  
Numerical Simulation ◽  
Harmonic Function ◽  
Parametric Excitation ◽  
Exciting Force ◽  
Mass System ◽  
Parameter Variations ◽  
Simulation Parameter ◽  
Top Mass ◽  
Theoretical Results ◽  
Good Agreement

Abstract The possibility of cancelling self-excited vibrations of a mechanical system using parametric excitation is discussed. A two-mass system is considered, with the top mass excited by a flow-generated self-exciting force. The parameter of the connecting stiffness between the base mass and the foundation is a harmonic function of time and represents a parametric excitation. For such a system general conditions for full vibration cancelling are derived and presented. By means of numerical simulation the system is investigated for several sets of parameters. The theoretical results are found to be in very good agreement with the results obtained by simulation. Parameter variations show the extent of the parameter space where significant vibration cancelling can be achieved and illustrate possible applications.

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