# harmonic mean

## Definitions

• WordNet 3.6
• n harmonic mean the mean of n numbers expressed as the reciprocal of the arithmetic mean of the reciprocals of the numbers
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Chambers's Twentieth Century Dictionary
• Harmonic mean the reciprocal of the arithmetical mean of the reciprocals of the quantities concerned
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## Etymology

Chambers's Twentieth Century Dictionary
O. Fr. meien (Fr. moyen)—L. medianus, enlarged form of medius.

## Usage

### In literature:

When you told me that you 'adored and worshipped' Doctor Harmon, did you mean it, or was that the delirium of fever?
"The Harvester" by Gene Stratton Porter
The only means of harmonizing your two wills is to arrange from the first that there shall be but one; and that will must be yours.
"The Marriage Contract" by Honore de Balzac
The new vibration by no means harmonizes.
"Fantasia of the Unconscious" by D. H. Lawrence
The formation of the harmonic basis, which is essentially in four parts, does not by any means devolve upon the wood-wind alone.
"Principles of Orchestration" by Nikolay Rimsky-Korsakov
But Preparation here means Friday, and noon is not the hour needed to harmonize with Mark.
"A Harmony of the Gospels for Students of the Life of Christ" by Archibald Thomas Robertson
It proves that, to produce its highest effects, sacred music must harmonize with the meaning of the words and with the environment.
"Increasing Personal Efficiency" by Russell H. Conwell
The attempt to harmonize different ideas means that in themselves they are discrepant.
"Essays in Experimental Logic" by John Dewey
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### In news:

The expression "one man's trash is another man's treasure" finds new meaning in the documentary "Landfill Harmonic".
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### In science:

Here, C\K has a Green function gK means that gK is continuous and subharmonic in C, harmonic in C\K with gK (z) − log |z | bounded as |z | → ∞, and gK = 0 on K .
Polynomial Interpolation and Approximation in C^d
In this paper we illustrate a method to test the statistical isotropy of the mean of the CMB temperature ﬂuctuations in the spherical harmonic space, and we apply it to the Wilkinson Microwave Anisotropic Probe (WMAP) seven-year observation data.
Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space
We carry out Monte Carlo simulations to test whether the temperature map observed by the WMAP has indeed zero mean in harmonic space.
Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space
It is worth studying how probable the observed inhomogeneous universe can create an apparently anisotropic signal in the mean of the CMB temperature ﬂuctuations in harmonic space through the gravitational lensing effect.
Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space
By applying the method to the WMAP seven-year observation data, We have found a signiﬁcant evidence for a non-zero mean of spherical harmonic coeﬃcients aℓm s at the multipole bin ℓ = 221-240, for the combined Q+V+W map at the 99.93% conﬁdence level with the KQ75y7 mask.
Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space
The centroid (mean position and momentum) follows the simple harmonic motion expected for the classical simple harmonic oscillator, and the Gaussian remains a minimumuncertainty state (with respect to uncertainty in position and momentum) so the Gaussian wavefunction has desirable properties.
Review of Entangled Coherent States
The ﬁrst of the equations (35) means that f +a is determined if one knows its lowest order term in harmonic variables.
Geometry and Harmonic Superspace: some recent progress
In the latter case, e.g., instead of an arithmetic mean of rewards we could use the geometric mean or a harmonic mean (to prevent from getting 0 when one agent scores 0).
On the influence of intelligence in (social) intelligence testing environments
In this paper the problem of harmonized spectrum access in TV whitespaces is addressed. Dynamic spectrum access is a means of managing spectrum enabled through Cognitive Radio . Cognitive radios (CRs) are seen as the solution to the current low usage of the radio spectrum , , .
Game Theoretical Modelling for Dynamic Spectrum Access in TV Whitespace
The F1 measure represents the harmonic mean of the precision and recall values.
Supervised Blockmodelling
The linear equation can be readily solved by standard techniques of separation of variables by means of spherical harmonics.
On the Prediction of Velocity Fields from Redshift Space Galaxy Samples
For large φ the potential is harmonic and there are six quadratic degrees of freedom, implying a mean energy of 3kB T for a classical gas; for a degenerate Bose gas the mean energy is 2.7 kB T .
Bose-Einstein Condensation of Atomic Hydrogen
Then the mean curvature vector of M is paral lel if and only if its Gauss map is a harmonic map.
A Bernstein theorem for special Lagrangian graphs
When we say that a property is a.e. true on ∂X we mean w. r. to some harmonic measure (that is the same, w. r. to every harmonic measure).
Strong and weak mean value properties on trees
Zucca F.: ‘The mean value property for harmonic functions on graphs and trees’, appearing on Ann.
Strong and weak mean value properties on trees
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