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What (who) is hourly basis - definition

NUMBER OF METEORS A SINGLE OBSERVER WOULD SEE IN AN HOUR OF PEAK ACTIVITY FOR THE METEOR SHOWER

Zenith Hourly Rate; Zenith hourly rate; Zenithal Hourly Rate

Standard basis

BASIS OF EUCLIDEAN SPACE CONSISTING OF ONE-HOT VECTORS

Standard bases; Standard basis vector; Kronecker basis; Standard unit vector

In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as \mathbb{R}^n or \mathbb{C}^n) is the set of vectors whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane \mathbb{R}^2 formed by the pairs of real numbers, the standard basis is formed by the vectors

https://en.wikipedia.org/wiki/Standard_basis

Basis (universal algebra)

STRUCTURE INSIDE OF SOME (UNIVERSAL) ALGEBRAS, WHICH ARE CALLED FREE ALGEBRAS. IT GENERATES ALL ALGEBRA ELEMENTS FROM ITS OWN ELEMENTS BY THE ALGEBRA OPERATIONS IN AN INDEPENDENT MANNER

Basis (Universal Algebra)

In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner.

https://en.wikipedia.org/wiki/Basis_(universal_algebra)

Dual basis

BASIS ON A DUAL VECTOR SPACE CANONICALLY ASSOCIATED TO A BASIS ON THE ORIGINAL VECTOR SPACE

Reciprocal basis

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), the dual set of B is a set B∗ of vectors in the dual space V∗ with the same index set I such that B and B∗ form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V∗.

https://en.wikipedia.org/wiki/Dual_basis

Wikipedia

Zenithal hourly rate

In astronomy, the zenithal hourly rate (ZHR) of a meteor shower is the number of meteors a single observer would see in an hour of peak activity if it was at the zenith, assuming the seeing conditions are excellent (when and where stars with apparent magnitudes up to 6.5 are visible to the naked eye). The rate that can effectively be seen is nearly always lower and decreases the closer the radiant is to the horizon.

The formula to calculate the ZHR is:

$ZHR={\cfrac {{\overline {HR}}\cdot F\cdot r^{6.5-lm}}{\sin(h_{R})}}$

where

${\overline {HR}}={\cfrac {N}{T_{eff}}}$

represents the hourly rate of the observer. N is the number of meteors observed, and T_eff is the effective observation time of the observer.

Example: If the observer detected 12 meteors in 15 minutes, their hourly rate was 48 (12 divided by 0.25 hours).

$F={\cfrac {1}{1-k}}$

This represents the field of view correction factor, where k is the percentage of the observer's field of view which is obstructed (by clouds, for example).

Example: If 20% of the observer's field of view were covered by clouds, k would be 0.2 and F would be 1.25. The observer should have seen 25% more meteors, therefore multiply by F = 1.25.

$r^{6.5-lm}$

This represents the limiting magnitude correction factor (Population index). For every change of 1 magnitude in the limiting magnitude of the observer, the number of meteors observed changes by a factor of r. Therefore, this must be taken into account.

Example: If r is 2, and the observer's limiting magnitude is 5.5, the hourly rate is multiplied by 2 (2 to the power 6.5–5.5), to know how many meteors they would have seen if their limiting magnitude was 6.5.

$\sin(h_{R})$

This represents the correction factor for the altitude of the radiant above the horizon (h_R). The number of meteors seen by an observer changes as the sine of the radiant height.

Example: If the radiant was at an average altitude of 30° during the observation period, the observer's hourly rate will need to be divided by 0.5 (sin 30°) to know how many meteors they would have seen if the radiant was at the zenith.

https://en.wikipedia.org/wiki/Zenithal hourly rate

Examples of use of hourly basis

1. The economy changes on a daily, even hourly basis.

2. Regulators have been in touch with Lehman on an almost hourly basis in recent days.

3. Advertisement Take for example workers who work on an hourly basis.

4. His condition is being monitored on an hourly basis,» Verma told mediapersons outside the hospital here.

5. In 1''', men earned 13 percent more than their female colleagues on an hourly basis.