delta
![]() delta |
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pronunciation | |||||||||||||||||||||||
antique | [ d ] | ||||||||||||||||||||||
modern | [ ð ] | ||||||||||||||||||||||
Equivalents | |||||||||||||||||||||||
Latin | D. | ||||||||||||||||||||||
Cyrillic | Д | ||||||||||||||||||||||
Hebrew | ד | ||||||||||||||||||||||
Arabic | د | ||||||||||||||||||||||
Phoenician | ? | ||||||||||||||||||||||
transcription | |||||||||||||||||||||||
From the ancient world | d | ||||||||||||||||||||||
From the modern | d | ||||||||||||||||||||||
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The delta ( Greek Δέλτα , capital letter : Δ, lower case letter : δ) is the fourth letter in the Greek alphabet and has the numerical value 4 according to the Milesian system .
origin
The sign comes from the Phoenician letter Daleth .
example
- Diogenes ( Διογένης )
use
In Greek
In the Greek number font lower-case letter represents δ the number 4 and together with subscript number sign as ͵δ the number 4000. Because of the shape of the capital letter Δ is (since Herodotus histories 2.13 and more often) the lying between the Nilarmen part Lower Egypt as Delta designated , as in the German river delta in general. In addition, the comedy writer Aristophanes uses Delta in Lysistrata verse 151 to denote female shame .
The Greek letter delta as such - and derived as a symbol for calculation quantities, parameters and the like - is also used in many different contexts and areas of knowledge .
mathematics
- The large delta (Δ) serves as the difference sign for
- the difference, see subtraction
- the difference operator - further parameters are derived from this
- the symmetrical difference of set theory
- the Laplace operator (the sum of the second partial derivatives in each spatial direction)
- The small delta (δ) denotes
- the derivative of variation or virtual displacement
- Dirac's δ 'function', see delta distribution
- the Kronecker Delta
- an infinitesimal (hence a small delta), path-dependent change (not a complete differential) of process variables that only occur when the state changes.
An inverted large delta ∇ is called a nabla . The symbol ( TeX ) that denotes a triangle is not a delta .
triangle
Science and Technology
- The large delta (Δ) is used
- in physics as an identifier for four baryons (Δ ++ , Δ + , Δ 0 and Δ - ).
- in molecular biology as a marking of deletions .
- as a term symbol for the characterization of energy states, for example in the singlet oxygen 1 Δ g
- The small delta (δ) denotes
- generally a small difference in arithmetic or measured variables , e.g. B. of times (mostly δt ) or distances ( δs ), in geodesy of small angle and vector differences , or in geometry and adjustment calculations of coordinate allowances (e.g. δx , δy )
- in NMR spectroscopy the chemical shift
- in electrical engineering the so-called loss angle , as well as the equivalent thickness of the conductive layer in the skin effect
- in chassis or vehicle technology, etc. a. the steering angle
- in anatomy, in Aδ fiber , a nerve fiber
- in electroplating the layer thickness
- a clast type in structural geology (see delta clast )
chemistry
- A large delta (Δ) indicates
- on a reaction arrow the supply of heat
- with one or more subsequent superscript locants the position of double bonds in
- partly hydrogenated cyclic compounds (e.g., Δ 3 -carene , Δ 9 -tetrahydrocannabinol , often in the literature for steroids and Indigo used derivatives)
- unsaturated fatty acids (such as Δ 9,12,15 -octadecatrienoic acid )
- A small delta (δ) denotes
- an atomic or molecular partial charge
- the δ bond , a metal-to-metal quadruple bond that occurs when two parallel d orbitals of two metals overlap
- as locant the distance of an atom from a reference atom or a linkage point ( e.g. δ-valerolactone )
- with a preceding locant and the following superscript number the position and number of cumulative double bonds based on an atom, see δ-convention
astronomy
- The small delta (δ) denotes the declination (astronomy) , one of the two equatorial coordinates of stars,
- as well as the third to fifth brightest star of each of the 88 constellations ,
- and the more detailed designation of some meteor streams in order to describe the position of the radiant more precisely in large constellations.
Named sizes and procedures
- Data processing:
- Delta coding , differential storage, a possibility of data compression
- Economics:
- in option theory, the first partial derivation of the option price model based on the price of the underlying asset or underlying.
- an indicator from the valuation of options; see option (economy) #Delta
- as a small delta (δ) the depreciation rate of a capital stock (compare Solow model ).
Others
In the Canadian syllabary there is one letter that looks like the great delta.