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Delta (/ ˈ d ɛ l t ə /; [1] uppercase Δ, lowercase δ; Greek: δέλτα, délta, ) [2] is the fourth letter of the Greek alphabet. In the system of Greek numerals , it has a value of four. It was derived from the Phoenician letter dalet 𐤃. [ 3 ]
Delta commonly refers to: Delta (letter) (Δ or δ), the fourth letter of the Greek alphabet; D (NATO phonetic alphabet: "Delta"), the fourth letter in the Latin ...
It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values 0 and 1. The mathematical rigor of the delta function was disputed until Laurent Schwartz developed the theory of distributions, where it is defined as a linear form acting on functions.
The definition is the same, except that the neighborhood |x − p| < δ now includes the point p, in contrast to the deleted neighborhood 0 < |x − p| < δ. This makes the definition of a non-deleted limit less general.
A river delta is so named because the shape of the Nile Delta approximates the triangular uppercase Greek letter delta.The triangular shape of the Nile Delta was known to audiences of classical Athenian drama; the tragedy Prometheus Bound by Aeschylus refers to it as the "triangular Nilotic land", though not as a "delta". [8]
The generalized Kronecker delta or multi-index Kronecker delta of order is a type (,) tensor that is completely antisymmetric in its upper indices, and also in its lower indices. Two definitions that differ by a factor of p ! {\displaystyle p!} are in use.
We can also say that the measure is a single atom at x; however, treating the Dirac measure as an atomic measure is not correct when we consider the sequential definition of Dirac delta, as the limit of a delta sequence [dubious – discuss]. The Dirac measures are the extreme points of the convex set of probability measures on X.
Mississippi Delta – green line marks boundary. The Mississippi Delta, also known as the Yazoo–Mississippi Delta, or simply the Delta, is the distinctive northwest section of the U.S. state of Mississippi (and portions of Arkansas and Louisiana) that lies between the Mississippi and Yazoo rivers.