Kronecker delta

[′krō·nek·ər ‚del·tə]

(mathematics)

The function or symbol δ_ijdependent upon the subscripts i and j which are usually integers; its value is 1 if i = j and 0 if i ≠ j.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Kronecker Delta

a function δ_nm that is dependent on two integral arguments n and m and is defined by

An example of the use of the Kronecker symbol is

The Kronecker symbol was introduced by L. Kronecker in 1866.

Mentioned in

References in periodicals archive

The number of separate terms in the expressions for the generalized Kronecker delta, if written only by using the standard Kronecker delta symbol, is given by the so-called double factorial (2n)!/(2"n!).

High-accuracy approximation of high-rank derivatives: isotropic finite differences based on lattice-Boltzmann stencils

Lemma 3.3 Let [[alpha].sub.i] = [C.sub.i-1] + [[delta].sub.i,1] where [[delta].sub.i,1] denotes the Kronecker delta. Then the central binomial coefficient is given by the sum

Number of cycles in the graph of 312-avoiding permutations

where [R.sub.out] = R(x, [y.sub.obs], z), [R.sub.in] = R(x, -[y.sub.obs], z), [[delta].sub.wg] is the Kronecker delta, g = [perpendicular to], [parallel] and w = [perpendicular to], [parallel] represent the incident and scattered wave polarization, respectively, and

GENERALIZED WAIT-HILL FORMULATION ANALYSIS OF LUMPED-ELEMENT PERIODICALLY-LOADED ORTHOGONAL WIRE GRID GENERIC FREQUENCY SELECTIVE SURFACES

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes system (1)-(2) response to Kronecker delta [delta](k - [k.sub.0]) at time [k.sub.1], i.e.

Generalised fractional indexes approximation with application to discrete-time generalised weyl symbol computation/Apibendrinta trupmeniniu indeksu aproksimacija naudojant apibendrintu Veilo simboliu skaiciavima

Let [[delta].sub.i] (j) be the Kronecker delta function on S, that is for i, j [member] S

A class of limit theorems for arbitrary information source on generalized random selection systems

[[delta].sub.ij] is the Kronecker delta tensor and [eta] is the viscosity.

Analysis of polymer flow in embossing stage during thermal nanoimprint lithography

where [[delta].sub.k-j] is the Kronecker delta function given by

Adaptive nonlinear model predictive control based on Wiener model

where the brackets <> denote the so-called projection, i.e., the inner product and where [delta] denotes the Kronecker delta. From these basis vectors, we define their tetrad components as

On a geometric theory of generalized chiral elasticity with discontinuities

where the Kronecker delta guarantees the neutrality of the system.

Exact Partition Function for the Random Walk of an Electrostatic Field