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In mathematics, the Kronecker sum of discrete Laplacians, named after Leopold Kronecker, is a discrete version of the separation of variables for the continuous...

properties, e.g., they are Kronecker sums of one-dimensional discrete Laplacians, see Kronecker sum of discrete Laplacians, in which case all its eigenvalues...

discrete Laplacian on a regular grid, which is presented as a Kronecker sum of discrete Laplacians in one-dimension. The index j represents the jth eigenvalue...

See the main article Kronecker sum of discrete Laplacians for details. Some mathematical programs are able to do separation of variables: Xcas among...

(also known as the Laplacian) takes f to the divergence of its gradient vector field, which is the sum of the n pure second derivatives of f with respect...

eigenvalues of discrete Laplace operator Kronecker sum of discrete Laplacians — used for Laplace operator in multiple dimensions Discrete Poisson equation...

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 is the cumulative summation of the Kronecker delta: H [ n ] = ∑ k = − ∞ n δ [ k ] {\displaystyle H[n]=\sum _{k=-\infty }^{n}\delta [k]} where δ...

the case that the discretized spatial domain is an arbitrary graph G = ( V , E ) {\displaystyle G=(V,E)} and the discrete laplacian L Z {\displaystyle...

of these shapes Babai's problem: which groups are Babai invariant groups? Brouwer's conjecture on upper bounds for sums of eigenvalues of Laplacians of...

\sum _{k=1}^{n}{\overline {z^{j\cdot k}}}\cdot z^{j'\cdot k}=n\cdot \delta _{j,j'}} where δ is the Kronecker delta and z is any primitive nth root of unity...

one could analogize the role of the Ricci curvature in Riemannian geometry to that of the Laplacian in the analysis of functions; in this analogy, the...

corresponds to a non-trivial zero of the Riemann zeta-function. The constant term of the pole at s = 1 is described by the Kronecker limit formula. The modified...

for any given dimension (size) of matrix. The matrix entries will be denoted aij. The table below uses the Kronecker delta δij for two integers i and...

the Kronecker delta (and the summation convention is again used). In place of the definition of the vector Laplacian used above, we now make use of an...

connected equidimensional arithmetic scheme of Kronecker dimension n can be factorized into the product of appropriately defined L-factors and an auxiliary...

dx^{i_{k}}\right)\\&=dg\wedge dx^{i_{1}}\wedge \cdots \wedge dx^{i_{k}}+g\sum _{p=1}^{k}(-1)^{p-1}\,dx^{i_{1}}\wedge \cdots \wedge dx^{i_{p-1}}\wedge...

(and its own natural filtration), where δij denotes the Kronecker delta. The spectral content of a stochastic process X t {\displaystyle X_{t}} can be found...

_{ij}=\lambda _{i}\,\delta _{ij}} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. We define Λ 1 / 2 {\displaystyle \Lambda ^{1/2}} as the diagonal...

(j)}\right)_{a'a}&=a\delta _{a',a}\end{aligned}}} where δ denotes the Kronecker delta. In components, with −m ≤ a, a′ ≤ m, −n ≤ b, b′ ≤ n, the representations...