Sentence examples for is in the kernel of from inspiring English sources

(2) It is clear that H Z a r 1 ( R, W ) is in the kernel of χ. □.

Since (mathbf{S}_{1}) is in the kernel of (b_{delta}^(cdot,cdot)), we conclude that inf_{mathbf{v}_{delta}^in V_{delta}^ bigl| mathbf{u}-mathbf{v}^_{delta}bigr| _leq inf_{v_{delta}in V_{delta}} |mathbf{u}_{r}-mathbf{v}_{delta}|.

It is easy to check that is in the kernel of L. Due to θ > 0, we know that 0 is a simple eigenvalue of L,which leads to ker ( L ) = span = X 1. Define the projection operator P = P ( μ, s ) : Y → X 1 as P ( y z ) = 1 ∫ Ω θ 2 ( x, μ ) d x [ ( 1 − s ) ∫ Ω θ y d x − s ∫ Ω θ z d x ].

By Equation 1, x∗ is in the kernel of the Laplacian matrix: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x^ \in \ker \mathcal {L}(G)$\end{document } x ∗ ∈ ker ℒ (G ).

Let moreover be the -linear subspace of containing all the functions which are in the kernel of the linear map, given by (3.17).

Let us denote first by the -linear subspace of such that all are in the kernel of the map, given by (3.16).

We give an integral representation of the series of generalized Jacobi polynomials P n0···0) which are in the kernel of the invariant operators of order greater than two on a root system BCp.

Finally, we describe all backward shift invariant subspaces which are in the kernels of Toeplitz operators with homogeneous type symbols.

But also the restriction of f i ′ to R i is non-zero, thus R i is not in the kernel of h i and therefore h i is an automorphism.

Apart from the home-help, he had to contend with Ophelia's extended Italian family, her mental-health nurse, the woman from the council, and of course Ophelia herself, who was to be found in the kernel of this nuthouse, curled up in a foetal ball on the sofa, making lowing sounds into a bottle of Bailey's.

This shows that U ′ ′ is a direct summand of X which is contained in the kernel of f.