Sentence examples for for a suitable function from inspiring English sources

We study the spectral functional A↦Trf(D+A) for a suitable function f, a self-adjoint operator D having compact resolvent, and a certain class of bounded self-adjoint operators A. Such functionals were introduce by Chamseddine and Connes in the context of noncommutative geometry.

The Caputo's derivative of fractional order for a suitable function is defined by (2.3).

For a suitable function f, the commutator is defined by ([b,T]f=bT f -T(bf)).

In this paper we use a non-local discrete Laplacian Ψ(L) defined for a suitable function Ψ by applying Fourier transform.

For a suitable function f : Ω ( r, s ) → R, we define for all n ∈ N 0 linear functionals via a discretized version of the continuous integral, namely T n ( r, s ) ( f ) : = ∑ k = − ∞ ∞ r q k ( r q k ) n f ( r q k ) + ∑ k = − ∞ ∞ s q k ( − s q k ) n f ( − s q k ).

Suppose that α is a stochastic process with right-continuous sample paths (or a pure jump process), finite-state space M = { 1, …, m 0 }, and x-dependent generator Q ( x ), so that for a suitable function f , Q ( x ) f ( x, ⋅ ) ( i ) = ∑ j ∈ M, j ≠ i q i j ( x ) ( f ( x, j ) − f ( x, i ) ) for each  i ∈ M. (1).

"I am clear, even with expert advice, that a quasi-judicial role such as this is not a suitable function for the executive.

This is a suitable function for modelling demand across virtual machine sizes, to a first approximation, for the following reasons.

For explaining more details of the reported gain coefficients, the g0 lAMP-parameter was introduced, where it was realized that with a good approximation a Gaussian profile is a suitable function for explaining the reported g0 lAMP-products.

To get a lower solution for (1.1), we will proceed with a limit process in, where is a classical solution of problem (1.10) (given by Theorem 1.6) with, is a suitable function and for and is such that in.

With this choice of path, it is known (see for example [44, Lemma 2.2] or [40, pp 99 101]) that (xrightarrow gamma (x,u,t)) is a (C^1) path, with Jacobian determinant begin{aligned} bigg |det frac{partial gamma }{partial x} x,u,t bigg |= 1 + psi (x,u,t), end{aligned}for a suitable function (psi (x,u,t)) satisfying begin{aligned} |psi (x,u,t)|le cr, text { on }Ktimes Q_epsilon times [0,cr].