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In this note, we shall investigate the Hölder continuity of matrix functions applied to normal matrices provided that the underlying scalar function is Hölder continuous..
The present material refers to an example of matrix functions, the exponential matrix function, used as a plane rotation operator.. In the case of the plane rotations we shall
As Ω in Lemma 3.1 becomes large, we can have a considerable but finite number of fundamental solutions belonging to different classes that satisfy the bounds.. We will see that
This yields explicit upper bounds on residues of Dedekind zeta func- tions of abelian number fields taking into account the behavior of small primes, and it as been explained how
We begin with an introductory section, where we define what this article will understand as a generalized Pascal matrix, as well as looking at the binomial transform, the Riordan
In addition to providing conditions for the existence of double positive solutions of (M 1) and (M 2), we also derive upper and lower bounds for the norms of these solutions..
As in deterministic case, the numerical stability in the quadratic mean-square sense for one-step numerical approximations does not tell us how to pick an appropriate step size ∆..
We will prove the twice continuous differentiability of these two different kinds of ruin probability and present their explicit expressions when the claims are
