Sentence examples for explicit estimates of from inspiring English sources

The following explicit estimates of Mittag-Leffler functions are useful in the sequel.

Explicit estimates of solutions and their derivatives allow us to restrict ourselves to a sufficiently large neighbourhood of the origin, when formulating these effective conditions.

Of course, for obtaining the explicit estimates of solutions and their derivatives, we should study, unlike in [22], exclusively the second-order Dirichlet boundary value problems.

One of the purposes of our paper is to shed light on the rate of assimilation across generations, and we provide explicit estimates of intergenerational transmission rates.

To provide spatial products for application in prioritization of management, we developed spatially explicit estimates of occurrence separately for encamped and traveling modes.

A major challenge is the lack of accurate and spatially explicit estimates of forest carbon storage over the entire urbanized area.

In this paper we give Banach fixed point theorems and explicit estimates on the rates of convergence of the transition function to the stationary distribution for a class of exponential ergodic Markov chains.

In §4, we will give explicit estimates on the size of the genus of a quaternion algebra over the field of rational functions of a split elliptic curve over a number field (cf. Theorem 4.1).

To overcome this drawback, a reduced-rank multistage Wiener filter design was proposed in [6], which relaxes the requirement on explicit estimate of the signal subspace.

Under general conditions, an explicit estimate of (lambda_{0}) is given such that the problem possesses a solution for any (|lambda|

Recently Pata in [14] introduced a fixed point theorem with weaker hypotheses than those of the Banach contraction principle with an explicit estimate of the convergence rate (see also [15]).