Sentence examples for mild approximation from inspiring English sources

We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function ψ G→C defines a closable multiplier on the reduced C⁎-algebra C⁎r(G) of G if and only if Schur multiplication by the function N G×G→C, given by N s,t)="ψ ts−1), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L2(G).

However, this rule is not true in a strict sense for arbitrary driving processes and requires some mild approximations to make it a more general statement.

In the case of very long filters, it turns out that even the mild approximations of the driving process are no longer required and thus less conservative step-size bounds are obtained.

Given that the specification imposes similar constraints on the 'low' and 'high' EYFP levels, and that these levels are under mild approximations proportional to the ratio κ eyfp /γ eyfp and κ eyfp /γ eyfp, respectively, one could have expected similar sensitivity indices for κ eyfp and κ eyfp.

We shall study the existence and approximation of mild solutions in the following sense.

This section is devoted to a proof of our main result on the existence and approximation of mild solutions of fractional order hybrid differential equations.

Section 3 is devoted to a proof of the existence and approximation of mild solutions of fractional order hybrid differential equations (1.1).

Using fixed point theorems developed by Dhage et al. in Applied Mathematics Letters 34, 76-80 (2014), we prove the existence and approximation of mild solutions.

But knowledge of dengue was based on incomplete reporting, a lack of data on mild cases, and crude approximations that produced "back-of-the-envelope estimates," Farrar says.

An asymptotic error analysis is conducted which shows that under very mild conditions the discrete approximations of the first- and second-order geometric differential operators have quadratic and linear convergence rates, respectively.

By constructing Picard successive approximation, Wang [17] established the approximate mild solutions of fractional stochastic differential equations.