Sentence examples for improper integrals of from inspiring English sources
In particular, HL integrability encompasses improper integrals of Bochner integrable mappings.
Different Engineering applications require dealing with improper integral on unbounded domains (improper integrals of the first kind).
Moreover HL integrability encloses improper integrals on finite intervals; HK integrability also on unbounded intervals.
Thus, g is HL integrable because HL integrability encloses improper integrals on finite intervals by Remarks 2.2.
One reason may be the difficulty of evaluating the MHC reaction rate, which is defined as an improper integral of the Marcus rate over the Fermi distribution of electron energies.
Note that the improper integral on the right is divergent.
Methods involving evaluation of real improper integrals by the use of the ideas of the theory of functions of real variables only are highlighted, and solutions of certain real singular integral equations of the Cauchy type have been re-derived.
It is with this idea in mind, in the present paper, that we have first reviewed the problems of evaluation of several real improper integrals (see[11]) by the help of the theory of functions of real variables only whilst the application of complex function theory is also demonstrated for these problems for comparison as well as for realizing the major differences of the analysis involved.
They applied their results to the approximation of certain improper integrals by quadrature sums of positive coefficients based on a finite number of equidistant nodes.
The Kramers Kronig dispersion relation, often used as a viscoelastic constitutive law for polymeric materials, is based on purely mathematical properties of linearity, convergence of improper integrals, and causality; thus, it may also be valid as a viscoelastic constitutive law for general structural materials.
The plan of this paper is as follows: In the 'Evaluation of real improper integrals' section, we consider some problems of real improper integrals and their solutions.
