Sentence examples for necessary definitions of from inspiring English sources

In Section 2, we introduce some necessary definitions of the fractional calculus.

For the convenience of the reader, we present here some necessary definitions of the fractional calculus.

2, we will give some necessary definitions of fractional q-calculus and deduce the new properties of the Green function.

In Section 2, we recall some necessary definitions of almost periodic time scales and introduce the concept of a Δ-sub-derivative on time scales to define ε-equivalent impulsive functional dynamic equations on almost periodic time scales.

Where necessary, definitions of code words were refined and categories expanded upon [ 29].

Here are some necessary definitions of the costs to clearly refer later: They are determined by the derivative of direct patient care, like: medication, hospitalization, diagnostic or therapeutic interventions, professional fees, transportation, mechanical aids for the patient, physiotherapy, as well as nursing value.

Attention is paid to the necessary definition of the respective development item, the threat-, handriskanalysis analysafetyafety concepts and their relation to architecture development, while the book also addresses the aspects of product realization in mechanics, electronics and software as well as for subsequent testing, verification, integration and validation phases.

As we progress further in increasing the numbers of postdocs and in developing the nature of the postdoctoral experience in Canada, I expect we'll begin to encounter a fine line between the overbureaucratization of the postdoctoral process and the necessary definition of the standards, rights, and responsibilities of all involved.

In this section, we give relation among the fractional order derivatives, Caputo, Reimann-Liouville and Grünwald-Letnikov fractional order derivatives, necessary definition of initial value problems of fractional order differential equations with these sense and a comparison result for Lyapunov-like functions.

For the convenience of the reader, we present some necessary definitions and lemmas of fractional q-calculus theory to facilitate analysis of the semipositone boundary value problem (1.1).

For convenience of the reader, we present some necessary definitions and lemmas of fractional q-calculus theory to facilitate analysis of problem (1.1).