Sentence examples for by introducing some definitions from inspiring English sources

We begin this section by introducing some definitions that are useful for the presentation of our approach.

In the following, we start by introducing some definitions related to impulsive semi-dynamic systems, which are used in this work.

We therefore being by introducing some notations and definitions which will be used throughout.

We start this section by introducing some notation and recalling the definition and relevant properties concerning CGR.

Leśniewski got around the problem by introducing auxiliary definitions which maneuvered the required variable slot into the right position with only one occurrence.

Particularly, the formulation recently proposed by the authors is here modified by introducing new definitions of the kinematic parameters and of the generalized deformations, and extended to the dynamic case.

To solve this problem, Ibragimov and Gandarias have extended the concept of self-adjoint equations by introducing the definitions of quasi-self-adjoint equations and weak self-adjoint equations [11 16].

By introducing precise definitions of such notions, these thinkers exposed ambiguities (e.g., such as with the word "infinite"), revealed interrelations between certain of them, and eliminated dubious notions that had previously caused confusion and paradoxes (such as those involved with the notion of an "infinitesimal").

By introducing two definitions for the decaying and regular states, the necessary conditions deduced form the reciprocal theorem, for the edge-data to induce only a decaying elastostatic are directly translated into the appropriate edge conditions for the existence of a rapidly decaying solution of the strips.

Nonetheless by introducing common definitions, technique and quantity of blood specimen acquisition, and uniform microbiological techniques at each center in the PNSN, our surveillance provide for baseline data for quality improvement initiatives.

We begin this section by introducing adequate new definitions of lower and upper solutions for problem (1).