Sentence examples for development of the integral from inspiring English sources

We further demonstrate the development of the integral vascular network of the definitive CP.

As the development of the singular integral operators, their commutators and multilinear operators have been well studied (see [1 3]).

Both approaches mentioned provide tools to deal also with the case where the integrand and integrator reveal the same irregularity as the standard Brownian motion or more general semimartingales (although the Young integral fails to exist in such case, and it was, historically, one of the main reasons for the development of the stochastic integral).

Along with the development of the theory of integral inequalities and the theory of difference equations, more attentions are drawn to some discrete versions of Gronwall type inequalities (e.g., [20 22] for some early works).

Along with the development of the theory of integral inequalities and the theory of difference equations, more attentions are paid to some discrete versions of Bellman-Gronwall type inequalities (e.g., [16 18]).

Along with the development of the theory of integral inequalities and the theory of difference equations, more attentions are paid to some discrete versions of Gronwall-Bellman-type inequalities (such as [9 11]).

But the major breakthrough came in 1960 when it occurred to the mathematical logician Abraham Robinson (1918 1974) that "the concepts and methods of contemporary Mathematical Logic are capable of providing a suitable framework for the development of the Differential and Integral Calculus by means of infinitely small and infinitely large numbers".

The research will involve design and optimization of the composite material for the roof, development of an integral weather protection layer for the roof, and structural design, analysis and testing of the roof system.

The results of the present study seem to indicate that the development of an integral risk map might be useful to help in making-decision processes concerning environmental pollutants.

Two years later he fled British India and found refuge in the French colony of Pondichéry (Puducherry) in southeastern India, where he devoted himself for the rest of his life to the development of his "integral" yoga, which was characterized by its holistic approach and its aim of a fulfilled and spiritually transformed life on earth.

As the development of singular integral operators (see [1, 2]), their commutators have been well studied.