Sentence examples for by using representation from inspiring English sources

for each τ ∈ ( 0, T ]. Proof The solutions of the direct problem (5) corresponding to the admissible coefficients k 1 ( x ), k 2 ( x ) ∈ K can be written at x = 0 as follows: respectively, by using representation (11).

By using representation (4.4) we have to investigate the boundedness of the operators J α 1, α 2 f, J α 1 S α 2 f, S α 1 J α 2 f, S α 1, α 2 f separately.

The philosophy behind the development of QRAS is to bridge communication and skill gaps between managers, engineers, and risk analysts by using representations of the risk model and analysis results that are easy to comprehend by each of those groups.

As compared with more traditional conversational technologies, like wikis and forums, CCSAV is designed to promote more critical thinking and evidence-based reasoning, by using representations that highlight conceptual relationships between contributions, and through computational analytics that assess the structural integrity of the network.

Potential theoretical solutions to this problem have been explored by Erickson using algebraic geometry [ 10], and by Sumner et al. using representation theory [ 23, 24].

It is inspired by the simplifications done by the travelers, using representations of their surrounding space.

By using such representation, Zero provides elegant use of statically typed higher-order methods.

These can be artificially imported by co-registration with MR angiography and by using 2D representation of real anatomy.

By using this representation, any non-uniform T2 FS can be represented by a function of two uniform T2 FSs.

Due to complexity of this system, the modeling process will become more complicated especially if modeled by using mathematical representation or white box approach.

This paper explains the NC specification dictionary structure by using EBNF representation, which is further implemented in tool command language, an embedded script language tool.