Sentence examples for basis for the complex from inspiring English sources

These universities usually developed the technical basis for the complex investment instruments used by investment banks.

This architectural divergence provides the structural basis for the complex regulatory roles and functional diversity of PIKKs.

Let X 1 1,..., X 1 n be a basis for g 1 and X 2 1,..., X 2 n a basis for g 2. Write Y 1 i = ( α 1 ) * X 1 i and Y 2 i = ( α 2 ) * X 2 i, then Y 1 1..., Y 1 n is a basis for the complex vector space g 1 ℂ and Y 2 1..., Y 2 n is a basis for the complex vector space g 2 ℂ.

By the mid- to late-1800s, William Hamilton had gone on to introduce ordered couples of reals as the first step in supplying a logical basis for the complex numbers and Karl Weierstrass, Richard Dedekind and Georg Cantor had all developed methods for founding the irrationals in terms of the rationals.

Improving clinical options for metastatic disease requires an understanding of the molecular basis for the complex behaviours of metastatic cells.

Analysis of the metabolic potential yielded interesting insights into the basis for the complex growth requirements of this fastidious organism [ 21].

An increasing repertoire of methodologies allows for the analysis of protein protein interactions, thereby providing an experimental basis for understanding the complex molecular interplay in a cell.

The structure provides a structural basis for understanding the complex assembly of mTORC1 and the regulatory mechanism of mTORC1 by its binding partners and those yet to be identified.

This study provides an important basis for deciphering the complex extracellular protein networks implicated in MSC cellular senescence and their interplay with the corresponding cytoplasmic signaling circuitry.

These data furnish a mechanistic explanation for the detrimental role of IFN I in pulmonary TB and form a basis for understanding the complex roles of IFN I in chronic inflammation.

Gene expression profiling continues to contribute to advances in clinical oncology, providing a basis for understanding the complex biology of tumors, improving the accuracy of disease diagnosis as well as disease prognosis, and providing tools to determine which targeted therapeutic agents are likely to be effective in the treatment of particular tumors.