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More precisely, the two new methods use LU and QR matrix factorizations, respectively, which consist in formulating high-dimensional optimization problems into several sequential polynomial and rational subproblems.
Secondly, we propose two Jacobi-like approaches using LU and QR matrix factorizations, respectively, which consist in formulating high-dimensional optimization problems into several sequential polynomial and rational subproblems.
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The approach consists in formulating a seismic model (WRW model) in wavenumber space and employ it for sound source reconstructions.
The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase.
A practical aspect of these monolayer investigations consisted in formulating principles of a convenient method of thorough electrokinetic characterization of nanoparticles and their monolayers.
It consists in formulating and solving one and the same problem within the framework of mutually related models with constructing equivalent analogs with fuzzy coefficients in objective functions alone.
The research methodology consists in formulating a set of hypotheses for a model sustained by empirical data obtained from a two-stage probabilistic sample design and analyzed with Partial Least Squares path modeling (PLS).
The third stage consisted in formulating themes by grouping together codes that reflected similar overarching ideas.
The task of the sciences, and of knowledge in general, is to study the facts and regularities of nature and society and to formulate the regularities as (descriptive) laws; explanations of phenomena can consist in no more than the subsuming of special cases under general laws.
Most of the art of science consists of formulating falsifiable propositions in just this spirit.
The difficulty consisted in the obligation to formulate a principle that is neither too restrictive for the important results in analysis, nor too liberal with respect to the formations of concept to be excluded by reason of Poincaré's philosophical position.
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