Sentence examples for fundamental decomposition from inspiring English sources

Given any fundamental decomposition X="−YU of X, the subspace Z can be written as the graph of a contraction A U→Y.

The representation (1.1) is called a fundamental decomposition of the Krein space K and is not unique in general.

Then with respect to this fixed fundamental decomposition, the inequality 〈 T x, T x 〉 K ≤ [ x, x ] K. holds.

In most of the existing audio coding techniques the fundamental decomposition components or building blocks are in the frequency domain with corresponding energy associated with them.

Second, the fundamental decomposition is identifiable because longitudinally linked employer‐employee data, whether sampled or from universes, provide a sufficiently rich description of the connectedness of the labor market.

The following lemma establishes a contractive-like relation for any T ∈ π p ( K ) with the constant π p ( T ) ≤ 1. Lemma 3.1 Let K be a Krein space with some fixed fundamental decomposition, and for 1 ≤ p < ∞, let T ∈ Π p ( K ) be such that π p ( T ) ≤ 1.

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used for reasoning about a building design process at micro-urban scale and defining strategies for making the search more efficient.

The algorithm is comprised of three fundamental steps: (i) decomposition of region D into subregions Di, (ii) packing of each subregion with a set of parallel tubes using appropriate circle-packing algorithms and finally, (iii) connection of the tubes, both within each subregion Di as well as between neighbouring regions.

The first contribution of this study is to formally prove that the time-asymptotic moments matching method applied to two-equation models is equivalent to a fundamental deterministic perturbation decomposition proposed in Quintard et al. (2001) [1] for mass transport and in Moyne et al. (2000) [2] for heat transfer.

The levels of the selected heavy metals from that study are similar to those found in some sludges, presenting a realistic approach on reduction in microbial activity fundamental to sludge decomposition.

The goal for this study was to establish if microbial succession was a fundamental property of decomposition.