Sentence examples for derived as a consequence of from inspiring English sources

In fact this is derived as a consequence of Thomson′s result for polynomials.

Kreisel has also noted that, in the opposite direction, the second incompleteness theorem can also be easily derived as a consequence of Löb's theorem.

The following version of Fatou's lemma is shown in [1], page 4, and [2], page 10, and can be derived as a consequence of Theorem 3.1.

The invertibility of (G x)) will be derived as a consequence of a series of lemmas, where we first consider (xin[-frac{a}{2},0]).

On the contrary, for Liouville-type results with scalar equations, it was shown in [1] that nonexistence in a half-space can be derived as a consequence of nonexistence in the whole space, without requiring stronger restrictions on the exponents (and actually the restriction becomes even weaker).

Normalization to unit \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} -norm can be derived as a consequence of the requirement of non-enhancement of local extrema.

> From the Holling equation, where parameters map directly to functional behavioural traits, many aspects of foraging behaviour can be intuitively derived as a direct consequence of search and handling (reviewed in Stephens et al. 2007).

We derive as a consequence that the odometer actions of Z that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures.

Sellers' conjecture then is derived as an immediate consequence (Corollary 2.12).

DNA DSB can occur via a variety of routes including exposure to exogenous ionising radiation during clinical anticancer radiotherapy (2), exposure to certain classes of anticancer chemotherapeutic drugs (3), and as a result of endogenously derived reactive oxygen species as a consequence of normal cellular metabolism (1).

The formalism also provides for detailed quantitative characterizations of signaling behavior, examples being that the bias factors β in the equiactive and pharmacological models can be derived as simple consequences of the analysis, and in calculating bias factors, the B 12 a model appropriately handles large transducer ratios that prove to be problematic for the pharmacological model.