In linear algebra and related areas of mathematics a function on a vector space V over the field F (which is either the real numbersR or the complex numbersC) is called sublinear if for all scalars γ and vectors x and y Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ... History Main article: History of mathematics In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. ... Please refer to Real vs. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ... The concept of a scalar is used in mathematics, physics, and computing. ...
In mathematics, given a vector space V over K, a norm on V is a function ||·||:V->R; x->||x|| with the following properties: For all a ∈ K and all u and v ∈ V, 1. ...
Sublinear shapes of the dose-response curve in the low-dose range of toxicity testing are often postulated to be indicative of a no-effect threshold.
We present statistical procedures to test sublinear dose responses in bioassays for carcinogenicity against the hypothesis of linearity and estimate a lower confidence limit for the dose at the postulated break point.
The proposed analysis may be useful to test sublinear sections of the dose response for the possibility of a threshold for carcinogens and to define dose levels that could be used as a starting point for setting exposure standards.
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