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In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin [1] for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology.
It involves. elds such as algebraic geometry and computational algebra. Though these themes are not as ubiquitous in biology as linear algebra is, they arise in a number of biological problems. Algebraic Biology is the sub eld that encompasses these problems, and the new mathematics that they spawn.
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Algebraic biology (also known as symbolic systems biology) applies the algebraic methods of symbolic computation to the study of biological problems, especially in genomics, proteomics, analysis of molecular structures and study of genes.
Oct 21, 2011 · Mathematical biology is a highly interdisciplinary area that defies classification into the usual categories of mathematical research, although it has involved all areas of mathematics (real and complex analysis, integral and differential systems, metamathematics, algebra, geometry, number theory, topology, probability and statistics, as well ...
Oct 9, 2017 · An algebraic space is a sheaf of sets $F$ in the étale topology of schemes satisfying the condition of local representability (in the étale topology): There exists a scheme $U$ and a sheaf morphism $\tilde U \rightarrow F$ such that for any scheme $V$ and morphism $\tilde V \rightarrow F$ the fibred product $\tilde U \times_F \tilde V$ is ...
Nov 5, 2018 · An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A form is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis.
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In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same structure.
