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Infinite descent, a method going back to Fermat to solve Diophantine equations; Descent (mathematics), an idea extending the notion of "gluing" in topology Hadamard's method of descent, a technique for solving partial differential equations
Descent theory tells conditions for which there is a fully faithful descent, and when this functor is an equivalence of categories. See also ...
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
The examples described below represent different modes of speciation and provide strong evidence for common descent. Not all speciation research directly observes divergence from "start-to-finish". This is by virtue of research delimitation and definition ambiguity, and occasionally leads research towards historical reconstructions.
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function . The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of ...
Common descent is a concept in evolutionary biology applicable when one species is the ancestor of two or more species later in time. According to modern evolutionary biology, all living beings could be descendants of a unique ancestor commonly referred to as the last universal common ancestor (LUCA) of all life on Earth .
A DNA segment is identical by state (IBS) in two or more individuals if they have identical nucleotide sequences in this segment. An IBS segment is identical by descent (IBD) in two or more individuals if they have inherited it from a common ancestor without recombination, that is, the segment has the same ancestral origin in these individuals.
Descant is a type of medieval polyphony characterized by relatively strict note-for-note counterpoint.It is found in the organum with a plainchant tenor (i.e. low voice; vox principis), and in the conductus without the requirement of a plainchant tenor.