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Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable ...
In mathematics, pseudoanalytic functions are functions introduced by Lipman Bers (1950, 1951, 1953, 1956) that generalize analytic functions and satisfy a weakened form of the Cauchy–Riemann equations.
In 1975, Leitzel, Madan, and Queen incorrectly claimed that there are only 7 function fields over finite fields with genus > 0 and class number 1, but in 2013 Stirpe found another; there are in fact exactly 8. Busemann–Petty problem.
A structure similar to LCGs, but not equivalent, is the multiple-recursive generator: X n = (a 1 X n−1 + a 2 X n−2 + ··· + a k X n−k) mod m for k ≥ 2. With a prime modulus, this can generate periods up to m k −1, so is a useful extension of the LCG structure to larger periods.
Pseudometric spaces were introduced by Đuro Kurepa [1] [2] in 1934. In the same way as every normed space is a metric space , every seminormed space is a pseudometric space. Because of this analogy, the term semimetric space (which has a different meaning in topology ) is sometimes used as a synonym, especially in functional analysis .
In algebra, given a 2-monad T in a 2-category, a pseudoalgebra for T is a 2-category-version of algebra for T, that satisfies the laws up to coherent isomorphisms. [ 1 ] See also
In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex.
[1] Every element x with the property x* = 0 (or equivalently, x** = 1) is called dense. Every element of the form x ∨ x* is dense. D(L), the set of all the dense elements in L is a filter of L. [1] [2] A distributive p-algebra is Boolean if and only if D(L) = {1}. [1] Pseudocomplemented lattices form a variety; indeed, so do ...