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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
In abstract algebra, the conjugacy problem for a group G with a given presentation is the decision problem of determining, given two words x and y in G, whether or not they represent conjugate elements of G. That is, the problem is to determine whether there exists an element z of G such that =.
In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial p K,α (x) of α over K. Conjugate elements are commonly called conjugates in contexts where this is not ambiguous.
It is an open problem whether every non-abelian p-group G has an automorphism of order p. The latter question has positive answer whenever G has one of the following conditions: G is nilpotent of class 2; G is a regular p-group; G / Z(G) is a powerful p-group
Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane. The complex conjugate is found by reflecting z {\displaystyle z} across the real axis. In mathematics , the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign .