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It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation: any index may appear at most twice and furthermore a raised index must contract with a lowered index ...
The number of each upper and lower indices of a tensor gives its type: a tensor with p upper and q lower indices is said to be of type (p, q), or to be a type-(p, q) tensor. The number of indices of a tensor, regardless of variance, is called the degree of the tensor (alternatively, its valence, order or rank, although rank is ambiguous).
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}} where q {\displaystyle q} is a prime, index calculus leads to a family of algorithms adapted to finite fields and to ...
Open Problems in Mathematics is a book, edited by John Forbes Nash Jr. and Michael Th. Rassias, published in 2016 by Springer (ISBN 978-3-319-32160-8). The book consists of seventeen expository articles, written by outstanding researchers, on some of the central open problems in the field of mathematics.
A numeric solution of the problem shows that the function is smooth and always decreasing to the left of =, and zero to the right. At η = 1 {\displaystyle \eta =1} , a slope discontinuity exists, a feature which the power series is incapable of rendering, for this reason the series solution continues decreasing to the right of η = 1 ...
If M is such that LCP(q, M) has a solution for every q, then M is a Q-matrix. If M is such that LCP(q, M) have a unique solution for every q, then M is a P-matrix. Both of these characterizations are sufficient and necessary. [4] The vector w is a slack variable, [5] and so is generally discarded after z is found. As such, the problem can also ...
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Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.