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Imaginary Worlds by Lin Carter, Ballantine Books, 1973. The Ballantine Adult Fantasy series was an imprint of American publisher Ballantine Books.Launched in 1969 (presumably in response to the growing popularity of Tolkien's works [1]), the series reissued a number of works of fantasy literature which were out of print or dispersed in back issues of pulp magazines (or otherwise not easily ...
Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots.
For example, the equation (+) = has no real solution, because the square of a real number cannot be negative, but has the two nonreal complex solutions + and . Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rule i 2 = − 1 {\displaystyle i^{2}=-1} along with the associative , commutative , and ...
The one-dimensional integrals can be generalized to multiple dimensions. [2] (+) = ()Here A is a real positive definite symmetric matrix.. This integral is performed by diagonalization of A with an orthogonal transformation = = where D is a diagonal matrix and O is an orthogonal matrix.
Autolux, a Los Angeles–based noise pop band, have a song "Science of Imaginary Solutions" on their second album Transit Transit. The composer Gavin Bryars has been a member of the Collège de 'Pataphysique since 1974; he was appointed Regent in 2001 and a Transcendent Satrap in 2015 at the pataphysical New Year's Eve Vigil E.P. 143 (7 ...
Optimal solutions for the Rubik's Cube are solutions that are the shortest in some sense. There are two common ways to measure the length of a solution. The first is to count the number of quarter turns. The second is to count the number of outer-layer twists, called "face turns".
A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not invertible for some or all values of the variables involved, which prevents the chain of logical implications from being bidirectional.
Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the ...