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The Impact of Different Severities of Anxiety on Decision-Making. [PDF]

Brain Behav
Ma Y, Tan Y, Xu F, Chen J, Chen Y, Liu F, Fan M, Han Q.   +7 more
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Efficient complex matrix multiplication

IEEE Transactions on Computers, 1988
Multiplication of the complex numbers x and y, where \(x=a+ib\) and \(y=c+id\), requires four real multiplications, while the identity \(xy=(a(c-d)+(a-b)d)+i(b(c+d)+(a-b)d)\) requires three real multiplications instead. The author observes that this identity could be used for multiplication of complex matrices.
A T Fam
exaly   +2 more sources

Complex Multiplication

, 2010
This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number ...
Reinhard Schertz
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Complex Multiplication

2005
In this chapter we present a method for finding a curve and the group order of its Jacobian which can be seen as complementary to those in Sections 17.2 and 17.3. Instead of trying several random curves over a fixed finite field until a good one is found and determining the group order by computing the characteristic polynomial of the Frobenius ...
Frey, G., Lange, T.
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On the asymptotic complexity of matrix multiplication

22nd Annual Symposium on Foundations of Computer Science (sfcs 1981), 1981
The main results of this paper have the following flavor: Given one algorithm for multiplying matrices, there exists another, better, algorithm.
Don Coppersmith, Shmuel Winograd
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Complexity and Multiple Complexes

2003
In this chapter we introduce the notion of the complexity of a module and explore some related ideas. Complexity was first defined by Jon Alperin in the late 1970’s and it helped to motivate much of the development of the homological properties of modules.
Jon F. Carlson, Lisa Townsley, Luis Valeri-Elizondo, Mucheng Zhang   +3 more
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Jacobians with complex multiplication

1991
In this paper we will say that a simple abelian variety X is of CM type if there is a number field K with [K: Q] = 2 dim(X) such that K ⊂ End°(X). If X is any abelian variety, then we will say that X is of CM type if all its simple factors are. Equivalently, X is of CM type if there are number fields K i such that Σ[K i: Q] = 2dim(X) and ⊕K i ⊂ End°(X).
Jong, A.J. de, Noot, R.
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On the Multiplication of Complex Numbers

The Mathematical Gazette, 1949
In the development of the theory of complex numbers, it is important to give a definition of them dependent only upon real numbers. In the usual algebraic treatments the product is postulated in the form or obtained from a matrix representation.
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On the Multiplicative Complexity of Boolean Functions

Fundamenta Informaticae, 2016
The multiplicative complexity μ(f) of a Boolean function f is the smallest number of & (of AND gates) in circuits in the basis {x&y, x⊕y, 1} such that each circuit implements the function f. By μ(S) we denote the number of & (of AND gates) in a circuit S in the basis {x&y, x ⊕ y, 1}. We present a method to construct circuits in the basis {x&y, x ⊕ y, 1}
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