Results 221 to 230 of about 16,145 (263)
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Jacobians with complex multiplication
1991In 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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Lower bounds for the multiplicative complexity of matrix multiplication
Computational Complexity, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Multiplication of Complex Numbers
The Mathematical Gazette, 1949In 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, 2016The 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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Rings of Low Multiplicative Complexity
Finite Fields and Their Applications, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joseph H. Silverman
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On the Additive Complexity of Matrix Multiplication
SIAM Journal on Computing, 1976A graph-theoretic model is introduced for bilinear algorithms. This facilitates in particular the investigation of the additive complexity of matrix multiplication. The number of additions/subtractions required for each of the problems defined by symmetric permutations on the dimensions of the matrices are shown to differ conversely as the size of each
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Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005., 2006
Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work, we consider the number of full and half adder cells required to realize those additions, and a novel complexity ...
Kenny Johansson +2 more
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Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work, we consider the number of full and half adder cells required to realize those additions, and a novel complexity ...
Kenny Johansson +2 more
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Algebras of Minimal Multiplicative Complexity [PDF]
2012 IEEE 27th Conference on Computational Complexity, 2012 We prove that an associative algebra $A$ has minimal rank if and only if the Alder -- Strassen bound is also tight for the multiplicative complexity of $A$, that is, the multiplicative complexity of $A$ is $2 \dim A - t_A$ where $t_A$ denotes the number of maximal two sided ideals of $A$. This generalizes a result by E.
Markus Bläser
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Multiple complexes of thrombin and heparin
Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology, 1986Fluorescence polarization has been used to study the interaction of thrombin and heparin, and the catalysis by heparin of the combination of thrombin and antithrombin. At low ionic strength (20 mM Tris, pH 7.4), the addition of heparins of known molecular weights to thrombin led to the formation of large complexes (defined as 'complex 1').
J R, Evington +3 more
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Circuit Complexity and Multiplicative Complexity of Boolean Functions
2010In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 - c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning
Arist Kojevnikov, Alexander S. Kulikov
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