Results 291 to 300 of about 498,616 (315)

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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Algebras Having Linear Multiplicative Complexities

Journal of the ACM, 1977
The foundations are laid for a theory of multiplicative complexity of algebras and it is shown how “multiplication problems” such as multiplication of matrices, polynomials, quaternions, etc., are instances of this theory. The usefulness of the theory is then demonstrated by utilizing algebraic ideas and results to derive complexity bounds.
Fiduccia, C. M., Zalcstein, Y.
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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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Multiple complexes in human spermatocytes

Chromosoma, 1978
Multiple complexes develop during metaphase I in normal human spermatocytes. Usually they form two separate bodies about 1 micron in diameter, composed of tripartite units and a denser matrix. The tripartite units are structurally identical to the components of the central space of synaptonemal complexes (SCs).
A J, Solari, O, Vilar
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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 ...
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Algebraic Complex Multiplication

1983
This chapter contains the first fundamental theory of complex multiplication. When an abelian variety has a sufficiently large ring of endomorphisms, then the Frobenius endomorphism of the variety mod p can be represented as the reduction mod p of an element in that ring, which is, say, the ring of integers in a number field K.
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Analytic Complex Multiplication

1983
This chapter is essentially elementary, and lays the foundations for the study of the endomorphisms of complex toruses known as complex multiplications. Let V be a vector space of dimension n over the complex numbers. Let Λ be a lattice in V. The quotient complex analytic group V/Λ is called a complex torus.
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Multiple, diverse, and complex

Science, 2018
Plant Science Calcium currents characterize the developing pollen tube in the small mustard plant Arabidopsis and correlate with growth at the tip of the pollen tube. This system constitutes a practical model for screening for Ca2+-signaling mechanisms in plants. Wudick et al.
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Multiple or Complex Fractures

2013
Description of the different types of fractures involving the axis vertebra are described; their mechanism, their diagnosis and treatment are presented.
Demetrios S. Korres, Andreas F. Mavrogenis   +1 more
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Multiplicative and Bilinear Complexity

1997
This chapter introduces the framework of the theory of bilinear complexity and is the basis for the study of Chap. 15–20. The language and concepts introduced here will, e. g., allow for a concise treatment of the fast matrix multiplication algorithms which we will discuss in the next chapter.
Peter Bürgisser, Michael Clausen, Mohammad Amin Shokrollahi   +2 more
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