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Abel, Niels Henrik (1802–29)

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 94 words.

who, at the age of 19, proved that the general equation of degree greater than 4 cannot be solved algebraically.

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Abel summation

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 37 words.

A method of computing the sum of a possibly *divergent series of *complex numbers as the limit, as

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Abel’s Limit Theorem

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 26 words.

For a *convergent series {ak }, the limit assigned by the Abel summation method exists and is

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Abel’s partial summation formula

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 26 words.

For two arbitrary sequences and with , the result that . This has some similarities with the formula for *

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Abel’s test

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 46 words.

A test for the convergence of an infinite series which states that if ∑a n is a convergent sequence,

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Abelian 1-Calabi–Yau Categories

Adam-Christiaan van Roosmalen.

in International Mathematics Research Notices

January 2008; p ublished online January 2008 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

In this paper, we show all k-linear abelian 1-Calabi–Yau categories over an algebraically closed field k are derived equivalent to either the category of coherent sheaves on an elliptic...

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Abelian Functions for Trigonal Curves of Genus Three

J. C. Eilbeck, V. Z. Enolski, S. Matsutani, Y. Ônishi and E. Previato.

in International Mathematics Research Notices

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

We develop the theory of generalized Weierstrass σ- and ℘-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential...

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abelian group

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 38 words.

Suppose that G is a *group with the operation ○. Then G is abelian if the operation ○ is

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abelian group

James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 38 words.

Suppose that G is a *group with the operation ○. Then G is abelian if the operation ○ is

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Abelian Varieties

D. Huybrechts.

in Fourier-Mukai Transforms in Algebraic Geometry

April 2006; p ublished online September 2007 .

Chapter. Subjects: Geometry. 19346 words.

Historically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this...

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