Gösta Mittag-Leffler

Stubhaug, Arild

doi:10.1007/978-3-642-11672-8

Cited by 20 publications

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“…Lars Edvard Phragmén (1863Phragmén ( -1937) was a Swedish mathematician, actuary and insurance executive. He began his mathematical university studies in Uppsala in 1882, but transferred in 1883 to Stockholm, where he became a student (and later confidant) of Gösta Mittag-Leffler [63]. In 1888, Phragmén was appointed coeditor of Mittag-Leffler's journal Acta Mathematica, where he immediately made an important contribution by finding an error in a paper by Henri Poincaré on the three-body problem.…”

Section: A Brief Biography Of Phragménmentioning

confidence: 99%

“…Moreover, he was a member of the Royal Commission on a Proportional Election Method 1902-1903 and of a new Royal Commission on the Proportional Election Method 1912-1913. For further information we refer the reader to the survey by Janson [26] and to the book by Stubhaug [63] (in particular for his relation with Mittag-Leffler).…”

Section: A Brief Biography Of Phragménmentioning

confidence: 99%

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Phragmén’s voting methods and justified representation

et al. 2023

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In the late 19th century, Swedish mathematician Edvard Phragmén proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants—one minimizing the maximum load and one minimizing the variance of loads—and a sequential variant. We study Phragmén ’s methods from an axiomatic point of view, focusing on properties capturing proportional representation. We show that the sequential variant satisfies proportional justified representation, which is a rare property for committee monotonic methods. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the computational complexity of Phragmén ’s methods and provide mixed-integer programming based algorithms for computing them.

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Section: A Brief Biography Of Phragménmentioning

confidence: 99%

Section: A Brief Biography Of Phragménmentioning

confidence: 99%

Phragmén’s voting methods and justified representation

et al. 2023

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“…10: Proof of Theorems of Pincherle) to revisit the original work of Pincherle; in particular, he wrote "Before we are going to prove this theorem, which is a special case of a more general theorem of Mr. Pincherle, we want to describe more closely the lines L over which the integration preferably is to be carried out" [free translation from German]. 1 More precisely, as we know from the recent biography of the Swedish mathematician Mittag-Leffler by Arild Stubhaug [22]: The final decision was to be made as to where the next international mathematics congress (in 1928) would be held; the options were Bologna and Stockholm. One strike against Stockholm was the strength of the Swedish currency; it was said that it would simply be too expensive in Stockholm.…”

Section: Pincherle and The Mellin-barnes Integralsmentioning

confidence: 99%

The Role of Salvatore Pincherle in the Development of Fractional Calculus

Mainardi

Pagnini²

2011

Mathematicians in Bologna 1861–1960

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We revisit two contributions by Salvatore Pincherle (Professor of Mathematics at the University of Bologna from 1880 to 1928) published (in Italian) in 1888 and 1902 in order to point out his possible role in the development of Fractional Calculus. Fractional Calculus is that branch of mathematical analysis dealing with pseudo-differential operators interpreted as integrals and derivatives of non-integer order. Even if the former contribution (published in two notes on Accademia dei Lincei) on generalized hypergeomtric functions does not concern Fractional Calculus it contains the first example in the literature of the use of the so called Mellin-Barnes integrals. These integrals will be proved to be a fundamental task to deal with all higher transcendental functions including the Meijer and Fox functions introduced much later. In particular, the solutions of differential equations of fractional order are suited to be expressed in terms of these integrals. In the second paper (published on Accademia delle Scienze di Bologna), the author is interested to insert in the framework of his operational theory the notion of derivative of non integer order that appeared in those times not yet well established. Unfortunately, Pincherle's foundation of Fractional Calculus seems still ignored.

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Chapter 1 Elliptic Functions

Bottazzini

Gray

2013

Hidden Harmony—Geometric Fantasies

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Gösta Mittag-Leffler

Cited by 20 publications

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Phragmén’s voting methods and justified representation

Phragmén’s voting methods and justified representation

The Role of Salvatore Pincherle in the Development of Fractional Calculus

Chapter 1 Elliptic Functions

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