In memory of Mikhail Alekseevich Lavrent'ev

Aleksandrov, P S; Bogolyubov, N. N.; Kolmogorov, A N; Lyusternik, L A; Marchuk, G. I.; Sobolev, S L; Shabat, B V

doi:10.1070/rm1981v036n02abeh002562

Cited by 3 publications

(1 citation statement)

References 2 publications

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“…They are contained in papers written by experts in the field, without any mention of Teichmüller's name and probably without any knowledge of the fact that they had already been discovered by him. 29 It is important to make straight the history of science and to attribute the origin of an idea to the person who discovered it first.…”

Section: On Teichmüller's Writingsmentioning

confidence: 99%

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

Papadopoulos

2017

Preprint

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The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the development of cartography, highlighting the main ideas that are related to quasiconformality. Some of these ideas were completely ignored in the previous historical surveys on quasiconformal mappings. We then survey early quasiconformal theory in the works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller, which are the 20th-century founders of the theory.The period we consider starts with Claudius Ptolemy (c. 100-170 A.D.) and ends with Oswald Teichmüller . We mention the works of several mathematicians-geographers done in this period, including Euler, Lagrange, Lambert, Gauss, Chebyshev, Darboux and others. We highlight in particular the work of Nicolas-Auguste Tissot (1824-1897), a French mathematician and geographer who (according to our knowledge) was the first to introduce the notion of a mapping which transforms infinitesimal circles into infinitesimal ellipses, studying parameters such as the ratio of the major to the minor axes of such an infinitesimal ellipse, its area divided by the area of the infinitesimal circle of which it is the image, and the inclination of its axis with respect to a fixed axis in the plane. We also give some information about the lives and works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller. The latter brought the theory of quasiconformal mappings to a high level of development. He used it in an essential way in his investigations of Riemann surfaces and their moduli and in function theory (in particular, in his work on the Bieberbach conjecture and the type problem). We survey in detail several of his results. We also discuss some aspects of his life and writings, explaining why his papers were not read and why some of his ideas are still unknown even to Teichmüller theorists.

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Section: On Teichmüller's Writingsmentioning

confidence: 99%

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

Papadopoulos

2017

Preprint

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SERGEI L'VOVICH SOBOLEV (on his sixtieth birthday)

Bitsadze¹,

Kantorovich²,

Lavrentʹev³

1968

Russ. Math. Surv.

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The conditions for propagation of a light-pulse-pair with nearly constant temporal and spatio-temporal parameters in nonlinear media are found in a broad range from quasi-cw to subpicosecond pulses. Because of the crucial dependence of the beam/pulse parameters from those of the complementary beam/pulse, the regime exhibits a symbiotic character. A set of balance solitary conditions are found between the signs and the values of the nonlinear susceptibilities for self-phase modulation, cross-phase modulation and the pump powers. The temporal and spatio-temporal modulation stability of the symbiotic light pair are discussed.

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Andrei Nikolaevich Kolmogorov (on his eightieth birthday)

Bogolyubov¹,

Гнеденко²,

Sobolev³

1983

Russ. Math. Surv.

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We derive an improved prescription for the merging of matrix elements with parton showers, extending the CKKW approach. A flavour-dependent phase space separation criterion is proposed. We show that this new method preserves the logarithmic accuracy of the shower, and that the original proposal can be derived from it. One of the main requirements for the method is a truncated shower algorithm. We outline the corresponding Monte Carlo procedures and apply the new prescription to QCD jet production in e + e − collisions and Drell-Yan lepton pair production. Explicit colour information from matrix elements obtained through colour sampling is incorporated in the merging and the influence of different prescriptions to assign colours in the large N C limit is studied. We assess the systematic uncertainties of the new method.

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In memory of Mikhail Alekseevich Lavrent'ev

Cited by 3 publications

References 2 publications

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

SERGEI L'VOVICH SOBOLEV (on his sixtieth birthday)

Andrei Nikolaevich Kolmogorov (on his eightieth birthday)

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