scholarly journals IX. The third elliptic integral and the ellipsotomic problem

1904 ◽  
Vol 203 (359-371) ◽  
pp. 217-304
Keyword(s):  
Elliptic Integral ◽  
Great Influence ◽  
Elliptic Functions ◽  
Mechanical Theory ◽  
The Third ◽  
History Of ◽  
Modern Analysis

The Abel Centennial Ceremony, held in Christiania, September, 1902, has directed the attention of mathematicians to the great influence of Abel on modern analysis, and. to the history of elliptic functions, and of the foundation by Crelle of the “ Journal für die reine und angewandte Mathematik.” Abel’s article in the first volume of ‘ Crelle’s Journal,' 1826, " Ueber die Integration der Differential-Formel ρdx ⁄ √R (A), wenn R und ρ gauze Functionen sind,” is of great importance as indicating the existence of what is now called the pseudo-elliptic integral; the present memoir is intended to show the utility of this integral in its application to mechanical theory.

XVIII. Researches on the geometrical properties of elliptic integrals

1852 ◽  
Vol 142 ◽  
pp. 311-416 ◽  
Keyword(s):  
Elliptic Integral ◽  
Plane Curve ◽  
Elliptic Functions ◽  
Elliptic Integrals ◽  
Mathematical Science ◽  
Third Order ◽  
Geometrical Properties ◽  
First Order ◽  
The Third ◽  
The Right

I. In placing before the Royal Society the following researches on the geometrical types of elliptic integrals, which nearly complete my investigations on this interesting subject, I may be permitted briefly to advert to what bad already been effected in this department of geometrical research. Legendre, to whom this important branch of mathematical science owes so much, devised a plane curve, whose rectification might be effected by an elliptic integral of the first order. Since that time many other geometers have followed his example, in contriving similar curves, to represent, either by their quadrature or rectification, elliptic functions. Of those who have been most successful in devising curves which should possess the required properties, may be mentioned M. Gudermann, M. Verhulst of Brussels, and M. Serret of Paris. These geometers however have succeeded in deriving from those curves scarcely any of the properties of elliptic integrals, even the most elementary. This barrenness in results was doubtless owing to the very artificial character of the genesis of those curves, devised, as they were, solely to satisfy one condition only of the general pro­blem. In 1841 a step was taken in the right direction. MM. Catalan and Gudermann, in the journals of Liouville and Crelle, showed how the arcs of spherical conic sec­tions might be represented by elliptic integrals of the third order and circular form. They did not, however, extend their investigations to the case of elliptic integrals of the third order and logarithmic form; nor even to that of the first order. These cases still remained, without any analogous geometrical representative, a blemish to the theory.

Interaction Behaviours Between Soliton and Cnoidal Periodic Waves for the Cubic Generalised Kadomtsev–Petviashvili Equation

2015 ◽  
Vol 70 (7) ◽  
pp. 539-544 ◽  
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Elliptic Integral ◽  
Elliptic Functions ◽  
Jacobi Elliptic Functions ◽  
Periodic Waves ◽  
The Third ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Kink Soliton

AbstractThe consistent tanh expansion (CTE) method is applied to the cubic generalised Kadomtsev–Petviashvili (CGKP) equation. The interaction solutions between one kink soliton and the cnoidal periodic waves are explicitly given. Some special concrete interaction solutions in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral are discussed both in analytical and graphical ways.

Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation

2016 ◽  
Vol 71 (4) ◽  
pp. 351-356 ◽  
Author(s):  
Wenguang Cheng ◽  
Biao Li
Keyword(s):  
Elliptic Integral ◽  
Wave Interaction ◽  
Elliptic Functions ◽  
Mkdv Equation ◽  
Jacobi Elliptic Functions ◽  
Cnoidal Wave ◽  
Residual Symmetry ◽  
The Third ◽  
Interaction Solutions ◽  
Consistent Riccati Expansion

AbstractThe truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV–mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV–mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV–mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton–cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.

A Universe of Societies

2018 ◽  
Author(s):  
Didier Debaise
Keyword(s):  
Spatial Relations ◽  
The Third ◽  
The Status ◽  
History Of ◽  
Temporal And Spatial

Which kind of relation exists between a stone, a cloud, a dog, and a human? Is nature made of distinct domains and layers or does it form a vast unity from which all beings emerge? Refusing at once a reductionist, physicalist approach as well as a vitalistic one, Whitehead affirms that « everything is a society » This chapter consequently questions the status of different domains which together compose nature by employing the concept of society. The first part traces the history of this notion notably with reference to the two thinkers fundamental to Whitehead: Leibniz and Locke; the second part defines the temporal and spatial relations of societies; and the third explores the differences between physical, biological, and psychical forms of existence as well as their respective ways of relating to environments. The chapter thus tackles the status of nature and its domains.

The Origins of Gritty Realism on British Television: Euston Films and Special Branch

2014 ◽  
Vol 11 (1) ◽  
pp. 23-40 ◽  
Author(s):  
Max Sexton
Keyword(s):  
Cultural Discourse ◽  
Technological Changes ◽  
Television Drama ◽  
The Third ◽  
Fourth Series ◽  
History Of

Euston Films was the first film subsidiary of a British television company that sought to film entirely on location. To understand how the ‘televisual imagination’ changed and developed in relationship to the parent institution's (Thames Television) economic and strategic needs after the transatlantic success of its predecessor, ABC Television, it is necessary to consider how the use of film in television drama was regarded by those working at Euston Films. The sources of realism and development of generic verisimilitude found in the British adventure series of the early 1970s were not confined to television, and these very diverse sources both outside and inside television are well worth exploring. Thames Television, which was formed in 1968, did not adopt the slickly produced adventure series style of ABC's The Avengers, for example. Instead, Thames emphasised its other ABC inheritance – naturalistic drama in the form of the studio-based Armchair Theatre – and was to give the adventure series a strong London lowlife flavour. Its film subsidiary, Euston Films, would produce ‘gritty’ programmes such as the third and fourth series of Special Branch. Amid the continuities and tensions between ABC and Thames, it is possible to discern how economic and technological changes were used as a cultural discourse of value that marks the production of Special Branch as a key transformative moment in the history of British television.

Displace of Documentary Heritage from the Soviet Union to Poland during the Third Decade of the XXth Century

2014 ◽  
Vol 3 ◽  
pp. 127-137
Author(s):  
Tatsiana Hiarnovich
Keyword(s):  
Soviet Union ◽  
International Agreements ◽  
Peace Treaty ◽  
Actual Process ◽  
Xxth Century ◽  
The Third ◽  
The Soviet Union ◽  
History Of ◽  
Selection Of

The paper explores the displace of Polish archives from the Soviet Union that was performed in 1920s according to the Riga Peace Treaty of 1921 and other international agreements. The aim of the research is to reconstruct the process of displace, based on the archival sources and literature. The object of the research is those documents that were preserved in the archives of Belarus and together with archives from other republics were displaced to Poland. The exploration leads to clarification of the selection of document fonds to be displaced, the actual process of movement and the explanation of the role that the archivists of Belarus performed in the history of cultural relationships between Poland and the Soviet Union. The articles of the Treaty of Riga had been formulated without taking into account the indivisibility of archive fonds that is one of the most important principles of restitution, which caused the failure of the treaty by the Soviet part.

The Question of Authority: Deracinating Race, Repositioning Religion, and Regenerating Gender in the History of African American Islam

2010 ◽  
Vol 4 (1-2) ◽  
pp. 213-227
Author(s):  
Rosemary Hicks
Keyword(s):  
African American ◽  
Review Essay ◽  
Oxford University ◽  
The Third ◽  
History Of ◽  
American Islam ◽  
African American Islam ◽  
Oxford University Press

A review essay devoted to Islam and the Blackamerican: Looking Toward the Third Resurrection by Sherman A. Jackson. Oxford University Press, 2005. 256 pages. Hb. $29.95/£22.50, ISBN-13: 9780195180817.

A Short Modern History of Studying Sacrobosco’s De sphaera

2020 ◽  
Vol 65 (Special Issue) ◽  
pp. 23-33
Author(s):  
Alin Constantin Corfu
Keyword(s):  
20Th Century ◽  
Modern History ◽  
13Th Century ◽  
The Third ◽  
History Of ◽  
University Of Paris ◽  
The University

"A Short Modern History of Studying Sacrobosco’s De sphaera. The treatise generally known as De sphaera offered at the beginning of the 13th century a general image of the structure of the cosmos. In this paper I’m first trying to present a triple stake with which this treaty of Johannes de Sacrobosco (c. 1195 - c. 1256). This effort is intended to draw a context upon the treaty on which I will present in the second part of this paper namely, a short modern history of studying this treaty starting from the beginning of the 20th century up to this day. The first stake consists in the well-known episode of translation of the XI-XII centuries in the Latin milieu of the Greek and Arabic treaties. The treatise De sphaera taking over, assimilating and comparing some of the new translations of the texts dedicated to astronomy. The second Consists in the fact that Sacrobosco`s work can be considered a response to a need of renewal of the curriculum dedicated to astronomy at the University of Paris. And the third consists in the novelty and the need to use the De sphaera treatise in the Parisian University’s curriculum of the 13th century. Keywords: astronomy, translation, university, 13th Century, Sacrobosco, Paris, curriculum"

Users behaviors: The Heritage of Digital World

2014 ◽  
Vol 13 (7) ◽  
pp. 4675-4682
Author(s):  
Atefeh Danesh Moghadam ◽  
Alireza Alagha
Keyword(s):  
Technology Development ◽  
Second Step ◽  
Information Communication ◽  
The Third ◽  
Digital World ◽  
New Concepts ◽  
Emerging Patterns ◽  
History Of ◽  
Fourth Step ◽  
Communication And Technology

In the advent of information era, not only digital world is going to expand its territories, it is going to penetrate into the traditional notions about the meaning of the words and also valorize new concepts. According to Oxford Dictionary, the word heritage is defined: The history, tradition and qualities that a country or society has had for many years and that are considered an important part of its character. In order to present how emerging patterns, as the consequences of technology development, are going to be considered as the new concept of heritage, we follow four steps. In the first step, we present the convergence of Information, Communication and Technology (ICT) and a concise history of its convergence. In the second step, we argue how convergence has culminated in emerging patterns and also has made changes in digital world. In the third step, the importance of users behaviors and its mining is surveyed. Finally, in the fourth step; we illustrate User Generated Contents (UGC) as the most prominent users behaviors in digital world.

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