Questions of generality as probes into nineteenth-century mathematical analysis

2017 ◽  
Author(s):  
Renaud Chorlay
Keyword(s):  
Nineteenth Century ◽  
Set Theory ◽  
Mathematical Analysis ◽  
Analytic Functions ◽  
Function Theory ◽  
The Third ◽  
Point Set

This article examines ways of expressing generality and epistemic configurations in which generality issues became intertwined with epistemological topics, such as rigor, or mathematical topics, such as point-set theory. In this regard, three very specific configurations are discussed: the first evolving from Niels Henrik Abel to Karl Weierstrass, the second in Joseph-Louis Lagrange’s treatises on analytic functions, and the third in Emile Borel. Using questions of generality, the article first compares two major treatises on function theory, one by Lagrange and one by Augustin Louis Cauchy. It then explores how some mathematicians adopted the sophisticated point-set theoretic tools provided for by the advocates of rigor to show that, in some way, Lagrange and Cauchy had been right all along. It also introduces the concept of embedded generality for capturing an approach to generality issues that is specific to mathematics.

Historical Fragments’ Mobile Echo

Transfers ◽  
2017 ◽  
Vol 7 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Susan E. Bell ◽  
Kathy Davis
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Eighteenth Century ◽  
Cultural Revolution ◽  
Ming Dynasty ◽  
Third Century ◽  
Refugee Crisis ◽  
The Third ◽  
Opium War ◽  
The Subject

Translocation – Transformation is an ambitious contribution to the subject of mobility. Materially, it interlinks seemingly disparate objects into a surprisingly unified exhibition on mobile histories and heritages: twelve bronze zodiac heads, silk and bamboo creatures, worn life vests, pressed Pu-erh tea, thousands of broken antique teapot spouts, and an ancestral wooden temple from the Ming dynasty (1368–1644) used by a tea-trading family. Historically and politically, the exhibition engages Chinese stories from the third century BCE, empires in eighteenth-century Austria and China, the Second Opium War in the nineteenth century, the Chinese Cultural Revolution of the mid-twentieth century, and today’s global refugee crisis.

Third Hankel determinants for two classes of analytic functions with real coefficients

2021 ◽  
Vol 33 (4) ◽  
pp. 973-986
Author(s):  
Young Jae Sim ◽  
Paweł Zaprawa
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Lower And Upper Bounds ◽  
Hankel Determinants ◽  
The Third ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

Abstract In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H 2 , 2 {H_{2,2}} or H 3 , 1 {H_{3,1}} over different subclasses of 𝒮 {\mathcal{S}} . Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 {\mathcal{T}} of typically real functions. The second object of our interest is 𝒦 ℝ ⁢ ( i ) {\mathcal{K}_{\mathbb{R}}(i)} , the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 721 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
The Third

Let SR * be the class of starlike functions with real coefficients, i.e., the class of analytic functions f which satisfy the condition f ( 0 ) = 0 = f ′ ( 0 ) − 1 , Re { z f ′ ( z ) / f ( z ) } > 0 , for z ∈ D : = { z ∈ C : | z | < 1 } and a n : = f ( n ) ( 0 ) / n ! is real for all n ∈ N . In the present paper, it is obtained that the sharp inequalities − 4 / 9 ≤ H 3 , 1 ( f ) ≤ 3 / 9 hold for f ∈ SR * , where H 3 , 1 ( f ) is the third Hankel determinant of order 3 defined by H 3 , 1 ( f ) = a 3 ( a 2 a 4 − a 3 2 ) − a 4 ( a 4 − a 2 a 3 ) + a 5 ( a 3 − a 2 2 ) .

Matter and Point Set Theory

1960 ◽  
Vol 117 (5) ◽  
pp. 1409-1409
Author(s):  
Ali Kyrala
Keyword(s):  
Set Theory ◽  
Point Set

Swedish Rural Society and Political Culture: The Eighteenth- and Nineteenth-Century Experience

Rural History ◽  
1992 ◽  
Vol 3 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Peter Aronsson
Keyword(s):  
Nineteenth Century ◽  
Political Culture ◽  
Rural Society ◽  
Final Decision ◽  
The Third ◽  
Legal Foundation ◽  
Local Parish ◽  
The Church

In 1776, baron Salomon von Otter, governor of the neighbouring county of Halland and jus patronatus of the local parish, stood opposite the men of Öja parish at a meeting outside the church. The powerful nobleman was for the third time arguing for the praiseworthy and legally required task of building a combined school and poor-house in cooperation with the neighbouring parish (where he happened to own most of the land). The peasants of Ö for a third time refused, both in writing and orally, on the grounds of their alleged right to self-government. The baron continued with his persuasions, and presented the support he had from the local nobility, among them the bishop. He was still met with a firm refusal. Eventually the baron ordered that they should build the house, referring (probably without much legal foundation) to his position as jus patronatus. Now everybody surrendered, except one farmer who refused to join in the final decision. This fact was carefully noted by the local clergyman, together with assurances that this unwise stubbornness would not suffice to impede the project.

Foundations of Point Set Theory

1934 ◽  
Vol 18 (231) ◽  
pp. 325
Author(s):  
P. J. D. ◽  
R. L. Moore
Keyword(s):  
Set Theory ◽  
Point Set

Lamennais

1947 ◽  
Vol 9 (2) ◽  
pp. 205-229 ◽  
Author(s):  
Waldemar Gurian
Keyword(s):  
Nineteenth Century ◽  
Catholic Church ◽  
Early Church ◽  
The Third ◽  
Vatican Council ◽  
Papal Infallibility ◽  
History Of ◽  
The Church ◽  
The Catholic Church

The history of the Catholic Church includes men who, after brilliant services to the Church, died outside her fold. Best known among them is Tertullian, the apologetic writer of the Early Church; less known is Ochino, the third vicar-general of the Capuchins, whose flight to Calvin's Geneva almost destroyed his order. In the nineteenth century there were two famous representatives of this group. Johann von Doellinger refused, when more than seventy years old, to accept the decision of the Vatican Council about papal infallibility. He passed away in 1890 unreconciled, though he had been distinguished for years as the outstanding German Catholic theologian. Félicité de la Mennais was celebrated as the new Pascal and Bossuet of his time before he became the modern Tertullian by breaking with the Church because Pope Gregory XVI rejected his views on the relations between the Church and die world. As he lay deathly ill, his niece, “Madame de Kertanguy asked him: ‘Féli, do you want a priest? Surely, you want a priest?’ Lamennais answered: ‘No.’ The niece repeated: ‘I beg of you.’ But he said with a stronger voice: ‘No, no, no.

The Gathering of A Community: The British-born of San Francisco in 1852 and 1872

1976 ◽  
Vol 10 (3) ◽  
pp. 279-312 ◽  
Author(s):  
R. A. Burchell
Keyword(s):  
Nineteenth Century ◽  
San Francisco ◽  
High Rate ◽  
Geographical Mobility ◽  
The Third ◽  
Human Effort ◽  
The Subject ◽  
Incomplete Picture ◽  
Do So

Studies of the Massachusetts communities of Newburyport and Boston have revealed a high rate of geographical mobility for their populations, in excess of what had been previously thought. Because of the difficulty in tracing out-migrants these works have concentrated on persisters, though to do so is to give an incomplete picture of communal progress. Peter R. Knights in his study of Boston between 1830 and 1860 attempted to follow his out-migrants but was only able to trace some 27 per cent of them. The problem of out-migration is generally regarded as being too large for solution through human effort, but important enough now to engage the computer. What follows bears on the subject of out-migration, for it is an analysis of where part of the migrating populations of the east went in the third quarter of the nineteenth century, namely to San Francisco.

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