C-Nodal Surfaces of Order Three

1983 ◽  
Vol 35 (1) ◽  
pp. 68-100
Author(s):  
Tibor Bisztriczky
Keyword(s):  
Nineteenth Century ◽  
Singular Point ◽  
Algebraic Surface ◽  
Partial Classification ◽  
Differentiability Condition ◽  
Nodal Surfaces

The problem of describing a surface of order three can be said to originate in the mid-nineteenth century when A. Cayley discovered that a non-ruled cubic (algebraic surface of order three) may contain up to twenty-seven lines. Besides a classification of cubics, not much progress was made on the problem until A. Marchaud introduced his theory of synthetic surfaces of order three in [9]. While his theory resulted in a partial classification of a now larger class of surfaces, it was too general to permit a global description. In [1], we added a differentiability condition to Marchaud's definition. This resulted in a partial classification and description of surfaces of order three with exactly one singular point in [2]-[5]. In the present paper, we examine C-nodal surfaces and thus complete this survey.

scholarly journals Complete algebraic vector fields on affine surfaces

2020 ◽  
Vol 31 (03) ◽  
pp. 2050018
Author(s):  
Shulim Kaliman ◽  
Frank Kutzschebauch ◽  
Matthias Leuenberger
Keyword(s):  
Algebraic Surface ◽  
Vector Fields ◽  
Algebraic Surfaces ◽  
Algebraic Vector ◽  
Dual Graphs ◽  
Holomorphic Automorphisms

Let [Formula: see text] be the subgroup of the group [Formula: see text] of holomorphic automorphisms of a normal affine algebraic surface [Formula: see text] generated by elements of flows associated with complete algebraic vector fields. Our main result is a classification of all normal affine algebraic surfaces [Formula: see text] quasi-homogeneous under [Formula: see text] in terms of the dual graphs of the boundaries [Formula: see text] of their SNC-completions [Formula: see text].

The Carabao and the Encounter of the Law in Nineteenth-Century Philippines

2019 ◽  
Vol 27 (3) ◽  
pp. 307-326
Author(s):  
Nicolo Paolo P. Ludovice
Keyword(s):  
Nineteenth Century ◽  
Legal Status ◽  
Water Buffalo ◽  
Private Property ◽  
Historical Context ◽  
The Philippines ◽  
Legal Research ◽  
Human Animal ◽  
Philippine History

AbstractThe place of the non-human animal in the legal world has been questioned. Animals’ legal status as property has been probed on how to best protect their welfare. While this is significant for animals who are not on the farm, it might not be effective when considering animals raised for food. The case of the carabao, or the water buffalo, in the Philippines is seen as a hybrid. This article traces the development of the carabao in Philippine history during the nineteenth century. Through historical, archival, and legal research on animals, the carabao is situated as private property. Colonial instruments of control were introduced to protect the carabao from criminals. In its proper historical context, the classification of carabaos as property indeed highlighted the animal’s status as legally owned, which did not necessarily demean the animal’s relationship with the human peasant nor the carabao’s quality as an animal.

scholarly journals The algebraic structure of relativistic wave equations

1978 ◽  
Vol 20 (4) ◽  
pp. 446-486 ◽  
Author(s):  
A. Cant ◽  
C. A. Hurst
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Mass Spectra ◽  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave ◽  
Partial Classification ◽  
The Family ◽  
Image Position

The algebraic structure of relativistic wave equations of the formis considered. This leads to the problem of finding all Lie algebrasLwhich contain the Lorentz Lie algebraso(3, 1) and also contain a “four-vector” αμa such anLgives rise to a family of wave equations. The simplest possibility is the Bhabha equations whereL≅so(5). Some authors have claimed that this is theonlyone, but it is shown that there are many other possibilities still in accord with physical requirements. Known facts about representations, along with Dynkin's theory of the embeddings of Lie algebras, are used to obtain a partial classification of wave equations. The discrete transformationsC, P, Tare also discussed, along with reality properties. Finally, a simple example of a family of wave equations based onL=sp(12) is considered in detail. Theso(3, 1) content and mass spectra are given for the low order members of the family, and the problem of causality is briefly discussed.

Review Lecture Periods of integrals and topology of algebraic varieties

1984 ◽  
Vol 391 (1801) ◽  
pp. 231-254
Keyword(s):  
Nineteenth Century ◽  
Singular Point ◽  
Algebraic Topology ◽  
Major Theme ◽  
Algebraic Varieties ◽  
Hodge Structures ◽  
Algebraic Functions ◽  
Several Variables ◽  
And Topology ◽  
Satisfactory Theory

A major theme of nineteenth century mathematics was the study of integrals of algebraic functions of one variable. This culminated in Riemann’s introduction of the surfaces that bear his name and analysis of periods of integrals on cycles on the surface. The creation of a correspondingly satisfactory theory for functions of several variables had to wait on the development of algebraic topology and its application by Lefschetz to algebraic varieties. These results were refined by Hodge’s theory of harmonic integrals. A closer analysis of Hodge structures by P. A. Griffiths and P. Deligne in recent years has led to unexpectedly strong restrictions on the topology of the variety and to a diversity of other applications. This advance is closely linked to the study of variation of integrals under deformations, particularly in the neighbourhood of a singular point.

Étienne Geoffroy Saint-Hilaire, Richard Owen and monotreme oviparity.

2019 ◽  
Vol 40 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Stewart Nicol
Keyword(s):  
Nineteenth Century ◽  
Social Context ◽  
Egg Laying ◽  
Social Classes ◽  
The Social ◽  
Late Eighteenth ◽  
Richard Owen ◽  
Initial Description ◽  
Social Conservatives

Most biologists, particularly Australian biologists, are aware that the initial description and attempts to classify the echidna and platypus were surrounded by controversy. Fewer are aware of the important roles played by two eminent scientists, Étienne Geoffroy Saint-Hilaire in Paris and Richard Owen in London, in the debate as to whether the platypus and echidna were really mammals, and whether they laid eggs. Geoffroy argued that they were egg-laying but could not possibly lactate; Owen argued that they lactated but could not possibly lay eggs. Because of these and many other aspects of their biology, monotremes featured prominently in debates about classification of animals and the transmutation of species, and involved many important scientists of the time. These arguments can only be understood in the context of the development of science in the late eighteenth and the nineteenth century, and how that was influenced by the social context. Early ideas of evolution, or transformism, were attractive to radical thinkers, whereas social conservatives were anxious to show that the boundaries between types of animals, just like the boundaries between social classes, were erected by God and could not be crossed.

scholarly journals Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms

2008 ◽  
Vol 23 (2) ◽  
pp. 137-162 ◽  
Author(s):  
M.J. Parker ◽  
I.N. Stewart ◽  
M.G.M. Gomes
Keyword(s):  
Partial Classification

scholarly journals Współistnienie języków na ziemiach byłego Wielkiego Księstwa Litewskiego w świetle prac Jana Karłowicza

2015 ◽  
Vol 37 ◽  
pp. 41-51
Author(s):  
Elżbieta Koniusz
Keyword(s):  
Nineteenth Century ◽  
The Social ◽  
Linguistic Interference ◽  
History Of ◽  
Polish Language ◽  
Grand Duchy Of Lithuania ◽  
Bilingualism And Multilingualism ◽  
Grand Duchy

Co-existence of languages in the area of the former Grand Duchy of Lithuania in the light of the works of Jan KarłowiczThe article discusses the issues of the co-existence of languages in the former Grand Duchy of Lithuania and the consequences of the phenomenon as documented in the works of Jan Karłowicz – the outstanding scholar of the second half of the nineteenth century, an expert and researcher of the “Lithuanian” version of Polish language. The article emphasizes the fact that the research on languages in the area of The Grand Duchy of Lithuania and results of their co-existence goes back to the second half of the nineteenth century and Jan Karłowicz was the pioneer of this research. He was the first to observe the following phenomena of their co-existence: interference; bilingualism and multilingualism; prioritization of co-existing languages with the unique role of the Polish language in focusing various functions in the history of The Grand Duchy of Lithuania; the diversity of Polish with sociolinguistic classification of its provincia­lisms and their division in the view of their origin; and the dangers to the Polish language in the period of Russification. Karłowicz struggled with the lack of terminology to describe the linguistic phenomena characteristic for the area. The article focuses on the classification of provincial qualities of the “Lithuanian” Polish language executed by Karłowicz in the social and ethnolinguistic area; and on the presentation of the phenomenon of linguistic interference visible in the provincial vocabulary in The Grand Duchy of Lithuania collected in “Dictionary of Polish dialects” by Karłowicz. Сосуществование языков на территории бывшего Великого княжества Литовского в свете произведений Яна КарловичаЦель данной статьи – показать сосуществование языков на землях бывшего Великого княжества Литовского (ВКЛ) и последствий этого явления, засвидетельствованных в работах Яна Карловича, видного ученого второй половины девятнадцатого века, знатока и исследователя „литовского” польского языка. Автор статьи указывает на то, что изучение языков в Великом княжестве Литовском, последствиям их сосуществования относятся ко второй половине девятнадцатого века, а их первым исследователем был Карлович. Им впервые были отмечены такие проявления этого сосуществования, как языковая интерференция, билингвизм и многоязычие, иерархия сосуществующих языков и диалектов. Выделена особая роль польского языка, объединившего целый ряд функций в истории ВКЛ, дифференциация внутри польского языка, социолингвистическая классификация его диалектизмов и их деление по происхождению, угрозы для польского языка в период сильной русификации. Особое внимание автор статьи сосредоточил на классификации провинциальных особенностей „литовского” польского языка, осуществлённой Карловичем в социальном и этнолингвистическом плане, а также на проявлениях интерференции в провинциальной лексике, ведущей своё происхождение из Великого княжества Литовского, собранной в „Словаре польских диалектов” Карловича.

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