scholarly journals The geometry of billiards in ellipses and their poncelet grids

2021 ◽  
Vol 112 (3) ◽  
Author(s):  
Hellmuth Stachel
Keyword(s):  
Continuous Variation ◽  
Initial Vertex

AbstractThe goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points which are located on confocal ellipses and hyperbolas. They define the associated Poncelet grid. If a billiard is periodic then it closes for any choice of the initial vertex on the ellipse. This gives rise to a continuous variation of billiards which is called billiard motion though it is neither a Euclidean nor a projective motion. The extension of this motion to the associated Poncelet grid leads to new insights and invariants.

Temporality and Truth

2013 ◽  
Vol 7 (3) ◽  
pp. 377-389 ◽  
Author(s):  
Daniel W. Smith
Keyword(s):  
Seventeenth Century ◽  
Laws Of Nature ◽  
Continuous Variation ◽  
Pure Form ◽  
The Other ◽  
Other Hand ◽  
The One ◽  
Time Image ◽  
Positive Light

This paper examines the intersecting of the themes of temporality and truth in Deleuze's philosophy. For the ancients, truth was something eternal: what was true was true in all times and in all places. Temporality (coming to be and passing away) was the realm of the mutable, not the eternal. In the seventeenth century, change began to be seen in a positive light (progress, evolution, and so on), but this change was seen to be possible only because of the immutable laws of nature that govern change. It was not until philosophers such as Bergson, James, Whitehead – and then Deleuze – that time began to be taken seriously on its own account. On the one hand, in Deleuze, time, freed from its subordination to movement, now becomes autonomous: it is the pure form of change (continuous variation) that lies at the basis of Deleuze's metaphysics in Difference and Repetition (and is explored more thematically in The Time-Image). As a result, on the other hand, the false, freed from its subordination to the form of the true, assumes a power of its own (the power of the false), which in turn implies a new ‘analytic of the concept’ that Deleuze develops in What Is Philosophy?

scholarly journals On randomly 3-axial graphs

1982 ◽  
Vol 25 (2) ◽  
pp. 187-206
Author(s):  
Yousef Alavi ◽  
Sabra S. Anderson ◽  
Gary Chartrand ◽  
S.F. Kapoor
Keyword(s):  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Complete Graphs ◽  
Initial Vertex ◽  
Complete Bipartite Graphs

A graph G, every vertex of which has degree at least three, is randomly 3-axial if for each vertex v of G, any ordered collection of three paths in G of length one with initial vertex v can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G. Randomly 3-axial graphs of order p > 4 are characterized for p ≢ 1 (mod 3), and are shown to be either complete graphs or certain regular complete bipartite graphs.

Continuous variation of iodine adlattices on Ag(111) electrodes: in situ STM and ex situ LEED studies

1996 ◽  
Vol 369 (1-3) ◽  
pp. 321-335 ◽  
Author(s):  
Taro Yamada ◽  
Katsuhiko Ogaki ◽  
Shinya Okubo ◽  
Kingo Itaya
Keyword(s):  
Continuous Variation ◽  
Ex Situ ◽  
In Situ Stm

scholarly journals Arguments Whose Strength Depends on Continuous Variation

2013 ◽  
Vol 33 (1) ◽  
pp. 33
Author(s):  
James Franklin
Keyword(s):  
Fuzzy Logic ◽  
Possible Worlds ◽  
Slippery Slope ◽  
Continuous Variation ◽  
Symbol Processing ◽  
Slippery Slope Arguments

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so that ignorance of their nature is profound.

scholarly journals Testing a continuous variation in preweaning expression of muscular hypertrophy in beef cattle using field data

2002 ◽  
Vol 45 (2) ◽  
pp. 139-149 ◽  
Author(s):  
F. Goyache ◽  
L. J. Royo ◽  
I. Alvarez ◽  
J. P. Gutierrez
Keyword(s):  
Field Data ◽  
Growth Traits ◽  
Major Gene ◽  
Continuous Variation ◽  
Muscular Hypertrophy ◽  
Index Method ◽  
Factors Affecting ◽  
Calving Season ◽  
Phenotypical Variability ◽  
Growth Ability

Abstract. The hypothesis of a continuous variation in the expression of muscular hypertrophy has been tested using field data. A modification of NEUVY and VISSAC's cularity index method (Culard Index) was assayed. Expression of muscular hypertrophy showed a broad phenotypical variability. Environmental factors affecting expression of muscular hypertrophy characterised by Culard Index were calving season, age of dam, sex of calf, muscularity of dam, muscularity of sire and age of calf at weaning. In addition, Culard Index influences significantly preweaning growth traits confirming double muscled calves’ higher preweaning growth ability. Culard Index score showed moderate heritability. Expression of muscular hypertrophy could be a relatively different trait with respect to latent muscular hypertrophy that would be, in turn, determined by a partially dominant major gene. Culard Index could be an interesting tool to make use of the observable differences in expression of muscular hypertrophy.

scholarly journals Reexamining the Classification of Theobroma cacao L. Using Molecular Markers

1994 ◽  
Vol 119 (5) ◽  
pp. 1073-1082 ◽  
Author(s):  
Antonio Figueira ◽  
Jules Janick ◽  
Morris Levy ◽  
Peter Goldsbrough
Keyword(s):  
Molecular Markers ◽  
Theobroma Cacao ◽  
Rapd Markers ◽  
Continuous Variation ◽  
Clear Distinction ◽  
Species Separation ◽  
Theobroma Cacao L ◽  
Rdna Polymorphism

Genetic similarities among eight Theobroma and two Herrania species, including 29 genotypes of T. cacao, were estimated by rDNA polymorphism. A phenogram based on these genetic similarities significantly separated two clusters: one cluster included all Herrania and Theobroma species, except T. cacao, while the second contained 28 of 29 T. cacao genotypes. There was no clear distinction between Herrania and Theobroma species. Separation of 29 T. cacao genotypes, representing all races and various origins, had no congruency with the conventional classification into three horticultural races: Criollo, Forastero, and Trinitario. Genetic similarities in T. cacao, estimated with RAPD markers, indicated continuous variation among the generally similar but heterogeneous genotypes. The wild genotypes formed an outgroup distinct from the cultivated genotypes, a distinction supported by the rDNA data. The phenograms constructed from RAPD and rDNA data were not similar within the wild and cultivated cacao subsets.

scholarly journals A Note on Hamiltonian Bypasses in Digraphs with Large Degrees

2020 ◽  
pp. 7-17
Author(s):  
Samvel Darbinyan
Keyword(s):  
Directed Graph ◽  
Hamiltonian Path ◽  
Terminal Vertex ◽  
Initial Vertex ◽  
Strongly Connected

Let D be a 2-strongly connected directed graph of order p ≥ 3. Suppose that d(x) ≥ p for every vertex x ∈ V (D) \ {x0}, where x0 is a vertex of D. In this paper, we show that if D is Hamiltonian or d(x0) > 2(p − 1)/5, then D contains a Hamiltonian path, in which the initial vertex dominates the terminal vertex.

Behaviour of some external characteristics in Essex pigs

1944 ◽  
Vol 34 (1) ◽  
pp. 16-21 ◽  
Author(s):  
T. M. Olbrycht
Keyword(s):  
Continuous Variation ◽  
Colour Pattern ◽  
External Characteristics

1. The colour pattern in the Essex breed shows continuous variation in width and in shape of the belt, in size and number of the distal white points, in pigmentation of the skin and in the occurrence of all-black colour.2. The variation in ear shape extends from long, hanging ears to small, erect (prick) ears.3. ‘Rose back’ was observed in a small percentage of pure-bred Essex pigs.4. Observed results of crossing Wessex with Essex pigs, and the similarity in variation of colour of the two breeds, indicate that the factors upon which the colour depends are the same in Essex and in Wessex, and that there is no genetical difference in colour in these two breeds.

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