scholarly journals Classification of $ \mathbf{(3 \!\mod 5)} $ arcs in $ \mathbf{ \operatorname{PG}(3,5)} $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sascha Kurz ◽  
Ivan Landjev ◽  
Assia Rousseva
Keyword(s):  
General Framework ◽  
Existence Proof ◽  
Partial Classification

<p style='text-indent:20px;'>The proof of the non-existence of Griesmer <inline-formula><tex-math id="M3">\begin{document}$ [104, 4, 82]_5 $\end{document}</tex-math></inline-formula>-codes is just one of many examples where extendability results are used. In a series of papers Landjev and Rousseva have introduced the concept of <inline-formula><tex-math id="M4">\begin{document}$ (t\mod q) $\end{document}</tex-math></inline-formula>-arcs as a general framework for extendability results for codes and arcs. Here we complete the known partial classification of <inline-formula><tex-math id="M5">\begin{document}$ (3 \mod 5) $\end{document}</tex-math></inline-formula>-arcs in <inline-formula><tex-math id="M6">\begin{document}$ \operatorname{PG}(3,5) $\end{document}</tex-math></inline-formula> and uncover two missing, rather exceptional, examples disproving a conjecture of Landjev and Rousseva. As also the original non-existence proof of Griesmer <inline-formula><tex-math id="M7">\begin{document}$ [104, 4, 82]_5 $\end{document}</tex-math></inline-formula>-codes is affected, we present an extended proof to fill this gap.</p>

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 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.

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 A novel framework for classification of selection mechanisms in epidemiological research

2019 ◽  
Author(s):  
Jonas Bjork ◽  
Anton Nilsson ◽  
Carl Bonander ◽  
Ulf Strömberg
Keyword(s):  
General Framework ◽  
Empirical Studies ◽  
Population Level ◽  
Epidemiological Studies ◽  
Three Dimensions ◽  
Epidemiological Research ◽  
Selection Processes ◽  
Selection Mechanisms

Abstract Background: Non-participation, losses to follow up and other types of study-specific selection mechanisms can be serious concerns in epidemiological studies. There are also selection processes that result in non-random groupings and changes in the composition of populations. These are continuously on-going irrespectively of whether they are subject to sampling in empirical studies. Such population selections are often overlooked, but may lead to lack of comparability of exposed and unexposed populations or decrease study validity in other ways. The overall aim of this study was to develop a simple but general framework for classifying various types of selection mechanisms of relevance for epidemiological research. Methods: We classify selection mechanisms in three dimensions: i) selection at the population level vs. selection that is study-specific, ii) type of mechanism (selection causing exposure vs. selection in population at risk), iii) timing of the selection (pre-exposure, during exposure or post-outcome). Results: Examples from the epidemiological literature of selection mechanisms are discussed and classified according to the three dimensions of the proposed framework. Conclusions: Increased mechanistic understanding of when, how, and why confusion of effects can occur because of selection is an important step towards improved validity of epidemiological research.

scholarly journals Antiautomorphisms and Biantiautomorphisms of Some Finite Abelian Groups

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 294
Author(s):  
Daniel López-Aguayo ◽  
Servando López Aguayo
Keyword(s):  
Lower Bound ◽  
Abelian Groups ◽  
Additive Group ◽  
Exact Formula ◽  
Finite Abelian Groups ◽  
Cyclic Groups ◽  
Partial Classification ◽  
Open Questions ◽  
Odd Order

We extend the concepts of antimorphism and antiautomorphism of the additive group of integers modulo n, given by Gaitanas Konstantinos, to abelian groups. We give a lower bound for the number of antiautomorphisms of cyclic groups of odd order and give an exact formula for the number of linear antiautomorphisms of cyclic groups of odd order. Finally, we give a partial classification of the finite abelian groups which admit antiautomorphisms and state some open questions.

scholarly journals On classification of super-modular categories of rank 8

2020 ◽  
pp. 2140017
Author(s):  
Paul Bruillard ◽  
Julia Plavnik ◽  
Eric C. Rowell ◽  
Qing Zhang
Keyword(s):  
Lower Rank ◽  
Partial Classification

We develop categorical and number-theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank [Formula: see text]. In particular we find three distinct families of prime categories in rank [Formula: see text] in contrast to the lower rank cases for which there is only one such family.

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