scholarly journals Algebras of Binary Isolating Formulas for Theories of Root Products of Graphs

2021 ◽  
Vol 37 ◽  
pp. 93-103
Author(s):  
D.Yu. Emel’yanov ◽  
Keyword(s):  
Finite Algebra ◽  
Regular Polygons ◽  
Natural Classification ◽  
Cayley Tables

Algebras of distributions of binary isolating and semi-isolating formulas are derived objects for given theory and reflect binary formula relations between realizations of 1-types. These algebras are associated with the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to the theories from this class and classify these algebras; 2) to classify theories from a given class depending on the algebras defined by these theories of isolating and semi-isolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semi-isolating formulas, which makes it possible to track the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulae for root products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems describing all algebras of binary formulae distributions for the root multiplication theory of regular polygons on an edge are formulated. It is shown that they are completely described by two algebras.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Dense Periodic Packings of Regular Polygons

1995 ◽  
Vol 5 (12) ◽  
pp. 1539-1550 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
A. Gervois ◽  
J. P. Troadec
Keyword(s):  
Regular Polygons

Random Close Packings of Regular Polygons

1997 ◽  
Vol 7 (10) ◽  
pp. 1181-1189 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
J. P. Troadec ◽  
A. Gervois
Keyword(s):  
Regular Polygons

scholarly journals Towards a Natural Classification of Hyphodontia Sensu Lato and the Trait Evolution of Basidiocarps within Hymenochaetales (Basidiomycota)

2021 ◽  
Vol 7 (6) ◽  
pp. 478
Author(s):  
Xue-Wei Wang ◽  
Tom W. May ◽  
Shi-Liang Liu ◽  
Li-Wei Zhou
Keyword(s):  
Phylogenetic Analyses ◽  
Taxonomic Status ◽  
Ancestral State ◽  
Trait Evolution ◽  
Natural Classification ◽  
Multiple Loci ◽  
The Family ◽  
Phylogenetic Perspective ◽  
Taxonomic Framework ◽  
First Time

Hyphodontia sensu lato, belonging to Hymenochaetales, accommodates corticioid wood-inhabiting basidiomycetous fungi with resupinate basidiocarps and diverse hymenophoral characters. Species diversity of Hyphodontia sensu lato has been extensively explored worldwide, but in previous studies the six accepted genera in Hyphodontia sensu lato, viz. Fasciodontia, Hastodontia, Hyphodontia, Kneiffiella, Lyomyces and Xylodon were not all strongly supported from a phylogenetic perspective. Moreover, the relationships among these six genera in Hyphodontia sensu lato and other lineages within Hymenochaetales are not clear. In this study, we performed comprehensive phylogenetic analyses on the basis of multiple loci. For the first time, the independence of each of the six genera receives strong phylogenetic support. The six genera are separated in four clades within Hymenochaetales: Fasciodontia, Lyomyces and Xylodon are accepted as members of a previously known family Schizoporaceae, Kneiffiella and Hyphodontia are, respectively, placed in two monotypic families, viz. a previous name Chaetoporellaceae and a newly introduced name Hyphodontiaceae, and Hastodontia is considered to be a genus with an uncertain taxonomic position at the family rank within Hymenochaetales. The three families emerged between 61.51 and 195.87 million years ago. Compared to other families in the Hymenochaetales, these ages are more or less similar to those of Coltriciaceae, Hymenochaetaceae and Oxyporaceae, but much older than those of the two families Neoantrodiellaceae and Nigrofomitaceae. In regard to species, two, one, three and 10 species are newly described from Hyphodontia, Kneiffiella, Lyomyces and Xylodon, respectively. The taxonomic status of additional 30 species names from these four genera is briefly discussed; an epitype is designated for X. australis. The resupinate habit and poroid hymenophoral configuration were evaluated as the ancestral state of basidiocarps within Hymenochaetales. The resupinate habit mainly remains, while the hymenophoral configuration mainly evolves to the grandinioid-odontioid state and also back to the poroid state at the family level. Generally, a taxonomic framework for Hymenochaetales with an emphasis on members belonging to Hyphodontia sensu lato is constructed, and trait evolution of basidiocarps within Hymenochaetales is revealed accordingly.

Natural classification

1981 ◽  
Vol 20 (1) ◽  
pp. 37-91 ◽  
Author(s):  
Scott Atran
Keyword(s):  
Natural Classification

New Theorems for Moments of Inertia

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach
Keyword(s):  
Regular Polygon ◽  
Moment Of Inertia ◽  
Regular Polygons ◽  
Centre Of Mass ◽  
Moments Of Inertia ◽  
The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

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