scholarly journals Weak separation, positivity and extremal Yangian invariants

2019 ◽  
Vol 2019 (9) ◽  
Author(s):  
Luke Lippstreu ◽  
Jorge Mago ◽  
Marcus Spradlin ◽  
Anastasia Volovich
Keyword(s):  
Weak Separation

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

scholarly journals The weak separation in higher dimensions

2021 ◽  
Vol 180 ◽  
pp. 105392
Author(s):  
Vladimir I. Danilov ◽  
Alexander V. Karzanov ◽  
Gleb A. Koshevoy
Keyword(s):  
Higher Dimensions ◽  
Weak Separation

scholarly journals Some New Separation Axioms Via β-I-Open Sets

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
N. Gowrisankar ◽  
A. Keskin ◽  
N. Rajesh
Keyword(s):  
Basic Properties ◽  
Separation Axioms ◽  
Weak Separation

Abstract In this paper, β-I-open sets are used to define some weak separation axioms and to study some of their basic properties. The implications of these axioms among themselves and with the known axioms are investigated

scholarly journals On generalized γµ-closed sets and related continuity

2021 ◽  
Vol 13 (2) ◽  
pp. 483-493
Author(s):  
Ritu Sen
Keyword(s):  
Topological Space ◽  
Main Interest ◽  
Closed Sets ◽  
Separation Axioms ◽  
Preservation Theorems ◽  
Generalized Topological Space ◽  
New Type ◽  
Weak Separation

Abstract In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

Weak Separation Problem for Tree Languages

2020 ◽  
Vol 31 (05) ◽  
pp. 583-593
Author(s):  
Saeid Alirezazadeh ◽  
Khadijeh Alibabaei
Keyword(s):  
Computer Science ◽  
Natural Extension ◽  
Classical Problem ◽  
Finite Alphabet ◽  
Direct Products ◽  
Separation Problem ◽  
Finite Algebras ◽  
Tree Languages ◽  
Weak Separation ◽  
Recognizable Language

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. A pseudovariety is a class of finite algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products. By looking at the syntactic congruence for monoids and as the natural extension in the case of forest algebras, we could define a version of syntactic congruence of a subset of the free forest algebra, not just a forest language. Let [Formula: see text] be a finite alphabet and [Formula: see text] be a pseudovariety of finite forest algebras. A language [Formula: see text] is [Formula: see text]-recognizable if its syntactic forest algebra belongs to [Formula: see text]. Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. Suppose that a forest language [Formula: see text] and a forest [Formula: see text] are given. We want to find if there exists any proof for that [Formula: see text] does not belong to [Formula: see text] just by using [Formula: see text]-recognizable languages, i.e. given such [Formula: see text] and [Formula: see text], if there exists a [Formula: see text]-recognizable language [Formula: see text] which contains [Formula: see text] and does not contain [Formula: see text]. In this paper, we present how one can use profinite forest algebra to separate a forest language and a forest term and also to separate two forest languages.

scholarly journals Does the genetic diversity among pubescent white oaks in southern Italy, Sicily and Sardinia islands support the current taxonomic classification?

2020 ◽  
Author(s):  
Romeo Di Pietro ◽  
Antonio Luca Conte ◽  
Piera Di Marzio ◽  
Paola Fortini ◽  
Emmanuele Farris ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Expressed Sequence Tag ◽  
Taxonomic Classification ◽  
Genetic Assignment ◽  
Molecular Analyses ◽  
Genetic Groups ◽  
Ecological Features ◽  
Weak Separation ◽  
Expressed Sequence ◽  
Simple Sequence

AbstractMolecular diversity analysis of deciduous pubescent oaks was conducted for populations from Calabria, Sicily and Sardinia. The aims of this study were twofold. First, to provide data on the genetic diversity of pubescent oaks from an understudied area which currently exhibits one of the highest concentrations of pubescent oak species in Europe. Second, to verify if these groups of oaks are genetically distinct and if their identification is in accordance with the current taxonomic classification. Molecular analyses of leaf material of 480 trees from seventeen populations belonging to putatively different pubescent oak species (Quercus amplifolia, Q. congesta, Q. dalechampii, Q. ichnusae, Q. leptobalanos, Q. virgiliana) were performed. Twelve gene-based Expressed Sequence Tag-Simple Sequence Repeat markers were selected, and genetic diversity and differentiation were calculated. The results showed relatively high values of allelic richness, heterozygosity and number of private alleles for the populations investigated. A weak but positive correlation between geographical and genetic distance was detected. Genetic assignment (STRUCTURE) and principle coordinate analyses exhibited a weak separation into two genetic groups which, however, did not correspond to the taxonomic, chorological and ecological features of the populations investigated. Sardinian populations formed one group which was separated from the Calabrian and Sicilian populations. In light of the results obtained, the taxonomic classification for the pubescent white oaks currently reported in the major Italian floras and checklists for the study area was not confirmed by molecular analyses.

Λsp-sets and some weak separation axioms

2004 ◽  
Vol 103 (3) ◽  
pp. 225-232 ◽  
Author(s):  
T. Noiri ◽  
E. Hatir
Keyword(s):  
Separation Axioms ◽  
Weak Separation
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