scholarly journals Quasi Semi-Border Singularities

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 495
Author(s):  
Fawaz Alharbi ◽  
Suliman Alsaeed
Keyword(s):  
Spectral Sequence ◽  
Equivalence Relation ◽  
Symplectic Geometry ◽  
Lagrangian Submanifolds ◽  
Natural Extension ◽  
Main Method ◽  
Equivalent Relation ◽  
Sequence Method ◽  
Artificial Nature

We obtain a list of simple classes of singularities of function germs with respect to the quasi m-boundary equivalence relation, with m ≥ 2 . The results obtained in this paper are a natural extension of Zakalyukin’s work on the new non-standard equivalent relation. In spite of the rather artificial nature of the definitions, the quasi relations have very natural applications in symplectic geometry. In particular, they are used to classify singularities of Lagrangian projections equipped with a submanifold. The main method that is used in the classification is the standard Moser’s homotopy technique. In addition, we adopt the version of Arnold’s spectral sequence method, which is described in Lemma 2. Our main results are Theorem 4 on the classification of simple quasi classes, and Theorem 5 on the classification of Lagrangian submanifolds with smooth varieties. The brief description of the main results is given in the next section.

A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq

1972 ◽  
Vol 24 (3) ◽  
pp. 426-431 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Equivalence Relation ◽  
Cohomology Ring

Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.

scholarly journals Quantum gravity, dynamical phase-space and string theory

2014 ◽  
Vol 23 (12) ◽  
pp. 1442006 ◽  
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
String Theory ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Symplectic Geometry ◽  
Complex Geometry ◽  
Hamiltonian Dynamics ◽  
Natural Extension ◽  
Dynamical Phase

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

scholarly journals Counting fuzzy subgroups of some finite groups by a new equivalence relation

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6151-6160
Author(s):  
Ardekani Kamali
Keyword(s):  
Group Theory ◽  
Finite Groups ◽  
Equivalence Relation ◽  
Theoretical Foundation ◽  
Dihedral Groups ◽  
Significant Aspect ◽  
Exact Number ◽  
Consistent Group ◽  
Fuzzy Subgroups

The study concerning the classification of the fuzzy subgroups of finite groups is a significant aspect of fuzzy group theory. In early papers, the number of distinct fuzzy subgroups of some nonabelian groups is calculated by the natural equivalence relation. In this paper, we treat to classifying fuzzy subgroups of some groups by a new equivalence relation which has a consistent group theoretical foundation. In fact, we determine exact number of fuzzy subgroups of finite non-abelian groups of order p3 and special classes of dihedral groups.

scholarly journals Quantitative spectral classification of late WC stars

1997 ◽  
Vol 180 ◽  
pp. 19-19
Author(s):  
Orsola de Marco ◽  
P. A. Crowther ◽  
M. J. Barlow
Keyword(s):  
Classification Scheme ◽  
Natural Extension ◽  
Optical Observations ◽  
Spectral Classification ◽  
High Quality ◽  
Definition Of

We present a revised classification scheme for late WC-type stars based on new high quality optical observations of seven stars. For consistency with the usual WC scheme (Smith, ApJ 358 229 1990), our principal diagnostic is Cvi λ5801/Ciii λ5696, while Ciii λ5696/Cii λ4267, and He II λ4686/He I λ5876 serve as secondary criteria. Our quantitative scheme forms an natural extension to the existing WC scheme and provides an unambiguous definition of subtypes, with natural breaks found between subclasses.

Ambitoric geometry I: Einstein metrics and extremal ambikähler structures

2016 ◽  
Vol 2016 (721) ◽  
Author(s):  
Vestislav Apostolov ◽  
David M. J. Calderbank ◽  
Paul Gauduchon
Keyword(s):  
Maxwell Equations ◽  
Einstein Metrics ◽  
Natural Extension ◽  
Torus Action ◽  
Local Geometry ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Bach Tensor ◽  
Extremal Kähler Metrics

AbstractWe present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kähler metrics which are toric with respect to a common 2-torus action. In the generic case, these “ambitoric” structures have an intriguing local geometry depending on a quadratic polynomialWe use this description to classify 4-dimensional Einstein metrics which are hermitian with respect to both orientations, as well as a class of solutions to the Einstein–Maxwell equations including riemannian analogues of the Plebański–Demiański metrics. Our classification can be viewed as a riemannian analogue of a result in relativity due to R. Debever, N. Kamran, and R. McLenaghan, and is a natural extension of the classification of selfdual Einstein hermitian 4-manifolds, obtained independently by R. Bryant and the first and third authors.These Einstein metrics are precisely the ambitoric structures with vanishing Bach tensor, and thus have the property that the associated toric Kähler metrics are extremal (in the sense of E. Calabi). Our main results also classify the latter, providing new examples of explicit extremal Kähler metrics. For both the Einstein–Maxwell and the extremal ambitoric structures,

scholarly journals GENETICALLY TURKISH OIKONYMS OF ODESSA REGION: MOTIVATED / UNMOTIVATED RENEWALS OF THE SOVIET PERIOD.

2021 ◽  
pp. 4-24
Author(s):  
Sviatoslav Verbych
Keyword(s):  
Semantic Analysis ◽  
Soviet Period ◽  
History Of ◽  
The Subject ◽  
Artificial Nature ◽  
Xix Century ◽  
Descriptive Method ◽  
Local Nature ◽  
Cultural Features

Introduction. The article analyzes the oikonyms of the modern Odessa region, which were formed during the Turkish-Tatar (Nogai) history of this region. The genetic Turkic names that the Bulgarian settlers moved to a new place of residence from their homeland (or from the territory of Turkey) during the end of the XVIII – first half of the XIX century are analyzed. These names were changed as a result of administrative intervention by the Soviet authorities, mainly during 1944–1945. Аim. The study aims to carry out etymological and structural-semantic analysis of genetically Turkic oikonyms of modern Odessa region. The object of the study is the genetically Turkic names of the settlements of Odesa region (local and transferred by Bulgarian settlers from across the Danube), which were changed administratively mainly after 1944; the subject of research is to find out the etymologies of the corresponding oikonyms and their structural and semantic characteristics. Research methods. For the analysis of oikonyms the descriptive method is applied by means of which the structure of both historical (genetically Turkic), and new (Soviet period) names is characterized, and also reception of the etymological analysis for establishment of etymons of genetically Turkic names of settlements. Research results. The article identifies word-forming models, presents the classification of genetically Turkic oikonyms of Odesa region, clarifies the dеonymic motivation of their creative bases; the structure of new (renamed) names is characterized. Conclusions. It is proved that most renamings do not take into account either the derivation model, which formed the original name of the settlement, or the appellate (onym) meaning of the creative bases, which convincingly testifies to their artificial nature, lack of connection with local nature, historical and cultural features of the region. It should be noted that it is necessary to change the names of the modern Odessa region, in particular the names with the Russian imperial connotation (Alexandrovka, Suvorov), as well as with the Russian-speaking structure (Udobne, Utkonosivka).  

scholarly journals Inversion as the Concept of Communicative Grammar

2019 ◽  
pp. 62-83
Author(s):  
Iryna Aribzhanova
Keyword(s):  
Basic Structure ◽  
Final Position ◽  
Sentence Structure ◽  
Main Method ◽  
Middle Position ◽  
Communicative Structure ◽  
Syntactic Status ◽  
Simple Sentences

The article considers the problem of the syntactic status of inversion. The material of the research is the simple sentences-utterances of the Ukrainian language. The concept of communicative inversion and the concept of formal inversion are defined. These concepts reflect different aspects of the division of a sentence – by communicative components (for example, rheme + theme) and by the members of a sentence (for example, predicate + subject). Two meanings of the concept of communicative inversion are defined: firstly, communicative inversion is the intonational-positional transfer of the most important semantic-informational part of a sentence (or the words of the syntactic group, or syntagma) from the final position to the initial or middle position (method of forming the utterance); secondly, communicative inversion is a sentence structure opposed to the basic structure as a derivative (expressive utterance). Communicative analysis shows that formal inversion is functionally subordinated to the communicative structure of the sentence-utterance. It serves as the main method of forming contextually dependent utter-ances (changes the actual division of a sentence). Formal inversion is optional in expressive utterances. The result of the study is the classification of the main types of basic sentences-utterances and the methods of forming communicative inversion (full and partial) in the Ukrainian language. The typology is implemented according to the following principles: communicative non-division / division, contextual independence / dependence of utterances, correlation of communicative components with the members of a sentence or connections of the members of a sentence. The first type combines basic sentences-utterances with an undivided predicative group. The second type includes basic sentences with a divided predicative group.

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