Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.4
2.2
Journals
Symmetry
Special Issues
Topological Structures and Analysis with Applications
share announcement

Topological Structures and Analysis with Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 12985

Special Issue Editors

Dr. Susmit Bagchi

E-Mail Website
Guest Editor
Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju 660701, Republic of Korea
Interests: topology; topological algebra; topological analysis and measure; discrete mathematics
Special Issues, Collections and Topics in MDPI journals
Dr. Anthony To-Ming Lau

E-Mail Website
Guest Editor
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
Interests: geometric; algebraic and topological properties

Special Issue Information

Dear Colleagues,

The applications of topology, topological groups, and analysis are in a wide array of domains ranging from the physical sciences (such as physics, chemistry, and biology) to the mathematical sciences. The presence of the concept of symmetry/asymmetry can be found in various natural observations. Algebraic as well as geometric topology includes various forms and aspects of symmetries/asymmetries within the space with computational applications. There can be two broad approaches to topology and topological group structures: (1) the presence of symmetry/asymmetry within a topological space itself and (2) the presence of symmetry/asymmetry of different algebraic structures contained within a topological space. This Special Issue on “Topological Structures and Analysis with Applications” invites original research papers and extended as well as analytical survey papers in this area. Authors are invited to submit papers on pure and applied topology, topological groups with applications, and topological analysis. Authors are invited to submit full-length manuscripts for publication in the Symmetry journal of MDPI.  All submitted manuscripts will go through the standard peer-review process by experts in the field.

Dr. Susmit Bagchi
Dr. Anthony To-Ming Lau
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topological spaces with symmetry/asymmetry
  • topological algebraic structures with applications
  • applied topology and topological groups
  • topological vector spaces with applications
  • homotopy and symmetry/asymmetry with applications
  • topological manifolds with applications
  • symmetry/asymmetry in geometric topology with applications

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

14 pages, 800 KiB  
Article
Between Soft Complete Continuity and Soft Somewhat-Continuity
by Samer Al Ghour and Jawaher Al-Mufarrij
Symmetry 2023, 15(11), 2056; https://doi.org/10.3390/sym15112056 - 13 Nov 2023
Cited by 5 | Viewed by 861
Abstract
This paper introduces two novel concepts of mappings over soft topological spaces: “soft somewhat-r-continuity” and “soft somewhat-r-openness”. We provide characterizations and discuss soft composition and soft subspaces. With the use of examples, we offer numerous connections between these two [...] Read more.
This paper introduces two novel concepts of mappings over soft topological spaces: “soft somewhat-r-continuity” and “soft somewhat-r-openness”. We provide characterizations and discuss soft composition and soft subspaces. With the use of examples, we offer numerous connections between these two notions and their accompanying concepts. We also offer extension theorems for them. Finally, we investigated a symmetry between our new concepts with their topological analogs. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
10 pages, 300 KiB  
Article
Generalizations of Topological Decomposition and Zeno Sequence in Fibered n-Spaces
by Susmit Bagchi
Symmetry 2022, 14(10), 2222; https://doi.org/10.3390/sym14102222 - 21 Oct 2022
Viewed by 1358
Abstract
The space-time geometry is rooted in the Minkowski 4-manifold. Minkowski and Euclidean topological 4-manifolds behave differently in view of compactness and local homogeneity. As a result, Zeno sequences are selectively admitted in such topological spaces. In this paper, the generalizations of topologically fibered [...] Read more.
The space-time geometry is rooted in the Minkowski 4-manifold. Minkowski and Euclidean topological 4-manifolds behave differently in view of compactness and local homogeneity. As a result, Zeno sequences are selectively admitted in such topological spaces. In this paper, the generalizations of topologically fibered n-spaces are proposed to formulate topological decomposition and the formation of projective fibered n-subspaces. The concept of quasi-compact fibering is introduced to analyze the formation of Zeno sequences in topological n-spaces (i.e., n-manifolds), where a quasi-compact fiber relaxes the Minkowski-type (algebraically) strict ordering relation under topological projections. The topological analyses of fibered Minkowski as well as Euclidean 4-spaces are presented under quasi-compact fibering and topological projections. The topological n-spaces endowed with quasi-compact fibers facilitated the detection of local as well as global compactness and the non-analytic behavior of a continuous function. It is illustrated that the 5-manifold with boundary embedding Minkowski 4-space transformed a quasi-compact fiber into a compact fiber maintaining generality. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
25 pages, 387 KiB  
Article
Geometry and Spectral Theory Applied to Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit Risk
by Simone Farinelli and Hideyuki Takada
Symmetry 2022, 14(7), 1330; https://doi.org/10.3390/sym14071330 - 27 Jun 2022
Cited by 2 | Viewed by 1580
Abstract
We apply Geometric Arbitrage Theory (GAT) to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. The remarkable aspect of the GAT is the gauge symmetry, which can be translated to the financial context, [...] Read more.
We apply Geometric Arbitrage Theory (GAT) to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. The remarkable aspect of the GAT is the gauge symmetry, which can be translated to the financial context, by packaging all of the asset model information into a (stochastic) principal fiber bundle. We obtain closed-form equations involving default intensities and loss-given defaults characterizing the no-free-lunch-with-vanishing-risk condition for government and corporate bond markets while relying on the spread-term structure with default intensity and loss-given default. Moreover, we provide a sufficient condition equivalent to the Novikov condition implying the absence of arbitrage. Furthermore, the generic dynamics for an isolated credit market allowing for arbitrage possibilities (and minimizing the total quantity of potential arbitrage) are derived, and arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed. The existence of an approximated risk-neutral measure allowing the definition of fundamental values for the assets is inferred through spectral theory. We show that instantaneous bond returns are serially uncorrelated and centered, that the expected value of credit bubbles remains constant for future times where no coupons are paid, and that the variance of the market portfolio nominals is concurrent with that of the corresponding bond deflators. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
14 pages, 866 KiB  
Article
A Novel 2D Clustering Algorithm Based on Recursive Topological Data Structure
by Ismael Osuna-Galán, Yolanda Pérez-Pimentel and Carlos Aviles-Cruz
Symmetry 2022, 14(4), 781; https://doi.org/10.3390/sym14040781 - 9 Apr 2022
Cited by 2 | Viewed by 2717
Abstract
In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric [...] Read more.
In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric space and takes into account the local and global topological properties of the data to be clustered. Taking into account cluster symmetry property, from a metric and mathematical-topological point of view, the analysis was carried out only in the positive region, reducing the number of calculations in the clustering process. The new clustering theory is inspired by the thermodynamics principle of energy. Thus, both topologies are recursively taken into account. The proposed model is based on the interaction of particles defined through measuring homogeneous-energy criterion. Based on the energy concept, both general and local topologies are taken into account for clustering. The effect of the integration of a new element into the cluster on homogeneous-energy criterion is analyzed. If the new element does not alter the homogeneous-energy of a group, then it is added; otherwise, a new cluster is created. The mathematical-topological theory and the results of its application on public benchmark datasets are presented. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
►▼ Show Figures

Figure 1

10 pages, 271 KiB  
Article
Topological Sigma-Semiring Separation and Ordered Measures in Noetherian Hyperconvexes
by Susmit Bagchi
Symmetry 2022, 14(2), 422; https://doi.org/10.3390/sym14020422 - 20 Feb 2022
Cited by 1 | Viewed by 2022
Abstract
The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed [...] Read more.
The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed in a sigma-semiring in a NHC under a topological ordering of NHCs. The topological ordering relation maintains the irreflexive and anti-symmetric algebraic properties while retaining the homeomorphism of NHCs. The monotonic measure sequence in a NHC determines the convexity and compactness of topological subspaces. Interestingly, the topological ordering in NHCs in two isomorphic topological spaces induces the corresponding ordering of measures in sigma-semirings. Moreover, the uniform topological measure spaces of NHCs need not always preserve the pushforward measures, and a NHC semiring is functionally separable by a set of inner-measurable functions. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
12 pages, 272 KiB  
Article
Topological Properties of Braid-Paths Connected 2-Simplices in Covering Spaces under Cyclic Orientations
by Susmit Bagchi
Symmetry 2021, 13(12), 2382; https://doi.org/10.3390/sym13122382 - 10 Dec 2021
Cited by 1 | Viewed by 2233
Abstract
In general, the braid structures in a topological space can be classified into algebraic forms and geometric forms. This paper investigates the properties of a braid structure involving 2-simplices and a set of directed braid-paths in view of algebraic as well as geometric [...] Read more.
In general, the braid structures in a topological space can be classified into algebraic forms and geometric forms. This paper investigates the properties of a braid structure involving 2-simplices and a set of directed braid-paths in view of algebraic as well as geometric topology. The 2-simplices are of the cyclically oriented variety embedded within the disjoint topological covering subspaces where the finite braid-paths are twisted as well as directed. It is shown that the generated homotopic simplicial braids form Abelian groups and the twisted braid-paths successfully admit several varieties of twisted discrete path-homotopy equivalence classes, establishing a set of simplicial fibers. Furthermore, a set of discrete-loop fundamental groups are generated in the covering spaces where the appropriate weight assignments generate multiplicative group structures under a variety of homological formal sums. Interestingly, the resulting smallest non-trivial group is not necessarily unique. The proposed variety of homological formal sum exhibits a loop absorption property if the homotopy path-products are non-commutative. It is considered that the topological covering subspaces are simply connected under embeddings with local homeomorphism maintaining generality. Full article
(This article belongs to the Special Issue Topological Structures and Analysis with Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop