Advances in Mathematics and Its Applications II

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (1 January 2024) | Viewed by 1780

Special Issue Editors


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Guest Editor

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Guest Editor
Department of Mathematics, Ankara Hacı Bayram Veli University, 06900 Ankara, Turkey
Interests: applications of matrix theory; graph theory; number theory and mathematical education based on projects and competencies
Special Issues, Collections and Topics in MDPI journals

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Guest Editor

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Department of Mathematics, Istanbul Beykent University, 34528 Istanbul, Turkey
Interests: differential geometry; kinematics; topology

Special Issue Information

Dear Colleagues,

Mathematical modeling is an active area of applied mathematics. At its beginning, engineers were the main practitioners of this area of mathematics, developing mathematical models for solving engineering problems in natural sciences.

However, analysis methods and models in social sciences are similar to those of nature sciences, including engineering, with the only difference that instead of using principles of nature, one uses principles or theories from experts in social sciences.

Models based on ordinary or partial differential equations describe a wide variety of phenomena, such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. Additionally, stochastic models have recently attracted increased attention. Indeed, some of these types of complex problems also require deep analysis of the tools utilized to solve these situations.

In this Special Issue, we try to integrate models, methods, and also applications, not only in the scope of traditional natural sciences, but also opening the scope to education and other social sciences. Theory- and data-driven models, even in a synergy that gives rise to producing fertile, multidisciplinary, and hybrid models, can be considered. Potential topics include, but are not limited to, the follo9wing:

  • Numerical and modelling analysis;
  • Optimization and evolutionary algorithms models and methods;
  • Deterministic differential equations: methods and models;
  • Random differential equations: methods and models;
  • Numerical solution of large systems of linear and non-linear equations;
  • Educational models and methods;
  • Social networks models and methods;
  • Engineering models and simulation;
  • Analysis modelling in economics and finance;
  • Algebraic models and methods with various applications;
  • Intelligent data analysis models and methods.

Before submission, authors should carefully read over the journal’s Author Guidelines, which can be found at the following link: https://www.mdpi.com/journal/axioms/instructions.

Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at the following link: https://susy.mdpi.com/.

Dr. Víctor Gayoso Martínez
Dr. Fatih Yilmaz
Prof. Dr. Araceli Queiruga-Dios
Prof. Dr. Jesús Martín Vaquero
Prof. Dr. Deolinda M. L. Dias Rasteiro
Dr. Mücahit Akbıyık
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. Axioms 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.

Published Papers (1 paper)

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Research

15 pages, 760 KiB  
Article
Geometric Properties of Planar and Spherical Interception Curves
by Yagub N. Aliyev
Axioms 2023, 12(7), 704; https://doi.org/10.3390/axioms12070704 - 20 Jul 2023
Viewed by 1255
Abstract
In this paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with the curve. These limits have some connections with [...] Read more.
In this paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with the curve. These limits have some connections with the lemniscate constants A,B and Gauss’s constant G, which are used to compare with the classical pursuit curve. The analogous spherical geometry problem is solved using a spherical curve defined by the Gudermannian function. It is shown that the results agree with the angle-preserving property of Mercator and Stereographic projections. The Mercator and Stereographic projections also reveal the symmetry of this curve with respect to Spherical and Logarithmic Spirals. The geometric properties of the spherical curve are proved in two ways, analytically and using a lemma about spherical angles. A similar lemma for the planar case is also mentioned. The paper shows symmetry/asymmetry between the spherical and planar cases and the derivation of properties of these curves as limiting cases of some plane and spherical geometry results. Full article
(This article belongs to the Special Issue Advances in Mathematics and Its Applications II)
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