Special Issue "Symmetry in Applied Mathematics"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 15 November 2019.

Special Issue Editors

Prof. Lorentz Jäntschi
E-Mail Website
Guest Editor
Department of Physics and Chemistry, Technical University of Cluj-Napoca, Romania
Interests: Applied mathematics; Applied informatics
Special Issues and Collections in MDPI journals
Prof. Dr. Sorana D. Bolboacă
E-Mail Website
Guest Editor
Department of Medical Informatics and Biostatistics, Iuliu Haţieganu University of Medicine and Pharmacy, Louis Pasteur Str., No. 6, 400349 Cluj-Napoca, Cluj, Romania
Interests: Applied & Computational Statistics; Molecular Modeling; Genetic Analysis; Statistical Modeling in Medicine; Integrated Health Informatics System; Medical Diagnostic Research; Statistical Inference; Medical Imaging Analysis; Assisted Decision Systems; Research Ethics; Social Media and Health Information; Evidence-Based Medicine
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, "Symmetry in Applied Mathematics" is open for submissions and welcomes papers from a broad interdisciplinary area, since 'applied mathematics' is a specific form of mathematics that involves creating and use of mathematical models in order to map out the mathematical core of a practical problem. There is probably no scientific field in which applied mathematics has not made its necessary presence. On the other hand, symmetry is about identification and use invariants to any of various transformations for any paired dataset and characterizations associated with. Inside applied mathematics, symmetry may work as a powerful tool for problems reduction and solving. Applications include probability theory (all probabilistic reasoning is ultimately based on judgments of symmetry), fractals (geometry), supersymmetry (physics), nanostructures (chemistry), taxonomy (biology), bilateral symmetry (medicine), and the list can go on.

Prof. Lorentz Jäntschi
Prof. Sorana D. BOLBOACĂ
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 papers will be 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 1400 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

  • Bayesian probability
  • Mathematical modeling
  • Topology (2D)
  • Geometry (2D and 3D)
  • Invariants
  • Symmetry groups

Published Papers (9 papers)

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Research

Open AccessArticle
One-Dimensional Optimal System for 2D Rotating Ideal Gas
Symmetry 2019, 11(9), 1115; https://doi.org/10.3390/sym11091115 - 03 Sep 2019
Abstract
We derive the one-dimensional optimal system for a system of three partial differential equations, which describe the two-dimensional rotating ideal gas with polytropic parameter γ > 2 . The Lie symmetries and the one-dimensional optimal system are determined for the nonrotating and rotating [...] Read more.
We derive the one-dimensional optimal system for a system of three partial differential equations, which describe the two-dimensional rotating ideal gas with polytropic parameter γ > 2 . The Lie symmetries and the one-dimensional optimal system are determined for the nonrotating and rotating systems. We compare the results, and we find that when there is no Coriolis force, the system admits eight Lie point symmetries, while the rotating system admits seven Lie point symmetries. Consequently, the two systems are not algebraic equivalent as in the case of γ = 2 , which was found by previous studies. For the one-dimensional optimal system, we determine all the Lie invariants, while we demonstrate our results by reducing the system of partial differential equations into a system of first-order ordinary differential equations, which can be solved by quadratures. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
Open AccessArticle
Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory
Symmetry 2019, 11(9), 1085; https://doi.org/10.3390/sym11091085 - 29 Aug 2019
Abstract
To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the [...] Read more.
To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems
Symmetry 2019, 11(7), 891; https://doi.org/10.3390/sym11070891 - 08 Jul 2019
Abstract
We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification [...] Read more.
We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested
Symmetry 2019, 11(6), 835; https://doi.org/10.3390/sym11060835 - 25 Jun 2019
Cited by 1
Abstract
One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling [...] Read more.
One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
A Continuous Coordinate System for the Plane by Triangular Symmetry
Symmetry 2019, 11(2), 191; https://doi.org/10.3390/sym11020191 - 09 Feb 2019
Abstract
The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only [...] Read more.
The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only discrete coordinate systems have been investigated. These have limited capabilities for some image-processing applications, including transformations like rotations or interpolation. In this paper, we introduce the continuous triangular coordinate system as an extension of the discrete triangular and hexagonal coordinate systems. The new system addresses each point of the plane with a coordinate triplet. Conversion between the Cartesian coordinate system and the new system is described. The sum of three coordinate values lies in the closed interval [−1, 1], which gives many other vital properties of this coordinate system. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations
Symmetry 2019, 11(2), 162; https://doi.org/10.3390/sym11020162 - 01 Feb 2019
Abstract
Coupled systems of Lane–Emden equations are of considerable interest as they model several physical phenomena, for instance population evolution, pattern formation, and chemical reactions. Assuming a complex variational structure, we classify the generalized system of Lane–Emden type equations in relation to Noether-like operators [...] Read more.
Coupled systems of Lane–Emden equations are of considerable interest as they model several physical phenomena, for instance population evolution, pattern formation, and chemical reactions. Assuming a complex variational structure, we classify the generalized system of Lane–Emden type equations in relation to Noether-like operators and associated first integrals. Various forms of functions appearing in the considered system are taken, and it is observed that the Noether-like operators form an Abelian algebra for the corresponding Euler–Lagrange-type systems. Interestingly, we find that in many cases, the Noether-like operators satisfy the classical Noether symmetry condition and become the Noether symmetries. Moreover, we observe that the classical Noetherian integrals and the first integrals we determine using the complex Lagrangian approach turn out to be the same for the underlying system of Lane–Emden equations. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
Open AccessArticle
Minimal Energy Configurations of Finite Molecular Arrays
Symmetry 2019, 11(2), 158; https://doi.org/10.3390/sym11020158 - 31 Jan 2019
Abstract
In this paper, we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attractive or repulsive forces given by a certain intermolecular potential. We limit ourselves to the cases of three particles [...] Read more.
In this paper, we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attractive or repulsive forces given by a certain intermolecular potential. We limit ourselves to the cases of three particles arranged in a triangular array and that of four particles in a tetrahedral array. The minimization is constrained to a fixed area in the case of the triangular array, and to a fixed volume in the tetrahedral case. For a general class of intermolecular potentials we give conditions for the homogeneous configuration (either an equilateral triangle or a regular tetrahedron) of the array to be stable that is, a minimizer of the potential energy of the system. To determine whether or not there exist other stable states, the system of first-order necessary conditions for a minimum is treated as a bifurcation problem with the area or volume variable as the bifurcation parameter. Because of the symmetries present in our problem, we can apply the techniques of equivariant bifurcation theory to show that there exist branches of non-homogeneous solutions bifurcating from the trivial branch of homogeneous solutions at precisely the values of the parameter of area or volume for which the homogeneous configuration changes stability. For the triangular array, we construct numerically the bifurcation diagrams for both a Lennard–Jones and Buckingham potentials. The numerics show that there exist non-homogeneous stable states, multiple stable states for intervals of values of the area parameter, and secondary bifurcations as well. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
Facility Location Problem Approach for Distributed Drones
Symmetry 2019, 11(1), 118; https://doi.org/10.3390/sym11010118 - 20 Jan 2019
Abstract
Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left [...] Read more.
Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Open AccessArticle
Khovanov Homology of Three-Strand Braid Links
Symmetry 2018, 10(12), 720; https://doi.org/10.3390/sym10120720 - 05 Dec 2018
Abstract
Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some [...] Read more.
Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some Khovanov homology groups of 3-strand braid links Δ 2 k + 1 = x 1 2 k + 2 x 2 x 1 2 x 2 2 x 1 2 x 2 2 x 1 2 x 1 2 , Δ 2 k + 1 x 2 , and Δ 2 k + 1 x 1 , where Δ is the Garside element x 1 x 2 x 1 , and which are three out of all six classes of the general braid x 1 x 2 x 1 x 2 with n factors. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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