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Symmetry
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Symmetry in Mathematical Analysis and Applications
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Symmetry in Mathematical Analysis and Applications

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

Deadline for manuscript submissions: closed (15 October 2019) | Viewed by 17762

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Luigi Rodino

E-Mail Website
Guest Editor
Department of Mathematics, University of Torino, 10124 Torino, TO, Italy
Interests: partial differential equations; Fourier analysis; operator theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics servant of Sciences, Mathematics queen of Sciences. This is the rough translation of a statement in Latin describing the role of mathematics in the scientific community. At the core of mathematics, mathematical analysis in the past centuries has provided applications in different disciplines, essential to reach modern knowledge, in both practical and theoretical aspects. In addition to applications, mathematics possesses a wonderful beauty: Fundamental formulas present deep links in symmetry, going beyond technical expressions.

The Special Issue of Symmetry will feature articles on mathematical analysis, its applications, and related computations. These include differential equations, integral equations, functional, Harmonic, Fourier and spectral analysis, function theory, stochastic analysis, and other subjects. Applications are not limited to physics, but may concern all the sciences. Preference will be given to results emphasizing deep relations and symmetries, in theoretical and applicative settings.

Prof. Luigi Rodino
Guest Editor

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

  • Differential equations
  • Functional analysis
  • Mathematical models
  • Computational analysis
  • Applications of Mathematical Analysis

Published Papers (6 papers)

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Research

12 pages, 268 KiB  
Article
Integral Inequalities of Chebyshev Type for Continuous Fields of Hermitian Operators Involving Tracy–Singh Products and Weighted Pythagorean Means
by Arnon Ploymukda and Pattrawut Chansangiam
Symmetry 2019, 11(10), 1256; https://doi.org/10.3390/sym11101256 - 09 Oct 2019
Viewed by 1350
Abstract
In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric [...] Read more.
In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric mean, and the harmonic mean. Every continuous field considered here is parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. Tracy-Singh product versions of the Chebyshev-Grüss inequality via oscillations are also obtained. Such integral inequalities reduce to discrete inequalities when the space is a finite space equipped with the counting measure. Moreover, our results include Chebyshev-type inequalities for tensor product of operators and Tracy-Singh/Kronecker products of matrices. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
13 pages, 1568 KiB  
Article
Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept
by Paweł Więcek, Daniel Kubek, Jan Hipolit Aleksandrowicz and Aleksandra Stróżek
Symmetry 2019, 11(6), 755; https://doi.org/10.3390/sym11060755 - 04 Jun 2019
Cited by 12 | Viewed by 3540
Abstract
Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, [...] Read more.
Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, in addition to criteria such as punctuality, the frequency of departures, and the number of transfers, a travelling comfort level is an important element for passengers. An overcrowded bus may discourage travelers from choosing this mode of transport and induce them to use a private car despite the existence of many other facilities offered by a given public transport system. Therefore, the forecasting of bus passenger demand, as well as bus occupancy at individual bus stops, is currently an important research direction. The main goal of the article is to present the conceptual framework for the Advanced Travel Information System with the prediction module. The proposed approach assumes that the prediction module is based on the use of the Markov Chain concept. The efficiency and accuracy of the obtained prediction were presented based on a real-life example, where the measurements of passengers boarding and alighting at bus stops were made in a selected Cracow bus line. The methodology presented in the paper and the obtained results can significantly contribute to the development of solutions and systems for a better management as well as a cost and energy consumption optimisation in the public transport system. Current and forecasted information related to bus occupancy, when properly used in the travel information system, may have a positive impact on the development of urban mobility patterns by encouraging the use of public transport. This article addresses the current and practical research problem using an adequate theoretical mathematical tool to describe it, reflecting the characteristics and nature of the phenomenon being studied. To the best of the authors’ knowledge, the article deals for the first time with the problem of prediction of onboard bus comfort levels based on in-vehicle occupancy. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
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22 pages, 341 KiB  
Article
On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls
by Manuel De la Sen
Symmetry 2019, 11(5), 712; https://doi.org/10.3390/sym11050712 - 24 May 2019
Cited by 2 | Viewed by 2358
Abstract
This paper links the celebrated Cauchy’s interlacing theorem of eigenvalues for partitioned updated sequences of Hermitian matrices with stability and convergence problems and results of related sequences of matrices. The results are also applied to sequences of factorizations of semidefinite matrices with their [...] Read more.
This paper links the celebrated Cauchy’s interlacing theorem of eigenvalues for partitioned updated sequences of Hermitian matrices with stability and convergence problems and results of related sequences of matrices. The results are also applied to sequences of factorizations of semidefinite matrices with their complex conjugates ones to obtain sufficiency-type stability results for the factors in those factorizations. Some extensions are given for parallel characterizations of convergent sequences of matrices. In both cases, the updated information has a Hermitian structure, in particular, a symmetric structure occurs if the involved vector and matrices are complex. These results rely on the relation of stable matrices and convergent matrices (those ones being intuitively stable in a discrete context). An epidemic model involving a clustering structure is discussed in light of the given results. Finally, an application is given for a discrete-time aggregation dynamic system where an aggregated subsystem is incorporated into the whole system at each iteration step. The whole aggregation system and the sequence of aggregated subsystems are assumed to be controlled via linear-output feedback. The characterization of the aggregation dynamic system linked to the updating dynamics through the iteration procedure implies that such a system is, generally, time-varying. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
14 pages, 1577 KiB  
Article
A Dynamic Simulation of the Immune System Response to Inhibit and Eliminate Abnormal Cells
by S. A. Alharbi and A. S. Rambely
Symmetry 2019, 11(4), 572; https://doi.org/10.3390/sym11040572 - 19 Apr 2019
Cited by 13 | Viewed by 3591
Abstract
Diet has long been considered a risk factor related to an increased risk of cancer. This challenges us to understand the relationship between the immune system and diet when abnormal cells appear in a tissue. In this paper, we propose and analyze a [...] Read more.
Diet has long been considered a risk factor related to an increased risk of cancer. This challenges us to understand the relationship between the immune system and diet when abnormal cells appear in a tissue. In this paper, we propose and analyze a model from the point of view of a person who follows a healthy diet, i.e., one correlated to the food pyramid, and a person who follows an unhealthy diet. Normal cells and immune cells are used in the design of the model, which aims to describe how the immune system functions when abnormal cells appear in a tissue. The results show that the immune system is able to inhibit and eliminate abnormal cells through the three following stages: the response stage, the interaction stage, and the recovery stage. Specifically, the failure of the immune system to accomplish the interaction stage occurs when a person follows an unhealthy diet. According to the analysis and simulation of our model, we can deduce that dietary pattern has a significant impact on the functioning of the immune system. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
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13 pages, 873 KiB  
Article
Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics
by Astha Chauhan, Rajan Arora and Mohd Junaid Siddiqui
Symmetry 2019, 11(4), 458; https://doi.org/10.3390/sym11040458 - 01 Apr 2019
Cited by 10 | Viewed by 2557
Abstract
Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, [...] Read more.
Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai’s technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai’s approach, we have constructed the solution in a power series of ( C / U ) 2 , where C is the velocity of sound in an ideal gas and U is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
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18 pages, 3817 KiB  
Article
Relationship between the Paradox of Enrichment and the Dynamics of Persistence and Extinction in Prey-Predator Systems
by Jawdat Alebraheem
Symmetry 2018, 10(10), 532; https://doi.org/10.3390/sym10100532 - 22 Oct 2018
Cited by 7 | Viewed by 3709
Abstract
The paradox of the enrichment phenomenon, considered one of the main counterintuitive observations in ecology, likely destabilizes predator–prey dynamics by increasing the nutrition of the prey. We use two systems to study the occurrence of the paradox of enrichment: The prey–predator system and [...] Read more.
The paradox of the enrichment phenomenon, considered one of the main counterintuitive observations in ecology, likely destabilizes predator–prey dynamics by increasing the nutrition of the prey. We use two systems to study the occurrence of the paradox of enrichment: The prey–predator system and the one prey, two predators system, with Holling type I and type II functional and numerical responses. We introduce a new approach that involves the connection between the occurrence of the enrichment paradox and persistence and extinction dynamics. We apply two main analytical techniques to study the persistence and extinction dynamics of two and three trophics, respectively. The linearity and nonlinearity of functional and numerical responses plays important roles in the occurrence of the paradox of enrichment. We derive the persistence and extinction conditions through the carrying capacity parameter, and perform some numerical simulations to demonstrate the effects of the paradox of enrichment when increasing carrying capacity. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
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