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State-of-the-Art Mathematical Applications in Europe
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State-of-the-Art Mathematical Applications in Europe

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 18385

Special Issue Editors

Dr. Irina Cristea

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Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
Interests: theory of algebraic hypercompositional structures
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yuriy Rogovchenko

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Department of Mathematical Sciences, University of Agder, P.O. Box 422, N-4604 Kristiansand, Norway
Interests: qualitative theory of ordinary, functional, and impulsive differential equations; mathematical modelling in medicine, biology and life sciences; undergraduate mathematics education
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gintautas Dzemyda

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Vilnius University Institute of Data Science and Digital Technologies, Akademijos St. 4, LT-08412 Vilnius, Lithuania
Interests: optimization; data analysis; multiple criteria decision analysis; data dimensionality reduction; visualization of multidimensional data; data mining; neural networks; image analysis
Prof. Dr. Patrick Siarry

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Guest Editor
University Paris-Est Creteil Images, Signals and Intelligent Systems Laboratory 61 avenue du Général de Gaulle, 94010 Creteil, France
Interests: artificial intelligence; soft grid; Internet of Things

Special Issue Information

Dear Colleague,

For this Special Issue, we invite original research articles and far-reaching survey papers that consolidate our understanding of the state of the art of mathematical applications in Europe. Acknowledging the importance of the rapid publication both for authors and editors, we will promptly process the manuscripts submitted to this Special Issue; all accepted papers will be published online upon their acceptance regardless of the Special Issue deadline.

The Special Issue will publish original research contributions and review papers. Potential topics include but are not limited to the following:

  • The use of mathematical and computational methods in natural and social sciences, technology, and engineering, including aerospace, atmospheric, automotive, chemical, computer, control, electrical, geophysical, industrial, informatics, manufacturing, mechanical, ocean, production, transportation, and other branches.
  • Stochastic and deterministic optimization.
  • Mathematical models and computational approaches in biology, ecology and life sciences.
  • Mathematics for finance, business, logistics and economics.
  • Fuzzy logic, fuzzy sets, and fuzzy systems.
  • Algorithms, data analysis, and computational methods in computer science.
  • Mathematical problems in physics and mechanics.
  • Continuous, discrete, and other types of dynamical systems and their applications.
  • Probability in the modeling of random phenomena in natural sciences, social sciences, and technology.
  • Stochastic models and statistical methods in medicine, epidemiology, telecommunications, inventories, reliability, queueing theory, statistical physics, optimization, operations research, and other areas.
  • Applications of algebra, geometry, and related fields such as differential geometry, global analysis, complex geometry, computational aspects, arithmetic, cryptography, topology, etc.

Dr. Irina Cristea
Prof. Dr. Yuriy Rogovchenko
Prof. Dr. Gintautas Dzemyda
Prof. Dr. Patrick Siarry
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 (13 papers)

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Research

Jump to: Review

22 pages, 443 KiB  
Article
On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems
by Luís P. Castro and Anabela S. Silva
Mathematics 2023, 11(2), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020297 - 06 Jan 2023
Cited by 2 | Viewed by 1008
Abstract
This article deals with a class of nonlinear fractional differential equations, with initial conditions, involving the Riemann–Liouville fractional derivative of order α∈(1,2). The main objectives are to obtain conditions for the existence and uniqueness of solutions [...] Read more.
This article deals with a class of nonlinear fractional differential equations, with initial conditions, involving the Riemann–Liouville fractional derivative of order α∈(1,2). The main objectives are to obtain conditions for the existence and uniqueness of solutions (within appropriate spaces), and to analyze the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias types. In fact, different conditions for the existence and uniqueness of solutions are obtained based on the analysis of an associated class of fractional integral equations and distinct fixed-point arguments. Additionally, using a Bielecki-type metric and some additional contractive arguments, conditions are also obtained to guarantee Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the problems under analysis. Examples are also included to illustrate the theory. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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22 pages, 463 KiB  
Article
Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution
by Srdjan Kadić, Božidar V. Popović and Ali İ. Genç
Mathematics 2023, 11(2), 290; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020290 - 05 Jan 2023
Cited by 2 | Viewed by 924
Abstract
In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some baseline distributions, such as exponential, Pareto [...] Read more.
In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some baseline distributions, such as exponential, Pareto and standard logistic distributions. We study in detail the properties of the two models resulting from the exponential baseline, among others. These two models have different shape characteristics. The model parameters are estimated by maximum likelihood, and related algorithms are proposed for the computation of the estimates. The existence of the maximum-likelihood estimators is discussed. Two applications prove its usefulness in real data fitting. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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15 pages, 327 KiB  
Article
Some Examples of BL-Algebras Using Commutative Rings
by Cristina Flaut and Dana Piciu
Mathematics 2022, 10(24), 4739; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244739 - 13 Dec 2022
Cited by 1 | Viewed by 749
Abstract
BL-algebras are algebraic structures corresponding to Hajek’s basic fuzzy logic. The aim of this paper is to analyze the structure of BL-algebras using commutative rings. Due to computational considerations, we are interested in the finite case. We present new ways to generate finite [...] Read more.
BL-algebras are algebraic structures corresponding to Hajek’s basic fuzzy logic. The aim of this paper is to analyze the structure of BL-algebras using commutative rings. Due to computational considerations, we are interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and provide summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equipped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings is established. Furthermore, we give examples of finite BL-rings for which the lattice of ideals is not an MV-algebra and, using these rings, we construct BL-algebras with 2r+1 elements, r≥2, and BL-chains with k elements, k≥4. In addition, we provide an explicit construction of isomorphism classes of BL-algebras of small n size (2≤n≤5). Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
16 pages, 3345 KiB  
Article
Quantification of Aversion to Uncertainty in Intertemporal Choice through Subjective Perception of Time
by Viviana Ventre and Roberta Martino
Mathematics 2022, 10(22), 4315; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224315 - 17 Nov 2022
Cited by 5 | Viewed by 1243
Abstract
Intertemporal choices are those decisions structured over several periods in which the effects only manifest themselves with the passage of time. The main mathematical reference for studying the behavior of individuals with respect to this type of decision is the Discounted Utility Model [...] Read more.
Intertemporal choices are those decisions structured over several periods in which the effects only manifest themselves with the passage of time. The main mathematical reference for studying the behavior of individuals with respect to this type of decision is the Discounted Utility Model which hypothesizes completely rational individuals. The empirical evidence that deviates from normative expectations has motivated the formulation of alternative models with the aim of better describing the behavior of individuals. The present paper investigates the characteristics behind hyperbolic discounting starting from the phenomenon of decision inconsistency, i.e., when individuals’ preferences vary over time. The mechanisms of inconsistency will be explored through the physical concept of relative time, proving the importance of uncertainty aversion in the hyperbolic trend of the discount function. The analysis of the mathematical characteristics of hyperbolic discounting and the relationship between decision inconsistency and subjective perception of time defines the maximum distance between rational and non-rational preferences. An experimental part empirically proves the relationship between uncertainty aversion and time inconsistency. The present paper contributes to the literature by defining a new characteristic of hyperbolic discounting and quantifying the impact of the subjective perception of time in the decision-making process. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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34 pages, 6480 KiB  
Article
Applications of a Group Theoretical Method on Biomagnetic Fluid Flow and Heat Transfer for Different Shapes of Fe3O4 Magnetic Particles under the Influence of Thermal Radiation and a Magnetic Dipole over a Cylinder
by Jahangir Alam, Ghulam Murtaza, Eugenia N. Petropoulou, Efstratios Em. Tzirtzilakis and Mohammad Ferdows
Mathematics 2022, 10(19), 3520; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193520 - 27 Sep 2022
Cited by 1 | Viewed by 1028
Abstract
The flow and heat characteristics of an unsteady, laminar biomagnetic fluid, namely blood containing Fe3O4 magnetic particles, under the influence of thermal radiation and a magnetic dipole over a cylinder with controlled boundary conditions using a group theory method are [...] Read more.
The flow and heat characteristics of an unsteady, laminar biomagnetic fluid, namely blood containing Fe3O4 magnetic particles, under the influence of thermal radiation and a magnetic dipole over a cylinder with controlled boundary conditions using a group theory method are investigated in the present study. The mathematical formulation of the problem is constructed with the aid of biomagnetic fluid dynamics (BFD) which combines principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD). It is assumed that blood exhibits polarization as well as electrical conductivity. Additionally, the shape of the magnetic particles, namely cylindrical and spherical, is also considered. Moreover, in this model, a group theoretical transformation, namely a two-parameter group technique, is applied. By applying this group transformation, the governing system of partial differential equations (PDEs) along with applicable boundary conditions are reduced to one independent variable and, consequently, converted into a system of ordinary differential equations (ODEs) with suitable boundary conditions. An efficient numerical technique is applied to solve the resultant ODEs and this technique is based on three essential features, namely (i) a common finite differences method with central differencing, (ii) tridiagonal matrix manipulation and (iii) an iterative procedure. The flow and heat characteristics of blood-Fe3O4 are found to be dependent on some physical parameters such as the particle volume fraction, the ferromagnetic interaction parameter, the magnetic field parameter, and the thermal radiation parameter. An ample parametric study is accomplished to narrate the influences of such physical parameters on velocity, temperature distributions as well as the coefficient of skin friction and rate of heat transfer. From the numerical results, it is deduced that the fluid velocity is enhanced for the ferromagnetic number and the temperature profile is decreased as the ferromagnetic number is gradually increased. It is also obtained that for the cylindrical shape of magnetic particles, the fluid temperature is more enhanced than that of the spherical shape. Both the skin friction coefficient and the local Nusselt number are increased for increasing values of the ferromagnetic interaction parameter, where the heat transfer rate of blood-Fe3O4 is significantly increased by approximately 33.2% compared to that of pure blood, whereas the coefficient of skin friction is reduced by approximately 6.82%. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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12 pages, 303 KiB  
Article
WSA-Supplements and Proper Classes
by Yılmaz Mehmet Demirci and Ergül Türkmen
Mathematics 2022, 10(16), 2964; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162964 - 17 Aug 2022
Cited by 1 | Viewed by 1070
Abstract
In this paper, we introduce the concept of wsa-supplements and investigate the objects of the class of short exact sequences determined by wsa-supplement submodules, where a submodule U of a module M is called a wsa-supplement in M if there is a submodule [...] Read more.
In this paper, we introduce the concept of wsa-supplements and investigate the objects of the class of short exact sequences determined by wsa-supplement submodules, where a submodule U of a module M is called a wsa-supplement in M if there is a submodule V of M with U+V=M and U∩V is weakly semiartinian. We prove that a module M is weakly semiartinian if and only if every submodule of M is a wsa-supplement in M. We introduce CC-rings as a generalization of C-rings and show that a ring is a right CC-ring if and only if every singular right module has a crumbling submodule. The class of all short exact sequences determined by wsa-supplement submodules is shown to be a proper class which is both injectively and co-injectively generated. We investigate the homological objects of this proper class along with its relation to CC-rings. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
12 pages, 887 KiB  
Article
An Interval-Simplex Approach to Determine Technological Parameters from Experimental Data
by Ilia Beloglazov and Kirill Krylov
Mathematics 2022, 10(16), 2959; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162959 - 16 Aug 2022
Cited by 17 | Viewed by 1310
Abstract
Statistical equations are widely used to describe the laws of various chemical technological processes. The values of constants and parameters included in these equations are determined by various methods. Methods that can determine the values of equation parameters using a limited amount of [...] Read more.
Statistical equations are widely used to describe the laws of various chemical technological processes. The values of constants and parameters included in these equations are determined by various methods. Methods that can determine the values of equation parameters using a limited amount of experimental data are of particular practical interest. In this manuscript, we propose a method to obtain simplex-interval equations. The proposed approach can be effectively used to control the values of technological process parameters. In this paper, we consider examples of chemical kinetics equation transformations and heterogeneous processes of solid particle dissolution. In addition, we describes mathematical model transformations, including equations for functions of the residence time distribution (RTD) of apparatus particles, the distribution of particles by size, etc. Finally, we apply the proposed approach to an example involving modeling of the calcination of coke in a tubular rotary kiln. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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14 pages, 791 KiB  
Article
A Note on Lagrange Interpolation of |x| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases
by Elías Berriochoa, Alicia Cachafeiro, Héctor García-Rábade and José Manuel García-Amor
Mathematics 2022, 10(15), 2558; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152558 - 22 Jul 2022
Viewed by 1088
Abstract
Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function [...] Read more.
Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function |x| on [−1,1], using Chebyshev and Chebyshev–Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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15 pages, 313 KiB  
Article
Supplements Related to Normal π-Projective Hypermodules
by Burcu Nişancı Türkmen, Hashem Bordbar and Irina Cristea
Mathematics 2022, 10(11), 1945; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111945 - 06 Jun 2022
Viewed by 1169
Abstract
In this study, the role of supplements in Krasner hypermodules is examined and related to normal π-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented [...] Read more.
In this study, the role of supplements in Krasner hypermodules is examined and related to normal π-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented and amply supplemented Krasner hypermodules. In the second part of the paper we relate the normal projectivity to direct summands and supplements in Krasner hypermodules. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
14 pages, 4339 KiB  
Article
Numerical Simulation of Solid and Porous Fins’ Impact on Heat Transfer Performance in a Differentially Heated Chamber
by Le Xuan Hoang Khoa, Ioan Pop and Mikhail A. Sheremet
Mathematics 2022, 10(2), 263; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020263 - 16 Jan 2022
Cited by 9 | Viewed by 1577
Abstract
The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is [...] Read more.
The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is devoted to the numerical analysis of natural convective energy transport in a differentially heated chamber with isothermal vertical walls and a fin system mounted on the heated wall. The developed in-house computational code has been comprehensively validated. The Forchheimer–Brinkman extended Darcy model has been employed for the numerical simulation of transport phenomena in a porous material. The partial differential equations written, employing non-primitive variables, have been worked out by the finite difference technique. Analysis has been performed for solid and porous fins with various fin materials, amounts and heights. It has been revealed that porous fins provide a very good technique for the intensification of energy removal from heated surfaces. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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12 pages, 3434 KiB  
Article
Thermogravitational Convective Flow and Energy Transport in an Electronic Cabinet with a Heat-Generating Element and Solid/Porous Finned Heat Sink
by Xuan Hoang Khoa Le, Ioan Pop and Mikhail A. Sheremet
Mathematics 2022, 10(1), 34; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010034 - 23 Dec 2021
Cited by 3 | Viewed by 2001
Abstract
Heat transfer enhancement poses a significant challenge for engineers in various practical fields, including energy-efficient buildings, energy systems, and aviation technologies. The present research deals with the energy transport strengthening using the viscous fluid and solid/porous fins. Numerical simulation of natural convective energy [...] Read more.
Heat transfer enhancement poses a significant challenge for engineers in various practical fields, including energy-efficient buildings, energy systems, and aviation technologies. The present research deals with the energy transport strengthening using the viscous fluid and solid/porous fins. Numerical simulation of natural convective energy transport of viscous fluid in a cooling cavity with a heat-generating element placed in a finned heat sink was performed. The heat-generating element is characterized by constant volumetric heat generation. The Darcy–Brinkman approach was employed for mathematical description of transport processes within the porous fins. The governing equations formulated using the non-primitive variables were solved by the finite difference method of the second-order accuracy. The influence of the fins material, number, and height on the flow structure and heat transfer was also studied. It was found that the mentioned parameters can be considered as control characteristics for heat transfer and fluid flow for the cooling system. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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20 pages, 3204 KiB  
Article
Dynamical Analysis of a Navigation Algorithm
by Mireya Cabezas-Olivenza, Ekaitz Zulueta, Ander Sánchez-Chica, Adrian Teso-Fz-Betoño and Unai Fernandez-Gamiz
Mathematics 2021, 9(23), 3139; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233139 - 06 Dec 2021
Cited by 6 | Viewed by 2860
Abstract
There is presently a need for more robust navigation algorithms for autonomous industrial vehicles. These have reasonably guaranteed the adequate reliability of the navigation. In the current work, the stability of a modified algorithm for collision-free guiding of this type of vehicle is [...] Read more.
There is presently a need for more robust navigation algorithms for autonomous industrial vehicles. These have reasonably guaranteed the adequate reliability of the navigation. In the current work, the stability of a modified algorithm for collision-free guiding of this type of vehicle is ensured. A lateral control and a longitudinal control are implemented. To demonstrate their viability, a stability analysis employing the Lyapunov method is carried out. In addition, this mathematical analysis enables the constants of the designed algorithm to be determined. In conjunction with the navigation algorithm, the present work satisfactorily solves the localization problem, also known as simultaneous localization and mapping (SLAM). Simultaneously, a convolutional neural network is managed, which is used to calculate the trajectory to be followed by the AGV, by implementing the artificial vision. The use of neural networks for image processing is considered to constitute the most robust and flexible method for realising a navigation algorithm. In this way, the autonomous vehicle is provided with considerable autonomy. It can be regarded that the designed algorithm is adequate, being able to trace any type of path. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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Review

Jump to: Research

16 pages, 823 KiB  
Review
Advances in Singular and Degenerate PDEs
by Salvatore Fragapane
Mathematics 2022, 10(24), 4760; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244760 - 14 Dec 2022
Viewed by 906
Abstract
This review was written with a dual purpose; on the one hand, to collect all the topics dealt with during the conference “Advances in Singular and Degenerate PDEs”. For this reason, in the first part of this work, the abstracts of the lectures [...] Read more.
This review was written with a dual purpose; on the one hand, to collect all the topics dealt with during the conference “Advances in Singular and Degenerate PDEs”. For this reason, in the first part of this work, the abstracts of the lectures during the workshop are shown. On the other hand, as well as the workshop, this work is a way to celebrate the career of Professor Maria Agostina Vivaldi. Professor Vivaldi’s long career and her work are hence highlighted in this work; moreover, some of the more recent results obtained by Professor Vivaldi about problems involving p-Laplace-type operators in fractal and pre-fractal boundary domains are here illustrated and discussed. In conclusion, some new recent outcomes and new perspectives are outlined. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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