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Mathematics
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Mathematical Methods in Applied Sciences
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Mathematical Methods in Applied Sciences

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (15 December 2019) | Viewed by 28523

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,

The book of nature is written in the language of mathematics. This famous statement of Galileo Galilei (1564–1642) may serve as introduction to this Special Issue. Of course, after four centuries, mathematics grew enormously, not only in the direction of differential calculus, but thanks to new disciplines, such as geometry, algebra, probability and statistics. Simultaneously, the range of the applications extended from mathematical physics to other fields, such as biomathematics, medicine and health, economy and social sciences.

The present Special Issue of Mathematics will feature articles on mathematical models, expressed in terms of any mathematical discipline, and addressed to all other sciences. New mathematical results are certainly welcome, but not requested. Rather, preference is given to papers emphasizing the beauty and the effectiveness of mathematical models in different aspects of the modern life.

Prof. Dr. 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. 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.

Keywords

  • Mathematical methods in applied sciences
  • Mathematical physics
  • Mathematical engineering
  • Computational methods

Published Papers (7 papers)

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Research

46 pages, 27580 KiB  
Article
Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation
by Fatin Amani Mohd Ali, Samsul Ariffin Abdul Karim, Azizan Saaban, Mohammad Khatim Hasan, Abdul Ghaffar, Kottakkaran Sooppy Nisar and Dumitru Baleanu
Mathematics 2020, 8(2), 159; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020159 - 22 Jan 2020
Cited by 21 | Viewed by 3111
Abstract
This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator [...] Read more.
This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R2). The higher R2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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21 pages, 956 KiB  
Article
Dynamic Modelling of Interactions between Microglia and Endogenous Neural Stem Cells in the Brain during a Stroke
by Awatif Jahman Alqarni, Azmin Sham Rambely and Ishak Hashim
Mathematics 2020, 8(1), 132; https://0-doi-org.brum.beds.ac.uk/10.3390/math8010132 - 16 Jan 2020
Cited by 6 | Viewed by 2767
Abstract
In this paper, we study the interactions between microglia and neural stem cells and the impact of these interactions on the brain cells during a stroke. Microglia cells, neural stem cells, the damage on brain cells from the stroke and the impacts these [...] Read more.
In this paper, we study the interactions between microglia and neural stem cells and the impact of these interactions on the brain cells during a stroke. Microglia cells, neural stem cells, the damage on brain cells from the stroke and the impacts these interactions have on living brain cells are considered in the design of mathematical models. The models consist of ordinary differential equations describing the effects of microglia on brain cells and the interactions between microglia and neural stem cells in the case of a stroke. Variables considered include: resident microglia, classically activated microglia, alternatively activated microglia, neural stem cells, tissue damage on cells in the brain, and the impacts these interactions have on living brain cells. The first model describes what happens in the brain at the stroke onset during the first three days without the generation of any neural stem cells. The second model studies the dynamic effect of microglia and neural stem cells on the brain cells following the generation of neural stem cells and potential recovery after this stage. We look at the stability and the instability of the models which are both studied analytically. The results show that the immune cells can help the brain by cleaning dead cells and stimulating the generation of neural stem cells; however, excessive activation may cause damage and affect the injured region. Microglia have beneficial and harmful functions after ischemic stroke. The microglia stimulate neural stem cells to generate new cells that substitute dead cells during the recovery stage but sometimes the endogenous neural stem cells are highly sensitive to inflammatory in the brain. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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17 pages, 4597 KiB  
Article
Evaluation of Elite Athletes Training Management Efficiency Based on Multiple Criteria Measure of Conditioning Using Fewer Data
by Aleksandras Krylovas, Natalja Kosareva, Rūta Dadelienė and Stanislav Dadelo
Mathematics 2020, 8(1), 66; https://0-doi-org.brum.beds.ac.uk/10.3390/math8010066 - 2 Jan 2020
Cited by 3 | Viewed by 2362
Abstract
Innovative solutions and techniques in the sports industry are commonly used and tested in real conditions. Elite athletes have to achieve their peak performance before the main competition of the year, which is the World Championship, and every fourth year before the Olympic [...] Read more.
Innovative solutions and techniques in the sports industry are commonly used and tested in real conditions. Elite athletes have to achieve their peak performance before the main competition of the year, which is the World Championship, and every fourth year before the Olympic Games, when the main competition of athletes takes place. The present study aims to analyze and evaluate the ability of elite kayakers to achieve the best form at the right times, with the Olympic Games taking the greatest importance. Target values for multiple measures of conditioning are compared to target values set by experts. A weighted least squares metric with weights varied by time period is developed as a measure of fulfillment of the athletes’ conditioning plans. The novelty of the paper is the idea of using linear combination of polynomials and trigonometric functions for approximating the target functions and application of the proposed methodology for the optimization and evaluation of athletic training. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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22 pages, 2807 KiB  
Article
Shift Scheduling with the Goal Programming Method: A Case Study in the Glass Industry
by Özlem Kaçmaz, Haci Mehmet Alakaş and Tamer Eren
Mathematics 2019, 7(6), 561; https://0-doi-org.brum.beds.ac.uk/10.3390/math7060561 - 20 Jun 2019
Cited by 8 | Viewed by 3960
Abstract
Nowadays, resource utilization and management are very important for businesses. They try to make a profit by providing high levels of efficiency from available sources. Their labor force is one of these sources. Therefore, scheduling based on personnel satisfaction has become an important [...] Read more.
Nowadays, resource utilization and management are very important for businesses. They try to make a profit by providing high levels of efficiency from available sources. Their labor force is one of these sources. Therefore, scheduling based on personnel satisfaction has become an important problem in recent years. In this study, a case study was carried out in a glass factory in Ankara which has 7 department and 80 personnel. The aim of the study is to provide better service by distributing personnel to shifts in a fair and balanced manner. Assignment points are different for the departments where the personnel will work. Every personnel member is assigned to the department as best as possible. A goal programming method was used, and the results were better than those obtained using other methods. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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12 pages, 1495 KiB  
Article
Chebyshev Spectral Collocation Method for Population Balance Equation in Crystallization
by Chunlei Ruan
Mathematics 2019, 7(4), 317; https://0-doi-org.brum.beds.ac.uk/10.3390/math7040317 - 28 Mar 2019
Cited by 3 | Viewed by 3108
Abstract
The population balance equation (PBE) is the main governing equation for modeling dynamic crystallization behavior. In the view of mathematics, PBE is a convection–reaction equation whose strong hyperbolic property may challenge numerical methods. In order to weaken the hyperbolic property of PBE, a [...] Read more.
The population balance equation (PBE) is the main governing equation for modeling dynamic crystallization behavior. In the view of mathematics, PBE is a convection–reaction equation whose strong hyperbolic property may challenge numerical methods. In order to weaken the hyperbolic property of PBE, a diffusive term was added in this work. Here, the Chebyshev spectral collocation method was introduced to solve the PBE and to achieve accurate crystal size distribution (CSD). Three numerical examples are presented, namely size-independent growth, size-dependent growth in a batch process, and with nucleation, and size-dependent growth in a continuous process. Through comparing the results with the numerical results obtained via the second-order upwind method and the HR-van method, the high accuracy of Chebyshev spectral collocation method was proven. Moreover, the diffusive term is also discussed in three numerical examples. The results show that, in the case of size-independent growth (PBE is a convection equation), the diffusive term should be added, and the coefficient of the diffusive term is recommended as 2G × 10−3 to G × 10−2, where G is the crystal growth rate. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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24 pages, 573 KiB  
Article
Surgical Operation Scheduling with Goal Programming and Constraint Programming: A Case Study
by Şeyda Gür, Tamer Eren and Hacı Mehmet Alakaş
Mathematics 2019, 7(3), 251; https://0-doi-org.brum.beds.ac.uk/10.3390/math7030251 - 11 Mar 2019
Cited by 20 | Viewed by 6330
Abstract
The achievement of health organizations’ goals is critically important for profitability. For this purpose, their resources, materials, and equipment should be efficiently used in the services they provide. A hospital has sensitive and expensive equipment, and the use of its equipment and resources [...] Read more.
The achievement of health organizations’ goals is critically important for profitability. For this purpose, their resources, materials, and equipment should be efficiently used in the services they provide. A hospital has sensitive and expensive equipment, and the use of its equipment and resources needs to be balanced. The utilization of these resources should be considered in its operating rooms, as it shares both expense expenditure and revenue generation. This study’s primary aim is the effective and balanced use of equipment and resources in hospital operating rooms. In this context, datasets from a state hospital were used via the goal programming and constraint programming methods. According to the wishes of hospital managers, three scenarios were separately modeled in both methods. According to the obtained results, schedules were compared and analyzed according to the current situation. The hospital-planning approach was positively affected, and goals such as minimization cost, staff and patient satisfaction, prevention over time, and less use were achieved. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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6 pages, 746 KiB  
Article
Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network
by Ioannis Dassios, Andrew Keane and Paul Cuffe
Mathematics 2019, 7(1), 106; https://0-doi-org.brum.beds.ac.uk/10.3390/math7010106 - 20 Jan 2019
Cited by 10 | Viewed by 4120
Abstract
Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These [...] Read more.
Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis. Full article
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
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