Special Issue "Mathematical Methods in Applied Sciences"

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

Deadline for manuscript submissions: 30 June 2019

Special Issue Editor

Guest Editor
Prof. Dr. Luigi Rodino

1. Department of Mathematics, University of Torino, Italy
2. RUDN University, Moscow, Russia
Website | E-Mail
Interests: partial differential equations; Fourier analysis; operator theory

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 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. Mathematics 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 850 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 (3 papers)

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Research

Open AccessArticle
Chebyshev Spectral Collocation Method for Population Balance Equation in Crystallization
Mathematics 2019, 7(4), 317; https://doi.org/10.3390/math7040317
Received: 18 February 2019 / Revised: 24 March 2019 / Accepted: 26 March 2019 / Published: 28 March 2019
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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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Open AccessArticle
Surgical Operation Scheduling with Goal Programming and Constraint Programming: A Case Study
Mathematics 2019, 7(3), 251; https://doi.org/10.3390/math7030251
Received: 13 November 2018 / Revised: 18 February 2019 / Accepted: 19 February 2019 / Published: 11 March 2019
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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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Open AccessArticle
Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network
Mathematics 2019, 7(1), 106; https://doi.org/10.3390/math7010106
Received: 29 November 2018 / Revised: 17 January 2019 / Accepted: 18 January 2019 / Published: 20 January 2019
Cited by 3 | PDF Full-text (746 KB) | HTML Full-text | XML Full-text
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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