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Mathematics and Its Applications in Science and Engineering
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Mathematics and Its Applications in Science and Engineering

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

Deadline for manuscript submissions: closed (9 May 2022) | Viewed by 40855

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

Special Issue Editors

Prof. Dr. Araceli Queiruga-Dios

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Guest Editor
Department of Applied Mathematics, School of Industrial Engineering, University of Salamanca, 37008 Salamanca, Spain
Interests: cryptography; algorithms; applied mathematics; applied and computational mathematics
Special Issues, Collections and Topics in MDPI journals
Dr. Maria Jesus Santos

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Guest Editor
Department of Applied Physics, Science Faculty, University of Salamanca, Plaza. de la Merced s / n, 37008 Salamanca, Spain
Interests: physics teaching
Dr. Fatih Yilmaz

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Guest Editor
Department of Mathematics, Ankara Hacı Bayram Veli University, 06900 Ankara, Turkey
Interests: applications of matrix theory; graph theory; number theory and mathematical education based on projects and competencies
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Deolinda M. L. Dias Rasteiro

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Guest Editor
Department of Mathematics and Physics, Coimbra Polytechnic—ISEC, 3045-093 Coimbra, Portugal
Interests: network optimization; image processing; research on new methods to present mathematics to students
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jesús Martín Vaquero

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Guest Editor
Department of Applied Mathematics, Institute of Fundamental Physics and Mathematics, Universidad de Salamanca, 37008 Salamanca, Spain
Interests: Runge–Kutta methods for nonlinear PDEs; approximation theory; mathematical education
Special Issues, Collections and Topics in MDPI journals
Dr. Víctor Gayoso Martínez

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Guest Editor
Data Research & Computation Group (DRACO), Centro Universitario de Tecnología y Arte Digital (U-Tad), Las Rozas de Madrid, 28290 Madrid, Spain
Interests: cryptography; elliptic curves; java; smart cards; biometrics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue invites papers on new and innovative proposals of Mathematics in science and engineering, i.e., the use of mathematics in non-mathematical contexts. This proposal aims to publish results from Mathematics applications, such as the use of differential equations to model structures, the shape of a machine or the growth of a population, or to ensure information security through cryptographic protocols.

The added value is that it will include results from recent years, which is of particular importance since mathematical education has been changing and acquiring a different role in undergraduate and graduate degrees in the past few years, and recent changes in the educational paradigm demand a comprehensive revision of the teaching and learning methodologies. Innovation in educational contexts should reach a consensus regarding how mathematical competencies are evaluated. In this Special Issue, our goal is to integrate different methodologies for mathematical education and how they are evaluated.

Potential topics include but are not limited to:

  • Mathematical modeling for science and engineering applications;
  • Optimization and control in engineering applications;
  • Numerical methods for science and engineering applications;
  • Mathematics in engineering and sciences studies;
  • Good practices in motivating students for learning mathematics during university studies;
  • Assessing mathematics using applications and projects;
  • Teaching and assessment methodologies in science and engineering.

Prof. Dr. Araceli Queiruga-Dios
Dr. Maria Jesus Santos
Dr. Fatih Yilmaz
Prof. Dr. Deolinda M. L. Dias Rasteiro
Prof. Dr. Jesús Martín Vaquero
Dr. Víctor Gayoso Martínez
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.

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Editorial

Jump to: Research

2 pages, 189 KiB  
Editorial
Mathematics and Its Applications in Science and Engineering
by Araceli Queiruga-Dios, María Jesus Santos Sánchez, Fatih Yilmaz, Deolinda M. L. Dias Rasteiro, Jesús Martín-Vaquero and Víctor Gayoso Martínez
Mathematics 2022, 10(19), 3412; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193412 - 20 Sep 2022
Viewed by 1377
Abstract
This book contains the successful submissions [...] Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)

Research

Jump to: Editorial

21 pages, 7690 KiB  
Article
Prediction of Splitting Tensile Strength of Self-Compacting Recycled Aggregate Concrete Using Novel Deep Learning Methods
by Jesús de-Prado-Gil, Osama Zaid, Covadonga Palencia and Rebeca Martínez-García
Mathematics 2022, 10(13), 2245; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132245 - 27 Jun 2022
Cited by 16 | Viewed by 1590
Abstract
The composition of self-compacting concrete (SCC) contains 60–70% coarse and fine aggregates, which are replaced by construction waste, such as recycled aggregates (RA). However, the complexity of its structure requires a time-consuming mixed design. Currently, many researchers are studying the prediction of concrete [...] Read more.
The composition of self-compacting concrete (SCC) contains 60–70% coarse and fine aggregates, which are replaced by construction waste, such as recycled aggregates (RA). However, the complexity of its structure requires a time-consuming mixed design. Currently, many researchers are studying the prediction of concrete properties using soft computing techniques, which will eventually reduce environmental degradation and other material waste. There have been very limited and contradicting studies regarding prediction using different ANN algorithms. This paper aimed to predict the 28-day splitting tensile strength of SCC with RA using the artificial neural network technique by comparing the following algorithms: Levenberg–Marquardt (LM), Bayesian regularization (BR), and Scaled Conjugate Gradient Backpropagation (SCGB). There have been very limited and contradicting studies regarding prediction by using and comparing different ANN algorithms, so a total of 381 samples were collected from various published journals. The input variables were cement, admixture, water, fine and coarse aggregates, and superplasticizer; the data were randomly divided into three sets—training (60%), validation (10%), and testing (30%)—with 10 neurons in the hidden layer. The models were evaluated by the mean squared error (MSE) and correlation coefficient (R). The results indicated that all three models have optimal accuracy; still, BR gave the best performance (R = 0.91 and MSE = 0.2087) compared with LM and SCG. BR was the best model for predicting TS at 28 days for SCC with RA. The sensitivity analysis indicated that cement (30.07%) was the variable that contributed the most to the prediction of TS at 28 days for SCC with RA, and water (2.39%) contributed the least. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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31 pages, 5392 KiB  
Article
A Refined Closed-Form Solution for the Large Deflections of Alekseev-Type Annular Membranes Subjected to Uniformly Distributed Transverse Loads: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation
by Bo Li, Qi Zhang, Xue Li, Xiao-Ting He and Jun-Yi Sun
Mathematics 2022, 10(12), 2121; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122121 - 17 Jun 2022
Cited by 2 | Viewed by 1167
Abstract
The Alekseev-type annular membranes here refer to annular membranes fixed at outer edges and connected with a movable, weightless, stiff, con-centric, circular thin plate at inner edges, which were proposed originally by Alekseev for bearing centrally concentrated loads. They are used to bear [...] Read more.
The Alekseev-type annular membranes here refer to annular membranes fixed at outer edges and connected with a movable, weightless, stiff, con-centric, circular thin plate at inner edges, which were proposed originally by Alekseev for bearing centrally concentrated loads. They are used to bear the pressure acting on both membranes and plates, which was proposed originally in our previous work for developing pressure sensors. The pressure is applied onto an Alekseev-type annular membrane, resulting in the parallel movement of the circular thin plate. Such a movement can be used to develop a capacitive pressure sensor using the circular thin plate as a movable electrode plate of a parallel plate capacitor. The pressure applied can be determined by measuring the change in capacitance of the parallel plate capacitor, based on the closed-form solution for the elastic behavior of Alekseev-type annular membranes. However, the previous closed-form solution is unsuitable for annular membranes with too large deflection, which limits the range of pressure operation of the developed sensors. A new and more refined closed-form solution is presented here by improving simultaneously the out-of-plane equilibrium equation and geometric equation, making it possible to develop capacitive pressure sensors with a wide range of pressure operations. The new closed-form solution is numerically discussed in its convergence and effectiveness and compared with the previous one. Additionally, its beneficial effect on developing the proposed capacitive pressure sensors is illustrated. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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19 pages, 3256 KiB  
Article
Team Control Problem in Virtual Ellipsoid and Its Numerical Simulations
by Zhiqing Dang, Zhaopeng Dai, Yang Yu, Long Zhang, Ang Su, Zhihang You and Hongwei Gao
Mathematics 2022, 10(12), 1970; https://0-doi-org.brum.beds.ac.uk/10.3390/math10121970 - 07 Jun 2022
Cited by 1 | Viewed by 1113
Abstract
There is tremendous interest in designing feedback strategy control for clusters in modern control theory. We propose a novel numerical solution to target team control problems by using the Hamilton formalism methods. In order to ensure the smooth wireless information exchange, all members [...] Read more.
There is tremendous interest in designing feedback strategy control for clusters in modern control theory. We propose a novel numerical solution to target team control problems by using the Hamilton formalism methods. In order to ensure the smooth wireless information exchange, all members of the team are located in a virtual ellipsoidal container during the whole movement process. An ellipsoidal container tube is constructed as the external state constraint of the team. The corresponding value function is then formulated based on collision avoidance conditions and energy constraints in the process of the team motion. Time-dependent partial differential equations are formulated based on Hamilton formalism, which have been solved numerically by using the traditional finite difference method (FDM). The objective of the presented method is to obtain optimal control and motion trajectory of the cluster at each moment. Lastly, we conduct a simulation study of unmanned aerial vehicles (UAVs) to demonstrate the performance of the proposed method. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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16 pages, 1125 KiB  
Article
Analysis of Industrial Engineering Students’ Perception after a Multiple Integrals-Based Activity with a Fourth-Year Student
by Anuar R. Giménez, Jesús Martín-Vaquero and Manuel Rodríguez-Martín
Mathematics 2022, 10(10), 1764; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101764 - 21 May 2022
Cited by 2 | Viewed by 1985
Abstract
In industrial engineering degrees in Spain, mathematics subjects are usually taught during the first two academic years. Consequently, it is often the case that students sometimes do not feel motivated to learn subjects such as Mathematics II (calculus). Nevertheless, this subject is fundamental [...] Read more.
In industrial engineering degrees in Spain, mathematics subjects are usually taught during the first two academic years. Consequently, it is often the case that students sometimes do not feel motivated to learn subjects such as Mathematics II (calculus). Nevertheless, this subject is fundamental for understanding other subjects in the degree study plan, as well as for the graduate’s future professional career as an engineer. To address this, a problem-based teaching methodology was carried out with the help of a fourth-year student who explained an activity to first-year students in a manner which was both friendly and approachable. In this experiment, the student went through a series of practical problems taken from different engineering subjects, which required multivariable integrals to be calculated and which he had learned in mathematics as a first-year student. In addition, a method based on pre-test and post-test assessments was applied. From this work, various benefits were observed in terms of learning, as well as an increase in the level of motivation of first-year students. There was a greater appreciation of the usefulness of calculus and computer programs to solve real-life problems, and the students generally responded positively to this type of activity. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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22 pages, 573 KiB  
Article
On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution
by Antonios Charalambopoulos, Theodore Gortsas and Demosthenes Polyzos
Mathematics 2022, 10(7), 1152; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071152 - 02 Apr 2022
Cited by 6 | Viewed by 1671
Abstract
The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient [...] Read more.
The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient parameters become zero. Through functional theory considerations, a solution representation of the one-intrinsic-parameter strain gradient elastostatic equation that comprises the classical elastic solution of the corresponding boundary value problem is rigorously provided for the first time. Next, that solution representation is employed to give an answer to contradictions arising by two well-known first-strain gradient elastic models proposed in the literature to describe the strain gradient elastostatic bending behavior of Bernoulli–Euler beams. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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29 pages, 4072 KiB  
Article
Novel Photovoltaic Empirical Mathematical Model Based on Function Representation of Captured Figures from Commercial Panels Datasheet
by Ola Hassan, Nahla Zakzouk and Ahmed Abdelsalam
Mathematics 2022, 10(3), 476; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030476 - 01 Feb 2022
Cited by 8 | Viewed by 2390
Abstract
Photovoltaic (PV) technology is gaining much interest as a clean, sustainable, noise-free source of energy. However, the non-linear behavior of PV modules and their dependency on varying environmental conditions require thorough study and analysis. Many PV modeling techniques have been introduced in the [...] Read more.
Photovoltaic (PV) technology is gaining much interest as a clean, sustainable, noise-free source of energy. However, the non-linear behavior of PV modules and their dependency on varying environmental conditions require thorough study and analysis. Many PV modeling techniques have been introduced in the literature, yet they exhibit several complexity levels for parameter extraction and constants estimation for PV power forecast. Comparatively, a simple, accurate, fast, and user friendly PV modeling technique is proposed in this paper featuring the least computational time and effort. Based on function representation of PV curves’ available in PV datasheets, an empirical mathematical equation is derived. The proposed formula is considered a generic tool capable of modeling any PV device under various weather conditions without either parameter estimation nor power prediction. The proposed model is validated using experimental data of commercial PV panels’ manufacturers under various environmental conditions for different power levels. The obtained results verified the effectiveness of the proposed PV model. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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20 pages, 4618 KiB  
Article
Improving Calculus Curriculum in Engineering Degrees: Implementation of Technological Applications
by María Teresa López-Díaz and Marta Peña
Mathematics 2022, 10(3), 341; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030341 - 23 Jan 2022
Cited by 4 | Viewed by 2571
Abstract
The teaching of mathematics has always concerned all the professionals involved in engineering degrees. Curently students have less interest in these studies, what has caused an increase of this concern. The lack of awareness of students about the significance of mathematics in their [...] Read more.
The teaching of mathematics has always concerned all the professionals involved in engineering degrees. Curently students have less interest in these studies, what has caused an increase of this concern. The lack of awareness of students about the significance of mathematics in their careers, provoke the decrease of undergraduate students’ motivation, which derives in a low interest in engineering degrees. The aim of this work is that engineering students achieve a greater motivation and involvement in first academic courses, through the implementation of real and technological applications related to their degrees in the learning of mathematical concepts. To this end, the 2019/2020 and 2020/2021 academics years, the seminar “Applications of Multivariable Calculus in Engineering” has been held in Universitat Politècnica de Catalunya-BarcelonaTech (UPC), based on the teaching of Multivariable Calculus by the execution of real problems where calculus concepts are necessary to solve them. With the aim of analyzing students’ motivation and assessment of the seminar, anonymous surveys and personal interviews have been conducted. The number of attending students to the sessions in each academic year has been 16 and all of them have been participants in the surveys and interviews. The results show that students’ responses were generally positive and they agree that their motivation to the subject Multivariable Calculus has increased with the use of real applications of mathematics. The execution of practical problems with engineering applications improves the acquirement of mathematical concepts, what could imply an increase of students’ performance and a decrease of the dropout in the first academic courses of engineering degrees. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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15 pages, 2291 KiB  
Article
Hybrid Statistical and Numerical Analysis in Structural Optimization of Silicon-Based RF Detector in 5G Network
by Tan Yi Liang, Nor Farhani Zakaria, Shahrir Rizal Kasjoo, Safizan Shaari, Muammar Mohamad Isa, Mohd Khairuddin Md Arshad, Arun Kumar Singh and Sharizal Ahmad Sobri
Mathematics 2022, 10(3), 326; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030326 - 21 Jan 2022
Cited by 4 | Viewed by 1809
Abstract
In this study, a hybrid statistical analysis (Taguchi method supported by analysis of variance (ANOVA) and regression analysis) and numerical analysis (utilizing a Silvaco device simulator) was implemented to optimize the structural parameters of silicon-on-insulator (SOI)-based self-switching diodes (SSDs) to achieve a high [...] Read more.
In this study, a hybrid statistical analysis (Taguchi method supported by analysis of variance (ANOVA) and regression analysis) and numerical analysis (utilizing a Silvaco device simulator) was implemented to optimize the structural parameters of silicon-on-insulator (SOI)-based self-switching diodes (SSDs) to achieve a high responsivity value as a radio frequency (RF) detector. Statistical calculation was applied to study the relationship between the control factors and the output performance of an RF detector in terms of the peak curvature coefficient value and its corresponding bias voltage. Subsequently, a series of numerical simulations were performed based on Taguchi’s experimental design. The optimization results indicated an optimized curvature coefficient and voltage peak of 26.4260 V−1 and 0.05 V, respectively. The alternating current transient analysis from 3 to 10 GHz showed the highest mean current at 5 GHz and a cut-off frequency of approximately 6.50 GHz, indicating a prominent ability to function as an RF detector at 5G related frequencies. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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24 pages, 1225 KiB  
Article
A Regularised Total Least Squares Approach for 1D Inverse Scattering
by Andreas Tataris and Tristan van Leeuwen
Mathematics 2022, 10(2), 216; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020216 - 11 Jan 2022
Cited by 4 | Viewed by 1485
Abstract
We study the inverse scattering problem for a Schrödinger operator related to a static wave operator with variable velocity, using the GLM (Gelfand–Levitan–Marchenko) integral equation. We assume to have noisy scattering data, and we derive a stability estimate for the error of the [...] Read more.
We study the inverse scattering problem for a Schrödinger operator related to a static wave operator with variable velocity, using the GLM (Gelfand–Levitan–Marchenko) integral equation. We assume to have noisy scattering data, and we derive a stability estimate for the error of the solution of the GLM integral equation by showing the invertibility of the GLM operator between suitable function spaces. To regularise the problem, we formulate a variational total least squares problem, and we show that, under certain regularity assumptions, the optimisation problem admits minimisers. Finally, we compute numerically the regularised solution of the GLM equation using the total least squares method in a discrete sense. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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18 pages, 1354 KiB  
Article
Formulation of Parsimonious Urban Flash Flood Predictive Model with Inferential Statistics
by Lloyd Ling, Sai Hin Lai, Zulkifli Yusop, Ren Jie Chin and Joan Lucille Ling
Mathematics 2022, 10(2), 175; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020175 - 06 Jan 2022
Cited by 3 | Viewed by 1652
Abstract
The curve number (CN) rainfall–runoff model is widely adopted. However, it had been reported to repeatedly fail in consistently predicting runoff results worldwide. Unlike the existing antecedent moisture condition concept, this study preserved its parsimonious model structure for calibration according to different ground [...] Read more.
The curve number (CN) rainfall–runoff model is widely adopted. However, it had been reported to repeatedly fail in consistently predicting runoff results worldwide. Unlike the existing antecedent moisture condition concept, this study preserved its parsimonious model structure for calibration according to different ground saturation conditions under guidance from inferential statistics. The existing CN model was not statistically significant without calibration. The calibrated model did not rely on the return period data and included rainfall depths less than 25.4 mm to formulate statistically significant urban runoff predictive models, and it derived CN directly. Contrarily, the linear regression runoff model and the asymptotic fitting method failed to model hydrological conditions when runoff coefficient was greater than 50%. Although the land-use and land cover remained the same throughout this study, the calculated CN value of this urban watershed increased from 93.35 to 96.50 as the watershed became more saturated. On average, a 3.4% increase in CN value would affect runoff by 44% (178,000 m3). This proves that the CN value cannot be selected according to the land-use and land cover of the watershed only. Urban flash flood modelling should be formulated with rainfall–runoff data pairs with a runoff coefficient > 50%. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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19 pages, 452 KiB  
Article
How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach
by Vicente Díaz-González, Alejandro Rojas-Palma and Marcos Carrasco-Benavides
Mathematics 2022, 10(1), 151; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010151 - 04 Jan 2022
Cited by 4 | Viewed by 2681
Abstract
This article presents a qualitative mathematical model to simulate the relationship between supplied water and plant growth. A novel aspect of the construction of this phenomenological model is the consideration of a structure of three phases: (1) The soil water availability, (2) the [...] Read more.
This article presents a qualitative mathematical model to simulate the relationship between supplied water and plant growth. A novel aspect of the construction of this phenomenological model is the consideration of a structure of three phases: (1) The soil water availability, (2) the available water inside the plant for its growth, and (3) the plant size or amount of dry matter. From these phases and their interactions, a model based on a three-dimensional nonlinear dynamic system was proposed. The results obtained showed the existence of a single equilibrium point, global and exponentially stable. Additionally, considering the framework of the perturbation theory, this model was perturbed by incorporating irrigation to the available soil water, obtaining some stability results under different assumptions. Later through the control theory, it was demonstrated that the proposed system was controllable. Finally, a numerical simulation of the proposed model was carried out, to depict the soil water content and plant growth dynamic and its agreement with the results of the mathematical analysis. In addition, a specific calibration for field data from an experiment with wheat was considered, and these parameters were then used to test the proposed model, obtaining an error of about 6% in the soil water content estimation. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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37 pages, 2547 KiB  
Article
Models of Privacy and Disclosure on Social Networking Sites: A Systematic Literature Review
by Lili Nemec Zlatolas, Luka Hrgarek, Tatjana Welzer and Marko Hölbl
Mathematics 2022, 10(1), 146; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010146 - 04 Jan 2022
Cited by 8 | Viewed by 3256
Abstract
Social networking sites (SNSs) are used widely, raising new issues in terms of privacy and disclosure. Although users are often concerned about their privacy, they often publish information on social networking sites willingly. Due to the growing number of users of social networking [...] Read more.
Social networking sites (SNSs) are used widely, raising new issues in terms of privacy and disclosure. Although users are often concerned about their privacy, they often publish information on social networking sites willingly. Due to the growing number of users of social networking sites, substantial research has been conducted in recent years. In this paper, we conducted a systematic review of papers that included structural equations models (SEM), or other statistical models with privacy and disclosure constructs. A total of 98 such papers were found and included in the analysis. In this paper, we evaluated the presentation of results of the models containing privacy and disclosure constructs. We carried out an analysis of which background theories are used in such studies and have also found that the studies have not been carried out worldwide. Extending the research to other countries could help with better user awareness of the privacy and self-disclosure of users on SNSs. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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19 pages, 2886 KiB  
Article
Entropy Analysis and Melting Heat Transfer in the Carreau Thin Hybrid Nanofluid Film Flow
by Kohilavani Naganthran, Roslinda Nazar, Zailan Siri and Ishak Hashim
Mathematics 2021, 9(23), 3092; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233092 - 30 Nov 2021
Cited by 11 | Viewed by 1481
Abstract
Melting heat transfer has a vital role in forming energy storage devices such as flexible thin film supercapacitors. This idea should be welcomed in the thin film theoretical models to sustain technological advancement, which could later benefit humankind. Hence, the present work endeavors [...] Read more.
Melting heat transfer has a vital role in forming energy storage devices such as flexible thin film supercapacitors. This idea should be welcomed in the thin film theoretical models to sustain technological advancement, which could later benefit humankind. Hence, the present work endeavors to incorporate the melting heat transfer effect on the Carreau thin hybrid nanofluid film flow over an unsteady accelerating sheet. The mathematical model that obeyed the boundary layer theory has been transformed into a solvable form via an apt similarity transformation. Furthermore, the collocation method, communicated through the MATLAB built-in bvp4c function, solved the model numerically. Non-uniqueness solutions have been identified, and solutions with negative film thickness are unreliable. The melting heat transfer effect lowers the heat transfer rate without affecting the liquid film thickness, while the Carreau hybrid nanofluid contributes more entropy than the Carreau nanofluid in the flow regime. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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12 pages, 919 KiB  
Article
Flow and Heat Transfer Past a Stretching/Shrinking Sheet Using Modified Buongiorno Nanoliquid Model
by Natalia C. Roşca, Alin V. Roşca, Emad H. Aly and Ioan Pop
Mathematics 2021, 9(23), 3047; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233047 - 27 Nov 2021
Cited by 12 | Viewed by 1497
Abstract
This paper studies the boundary layer flow and heat transfer characteristics past a permeable isothermal stretching/shrinking surface using both nanofluid and hybrid nanofluid flows (called modified Buongiorno nonliquid model). Using appropriate similarity variables, the PDEs are transformed into ODEs to be solved numerically [...] Read more.
This paper studies the boundary layer flow and heat transfer characteristics past a permeable isothermal stretching/shrinking surface using both nanofluid and hybrid nanofluid flows (called modified Buongiorno nonliquid model). Using appropriate similarity variables, the PDEs are transformed into ODEs to be solved numerically using the function bvp4c from MATLAB. It was found that the solutions of the resulting system have two branches, upper and lower branch solutions, in a certain range of the suction, stretching/shrinking and hybrid nanofluids parameters. Both the analytic and numerical results are obtained for the skin friction coefficient, local Nusselt number, and velocity and temperature distributions, for several values of the governing parameters. It results in the governing parameters considerably affecting the flow and heat transfer characteristics. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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14 pages, 7629 KiB  
Article
Influence of MHD Hybrid Ferrofluid Flow on Exponentially Stretching/Shrinking Surface with Heat Source/Sink under Stagnation Point Region
by Nur Syazana Anuar, Norfifah Bachok and Ioan Pop
Mathematics 2021, 9(22), 2932; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222932 - 17 Nov 2021
Cited by 24 | Viewed by 1792
Abstract
The numerical investigations of hybrid ferrofluid flow with magnetohydrodynamic (MHD) and heat source/sink effects are examined in this research. The sheet is assumed to stretch or shrink exponentially near the stagnation region. Two dissimilar magnetic nanoparticles, namely cobalt ferrite, CoFe2O4 [...] Read more.
The numerical investigations of hybrid ferrofluid flow with magnetohydrodynamic (MHD) and heat source/sink effects are examined in this research. The sheet is assumed to stretch or shrink exponentially near the stagnation region. Two dissimilar magnetic nanoparticles, namely cobalt ferrite, CoFe2O4 and magnetite, Fe3O4, are considered with water as a based fluid. Utilizing the suitable similarity transformation, the governing equations are reduced to an ordinary differential equation (ODE). The converted ODEs are numerically solved with the aid of bvp4c solver from Matlab. The influences of varied parameters on velocity profile, skin friction coefficient, temperature profile and local Nusselt number are demonstrated graphically. The analysis evident the occurrence of non-unique solution for a shrinking sheet and it is confirmed from the analysis of stability that only the first solution is the stable solution. It is also found that for a stronger heat source, heat absorption is likely to happen at the sheet. Further, hybrid ferrofluid intensifies the heat transfer rate compared to ferrofluid. Moreover, the boundary layer separation is bound to happen faster with an increment of magnetic parameter, while it delays when CoFe2O4 nanoparticle volume fraction increases. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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9 pages, 250 KiB  
Article
On Leonardo Pisano Hybrinomials
by Ferhat Kürüz, Ali Dağdeviren and Paula Catarino
Mathematics 2021, 9(22), 2923; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222923 - 17 Nov 2021
Cited by 12 | Viewed by 1675
Abstract
A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials. Furthermore, we also describe the basic algebraic properties and some [...] Read more.
A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials. Furthermore, we also describe the basic algebraic properties and some identities of the Leonardo Pisano polynomials and hybrinomials. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
14 pages, 287 KiB  
Article
On Third-Order Bronze Fibonacci Numbers
by Mücahit Akbiyik and Jeta Alo
Mathematics 2021, 9(20), 2606; https://0-doi-org.brum.beds.ac.uk/10.3390/math9202606 - 16 Oct 2021
Cited by 7 | Viewed by 1770
Abstract
In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then, we define the generalized third-order Bronze Fibonacci sequence and [...] Read more.
In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then, we define the generalized third-order Bronze Fibonacci sequence and calculate the De Moivre-type identities for these sequences. Moreover, we find the generating functions, Binet’s formulas, Cassini’s identities and matrix representations of these sequences and examine some interesting identities related to the third-order Bronze Fibonacci sequences. Finally, we present an encryption and decryption application that uses our obtained results and we present an illustrative example. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
13 pages, 1863 KiB  
Article
Flow towards a Stagnation Region of a Curved Surface in a Hybrid Nanofluid with Buoyancy Effects
by Iskandar Waini, Anuar Ishak and Ioan Pop
Mathematics 2021, 9(18), 2330; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182330 - 20 Sep 2021
Cited by 13 | Viewed by 1669
Abstract
This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO2) and alumina (Al2O3) nanoparticles are added into water to form SiO2-Al2O3/water hybrid [...] Read more.
This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO2) and alumina (Al2O3) nanoparticles are added into water to form SiO2-Al2O3/water hybrid nanofluid. Both buoyancy-opposing and -assisting flows are considered. The governing partial differential equations are reduced to a set of ordinary differential equations, before being coded in MATLAB software to obtain the numerical solutions. Findings show that the solutions are not unique, where two solutions are obtained, for both buoyancy-assisting and -opposing flow cases. The local Nusselt number increases in the presence of the hybrid nanoparticles. The temporal stability analysis shows that only one of the solutions is stable over time. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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15 pages, 1018 KiB  
Article
A Predictive Control Strategy for Aerial Payload Transportation with an Unmanned Aerial Vehicle
by Norberto Urbina-Brito, María-Eusebia Guerrero-Sánchez, Guillermo Valencia-Palomo, Omar Hernández-González, Francisco-Ronay López-Estrada and José Antonio Hoyo-Montaño
Mathematics 2021, 9(15), 1822; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151822 - 01 Aug 2021
Cited by 15 | Viewed by 2759
Abstract
This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving [...] Read more.
This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving a good balance between fast stabilization times and small swing angles. The mathematical model is based on the Euler–Lagrange formulation and considers the dynamics of the vehicle, the cable, and the load. Then, the mathematical model is represented as an input-affine system to obtain the linear model for the control design. A constrained MPC strategy was designed and compared with an unconstrained MPC and an algorithm from the literature for the case of study. The constraints to be considered include the limits on the swing angles and the quadrotor position. The constrained control algorithm was constructed to stabilize the aerial vehicle. It aims to track a trajectory reference while attenuating the load swing, considering a maximum swing range of ±10∘. Numerical simulations were carried out to validate the control strategy. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)
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