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Mathematics and Its Applications in Science and Engineering II

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 22078

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Prof. Dr. Araceli Queiruga-Dios

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Department of Applied Mathematics, School of Industrial Engineering, University of Salamanca, 37008 Salamanca, Spain
Interests: cryptography; algorithms; applied mathematics; applied and computational mathematics
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Dr. Fatih Yilmaz

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Department of Mathematics, Ankara Hacı Bayram Veli University, Çankaya, Ankara 06570, Turkey
Interests: matrix theory; number theory; graph theory; combinatorics
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Dr. Ion Mierlus-Mazilu

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Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania
Interests: applications of probability and statistics; operational research; numerical analysis and numerical methods; mathematical and informatics education based on e/m/u-Learning
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Prof. Dr. Deolinda M. L. Dias Rasteiro

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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
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Prof. Dr. Jesús Martín Vaquero

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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
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Special Issue Information

Dear Colleagues,

This Special Issue accepts papers about new and innovative implementations of mathematics in science and engineering, i.e., the use of mathematics in non-mathematical contexts is considered. This proposal wants to publish results from mathematical applications, such as the use of differential equations to model structures, the shape of a machine or the growing of a population, or to assure information security through cryptographic protocols.

The added value is that it will include results from recent years, which will allow readers to keep up to date.

In recent years, mathematical education has changed and is performing a different role in undergraduate and graduate degrees. Recent changes in the educational paradigm demands a comprehensive revision of the teaching and learning methodologies. The innovation in educational contexts should reach a consensus in the way mathematical competencies are evaluated. In this Special Issue, we try 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. Fatih Yilmaz
Dr. Ion Mierlus-Mazilu
Prof. Dr. Deolinda M. L. Dias Rasteiro
Prof. Dr. Jesús Martín Vaquero
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.

Related Special Issue

Mathematics and Its Applications in Science and Engineering, 3rd Edition in Mathematics

Published Papers (12 papers)

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12 pages, 303 KiB

Open AccessFeature PaperArticle

On Hybrid Numbers with Gaussian Leonardo Coefficients

by Nagihan Kara and Fatih Yilmaz

Mathematics 2023, 11(6), 1551; https://doi.org/10.3390/math11061551 - 22 Mar 2023

Cited by 2 | Viewed by 1240

Abstract

We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid Gaussian Leonardo numbers and obtain some of their particular [...] Read more.

n n

Hessenberg matrices whose permanents yield the Leonardo and Gaussian Leonardo sequences. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

34 pages, 1565 KiB

Open AccessArticle

On the Practicality of the Analytical Solutions for all Third- and Fourth-Degree Algebraic Equations with Real Coefficients

by Mauricio Chávez-Pichardo, Miguel A. Martínez-Cruz, Alfredo Trejo-Martínez, Ana Beatriz Vega-Cruz and Tanya Arenas-Resendiz

Mathematics 2023, 11(6), 1447; https://doi.org/10.3390/math11061447 - 16 Mar 2023

Cited by 1 | Viewed by 1350

Abstract

In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that satisfies the following two conditions at the same time: (1) Its discriminant is identical to the discriminant of the general quartic equation. (2) It has at least one positive real root whenever the general quartic equation is non-biquadratic. This unique special form of the resolvent cubic is defined here as the “Standard Form of the Resolvent Cubic”, which becomes relevant since it allows us to reveal the relationship between the nature of the roots of the general quartic equation and the nature of the roots of all the forms of the resolvent cubic. Finally, this new analysis is the basis for designing and programming efficient algorithms that analytically solve all algebraic equations of the fourth and lower degree with real coefficients, always avoiding the application of complex arithmetic operations, even when these equations have non-real complex roots. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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10 pages, 258 KiB

Open AccessArticle

Submanifolds of Almost-Complex Metallic Manifolds

by Ayşe Torun and Mustafa Özkan

Mathematics 2023, 11(5), 1172; https://doi.org/10.3390/math11051172 - 27 Feb 2023

Cited by 1 | Viewed by 941

Abstract

Our paper aims to study the geometry of submanifolds of an almost-complex metallic manifold. We give an example of this type of manifold, and reveal the fundamental properties of structure induced on submanifolds. We establish subsets of submanifolds in almost-complex metallic manifolds, such [...] Read more.

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

15 pages, 289 KiB

Open AccessArticle

On Harmonic Complex Balancing Numbers

by Fatih Yılmaz, Aybüke Ertaş and Jiteng Jia

Mathematics 2023, 11(1), 210; https://doi.org/10.3390/math11010210 - 31 Dec 2022

Viewed by 1288

Abstract

In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini identity, etc. In addition, one type of symmetric matrix family whose entries are harmonic complex balancing numbers is constructed. Additionally, some linear algebraic properties are obtained. Furthermore, some inequalities are stated by exploiting the well-known inequalities between various matrix norms. Finally, we illustrate the results with some numerical examples. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

14 pages, 336 KiB

Open AccessArticle

About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals

by Ion Mierluș-Mazilu and Lucian Niță

Mathematics 2022, 10(24), 4825; https://doi.org/10.3390/math10244825 - 19 Dec 2022

Viewed by 824

Abstract

If X is a Hilbert space, one can consider the space

cabv (X)

of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich [...] Read more.

If X is a Hilbert space, one can consider the space

cabv (X)

of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm. Our first goal was to introduce a Monge–Kantorovich type norm on

cabv (X)

, where X is a Banach space, but not necessarily a Hilbert space. Thus, we introduced here the Monge–Kantorovich type norm on

cabv (L^{q} ([0, 1])), (1 < q < \infty)

. We obtained some properties of this norm and provided some examples. Then, we used the Monge–Kantorovich norm on

cabv (K^{n}) (K

being

R

C)

to obtain convergence properties for sequences of fractal sets and fractal vector measures associated to a sequence of iterated function systems. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

25 pages, 7548 KiB

Open AccessArticle

Concrelife: A Software to Solve the Chloride Penetration in Saturated and Unsaturated Reinforced Concrete

by Juan Francisco Sánchez-Pérez, Pilar Hidalgo and Francisco Alhama

Mathematics 2022, 10(24), 4810; https://doi.org/10.3390/math10244810 - 17 Dec 2022

Cited by 2 | Viewed by 1346

Abstract

This paper presents new software (Concrelife) capable of reliably simulating chloride ions penetration in reinforced concrete from different environments in the most common 1-D rectangular geometry scenarios. Its numerical solution is obtained from the simulation of models whose structure is based on Network Simulation Method. These models are generated by the program itself and run in the powerful free code NgSpice. The mathematical model of the problem includes the formation of bound chloride, precipitated chloride, reduction of porosity, saturated and unsaturated conditions, etc. All this allows tackling all kinds of scenarios, such as successive changes in concentration and temperature at the boundary, wet-drying cycles, washing of structures, etc. Concrelife has been developed with a pleasant window environment, intuitive and easy for a user not expert in numerical techniques, both for the introduction of data and for the graphic representation of the results, which include the spatial and temporal concentration of all species of chloride, porosity, water content in pores etc. To test and verify the results of the software, applications are presented to real scenarios. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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22 pages, 3510 KiB

Open AccessArticle

A Lagrange Programming Neural Network Approach with an ℓ₀-Norm Sparsity Measurement for Sparse Recovery and Its Circuit Realization

by Hao Wang, Ruibin Feng, Chi-Sing Leung, Hau Ping Chan and Anthony G. Constantinides

Mathematics 2022, 10(24), 4801; https://doi.org/10.3390/math10244801 - 16 Dec 2022

Cited by 2 | Viewed by 1068

Abstract

Many analog neural network approaches for sparse recovery were based on using

ℓ_{1}

-norm as the surrogate of

ℓ_{0}

-norm. This paper proposes an analog neural network model, namely the Lagrange programming neural network with

ℓ_{p}

objective and quadratic constraint [...] Read more.

Many analog neural network approaches for sparse recovery were based on using

ℓ_{1}

-norm as the surrogate of

ℓ_{0}

-norm. This paper proposes an analog neural network model, namely the Lagrange programming neural network with

ℓ_{p}

objective and quadratic constraint (LPNN-LPQC), with an

ℓ_{0}

-norm sparsity measurement for solving the constrained basis pursuit denoise (CBPDN) problem. As the

ℓ_{0}

-norm is non-differentiable, we first use a differentiable

ℓ_{p}

-norm-like function to approximate the

ℓ_{0}

-norm. However, this

ℓ_{p}

-norm-like function does not have an explicit expression and, thus, we use the locally competitive algorithm (LCA) concept to handle the nonexistence of the explicit expression. With the LCA approach, the dynamics are defined by the internal state vector. In the proposed model, the thresholding elements are not conventional analog elements in analog optimization. This paper also proposes a circuit realization for the thresholding elements. In the theoretical side, we prove that the equilibrium points of our proposed method satisfy Karush Kuhn Tucker (KKT) conditions of the approximated CBPDN problem, and that the equilibrium points of our proposed method are asymptotically stable. We perform a large scale simulation on various algorithms and analog models. Simulation results show that the proposed algorithm is better than or comparable to several state-of-art numerical algorithms, and that it is better than state-of-art analog neural models. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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16 pages, 4289 KiB

Open AccessArticle

A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems

by Li-Dan Hong, Cheng-Yu Ku and Chih-Yu Liu

Mathematics 2022, 10(24), 4694; https://doi.org/10.3390/math10244694 - 11 Dec 2022

Cited by 2 | Viewed by 1272

Abstract

In this study, a novel space-time (ST) marching method is presented to solve linear and nonlinear transient flow problems in porous media. The method divides the ST domain into subdomains along the time axis. The solutions are approximated using ST polyharmonic radial polynomial basis functions (RPBFs) in the ST computational domain. In order to proceed along the time axis, we use the numerical solution at the current timespan of the two ST subdomains in the computational domain as the initial conditions of the next stage. The fictitious time integration method (FTIM) is subsequently employed to solve the nonlinear equations. The novelty of the proposed method is attributed to the division of the ST domain along the time axis into subdomains such that the dense and ill-conditioned matrices caused by the excessive number of boundary and interior points and the large ST radial distances can be avoided. The results demonstrate that the proposed method achieves a high accuracy in solving linear and nonlinear transient problems. Compared to the conventional time marching and ST methods, the proposed meshless approach provides more accurate solutions and reduces error accumulation. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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19 pages, 9268 KiB

Open AccessArticle

Entropy Generation Due to Magneto-Convection of a Hybrid Nanofluid in the Presence of a Wavy Conducting Wall

by Bengisen Pekmen Geridonmez and Hakan F. Oztop

Mathematics 2022, 10(24), 4663; https://doi.org/10.3390/math10244663 - 08 Dec 2022

Cited by 3 | Viewed by 1110

Abstract

The two-dimensional, time-independent conjugate natural convection flow and entropy generation are numerically investigated in three different cases of a wavy conducting solid block attached to the left wall of a square cavity. A hybrid nanofluid with titania (TiO₂) and copper (Cu) nanoparticles and base fluid water in the fluid part is considered in the presence of a uniform inclined magnetic field. The leftmost wall of the cavity is the hot one and the rightmost one is the cold one. Radial-basis-function-based finite difference (RBF-FD) is performed on an appropriate designed grid distribution. Numerical results in view of streamlines and isotherms, as well as average Nusselt number in an interface and total entropy generation are presented. The related parameters such as Hartmann number, Rayleigh number, conductivity ratio, amplitude in wavy wall, number of waviness, and inclination angle of magnetic field are observed. Convective heat transfer in the fluid part is an increasing function of

k r, R a, γ

, while it deflates with the rise in

H a

in each case. Total entropy generation increases with the increase in

R a

and

k r

but it decreases with

H a

values. Average Bejan number ascends with the rise in

H a

and descends with the rise in

R a

. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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41 pages, 7291 KiB

Open AccessArticle

Bayesian and Frequentist Approaches for a Tractable Parametric General Class of Hazard-Based Regression Models: An Application to Oncology Data

by Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, Afrah Al-Bossly and Mahmoud El-Morshedy

Mathematics 2022, 10(20), 3813; https://doi.org/10.3390/math10203813 - 15 Oct 2022

Cited by 4 | Viewed by 2112

Abstract

In this study, we consider a general, flexible, parametric hazard-based regression model for censored lifetime data with covariates and term it the “general hazard (GH)” regression model. Some well-known models, such as the accelerated failure time (AFT), and the proportional hazard (PH) models, as well as the accelerated hazard (AH) model accounting for crossed survival curves, are sub-classes of this general hazard model. In the proposed class of hazard-based regression models, a covariate’s effect is identified as having two distinct components, namely a relative hazard ratio and a time-scale change on hazard progression. The new approach is more adaptive to modelling lifetime data and could give more accurate survival forecasts. The nested structure that includes the AFT, AH, and PH models in the general hazard model may offer a numerical tool for identifying which of them is most appropriate for a certain dataset. In this study, we propose a method for applying these various parametric hazard-based regression models that is based on a tractable parametric distribution for the baseline hazard, known as the generalized log-logistic (GLL) distribution. This distribution is closed under all the PH, AH, and AFT frameworks and can incorporate all of the basic hazard rate shapes of interest in practice, such as decreasing, constant, increasing, V-shaped, unimodal, and J-shaped hazard rates. The Bayesian and frequentist approaches were used to estimate the model parameters. Comprehensive simulation studies were used to evaluate the performance of the proposed model’s estimators and its nested structure. A right-censored cancer dataset is used to illustrate the application of the proposed approach. The proposed model performs well on both real and simulation datasets, demonstrating the importance of developing a flexible parametric general class of hazard-based regression models with both time-independent and time-dependent covariates for evaluating the hazard function and hazard ratio over time. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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32 pages, 6088 KiB

Open AccessArticle

A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

by Fei-Yan Li, Xue Li, Qi Zhang, Xiao-Ting He and Jun-Yi Sun

Mathematics 2022, 10(16), 3025; https://doi.org/10.3390/math10163025 - 22 Aug 2022

Cited by 4 | Viewed by 1342

Abstract

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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Review

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34 pages, 1942 KiB

Open AccessReview

Student Engagement with Technology-Enhanced Resources in Mathematics in Higher Education: A Review

by Caitríona Ní Shé, Eabhnat Ní Fhloinn and Ciarán Mac an Bhaird

Mathematics 2023, 11(3), 787; https://doi.org/10.3390/math11030787 - 03 Feb 2023

Cited by 4 | Viewed by 6682

Abstract

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)

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