Mathematics

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18 pages, 1910 KiB

Open AccessArticle

Compartmental Learning versus Joint Learning in Engineering Education

by María Jesús Santos, Alejandro Medina, José Miguel Mateos Roco and Araceli Queiruga-Dios

Mathematics 2021, 9(6), 662; https://doi.org/10.3390/math9060662 - 20 Mar 2021

Cited by 2 | Viewed by 3128

Sophomore students from the Chemical Engineering undergraduate Degree at the University of Salamanca are involved in a Mathematics course during the third semester and in an Engineering Thermodynamics course during the fourth one. When they participate in the latter they are already familiar [...] Read more.

Sophomore students from the Chemical Engineering undergraduate Degree at the University of Salamanca are involved in a Mathematics course during the third semester and in an Engineering Thermodynamics course during the fourth one. When they participate in the latter they are already familiar with mathematical software and mathematical concepts about numerical methods, including non-linear equations, interpolation or differential equations. We have focused this study on the way engineering students learn Mathematics and Engineering Thermodynamics. As students use to learn each matter separately and do not associate Mathematics and Physics, they separate each matter into different and independent compartments. We have proposed an experience to increase the interrelationship between different subjects, to promote transversal skills, and to make the subjects closer to real work. The satisfactory results of the experience are exposed in this work. Moreover, we have analyzed the results obtained in both courses during the academic year 2018–2019. We found that there is a relation between both courses and student’s final marks do not depend on the course. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

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15 pages, 290 KiB

Open AccessArticle

One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms

by Seda Yamaç Akbiyik, Mücahit Akbiyik and Fatih Yilmaz

Mathematics 2021, 9(5), 539; https://doi.org/10.3390/math9050539 - 4 Mar 2021

Cited by 6 | Viewed by 2018

Abstract

The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are [...] Read more.

The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell numbers and its Hadamard exponential matrix. We investigate some linear algebraic properties and obtain inequalities by using matrix norms. Furthermore, some summation identities for harmonic Pell numbers are obtained. Finally, we give a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

18 pages, 3380 KiB

Open AccessArticle

Differential and Integral Calculus in First-Year Engineering Students: A Diagnosis to Understand the Failure

by Maria Emília Bigotte de Almeida, Araceli Queiruga-Dios and María José Cáceres

Mathematics 2021, 9(1), 61; https://doi.org/10.3390/math9010061 - 29 Dec 2020

Cited by 18 | Viewed by 7615

Abstract

Difficulties in the curricular units (CU) of the mathematical science area, particularly those related to differential and integral calculus (DIC), are often found among students of engineering degrees, leading to high failure rates. A research work was developed with the objective of finding [...] Read more.

Difficulties in the curricular units (CU) of the mathematical science area, particularly those related to differential and integral calculus (DIC), are often found among students of engineering degrees, leading to high failure rates. A research work was developed with the objective of finding the reasons that lead the students to fail in the CU of DIC (CU-DIC) taught in the 1st year of the engineering undergraduate degrees at the Coimbra Engineering Institute (ISEC), in Portugal. Applying a case study methodology, this article will present a current diagnosis with the objective to establish relationships between teaching methods and students’ learning strategies, and besides, we propose to build learning environments that lead to higher success. The analysis of collected data allows us to conclude that the CU-DIC in the ISEC maintain an identical distribution in the hourly load in several engineering degrees, where contents are adjusted to each context taking into account the CUs of each degree. The data analysis found better results in the academic year that includes two examination moments without any relationship between class attendance, dropout and pass rates. We propose some different teaching/learning strategies in CU-DIC and new learning environments that enhance freshmen students’ engagement and participation in their own learning process. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

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15 pages, 243 KiB

Open AccessArticle

A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients

by Emel Karaca, Fatih Yılmaz and Mustafa Çalışkan

Mathematics 2020, 8(12), 2149; https://doi.org/10.3390/math8122149 - 2 Dec 2020

Cited by 4 | Viewed by 2610

Abstract

This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two quaternions. Taking into account some results obtained [...] Read more.

This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two quaternions. Taking into account some results obtained by Karaca, E. et al., 2020, each of these quaternions is studied and some important differences are remarked on. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

10 pages, 247 KiB

Open AccessArticle

Fixed Point Results of Expansive Mappings in Metric Spaces

by Seher Sultan Yeşilkaya and Cafer Aydın

Mathematics 2020, 8(10), 1800; https://doi.org/10.3390/math8101800 - 16 Oct 2020

Cited by 4 | Viewed by 2478

Abstract

In this study, we introduce the concept of

θ

-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for

θ

-expansive mapping in metric spaces and prove fixed point theorems for [...] Read more.

In this study, we introduce the concept of

θ

-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for

θ

-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

13 pages, 265 KiB

Open AccessArticle

Several Theorems on Single and Set-Valued Prešić Type Mappings

by Seher Sultan Yeşilkaya and Cafer Aydın

Mathematics 2020, 8(9), 1616; https://doi.org/10.3390/math8091616 - 18 Sep 2020

Cited by 2 | Viewed by 2199

Abstract

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show [...] Read more.

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

13 pages, 257 KiB

Open AccessArticle

Generalized Quasi-Einstein Manifolds in Contact Geometry

by İnan Ünal

Mathematics 2020, 8(9), 1592; https://doi.org/10.3390/math8091592 - 16 Sep 2020

Cited by 4 | Viewed by 2568

Abstract

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It [...] Read more.

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to

M

-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold

S^{2 n + 1} (1) \times S^{1}

. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

8 pages, 517 KiB

Open AccessArticle

Modelling Tap Water Consumer Ratio

by Meltem Ekiz and Osman Ufuk Ekiz

Mathematics 2020, 8(9), 1557; https://doi.org/10.3390/math8091557 - 10 Sep 2020

Cited by 1 | Viewed by 1904

Abstract

Increasing population and the rising air temperatures are known as factors that cause water depletion in the watersheds. Therefore, it is important to accurately predict the future ratios of tap water consumers using the same watershed to the population living in the specified [...] Read more.

Increasing population and the rising air temperatures are known as factors that cause water depletion in the watersheds. Therefore, it is important to accurately predict the future ratios of tap water consumers using the same watershed to the population living in the specified area, to produce better water policies and to take the necessary measures. Predictions can be made by a growth curve model (GCM). Parameter estimations of the GCM are usually based on the ordinary least square (OLS) estimator. However, the outlier presence affects the estimations and the predictions, which are obtained by using the estimated model. The present article attempts to construct first- and third-order GCMs with robust least median square (LMS) and M estimators to make short-term predictions of ratios of tap water consumers. According to the findings, parameter estimations of the models, the outliers, and the predictions vary with respect to the estimators. The M estimator for short-term predictions is suggested for use, due to its robustness against outlier points. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

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