Mathematical and Computational Applications

19 pages, 1272 KiB

Open AccessArticle

Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach

by Kalyan Das, M. N. Srinivas and Nurul Huda Gazi

Math. Comput. Appl. 2019, 24(4), 103; https://doi.org/10.3390/mca24040103 - 17 Dec 2019

Cited by 1 | Viewed by 1893

The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator–prey system. The predator dependence is one of the main concerns of the system. The stability analysis of this 2-dimensional map was carried out analytically. Numerical simulation was carried out to verify [...] Read more.

The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator–prey system. The predator dependence is one of the main concerns of the system. The stability analysis of this 2-dimensional map was carried out analytically. Numerical simulation was carried out to verify the analytical results. We analyzed some specific features that could arise in discrete system. Basin of attraction was found for the endemic equilibrium state. We extended the numerical simulation for the maximal Lyapunov exponent. The presence of positive Lyapunov exponent indicated chaotic behavior of the map. The sensitive dependence on initial condition is one of the criteria for a discrete system. We showed that the system is sensitive on the initial conditions. We also carried out the analysis of diffusion and impact of noise. Full article

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34 pages, 1279 KiB

Open AccessArticle

Decision Making Approach under Pythagorean Dombi Fuzzy Graphs for Selection of Leading Textile Industry

by Muhammad Akram, Jawaria Mohsan Dar and Sundas Shahzadi

Math. Comput. Appl. 2019, 24(4), 102; https://doi.org/10.3390/mca24040102 - 13 Dec 2019

Cited by 2 | Viewed by 2126

Abstract

Graphs play a pivotal role in structuring real-world scenarios such as network security and expert systems. Numerous extensions of graph theoretical conceptions have been established for modeling uncertainty in graphical network situations. The Pythagorean Dombi fuzzy graph (PDFG), a generalization of the fuzzy [...] Read more.

Graphs play a pivotal role in structuring real-world scenarios such as network security and expert systems. Numerous extensions of graph theoretical conceptions have been established for modeling uncertainty in graphical network situations. The Pythagorean Dombi fuzzy graph (PDFG), a generalization of the fuzzy Dombi graph (FDG), is very useful in representing vague relations between several objects, whereas the operational parameter has a flexible nature in decision-making problems. The main objective of this research study is to expand the area of discussion on PDFGs by establishing fruitful results and notions related to operations such as the direct product, Cartesian product, semi-strong product, strong product, and composition on PDFGs. Certain concepts, including the degree of vertices and total degree, are discussed as its modifications. Meanwhile, these outcomes are considered on PDFGs maintaining the strongness property. At the end, an algorithm for Pythagorean Dombi fuzzy multi-criteria decision-making is given, and a numerical example based on the selection of a leading textile industry is put forward to clarify the suitability of the proposed approach. Full article

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18 pages, 3249 KiB

Open AccessFeature PaperArticle

Meshless Local Petrov–Galerkin Formulation of Inverse Stefan Problem via Moving Least Squares Approximation

by A. Karami, Saeid Abbasbandy and E. Shivanian

Math. Comput. Appl. 2019, 24(4), 101; https://doi.org/10.3390/mca24040101 - 10 Dec 2019

Cited by 4 | Viewed by 2234

Abstract

In this paper, we study the meshless local Petrov–Galerkin (MLPG) method based on the moving least squares (MLS) approximation for finding a numerical solution to the Stefan free boundary problem. Approximation of this problem, due to the moving boundary, is difficult. To overcome [...] Read more.

In this paper, we study the meshless local Petrov–Galerkin (MLPG) method based on the moving least squares (MLS) approximation for finding a numerical solution to the Stefan free boundary problem. Approximation of this problem, due to the moving boundary, is difficult. To overcome this difficulty, the problem is converted to a fixed boundary problem in which it consists of an inverse and nonlinear problem. In other words, the aim is to determine the temperature distribution and free boundary. The MLPG method using the MLS approximation is formulated to produce the shape functions. The MLS approximation plays an important role in the convergence and stability of the method. Heaviside step function is used as the test function in each local quadrature. For the interior nodes, a meshless Galerkin weak form is used while the meshless collocation method is applied to the the boundary nodes. Since MLPG is a truly meshless method, it does not require any background integration cells. In fact, all integrations are performed locally over small sub-domains (local quadrature domains) of regular shapes, such as intervals in one dimension, circles or squares in two dimensions and spheres or cubes in three dimensions. A two-step time discretization method is used to deal with the time derivatives. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments. Full article

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21 pages, 926 KiB

Open AccessArticle

Hypergraphs Based on Pythagorean Fuzzy Soft Model

by Gulfam Shahzadi and Muhammad Akram

Math. Comput. Appl. 2019, 24(4), 100; https://doi.org/10.3390/mca24040100 - 23 Nov 2019

Cited by 8 | Viewed by 1973

Abstract

A Pythagorean fuzzy soft set (PFSS) model is an extension of an intuitionistic fuzzy soft set (IFSS) model to deal with vague knowledge according to different parameters. The PFSS model is a more powerful tool for expressing uncertain information when making decisions and [...] Read more.

A Pythagorean fuzzy soft set (PFSS) model is an extension of an intuitionistic fuzzy soft set (IFSS) model to deal with vague knowledge according to different parameters. The PFSS model is a more powerful tool for expressing uncertain information when making decisions and it relaxes the constraint of IFSS. Hypergraphs are helpful to handle the complex relationships among objects. Here, we apply the concept of PFSSs to hypergraphs, and present the notion of Pythagorean fuzzy soft hypergraphs (PFSHs). Further, we illustrate some operations on PFSHs. Moreover, we describe the regular PFSHs, perfectly regular PFSHs and perfectly irregular PFSHs. Finally, we consider the application of PFSHs for the selection of a team of workers for business and got the appropriate result by using score function. Full article

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31 pages, 5367 KiB

Open AccessArticle

Factors for Marketing Innovation in Portuguese Firms CIS 2014

by Patrícia Monteiro, Aldina Correia and Vítor Braga

Math. Comput. Appl. 2019, 24(4), 99; https://doi.org/10.3390/mca24040099 - 22 Nov 2019

Cited by 4 | Viewed by 5615

Abstract

Globalization, radical and frequent changes as well as the increasing importance of applying knowledge through the efficient implementation of innovation is critical under the current circumstances. Innovation has been the source of businesses competitive advantage, but it is not restricted to technological innovations, [...] Read more.

Globalization, radical and frequent changes as well as the increasing importance of applying knowledge through the efficient implementation of innovation is critical under the current circumstances. Innovation has been the source of businesses competitive advantage, but it is not restricted to technological innovations, and thus marketing innovation also plays a central role. This is a significant topic in the marketing field and not yet deeply analysed in academic research. The main objective of this study is to understand what factors influence marketing innovation and to establish a business profile of firms that innovate or do not in marketing. We used multivariate statistical techniques, such as, multiple linear regression (with the Marketing Innovation Index as dependent variable) and discriminant analysis where the dependent variable is a dummy variable indicating if the firm innovates or not in marketing. The results suggest that there are several factors explaining marketing innovation, although in this study, we find that the factors contributing the most for marketing innovation are: the Organizational Innovation Index, customer and/or user suggestions, and intellectual property rights and licensing (IPRL). Most of the literature has studied these factors separately. This research studied such factors together, and it is clear that both organizational innovation and IPRL play an important role that drives firms to innovate in marketing, which differs from some literature; customer suggestions help in the process of marketing innovation, as some authors argue that customers do not always know what they want until they have it. In parallel, this study proved to be useful in understanding that the different values for the Marketing Innovation Index display no influence on the results, since they were equivalent when a dummy variable (innovated/not innovated in marketing) was used as a dependent variable. In practice, we realize that the factors are useful to clarify what Portuguese firms innovate or not in marketing, with no different results when we the four marketing innovation levels (design, distribution, advertising and price) are considered. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

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20 pages, 9575 KiB

Open AccessArticle

Less Is Enough: Assessment of the Random Sampling Method for the Analysis of Magnetoencephalography (MEG) Data

by Cristina Campi, Annalisa Pascarella and Francesca Pitolli

Math. Comput. Appl. 2019, 24(4), 98; https://doi.org/10.3390/mca24040098 - 19 Nov 2019

Cited by 1 | Viewed by 2051

Abstract

Magnetoencephalography (MEG) aims at reconstructing the unknown neuroelectric activity in the brain from non-invasive measurements of the magnetic field induced by neural sources. The solution of this ill-posed, ill-conditioned inverse problem is usually dealt with using regularization techniques that are often time-consuming, and [...] Read more.

Magnetoencephalography (MEG) aims at reconstructing the unknown neuroelectric activity in the brain from non-invasive measurements of the magnetic field induced by neural sources. The solution of this ill-posed, ill-conditioned inverse problem is usually dealt with using regularization techniques that are often time-consuming, and computationally and memory storage demanding. In this paper we analyze how a slimmer procedure, random sampling, affects the estimation of the brain activity generated by both synthetic and real sources. Full article

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13 pages, 856 KiB

Open AccessFeature PaperArticle

Optimizing the Maximal Perturbation in Point Sets while Preserving the Order Type

by Luis Gerardo de la Fraga and Heriberto Cruz Hernández

Math. Comput. Appl. 2019, 24(4), 97; https://doi.org/10.3390/mca24040097 - 16 Nov 2019

Viewed by 2228

Abstract

Recently a new kind of fiducial marker based on order type (OT) has been proposed. Using OT one can unequivocally identify a set of points through its triples of point orientation, and therefore, there is no need to use metric information. These proposed [...] Read more.

Recently a new kind of fiducial marker based on order type (OT) has been proposed. Using OT one can unequivocally identify a set of points through its triples of point orientation, and therefore, there is no need to use metric information. These proposed order type tags (OTTs) are invariant under a projective transformation which allows identification of them directly from a photograph. The magnitude of noise in the point positions that a set of points can support without changing its OT, is named the maximal perturbation (MP) value. This value represents the maximal displacement that any point in the set can have in any direction without changing the triplet’s orientation in the set. A higher value of the MP makes an OTT instance more robust to perturbations in the points positions. In this paper, we address the problem of how to improve the MP value for sets of points. We optimize “by hand” the MP for all the 16 subsets of points in the set of OTs composed of six points, and we also propose a general algorithm to optimize all the sets of OTs composed of six, seven, and eight points. Finally, we show several OTTs with improved MP values, and their use in an augmented reality application. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2019)

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12 pages, 385 KiB

Open AccessArticle

Almost Exact Computation of Eigenvalues in Approximate Differential Problems

by José M. A. Matos and Maria João Rodrigues

Math. Comput. Appl. 2019, 24(4), 96; https://doi.org/10.3390/mca24040096 - 14 Nov 2019

Cited by 2 | Viewed by 1879

Abstract

Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab [...] Read more.

Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab toolbox was recently presented and here we explore its potential use and suitability for this problem. The first step is to translate the eigenvalue differential problem into an algebraic approximated eigenvalues problem. In a second step, making use of symbolic computations, we arrive at the exact polynomial expression of the determinant of the algebraic problem matrix, allowing us to get high accuracy approximations of differential eigenvalues. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

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2 pages, 196 KiB

Open AccessCorrection

Correction: Kunc, O.; Fritzen, F. Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling. Math. Comput. Appl. 2019, 24, 56

by Oliver Kunc and Felix Fritzen

Math. Comput. Appl. 2019, 24(4), 95; https://doi.org/10.3390/mca24040095 - 06 Nov 2019

Cited by 1 | Viewed by 1584

Abstract

The authors wish to make a correction to Formula (42) of the paper [...] Full article

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)

25 pages, 3145 KiB

Open AccessFeature PaperArticle

A Continuation Procedure for the Quasi-Static Analysis of Materially and Geometrically Nonlinear Structural Problems

by Davide Bellora and Riccardo Vescovini

Math. Comput. Appl. 2019, 24(4), 94; https://doi.org/10.3390/mca24040094 - 02 Nov 2019

Cited by 1 | Viewed by 2437

Abstract

Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material [...] Read more.

Discussed is the implementation of a continuation technique for the analysis of nonlinear structural problems, which is capable of accounting for geometric and dissipative requirements. The strategy can be applied for solving quasi-static problems, where nonlinearities can be due to geometric or material response. The main advantage of the proposed approach relies in its robustness, which can be exploited for tracing the equilibrium paths for problems characterized by complex responses involving the onset and propagation of cracks. A set of examples is presented and discussed. For problems involving combined material and geometric nonlinearties, the results illustrate the advantages of the proposed hybrid continuation technique in terms of efficiency and robustness. Specifically, less iterations are usually required with respect to similar procedures based on purely geometric constraints. Furthermore, bifurcation plots can be easily traced, furnishing the analyst a powerful tool for investigating the nonlinear response of the structure at hand. Full article

(This article belongs to the Special Issue Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications)

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14 pages, 573 KiB

Open AccessArticle

A New Approach to Non-Singular Plane Cracks Theory in Gradient Elasticity

by Sergey A. Lurie, Dmitriy B. Volkov-Bogorodsky and Valery V. Vasiliev

Math. Comput. Appl. 2019, 24(4), 93; https://doi.org/10.3390/mca24040093 - 26 Oct 2019

Cited by 7 | Viewed by 2113

Abstract

A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the function on the right [...] Read more.

A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the function on the right side of the Helmholtz equation is a singular classical solution. An assertion is proved that allows us to propose a new solution for displacements and stresses at the crack tip through the vector harmonic potential, which determines by the Papkovich-Neuber representation. One of the goals of this work is a definition of a new representation of the solution of the plane problem of the theory of elasticity through the complex-valued harmonic potentials included in the Papkovich-Neuber relations represented in a symmetric form, which is convenient for applications. It is shown here that this new representation of the solution for the mechanics of cracks can be written through one harmonic complex-valued potential. The explicit potential value is found by comparing the new solution with the classical representation of the singular solution at the crack tip constructed using the complex potentials of Kolosov-Muskhelishvili. A generalized solution of the singular problem of fracture mechanics is reduced to a non-singular stress concentration problem, which allows one to implement a new concept of non-singular fracture mechanics, where the scale parameter along with ultimate stresses determines the fracture criterion and is determined by experiments. Full article

(This article belongs to the Special Issue Related Problems of Continuum Mechanics)

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14 pages, 1009 KiB

Open AccessArticle

Privacy-Preserved Approximate Classification Based on Homomorphic Encryption

by Xiaodong Xiao, Ting Wu, Yuanfang Chen and Xingyue Fan

Math. Comput. Appl. 2019, 24(4), 92; https://doi.org/10.3390/mca24040092 - 26 Oct 2019

Cited by 3 | Viewed by 2619

Abstract

Privacy is a crucial issue for outsourcing computation, which means that clients utilize cloud infrastructure to perform online prediction without disclosing sensitive information. Homomorphic encryption (HE) is one of the promising cryptographic tools resolving privacy issue in this scenario. However, a bottleneck in [...] Read more.

Privacy is a crucial issue for outsourcing computation, which means that clients utilize cloud infrastructure to perform online prediction without disclosing sensitive information. Homomorphic encryption (HE) is one of the promising cryptographic tools resolving privacy issue in this scenario. However, a bottleneck in application of HE is relatively high computational overhead. In this paper, we study the privacy-preserving classification problem. To this end, we propose a novel privacy-preserved approximate classification algorithm. It exploits a set of decision trees to reduce computational complexity during homomorphic evaluation computation formula, the time complexity of evaluating a polynomial is degraded from

O (n)

to

O (log n)

. As a result, for an MNIST dataset, the Micro-

f 1

score of the proposed algorithm is

0.882

, compared with

0.912

of the standard method. For the Credit dataset, the algorithm achieves

0.601

compared with

0.613

of the method. These results show that our algorithm is feasible and practical in real world problems. Full article

(This article belongs to the Section Engineering)

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10 pages, 858 KiB

Open AccessArticle

Solving Nonholonomic Systems with the Tau Method

by Alexandra Gavina, José M. A. Matos and Paulo B. Vasconcelos

Math. Comput. Appl. 2019, 24(4), 91; https://doi.org/10.3390/mca24040091 - 19 Oct 2019

Cited by 2 | Viewed by 2053

Abstract

A numerical procedure based on the spectral Tau method to solve nonholonomic systems is provided. Nonholonomic systems are characterized as systems with constraints imposed on the motion. The dynamics is described by a system of differential equations involving control functions and several problems [...] Read more.

A numerical procedure based on the spectral Tau method to solve nonholonomic systems is provided. Nonholonomic systems are characterized as systems with constraints imposed on the motion. The dynamics is described by a system of differential equations involving control functions and several problems that arise from nonholonomic systems can be formulated as optimal control problems. Applying the Pontryagins maximum principle, the necessary optimality conditions along with the transversality condition, a boundary value problem is obtained. Finally, a numerical approach to tackle the boundary value problem is required. Here we propose the Lanczos spectral Tau method to obtain an approximate solution of these problems exploiting the Tau toolbox software library, which allows for ease of use as well as accurate results. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

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15 pages, 10871 KiB

Open AccessArticle

Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

by Wojciech Śmiechowicz, Théo Loup and Paweł Olejnik

Math. Comput. Appl. 2019, 24(4), 90; https://doi.org/10.3390/mca24040090 - 16 Oct 2019

Cited by 8 | Viewed by 2632

Abstract

This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined [...] Read more.

This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Full article

(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)

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14 pages, 323 KiB

Open AccessArticle

The Invariant Two-Parameter Function of Algebras ψ

by José María Escobar, Juan Núñez-Valdés and Pedro Pérez-Fernández

Math. Comput. Appl. 2019, 24(4), 89; https://doi.org/10.3390/mca24040089 - 14 Oct 2019

Cited by 1 | Viewed by 1729

Abstract

At present, the research on invariant functions for algebras is very extended since Hrivnák and Novotný defined in 2007 the invariant functions

ψ

and

φ

as a tool to study the Inönü–Wigner contractions (IW-contractions), previously introduced by those authors in 1953. In this [...] Read more.

At present, the research on invariant functions for algebras is very extended since Hrivnák and Novotný defined in 2007 the invariant functions

ψ

and

φ

as a tool to study the Inönü–Wigner contractions (IW-contractions), previously introduced by those authors in 1953. In this paper, we introduce a new invariant two-parameter function of algebras, which we call

\bar{ψ},

as a tool which makes easier the computations and allows researchers to deal with contractions of algebras. Our study of this new function is mainly focused in Malcev algebras of the type Lie, although it can also be used with any other types of algebras. The main goal of the paper is to prove, by means of this function, that the five-dimensional classical-mechanical model built upon certain types of five-dimensional Lie algebras cannot be obtained as a limit process of a quantum-mechanical model based on a fifth Heisenberg algebra. As an example of other applications of the new function obtained, its computation in the case of the Lie algebra induced by the Lorentz group

S O (3, 1)

is shown and some open physical problems related to contractions are also formulated. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

15 pages, 556 KiB

Open AccessFeature PaperArticle

Uniqueness of Closed Equilibrium Hypersurfaces for Anisotropic Surface Energy and Application to a Capillary Problem

by Miyuki Koiso

Math. Comput. Appl. 2019, 24(4), 88; https://doi.org/10.3390/mca24040088 - 10 Oct 2019

Cited by 3 | Viewed by 2125

Abstract

We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was introduced to model the [...] Read more.

We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was introduced to model the surface tension of a small crystal. The purpose of this paper is two-fold. First, we give uniqueness and nonuniqueness results for closed equilibria under weaker assumptions on the regularity of both considered hypersurfaces and the anisotropic surface energy density than previous works and apply the results to the anisotropic mean curvature flow. This part is an announcement of two forthcoming papers by the author. Second, we give a new uniqueness result for stable anisotropic capillary surfaces in a wedge in the three-dimensional Euclidean space. Full article

(This article belongs to the Special Issue Related Problems of Continuum Mechanics)

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17 pages, 1597 KiB

Open AccessArticle

Bridging Symbolic Computation and Economics: A Dynamic and Interactive Tool to Analyze the Price Elasticity of Supply

by Jorge M. Andraz, Renato Candeias and Ana C. Conceição

Math. Comput. Appl. 2019, 24(4), 87; https://doi.org/10.3390/mca24040087 - 10 Oct 2019

Cited by 2 | Viewed by 3921

Abstract

It is not possible to achieve the objectives and skills of a program in economics, at the secondary and undergraduate levels, without resorting to graphic illustrations. In this way, the use of educational software has been increasingly recognized as a useful tool to [...] Read more.

It is not possible to achieve the objectives and skills of a program in economics, at the secondary and undergraduate levels, without resorting to graphic illustrations. In this way, the use of educational software has been increasingly recognized as a useful tool to promote students’ motivation to deal with, and understand, new economic concepts. Current digital technology allows students to work with a large number and variety of graphics in an interactive way, complementing the theoretical results and the so often used paper and pencil calculations. The computer algebra system Mathematica is a very powerful software that allows the implementation of many interactive visual applications. Thanks to the symbolic and numerical capabilities of Mathematica, these applications allow the user to interact with the graphical and analytical information in real time. However, Mathematica is a commercially distributed application which makes it difficult for teachers and students to access. The main goal of this paper is to present a new dynamic and interactive tool, created with Mathematica and available in the Computable Document Format. This format allows anyone with a computer to use, at no cost, the PES(Linear)-Tool, even without an active Wolfram Mathematica license. The PES(Linear)-Tool can be used as an active learning tool to promote better student activity and engagement in the learning process, among students enrolled in socio-economic programs. This tool is very intuitive to use which makes it suitable for less experienced users. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

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14 pages, 2286 KiB

Open AccessArticle

Adaptive Control of Resistance Spot Welding Based on a Dynamic Resistance Model

by Ziyad Kas and Manohar Das

Math. Comput. Appl. 2019, 24(4), 86; https://doi.org/10.3390/mca24040086 - 28 Sep 2019

Cited by 4 | Viewed by 4314

Abstract

Resistance spot welding is a process commonly used for joining a stack of two or three metal sheets at desired spots. Such welds are accomplished by holding the metallic workpieces together by applying pressure through the tips of a pair of electrodes and [...] Read more.

Resistance spot welding is a process commonly used for joining a stack of two or three metal sheets at desired spots. Such welds are accomplished by holding the metallic workpieces together by applying pressure through the tips of a pair of electrodes and then passing a strong electric current for a short duration. This kind of welding process often suffers from two common drawbacks, namely, inconsistent weld quality and inadequate nugget size. In order to address these problems, a new theoretical approach of controlling resistance spot welding processes is proposed in this paper. The proposed controller is based on a simplified dynamical model of the resistance spot welding process and employs the principle of adaptive one-step-ahead control. It is essentially an adaptive tracking controller that estimates the unknown process parameters and adjusts the welding voltage continuously to make sure that the nugget resistance tracks a desired reference resistance profile. The modeling and controller design methodologies are discussed in detail. Also, the results of a simulation study to evaluate the performance of the proposed controller are presented. The proposed control scheme is expected to reduce energy consumption and produce consistent welds. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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16 pages, 1104 KiB

Open AccessArticle

Light Robust Goal Programming

by Emmanuel Kwasi Mensah and Matteo Rocca

Math. Comput. Appl. 2019, 24(4), 85; https://doi.org/10.3390/mca24040085 - 28 Sep 2019

Cited by 3 | Viewed by 2349

Abstract

Robust goal programming (RGP) is an emerging field of research in decision-making problems with multiple conflicting objectives and uncertain parameters. RGP combines robust optimization (RO) with variants of goal programming techniques to achieve stable and reliable goals for previously unspecified aspiration levels of [...] Read more.

Robust goal programming (RGP) is an emerging field of research in decision-making problems with multiple conflicting objectives and uncertain parameters. RGP combines robust optimization (RO) with variants of goal programming techniques to achieve stable and reliable goals for previously unspecified aspiration levels of the decision-maker. The RGP model proposed in Kuchta (2004) and recently advanced in Hanks, Weir, and Lunday (2017) uses classical robust methods. The drawback of these methods is that they can produce optimal values far from the optimal value of the “nominal” problem. As a proposal for overcoming the aforementioned drawback, we propose light RGP models generalized for the budget of uncertainty and ellipsoidal uncertainty sets in the framework discussed in Schöbel (2014) and compare them with the previous RGP models. Conclusions regarding the use of different uncertainty sets for the light RGP are made. Most importantly, we discuss that the total goal deviations of the decision-maker are very much dependent on the threshold set rather than the type of uncertainty set used. Full article

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Math. Comput. Appl., Volume 24, Issue 4 (December 2019) – 19 articles

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