Special Issue "Numerical and Symbolic Computation: Developments and Applications"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (30 September 2019).

Special Issue Editors

Dr. Maria Amélia Ramos Loja
E-Mail Website
Guest Editor
Grupo de Investigação em Modelação e Optimização de Sistemas Multifuncionais (GI-MOSM), Instituto Superior de Engenharia de Lisboa (ISEL), Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Interests: numerical modeling and simulation of composite structures and functionally gradient materials; control of behavior of structures; stochastic optimization of structures; reconstruction of 3D / solids surfaces
Prof. Dr. Joaquim Infante Barbosa
E-Mail Website
Guest Editor
Grupo de Investigação em Modelação e Optimização de Sistemas Multifuncionais (GI-MOSM), Instituto Superior de Engenharia de Lisboa (ISEL), Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Interests: structural optimization; composite materials

Special Issue Information

Dear Colleagues,

This Special Issue will mainly consist of selected papers presented at the "4th International Conference on Numerical and Symbolic Computation: Developments and Applications" (http://symcomp2019.dem.isel.pt/). Papers considered to fit the scope of the journal and of sufficient quality, after evaluation by the reviewers, will be published free of charge.

Dr. Maria Amélia Ramos Loja
Prof. Dr. Joaquim Infante Barbosa
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 papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access quarterly 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 1000 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.

Published Papers (5 papers)

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Research

Open AccessArticle
Factors for Marketing Innovation in Portuguese Firms CIS 2014
Math. Comput. Appl. 2019, 24(4), 99; https://doi.org/10.3390/mca24040099 - 22 Nov 2019
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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Open AccessArticle
Almost Exact Computation of Eigenvalues in Approximate Differential Problems
Math. Comput. Appl. 2019, 24(4), 96; https://doi.org/10.3390/mca24040096 - 14 Nov 2019
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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Open AccessArticle
Solving Nonholonomic Systems with the Tau Method
Math. Comput. Appl. 2019, 24(4), 91; https://doi.org/10.3390/mca24040091 - 19 Oct 2019
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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Open AccessArticle
The Invariant Two-Parameter Function of Algebras ψ
Math. Comput. Appl. 2019, 24(4), 89; https://doi.org/10.3390/mca24040089 - 14 Oct 2019
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 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)
Open AccessArticle
Bridging Symbolic Computation and Economics: A Dynamic and Interactive Tool to Analyze the Price Elasticity of Supply
Math. Comput. Appl. 2019, 24(4), 87; https://doi.org/10.3390/mca24040087 - 10 Oct 2019
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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