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) | Viewed by 25030

Special Issue Editors

Centro de Investigação em Modelação e Optimização de Sistemas Multifuncionais (CIMOSM), Instituto Superior de Engenharia de Lisboa (ISEL), Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Interests: Composite materials; Advamced composites; Numerical modeling; structural optimization; Reverse Engineering
Special Issues, Collections and Topics in MDPI journals
1. CIMOSM, ISEL—Centro de Investigação em Modelação e Optimização de Sistemas Multifuncionais, Instituto Superior de Engenharia de Lisboa, Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
2. IDMEC, IST—Instituto de Engenharia Mecânica, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal
Interests: finite element method; structural optimization; computational mechanics; symbolic computation; composite materials; functionally graded materials
Special Issues, Collections and Topics in MDPI journals

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

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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.

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Editorial

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2 pages, 211 KiB  
Editorial
Preface to Numerical and Symbolic Computation: Developments and Applications—2019
by Maria Amélia R. Loja and Joaquim I. Barbosa
Math. Comput. Appl. 2020, 25(2), 28; https://doi.org/10.3390/mca25020028 - 11 May 2020
Viewed by 1508
Abstract
This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications—2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and [...] Read more.
This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications—2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and Symbolic Computation—SYMCOMP 2019—that took place in Porto, Portugal, from April 11th to April 12th 2019 [...] Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)

Research

Jump to: Editorial

22 pages, 8799 KiB  
Article
Isogeometric Analysis for Fluid Shear Stress in Cancer Cells
by José A. Rodrigues
Math. Comput. Appl. 2020, 25(2), 19; https://doi.org/10.3390/mca25020019 - 03 Apr 2020
Cited by 4 | Viewed by 2687
Abstract
The microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. [...] Read more.
The microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. The mathematical models have the potential to elucidate the metastatic behavior of the cells’ membrane exposed to these microenvironment forces. Due to the shape configuration of the cancer cells, Non-uniform Rational B-splines (NURBS) lines are very adequate to define its geometric model. The Isogeometric Analysis allows a simplified transition of exact CAD models into the analysis avoiding the geometrical discontinuities of the traditional Galerkin traditional techniques. In this work, we use an isogeometric analysis to model the fluid-generated forces that tumor cells are exposed to in the vascular and tumor microenvironments, in the metastatic process. Using information provided by experimental tests in vitro, we present a suite of numerical experiments which indicate, for standard configurations, the metastatic behavior of cells exposed to such forces. The focus of this paper is strictly on geometrical sensitivities to the shear stress’ exhibition for the cell membrane, this being its innovation. Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)
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20 pages, 1036 KiB  
Article
Numerical Optimal Control of HIV Transmission in Octave/MATLAB
by Carlos Campos, Cristiana J. Silva and Delfim F. M. Torres
Math. Comput. Appl. 2020, 25(1), 1; https://doi.org/10.3390/mca25010001 - 19 Dec 2019
Cited by 15 | Viewed by 5350
Abstract
We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on [...] Read more.
We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article. Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)
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31 pages, 5367 KiB  
Article
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 5487
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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12 pages, 385 KiB  
Article
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 1820
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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10 pages, 858 KiB  
Article
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 1971
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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14 pages, 323 KiB  
Article
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 1673
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)
17 pages, 1597 KiB  
Article
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 3838
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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