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Volume 25, December

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Math. Comput. Appl., Volume 25, Issue 1 (March 2020) – 12 articles

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Open AccessFeature PaperArticle
Certified Motorcycle Helmets: Computational Evaluation of the Efficacy of Standard Requirements with Finite Element Models
Math. Comput. Appl. 2020, 25(1), 12; https://doi.org/10.3390/mca25010012 - 16 Feb 2020
Viewed by 165
Abstract
Every year, thousands of people die in the European Union as a direct result of road accidents. Helmets are one of the most important types of personal safety gear. The ECE R22.05 standard, adopted in 2000, is responsible for the certification of motorcycle [...] Read more.
Every year, thousands of people die in the European Union as a direct result of road accidents. Helmets are one of the most important types of personal safety gear. The ECE R22.05 standard, adopted in 2000, is responsible for the certification of motorcycle helmets in the European Union and in many other countries. Two decades later, it is still being used with the same requirements, without any update. The aim of this work is to evaluate the efficacy of a motorcycle helmet certified by such standard, using computational models as an assessment tool. First, a finite element model of a motorcycle helmet available on the market was developed and validated by simulating the same impacts required by the standard. Then, a finite element model of the human head is used as an injury prediction tool to assess its safety performance. Results indicate a significant risk of brain injury, which is in accordance with previous studies available in the literature. Therefore, this work underlines and emphasizes the need of improving the requirements of ECE R22.05. Full article
(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)
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Open AccessFeature PaperArticle
Reduced-Order Model of Rotor Cage in Multiphase Induction Machines: Application on the Prediction of Torque Pulsations
Math. Comput. Appl. 2020, 25(1), 11; https://doi.org/10.3390/mca25010011 - 29 Jan 2020
Viewed by 211
Abstract
For three-phase induction machines supplied by sinusoidal current, it is usual to model the n-bar squirrel-cage by an equivalent two-phase circuit. For a multiphase induction machine which can be supplied with different harmonics of current, the reduced-order model of the rotor must be [...] Read more.
For three-phase induction machines supplied by sinusoidal current, it is usual to model the n-bar squirrel-cage by an equivalent two-phase circuit. For a multiphase induction machine which can be supplied with different harmonics of current, the reduced-order model of the rotor must be more carefully chosen in order to predict the pulsations of torque. The proposed analysis allows to avoid a wrong design with non-sinusoidal magnetomotive forces. An analytical approach is proposed and confirmed by Finite-Element modelling at first for a three-phase induction machine and secondly for a five-phase induction machine. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Open AccessArticle
Maximal Product of Graphs under Vague Environment
Math. Comput. Appl. 2020, 25(1), 10; https://doi.org/10.3390/mca25010010 - 23 Jan 2020
Viewed by 172
Abstract
Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we [...] Read more.
Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we present a new product of graphs, namely, maximal product of two vague graphs. Then we describe certain concepts, including strongly, completely, regularity and connectedness on a maximal product of vague graphs. Further, we consider some results of edge regular and totally edge regular in a maximal product of vague graphs. Finally, we present an application for optimization of the biomass based on a maximal product of vague graphs. Full article
Open AccessArticle
Added-Mass Based Efficient Fluid–Structure Interaction Model for Dynamics of Axially Moving Panels with Thermal Expansion
Math. Comput. Appl. 2020, 25(1), 9; https://doi.org/10.3390/mca25010009 - 22 Jan 2020
Viewed by 178
Abstract
The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The [...] Read more.
The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement. Then, the panel displacement, accounting also for the fluid–structure interaction, is analyzed with the help of the weak form of the governing partial differential equation, using a Galerkin method. In the first part of this paper, we represent the traveling panel by a single partial differential equation in weak form, using an added-mass approximation of the exact fluid reaction. In the second part, we apply a Galerkin method for dynamic stability analysis of the panel, and present an analytical investigation of static stability loss (divergence, buckling) based on the added-mass model. Full article
(This article belongs to the Special Issue Coupled CFD Problems with Moving Boundaries and Interfaces)
Open AccessArticle
Spherical Fuzzy Graphs with Application to Decision-Making
Math. Comput. Appl. 2020, 25(1), 8; https://doi.org/10.3390/mca25010008 - 20 Jan 2020
Viewed by 187
Abstract
In a network model, the evaluation information given by decision makers are occasionally of types: yes, abstain, no, and refusal. To deal with such problems, we use mathematical models based on picture fuzzy sets. The spherical fuzzy model is more versatile than the [...] Read more.
In a network model, the evaluation information given by decision makers are occasionally of types: yes, abstain, no, and refusal. To deal with such problems, we use mathematical models based on picture fuzzy sets. The spherical fuzzy model is more versatile than the picture fuzzy model as it broadens the space of uncertain and vague information, due to its outstanding feature of vast space of participation of acceptable triplets. Graphs are a mathematical representation of networks. Thus to deal with many real-world phenomena represented by networks, spherical fuzzy graphs can be used to model different practical scenarios in a more flexible manner than picture fuzzy graphs. In this research article, we discuss two operations on spherical fuzzy graphs (SFGs), namely, symmetric difference and rejection; and develop some results regarding their degrees and total degrees. We describe certain concepts of irregular SFGs with several important properties. Further, we present an application of SFGs in decision making. Full article
Open AccessArticle
Evolutionary Algorithms Enhanced with Quadratic Coding and Sensing Search for Global Optimization
Math. Comput. Appl. 2020, 25(1), 7; https://doi.org/10.3390/mca25010007 - 16 Jan 2020
Viewed by 245
Abstract
Enhancing Evolutionary Algorithms (EAs) using mathematical elements significantly contribute to their development and control the randomness they are experiencing. Moreover, the automation of the primary process steps of EAs is still one of the hardest problems. Specifically, EAs still have no robust automatic [...] Read more.
Enhancing Evolutionary Algorithms (EAs) using mathematical elements significantly contribute to their development and control the randomness they are experiencing. Moreover, the automation of the primary process steps of EAs is still one of the hardest problems. Specifically, EAs still have no robust automatic termination criteria. Moreover, the highly random behavior of some evolutionary operations should be controlled, and the methods should invoke advanced learning process and elements. As follows, this research focuses on the problem of automating and controlling the search process of EAs by using sensing and mathematical mechanisms. These mechanisms can provide the search process with the needed memories and conditions to adapt to the diversification and intensification opportunities. Moreover, a new quadratic coding and quadratic search operator are invoked to increase the local search improving possibilities. The suggested quadratic search operator uses both regression and Radial Basis Function (RBF) neural network models. Two evolutionary-based methods are proposed to evaluate the performance of the suggested enhancing elements using genetic algorithms and evolution strategies. Results show that for both the regression, RBFs and quadratic techniques could help in the approximation of high-dimensional functions with the use of a few adjustable parameters for each type of function. Moreover, the automatic termination criteria could allow the search process to stop appropriately. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2019)
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Open AccessEditorial
Acknowledgement to Reviewers of MCA in 2019
Math. Comput. Appl. 2020, 25(1), 6; https://doi.org/10.3390/mca25010006 - 16 Jan 2020
Viewed by 209
Abstract
The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not[...] Full article
Open AccessFeature PaperArticle
Jacob’s Ladder: Prime Numbers in 2D
Math. Comput. Appl. 2020, 25(1), 5; https://doi.org/10.3390/mca25010005 - 11 Jan 2020
Viewed by 394
Abstract
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we [...] Read more.
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we present a simple representation of prime numbers in two dimensions that allows us to formulate a number of conjectures that may lead to important avenues in the field of research on prime numbers. In particular, although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps between them present a remarkable and intriguing property: a clear exponential decay in the frequency of gaps vs. gap size. The smaller the gaps, the more frequently they appear. Additionally, the sequence of zeroes, despite being non-consecutive numbers, contains a number of primes approximately equal to n / log n , n being the number of terms in the sequence. Full article
(This article belongs to the Section Natural Sciences)
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Open AccessArticle
Cost Efficiency Evaluation Based on a Data Envelopment Analysis Approach by Considering Undesirable Outputs on the Basis of the Semi-Disposability Assumption
Math. Comput. Appl. 2020, 25(1), 4; https://doi.org/10.3390/mca25010004 - 10 Jan 2020
Viewed by 247
Abstract
It is considerably important to calculate the cost efficiency in data envelopment analysis for the efficiency evaluation of decision-making units. The present paper develops the classical cost efficiency model in which all the input prices are constant and certain for each decision-making unit, [...] Read more.
It is considerably important to calculate the cost efficiency in data envelopment analysis for the efficiency evaluation of decision-making units. The present paper develops the classical cost efficiency model in which all the input prices are constant and certain for each decision-making unit, considering undesirable outputs under the semi-disposability assumption. The proposed models are interval and uncertain under the constant returns to scale and also variable returns to scale assumptions, for the easy solution of which, their lower and upper bounds are obtained on the basis of the theorem presented in the text. In order to simulate the proposed models and show their scientific capabilities, additionally, 56 electricity producing thermal power plants in Iran were studied in 2015. Results of the present study show that under both assumptions of constant returns to scale and variable returns to scale, the highest cost efficiency bounds belonged to the combined and steam cycle power plants. Moreover, the average of lower and upper cost efficiency bounds of the power plants under study were 34% and 35%, respectively, in 2015, under the constant returns to scale assumption, and 52% and 54%, respectively, under the variable returns to scale assumption. Full article
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Open AccessFeature PaperArticle
Non-Epsilon Dominated Evolutionary Algorithm for the Set of Approximate Solutions
Math. Comput. Appl. 2020, 25(1), 3; https://doi.org/10.3390/mca25010003 - 08 Jan 2020
Viewed by 228
Abstract
In this paper, we present a novel evolutionary algorithm for the computation of approximate solutions for multi-objective optimization problems. These solutions are of particular interest to the decision-maker as backup solutions since they can provide solutions with similar quality but in different regions [...] Read more.
In this paper, we present a novel evolutionary algorithm for the computation of approximate solutions for multi-objective optimization problems. These solutions are of particular interest to the decision-maker as backup solutions since they can provide solutions with similar quality but in different regions of the decision space. The novel algorithm uses a subpopulation approach to put pressure towards the Pareto front while exploring promissory areas for approximate solutions. Furthermore, the algorithm uses an external archiver to maintain a suitable representation in both decision and objective space. The novel algorithm is capable of computing an approximation of the set of interest with good quality in terms of the averaged Hausdorff distance. We underline the statements on some academic problems from literature and an application in non-uniform beams. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2019)
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Open AccessFeature PaperArticle
Efficient Methods to Calculate Partial Sphere Surface Areas for a Higher Resolution Finite Volume Method for Diffusion-Reaction Systems in Biological Modeling
Math. Comput. Appl. 2020, 25(1), 2; https://doi.org/10.3390/mca25010002 - 23 Dec 2019
Viewed by 316
Abstract
Computational models for multicellular biological systems, in both in vitro and in vivo environments, require solving systems of differential equations to incorporate molecular transport and their reactions such as release, uptake, or decay. Examples can be found from drugs, growth nutrients, and signaling [...] Read more.
Computational models for multicellular biological systems, in both in vitro and in vivo environments, require solving systems of differential equations to incorporate molecular transport and their reactions such as release, uptake, or decay. Examples can be found from drugs, growth nutrients, and signaling factors. The systems of differential equations frequently fall into the category of the diffusion-reaction system due to the nature of the spatial and temporal change. Due to the complexity of equations and complexity of the modeled systems, an analytical solution for the systems of the differential equations is not possible. Therefore, numerical calculation schemes are required and have been used for multicellular biological systems such as bacterial population dynamics or cancer cell dynamics. Finite volume methods in conjunction with agent-based models have been popular choices to simulate such reaction-diffusion systems. In such implementations, the reaction occurs within each finite volume and finite volumes interact with one another following the law of diffusion. The characteristic of the reaction can be determined by the agents in the finite volume. In the case of cancer cell growth dynamics, it is observed that cell behavior can be different by a matter of a few cell size distances because of the chemical gradient. Therefore, in the modeling of such systems, the spatial resolution must be comparable to the cell size. Such spatial resolution poses an extra challenge in the development and execution of the computational model due to the agents sitting over multiple finite volumes. In this article, a few computational methods for cell surface-based reaction for the finite volume method will be introduced and tested for their performance in terms of accuracy and computation speed. Full article
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Open AccessFeature PaperArticle
Numerical Optimal Control of HIV Transmission in Octave/MATLAB
Math. Comput. Appl. 2020, 25(1), 1; https://doi.org/10.3390/mca25010001 - 19 Dec 2019
Viewed by 479
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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