Mathematical and Computational Applications doi: 10.3390/mca25020030

Authors: Aline Hosry Roger Nakad Sachin Bhalekar

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing the efficiency and validity of the method that we introduce.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020029

Authors: Adair Nagimova Jaeger

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton&rsquo;s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020028

Authors: Maria Amélia R. Loja Joaquim I. Barbosa

This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications&mdash;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&mdash;SYMCOMP 2019&mdash;that took place in Porto, Portugal, from April 11th to April 12th 2019 [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25020027

Authors: Aliyu Muhammed Awwal Lin Wang Poom Kumam Hassan Mohammad Wiboonsak Watthayu

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve ℓ 1 -norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020026

Authors: Muhammad Akram Shumaiza José Alcantud

The Analytical Hierarchy Process (AHP) is arguably the most popular and factual approach for computing the weights of attributes in the multi-attribute decision-making environment. The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking family of multi-criteria decision-making techniques for evaluating a finite set of alternatives, that relies on multiple and inconsistent criteria. One of its main advantages is the variety of admissible preference functions that can measure the differences between alternatives, in response to the type and nature of the criteria. This research article studies a version of the PROMETHEE technique that encompasses multipolar assessments of the performance of each alternative (relative to the relevant criteria). As is standard practice, first we resort to the AHP technique in order to quantify the normalized weights of the attributes by the pairwise comparison of criteria. Afterwards the m-polar fuzzy PROMETHEE approach is used to rank the alternatives on the basis of conflicting criteria. Six types of generalized criteria preference functions are used to measure the differences or deviations of every pair of alternatives. A partial ranking of alternatives arises by computing the positive and negative outranking flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ranking of alternatives is achieved by the inspection of the net flow of alternatives, and this is known as PROMETHEE II. Two comparative analysis are performed. A first study checks the impact of different types of preference functions. It considers the usual criterion preference function for all criteria. In addition, we compare the technique that we develop with existing multi-attribute decision-making methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020025

Authors: Ana F. Mota Maria Amélia R. Loja Joaquim I. Barbosa José A. Rodrigues

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and the corresponding estimations of their material properties&mdash;in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure&rsquo;s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020023

Authors: Diana Gamboa Carlos E. Vázquez Paul J. Campos

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic &beta; -cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey&ndash;predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic &beta; -cell population growth and leukocyte population growth via the immune response. In this scenario, &beta; -cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and &beta; -cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell&ndash;cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the &beta; -cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness&mdash;that is, a condition wherein the pancreatic &beta; -cell population holds and there are no antigen cells labeled by the activated macrophages.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020024

Authors: Yue Wang Jinchuan Zhou Jingyong Tang

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020022

Authors: Milan Toma Rosalyn Chan-Akeley Christopher Lipari Sheng-Han Kuo

Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method of smoothed particle hydrodynamics is used to simulate the fluid flow, induced by the impact, simultaneously with finite element analysis to solve the large deformations in the brain model. Main Outcomes and Results: Mechanism of injury resulting in concussion is demonstrated. The locations with the highest stress values on the brain parenchyma are shown. Conclusions: Our simulations found that the damage to the brain resulting from the contrecoup injury is more severe than that resulting from the coup injury. Additionally, we show that the contrecoup injury does not always appear on the side opposite from where impact occurs.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020021

Authors: Mohammad Hosseini-Farid MaryamSadat Amiri-Tehrani-Zadeh Mohammadreza Ramzanpour Mariusz Ziejewski Ghodrat Karami

Knowing the precise material properties of intracranial head organs is crucial for studying the biomechanics of head injury. It has been shown that these biological tissues are significantly rate-dependent; hence, their material properties should be determined with respect to the range of deformation rate they experience. In this paper, a validated finite element human head model is used to investigate the biomechanics of the head in impact and blast, leading to traumatic brain injuries (TBI). We simulate the head under various directions and velocities of impacts, as well as helmeted and unhelmeted head under blast shock waves. It is demonstrated that the strain rates for the brain are in the range of 36 to 241 s&minus;1, approximately 1.9 and 0.86 times the resulting head acceleration under impacts and blast scenarios, respectively. The skull was found to experience a rate in the range of 14 to 182 s&minus;1, approximately 0.7 and 0.43 times the head acceleration corresponding to impact and blast cases. The results of these incident simulations indicate that the strain rates for brainstem and dura mater are respectively in the range of 15 to 338 and 8 to 149 s&minus;1. These findings provide a good insight into characterizing the brain tissue, cranial bone, brainstem and dura mater, and also selecting material properties in advance for computational dynamical studies of the human head.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020020

Authors: Francisco Solis Silvia Jerez Roberto Ku-Carrillo Sandra Delgadillo

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We discover an unexpected oscillatory parametrical behavior of the perturbed family.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020019

Authors: José A. Rodrigues

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&rsquo; 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&rsquo; exhibition for the cell membrane, this being its innovation.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020018

Authors: Weiming Zhang Dapan Li Xuyang Lou Dezhi Xu

In this paper, a prescribed performance adaptive backstepping control (PPABC) strategy is proposed to control the speed of a winding segmented permanent magnet linear synchronous motor (WS-PMLSM) with variable parameters and an unknown load disturbance. Firstly, a mathematical model of WS-PMLSM is provided. Then, the prescribed performance technique is introduced in the adaptive backstepping control to improve the transient performance and ensures the tracking error converges within a predetermined range. In addition, a constrained command filter is introduced to address the problem of differential expansion which exists in the traditional backstepping method, and a filter compensation signal is designed against the filter error. Moreover, the adaptive law is designed based on Lyapunov stability theory to estimate the uncertainties caused by parameter changes and load disturbances. The stability of the proposed control strategy is given and the simulation of the control system is carried out under the proposed PPABC in contrast with another backstepping control and traditional PI control. Finally, the experiment is conducted to further show the effectiveness of the proposed controller.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010017

Authors: Majid Ebrahimi Moghadam Hamid Falaghi Mahdi Farhadi

One of the effective ways of reducing power system losses is local compensation of part of the reactive power consumption by deploying shunt capacitor banks. Since the capacitor&rsquo;s impedance is frequency-dependent and it is possible to generate resonances at harmonic frequencies, it is important to provide an efficient method for the placement of capacitor banks in the presence of nonlinear loads which are the main cause of harmonic generation. This paper proposes a solution for a multi-objective optimization problem to address the optimal placement of capacitor banks in the presence of nonlinear loads, and it establishes a reasonable reconciliation between costs, along with improvement of harmonic distortion and a voltage index. In this paper, while using the harmonic power flow method to calculate the electrical quantities of the grid in terms of harmonic effects, the non-dominated sorting genetic (NSGA)-II multi-objective genetic optimization algorithm was used to obtain a set of solutions named the Pareto front for the problem. To evaluate the effectiveness of the proposed method, the problem was tested for an IEEE 18-bus system. The results were compared with the methods used in eight other studies. The simulation results show the considerable efficiency and superiority of the proposed flexible method over other methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010016

Authors: Corina Plata Pablo J. Prieto Ramon Ramirez-Villalobos Luis N. Coria

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010015

Authors: Daniele Polucci Michele Marchetti Simone Fiori

The present paper deals with nonlinear, non-monotonic data regression. This paper introduces an efficient algorithm to perform data transformation from non-monotonic to monotonic to be paired with a statistical bivariate regression method. The proposed algorithm is applied to a number of synthetic and real-world non-monotonic data sets to test its effectiveness. The proposed novel non-isotonic regression algorithm is also applied to a collection of data about strontium isotope stratigraphy and compared to a LOWESS regression tool.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010014

Authors: Youcef Benmessaoud Daoud Ouamara Frédéric Dubas Mickael Hilairet

This paper investigates the permanent-magnet (PM) eddy-current losses in multi-phase PM synchronous machines (PMSM) with concentric winding and surface-mounted PMs. A hybrid multi-layer model, combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell&ndash;Fourier method (i.e., the formal resolution of Maxwell&rsquo;s equations by using the separation of variables method and the Fourier&rsquo;s series), performs the eddy-current loss calculations. First, the magnetic flux density was obtained from the 2-D generic MEC and then subjected to the Fast Fourier Transform (FFT). The semi-analytical model includes the automatic mesh of static/moving zones, the saturation effect and zones connection in accordance with rotor motion based on a new approach called &ldquo;Air-gap sliding line technic&rdquo;. The results of the hybrid multi-layer model were compared with those obtained by three-dimensional (3-D) nonlinear finite-element analysis (FEA). The PM eddy-current losses were estimated on different paths for different segmentations as follow: (i) one segment (no segmentation), (ii) five axial segments, and (iii) two circumferential segments, where the non-uniformity loss distribution is shown. The top of PMs presents a higher quantity of losses compared to the bottom.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010013

Authors: Vania Lara-Ortiz Ivan Salgado David Cruz-Ortiz Alejandro Guarneros Misael Magos-Sanchez Isaac Chairez

This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state restrictions in the device articulations; this means the maximum and minimum angular ranges, to avoid any possible damage to the structure. The controller uses an active compensation method to estimate the unknown dynamics of the WBRD by means of an extended state observer. The sequence of movements for the gait cycle of a WBRD is represented as a class of hybrid system by alternative reference frameworks placed at the first and the last link. The stability analysis employs a class of Hybrid Barrier Lyapunov Function to ensure the fulfillment of the angular restrictions in the robotic device. The proposed controller is evaluated using a numerical simulation system based on the virtual version of the WBRD. Moreover, experimental results confirmed that the H-ADRC may endorse the realization of the proposed gait cycle despite the presence of perturbations and modeling uncertainties. The H-ADRC is compared against a proportional derivative (PD) controller and a proportional-integral-derivative (PID) controller. The H-ADRC shows a superior performance as a consequence of the estimation provided by the homogeneous extended state observer.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010012

Authors: Fábio A. O. Fernandes Ricardo J. Alves de Sousa Mariusz Ptak Johannes Wilhelm

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010011

Authors: Abdelhak Mekahlia Eric Semail Franck Scuiller Hussein Zahr

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010010

Authors: Behnaz Sheikh Hoseini Muhammad Akram Mehrnaz Sheikh Hosseini Hossein Rashmanlou Rajab Ali Borzooei

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010009

Authors: Nikolay Banichuk Svetlana Ivanova Evgeny Makeev Juha Jeronen Tero Tuovinen

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&ndash;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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010008

Authors: Muhammad Akram Danish Saleem Talal Al-Hawary

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010007

Authors: Abdel-Rahman Hedar Wael Deabes Majid Almaraashi Hesham H. Amin

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010006

Authors: MCA Editorial Office

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[...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25010005

Authors: Alberto Fraile Roberto Martínez Daniel Fernández

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010004

Authors: Mehdi Karami Khorramabadi Majid Yarahmadi Mojtaba Ghiyasi

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010003

Authors: Carlos Ignacio Hernández Castellanos Oliver Schütze Jian-Qiao Sun Sina Ober-Blöbaum

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010002

Authors: Abigail Bowers Jared Bunn Myles Kim

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010001

Authors: Carlos Campos Cristiana J. Silva Delfim F. M. Torres

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&rsquo;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&ndash;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&ndash;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&ndash;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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040103

Authors: Kalyan Das M. N. Srinivas Nurul Huda Gazi

The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator&ndash;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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040102

Authors: Muhammad Akram Jawaria Mohsan Dar Sundas Shahzadi

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040101

Authors: A. Karami Saeid Abbasbandy E. Shivanian

In this paper, we study the meshless local Petrov&ndash;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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040100

Authors: Gulfam Shahzadi Muhammad Akram

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040099

Authors: Patrícia Monteiro Aldina Correia Vítor Braga

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040098

Authors: Cristina Campi Annalisa Pascarella Francesca Pitolli

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040097

Authors: Luis Gerardo de la Fraga Heriberto Cruz Hernández

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&rsquo;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 &ldquo;by hand&rdquo; 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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040096

Authors: José M. A. Matos Maria João Rodrigues

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040095

Authors: Oliver Kunc Felix Fritzen

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

]]>Mathematical and Computational Applications doi: 10.3390/mca24040094

Authors: Davide Bellora Riccardo Vescovini

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040093

Authors: Sergey A. Lurie Dmitriy B. Volkov-Bogorodsky Valery V. Vasiliev

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040092

Authors: Xiaodong Xiao Ting Wu Yuanfang Chen Xingyue Fan

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040091

Authors: Alexandra Gavina José M. A. Matos Paulo B. Vasconcelos

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040090

Authors: Śmiechowicz Loup Olejnik

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 Poincar&eacute; 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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040089

Authors: José María Escobar Juan Núñez-Valdés Pedro Pérez-Fernández

At present, the research on invariant functions for algebras is very extended since Hrivn&aacute;k and Novotn&yacute; defined in 2007 the invariant functions &psi; and &phi; as a tool to study the In&ouml;n&uuml;&ndash;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 &psi; &macr; , 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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040088

Authors: Miyuki Koiso

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040087

Authors: Jorge M. Andraz Renato Candeias Ana C. Conceição

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&rsquo; 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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040086

Authors: Ziyad Kas Manohar Das

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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24040085

Authors: Emmanuel Kwasi Mensah Matteo Rocca

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 &ldquo;nominal&rdquo; 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 Sch&ouml;bel (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.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030084

Authors: Padraig Corcoran

A model for tracking objects whose topological properties change over time is proposed. Such changes include the splitting of an object into multiple objects or the merging of multiple objects into a single object. The proposed model employs a novel formulation of the tracking problem in terms of homology theory whereby 0-dimensional homology classes, which correspond to connected components, are tracked. A generalisation of this model for tracking spatially close objects lying in an ambient metric space is also proposed. This generalisation is particularly suitable for tracking spatial-temporal phenomena such as rain clouds. The utility of the proposed model is demonstrated with respect to tracking communities in a social network and tracking rain clouds in radar imagery.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030083

Authors: Tashi AMM Sharif Ullah Akihiko Kubo

Previous studies have reported that a recursive process called the point cloud creation algorithm (PCA) that generates a point cloud is useful for reverse engineering a planner shape. This study elucidates the characteristics of the parameters used in the recursive process as well as its ability in geometric modeling and 3D printing of 3D shapes. In the recursive process, three constants (center point, initial distance, and initial angle) and two variables (instantaneous distance and instantaneous rotational angle) are employed. The shape-modeling characteristics of the constants and variables are elucidated using some commonly used shapes (straight-line, circle, ellipses, spiral, astroid, S-shape, and leaf-shape). In addition, the shape-modeling capability of the recursive process as a whole is quantified using two parameters called the radius of curvature and aesthetic value. Moreover, an illustrative example that shows the efficacy of the recursive process in virtual and physical prototyping of a relatively complex 3D object is presented. The results show that reverse engineering performed by the recursive-process-created point cloud is free from computational complexity compared to reverse engineering performed by the 3D-scanner-created point cloud. As such, the outcomes of this study enrich the field of reverse engineering.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030082

Authors: Oliver Cuate Oliver Schütze

The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations&rsquo; approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030081

Authors: Abouzar Ebrahimi Mohammad Saeed Seif Ali Nouri-Borujerdi

The noise emitted by ships is one of the most important noises in the ocean, and the propeller noise is one of the major components of the ship noise. Measuring the propeller noise in a laboratory, despite the high accuracy and good reliability, has high costs and is very time-consuming. For this reason, the calculation of propeller noise using numerical methods has been considered in recent years. In this study, the noise of a propeller in non-cavitating conditions is calculated by the combination of the panel method (boundary element method) and solving the Ffowcs Williams-Hawkings (FW-H) equations. In this study, a panel method code is developed, and the results are validated by the experimental results of the model tests carried out in the cavitation tunnel of the Sharif University of Technology. Software for numerical calculation of propeller noise, based on FW-H equations, is also developed and the results are validated by experimental results. This study shows that the results of the panel method code have good agreement with experimental results, and that the maximum error of this code for the thrust and torque coefficients is 4% and 7%, respectively. The results of the FW-H noise code are also in good agreement with the experimental data.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030080

Authors: Prasert Sriboonchandr Nuchsara Kriengkorakot Preecha Kriengkorakot

This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to the meta-heuristics from the literature review. For FJSP, by comparing the problem group with the makespan and the mean relative errors (MREs), it was found that for small-sized Kacem problems, value adjusting with &ldquo;DE/rand/1&rdquo; and exponential crossover at position 2. Moreover, value adjusting with &ldquo;DE/best/2&rdquo; and exponential crossover at position 2 gave an MRE of 3.25. For medium-sized Brandimarte problems, value adjusting with &ldquo;DE/best/2&rdquo; and exponential crossover at position 2 gave a mean relative error of 7.11. For large-sized Dauzere-Peres and Paulli problems, value adjusting with &ldquo;DE/best/2&rdquo; and exponential crossover at position 2 gave an MRE of 4.20. From the comparison of the DE results with other methods, it was found that the MRE was lower than that found by Girish and Jawahar with the particle swarm optimization (PSO) method (7.75), which the improved DE was 7.11. For large-sized problems, it was found that the MRE was lower than that found by Warisa (1ST-DE) method (5.08), for which the improved DE was 4.20. The results further showed that basic DE and improved DE with jump search are effective methods compared to the other meta-heuristic methods. Hence, they can be used to solve the FJSP.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030079

Authors: George L. Brovko

In the Newtonian approach to mechanics, the concepts of objective tensors of various ranks and types are introduced. The tough classification of objective tensors is given, including tensors of material and spatial types. The diagrams are constructed for non-degenerate (&ldquo;analogous&rdquo;) relations between tensors of one and the same (any) rank, and of various types of objectivity. Mappings expressing dependence between objective tensor processes of various ranks and types are considered. The fundamental concept of frame-independence of such mappings is introduced as being inherent to constitutive relations of various physical and mechanical properties in the Newtonian approach. The criteria are established for such frame-independence. The mathematical restrictions imposed on the frame-independent mappings by the objectivity types of connected tensors are simultaneously revealed. The absence of such restrictions is established exclusively for mappings and equations linking tensors of material types. Using this, a generalizing concept of objective differentiation of tensor processes in time, and a new concept of objective integration, are introduced. The axiomatic construction of the generalized theory of stress and strain tensors in continuum mechanics is given, which leads to the emergence of continuum classes and families of new tensor measures. The axioms are proposed and a variant of the general theory of constitutive relations of mechanical properties of continuous media is constructed, generalizing the known approaches by Ilyushin and Noll, taking into account the possible presence of internal kinematic constraints and internal body-forces in the body. The concepts of the process image and the properties of the five-dimensional Ilyushin&rsquo;s isotropy are generalized on the range of finite strains.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030078

Authors: Perla Juárez-Smith Leonardo Trujillo Mario García-Valdez Francisco Fernández de Vega Francisco Chávez

This work presents a unique genetic programming (GP) approach that integrates a numerical local search method and a bloat-control mechanism within a distributed model for evolutionary algorithms known as EvoSpace. The first two elements provide a directed search operator and a way to control the growth of evolved models, while the latter is meant to exploit distributed and cloud-based computing architectures. EvoSpace is a Pool-based Evolutionary Algorithm, and this work is the first time that such a computing model has been used to perform a GP-based search. The proposal was extensively evaluated using real-world problems from diverse domains, and the behavior of the search was analyzed from several different perspectives. The results show that the proposed approach compares favorably with a standard approach, identifying promising aspects and limitations of this initial hybrid system.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030077

Authors: Mohammed Mazen Alhato Soufiene Bouallègue

This study presents an intelligent metaheuristics-based design procedure for the Proportional-Integral (PI) controllers tuning in the direct power control scheme for 1.5 MW Doubly Fed Induction Generator (DFIG) based Wind Turbine (WT) systems. The PI controllers&rsquo; gains tuning is formulated as a constrained optimization problem under nonlinear and non-smooth operational constraints. Such a formulated tuning problem is efficiently solved by means of the proposed Thermal Exchange Optimization (TEO) algorithm. To evaluate the effectiveness of the introduced TEO metaheuristic, an empirical comparison study with the homologous particle swarm optimization, genetic algorithm, harmony search algorithm, water cycle algorithm, and grasshopper optimization algorithm is achieved. The proposed TEO algorithm is ensured to perform several desired operational characteristics of DFIG for the active/reactive power and DC-link voltage simultaneously. This is performed by solving a multi-objective function optimization problem through a weighted-sum approach. The proposed control strategy is investigated in MATLAB/environment and the results proved the capabilities of the proposed control system in tracking and control under different scenarios. Moreover, a statistical analysis using non-parametric Friedman and Bonferroni&ndash;Dunn&rsquo;s tests demonstrates that the TEO algorithm gives very competitive results in solving global optimization problems in comparison to the other reported metaheuristic algorithms.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030076

Authors: Jürgen Geiser Amirbahador Nasari

In this paper, we discuss the different splitting approaches to numerically solve the Gross&ndash;Pitaevskii equation (GPE). The models are motivated from spinor Bose&ndash;Einstein condensate (BEC). This system is formed of coupled mean-field equations, which are based on coupled Gross&ndash;Pitaevskii equations. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators and combine these schemes with different splitting approaches. The numerical solutions are compared based on the conservation of the L 2 -norm with the analytical solutions. The advantages of the novel splitting methods for large time-domains are based on the asymptotic conservation of the solution of the soliton&rsquo;s applications. Furthermore, we have the benefit of larger local time-steps and therefore obtain faster numerical schemes.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030075

Authors: Musawenkhosi Mkhatshwa Sandile Motsa Precious Sibanda

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag&ndash;water nanofluid has higher skin friction and surface temperature than the Cu&ndash;water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030074

Authors: Samuil R. Aleksandrov Timo T. Overboom Elena A. Lomonova

This paper presents a 2D hybrid steady-state magnetic field model, capable of accurately modeling the electromagnetic behavior in a linear induction motor, including primary slotting, finite yoke length, and longitudinal end-effects by primary motion. This model integrates a complex harmonic modeling technique with a discretized magnetic equivalent circuit model. The Fourier model is applied to regions with homogeneous material properties, e.g., air regions and the track of the motor, while the magnetic equivalent circuit (MEC) approach is used for the regions containing non-homogeneous material properties, e.g., the primary of the linear induction motor (LIM). By only meshing the domains containing highly-permeable materials, the computational effort is reduced in comparison with the finite element method (FEM). The model is applied to a double-layer single-sided LIM, and the resulting thrust and normal forces show an excellent agreement with respect to finite element analysis and measurement data.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030073

Authors: Muhammad Akram Sumera Naz

A complex Pythagorean fuzzy set (CPFS) is an extension of a Pythagorean fuzzy set that is used to handle the vagueness with the degrees whose ranges are enlarged from real to complex subset with unit disc. In this research study, we propose the innovative concept of complex Pythagorean fuzzy graphs (CPFGs). Further, we present the concepts of regular and edge regular graphs in a complex Pythagorean fuzzy environment. Moreover, we develop a complex Pythagorean fuzzy graph based multi-attribute decision making an approach to handling the situations in which the graphic structure of attributes is obscure. A numerical example concerning information technology improvement project selection is utilized to illustrate the availability of the developed approach.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030072

Authors: Yunan Prawoto Agus Suhartono

Probabilistic engineering mechanics is used to relate the value of &pi; with one of the main parameters in fracture mechanics. It proposes an engineering method to obtain the value of it from engineering data without involving any geometrical Euclidian&rsquo;s circle&rsquo;s data measurement or analysis. It is the first trial in studying the use of fracture mechanics to determine the value of ratio of circumference and diameter of Euclidean&rsquo;s circles indirectly, and subsequently evaluate the number of the digits actually needed in fracture mechanics and engineering purposes.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030071

Authors: Samuel Asante Gyamerah Philip Ngare Dennis Ikpe

The effects of weather on agriculture in recent years have become a major global concern. Hence, an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties is needed. However, most smallholder farmers and agricultural stakeholders are unwilling to pay for the price of weather derivatives (WD) because of the presence of basis risks (product-design and geographical) in the pricing models. To eliminate product-design basis risks, a machine learning ensemble technique was used to determine the relationship between maize yield and weather variables. The results revealed that the most significant weather variable that affected the yield of maize was average temperature. A mean-reverting model with a time-varying speed of mean reversion, seasonal mean, and local volatility that depended on the local average temperature was then proposed. The model was extended to a multi-dimensional model for different but correlated locations. Based on these average temperature models, pricing models for futures, options on futures, and basket futures for cumulative average temperature and growing degree-days are presented. Pricing futures on baskets reduces geographical basis risk, as buyers have the opportunity to select the most appropriate weather stations with their desired weight preference. With these pricing models, farmers and agricultural stakeholders can hedge their crops against the perils of extreme weather.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030070

Authors: Conrad Sanderson Ryan Curtin

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of the underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by these issues, we present a user-friendly and open-source sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely-used MATLAB language. This facilitates prototyping directly in C++ and aids the conversion of research code into production environments. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, red-black tree, coordinate list) depending on which format is best suited and/or available for specific operations, and (ii) a template-based meta-programming framework to automatically detect and optimise the execution of common expression patterns. Empirical evaluations on large sparse matrices with various densities of non-zero elements demonstrate the advantages of the hybrid storage framework and the expression optimisation mechanism.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030069

Authors: Mikhail U. Nikabadze Armine R. Ulukhanyan Tamar Moseshvili Ketevan Tskhakaia Nodar Mardaleishvili Zurab Arkania

Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-layer thin prismatic bodies are considered. From here, we can easily get the statements of the initial-boundary value problems for the five-layer thin prismatic bodies.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030068

Authors: María Susana Torre Anais Acquaviva Jean-Marc Boyer Jorge Tredicce

We study the dynamical behavior of a model commonly used to describe the infection of mice due to hantavirus (and, therefore, its possibility of propagation into human populations) when a parameter is changed in time. In particular, we study the situation when the ecological conditions (e.g., climate benignity, food availability, and so on) change periodically in time. We show that the density of infected mice increases abruptly as the parameter crosses a critical value. We correlate such a situation with the observed sudden outbreaks of hantavirus. Finally, we discuss the possibility of preventing a hantavirus epidemic.

]]>Mathematical and Computational Applications doi: 10.3390/mca24030067

Authors: Daoud Ouamara Frédéric Dubas

Eddy-current analysis is an important research field. This phenomenon occurs in multiple areas and has several applications: electromagnetic braking, repulsive effects, levitation, etc. Thereby, this paper is limited to eddy-current study in rotating electrical machines. In the design process, if the permanent-magnet (PM) loss calculation is very important, the overheating due to eddy-currents must be taken into account. The content of this paper includes sources, calculation methods, reduction techniques, and thermal analysis of PM eddy-current losses. This review aims to act as a guide for the reader to learn about the different aspects and points to consider in studying the eddy-current.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020066

Authors: Gilberto M. Nakamura Brenno Cabella Alexandre S. Martinez

Superradiance describes the coherent collective radiation caused by the interaction between many emitters, mediated by a shared electromagnetic field. Recent experiments involving Bose&ndash;Einstein condensates coupled to high-finesse cavities and interacting quantum dots in condensed-matter have attracted attention to the superradiant regime as a fundamental step to create quantum technologies. Here, we consider a simplified description of superradiance that allows the evaluation of statistical moments. A correspondence with the classical birthday problem recovers the statistical moments for discrete time and an arbitrary number of emitters. In addition, the correspondence provides a way to calculate the degeneracy of the problem.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020065

Authors: José Carlos Garcia Pereira Jorge Cruz Fernandes Luís Guerra Rosa

High-flux solar furnaces distributed throughout the world have been designed and constructed individually, i.e., on a one-by-one basis because there are several possible optical configurations that must take into account the geographical location and the maximum power to be attained. In this work, three ray-tracing models were developed to simulate the optical paths travelled by sun rays in solar furnaces of high concentration using as an example, the solar furnace SF60 of the Plataforma Solar de Almer&iacute;a, in Spain. All these simulation models are supported by mathematical constructions, which are also presented. The first model assumes a random distribution of sun rays coming from a concentrator with spherical curvature. The second model assumes that a random distribution of parallel rays coming from the heliostat is reflected by a concentrator with spherical curvature. Finally, the third model considers that the random parallel rays are reflected by a concentrator with a paraboloid curvature. The three models are all important in optical geometry, although the paraboloid model is more adequate to optimize solar furnaces. The models are illustrated by studying the influence of mirror positioning and shutter attenuation. Additionally, ray-tracing simulations confirmed the possibility to attain homogenous distribution of flux by means of double reflexion using two paraboloid surfaces.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020064

Authors: Ali A. Noroozi Jaber Karimpour Ayaz Isazadeh

Preserving the confidentiality of information is a growing concern in software development. Secure information flow is intended to maintain the confidentiality of sensitive information by preventing them from flowing to attackers. This paper discusses how to ensure confidentiality for multi-threaded programs through a property called observational determinism. Operational semantics of multi-threaded programs are modeled using Kripke structures. Observational determinism is formalized in terms of divergence weak low-bisimulation. Bisimulation is an equivalence relation associating executions that simulate each other. The new property is called bisimulation-based observational determinism. Furthermore, a model checking method is proposed to verify the new property and ensure that secure information flow holds in a multi-threaded program. The model checking method successively refines the Kripke model of the program until the quotient of the model with respect to divergence weak low-bisimulation is reached. Then, bisimulation-based observational determinism is checked on the quotient, which is a minimized model of the concrete Kripke model. The time complexity of the proposed method is polynomial in the size of the Kripke model. The proposed approach has been implemented on top of PRISM, a probabilistic model checking tool. Finally, a case study is discussed to show the applicability of the proposed approach.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020063

Authors: Ephraim Agyingi Tamas Wiandt

There are several types of deterministic compartmental models for disease epidemiology such as SIR, SIS, SEIS, SEIR, etc. The exposed population group in, for example SEIS or SEIR, usually represents individuals in the incubation class. Time delays (of which there are several types) when incorporated into a SIR or SIS model, also fulfil the role of the incubation period without necessarily adding another compartment to the model. This paper incorporates time delays into a SIS model that describes the transmission dynamics of cutaneous leishmaniasis. The time lags account for the incubation periods within the sandflies vector, the human hosts and the different animal groups that serve as reservoir hosts. A threshold value, R 0 , of the model is computed and used to study the disease-free equilibrium and endemic equilibrium of the system. Analysis demonstrating local and global stability of the disease-free equilibrium when R 0 &lt; 1 is provided for all n + 1 population groups involved is provided. The existence of an endemic equilibrium is only guaranteed when R 0 &gt; 1 and numerical analysis of the endemic equilibrium for a human host, a vector host and a single animal reservoir host that is globally stable is also provided.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020062

Authors: Anthony Overmars Sitalakshmi Venkatraman

For several centuries, prime factorisation of large numbers has drawn much attention due its practical applications and the associated challenges. In computing applications, encryption algorithms such as the Rivest&ndash;Shamir&ndash;Adleman (RSA) cryptosystems are widely used for information security, where the keys (public and private) of the encryption code are represented using large prime factors. Since prime factorisation of large numbers is extremely hard, RSA cryptosystems take advantage of this property to ensure information security. A semi-prime being, a product of two prime numbers, has wide applications in RSA algorithms and pseudo number generators. In this paper, we consider a semi-prime number whose construction consists of primes, N = p 1 p 2 , being Pythagorean and having a representation on the Cartesian plane such that, p = x 2 + y 2 . We prove that the product of two such primes can be represented as the sum of four squares, and further, that the sums of two squares can be derived. For such a semi-prime, if the original construction is unknown and the sum of four squares is known, by Euler&rsquo;s factorisation the original construction p 1 p 2 can be found. By considering the parity of each of the squares, we propose a new method of factorisation of semi-primes. Our factorisation method provides a faster alternative to Euler&rsquo;s method by exploiting the relationship between the four squares. The correctness of the new factorisation method is established with mathematical proofs and its practical value is demonstrated by generating RSA-768 efficiently.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020061

Authors: Estefanía Piegari Silvina Ponce Dawson

The specificity and universality of intracellular Ca 2 + signals rely on the variety of spatio-temporal patterns that the Ca 2 + concentration can display. Ca 2 + release into the cytosol through inositol 1,4,5-trisphosphate receptors (IP 3 Rs) is key for this variety. The opening probability of IP 3 Rs depends on the cytosolic Ca 2 + concentration. All of the dynamics are then well described by an excitable system in which the signal propagation depends on the ability of the Ca 2 + released through one IP 3 R to induce the opening of other IP 3 Rs. In most cell types, IP 3 Rs are organized in clusters, i.e., the cytosol is a &ldquo;patchy&rdquo; excitable system in which the signals can remain localized (i.e., involving the release through one or more IP 3 Rs in a cluster), or become global depending on the efficiency of the Ca 2 + -mediated coupling between clusters. The spatial range over which the signals propagate determines the responses that the cell eventually produces. This points to the importance of understanding the mechanisms that make the propagation possible. Our previous qualitative comparison between experiments and numerical simulations seemed to indicate that Ca 2 + release not only occurs within the close vicinity of the clearly identifiable release sites (IP 3 R clusters) but that there are also functional IP 3 Rs in between them. In this paper, we present a quantitative comparison between experiments and models that corroborate this preliminary conclusion. This result has implications on how the Ca 2 + -mediated coupling between clusters works and how it can eventually be disrupted by the different Ca 2 + trapping mechanisms.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020060

Authors: Youcef Benmessaoud Frédéric Dubas Mickael Hilairet

In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020059

Authors: Parimala Sivakumar Jayakumar Jayaraman

Three new iterative methods for solving scalar nonlinear equations using weight function technique are presented. The first one is a two-step fifth order method with four function evaluations which is improved from a two-step Newton&rsquo;s method having same number of function evaluations. By this, the efficiency index of the new method is improved from 1.414 to 1.495. The second one is a three step method with one additional function evaluation producing eighth order accuracy with efficiency index 1.516. The last one is a new fourth order optimal two-step method with efficiency index 1.587. All these three methods are better than Newton&rsquo;s method and many other equivalent higher order methods. Convergence analyses are established so that these methods have fifth, eighth and fourth order respectively. Numerical examples ascertain that the proposed methods are efficient and demonstrate better performance when compared to some equivalent and optimal methods. Seven application problems are solved to illustrate the efficiency and performance of the proposed methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020058

Authors: Hovik A. Matevossian

We study the properties of solutions of the mixed Dirichlet&ndash;Robin and Neumann&ndash;Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020057

Authors: Julian Lißner Felix Fritzen

An image based prediction of the effective heat conductivity for highly heterogeneous microstructured materials is presented. The synthetic materials under consideration show different inclusion morphology, orientation, volume fraction and topology. The prediction of the effective property is made exclusively based on image data with the main emphasis being put on the 2-point spatial correlation function. This task is implemented using both unsupervised and supervised machine learning methods. First, a snapshot proper orthogonal decomposition (POD) is used to analyze big sets of random microstructures and, thereafter, to compress significant characteristics of the microstructure into a low-dimensional feature vector. In order to manage the related amount of data and computations, three different incremental snapshot POD methods are proposed. In the second step, the obtained feature vector is used to predict the effective material property by using feed forward neural networks. Numerical examples regarding the incremental basis identification and the prediction accuracy of the approach are presented. A Python code illustrating the application of the surrogate is freely available.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020056

Authors: Oliver Kunc Felix Fritzen

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5&ndash;100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020055

Authors: Abdelouahed Hamdi Lotfi Tadj

Component commonality is a well-known approach in manufacturing, where the same components are used for multiple products. It has been implemented by many established companies such as Airbus, Kodak, Toyota, etc. We consider a standard two-product inventory model with a common component. The demands for the products are independent random variables. Instead of the usual approach to minimize the total shortage quantity, we propose to minimize the total shortage cost. The resulting problem is a non-convex nonlinear mathematical program. We illustrate the use of a primal-dual proximal method to solve this problem by obtaining numerically the optimal allocations of components. In particular, we show that a higher unit shortage cost induces a higher allocation.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020054

Authors: Marjan Uddin Hazrat Ali Muhammad Taufiq

A localized radial basis function meshless method is applied to approximate a nonlinear biological population model with highly satisfactory results. The method approximates the derivatives at every point corresponding to their local support domain. The method is well suited for arbitrary domains. Compared to the finite element and element free Galerkin methods, no integration tool is required. Four examples are demonstrated to check the efficiency and accuracy of the method. The results are compared with an exact solution and other methods available in literature.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020053

Authors: Ugur Duran Mehmet Acikgoz

In this paper, we introduce the &rho; , q -analog of the p-adic factorial function. By utilizing some properties of &rho; , q -numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic &rho; , q -gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2 . We also derive more representations of the p-adic &rho; , q -gamma function in general case. Moreover, we consider the p-adic &rho; , q -Euler constant derived from the derivation of p-adic &rho; , q -gamma function at x = 1 . Furthermore, we provide a limit representation of aforementioned Euler constant based on &rho; , q -numbers. Finally, we consider &rho; , q -extension of the p-adic beta function via the p-adic &rho; , q -gamma function and we then investigate various formulas and identities.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020052

Authors: Michele Bacciocchi Angelo Tarantino

This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose. The main novelty of the research is the modelling of the reinforcing fibers of the orthotropic layers assuming a non-uniform distribution in the thickness direction. The Halpin–Tsai approach is employed to define the overall mechanical properties of the composite layers starting from the features of the two constituents (fiber and epoxy resin). Several functions are introduced to describe the dependency on the thickness coordinate of their volume fraction. The analyses are carried out in the theoretical framework provided by the first-order shear deformation theory (FSDT) for laminated thick plates. Nevertheless, the same approach is used to deal with the vibration analysis of thin plates, neglecting the shear stiffness of the structure. This objective is achieved by properly choosing the value of the shear correction factor, without any modification in the formulation. The results prove that the dynamic response of thin and thick plates, in terms of natural frequencies and mode shapes, is affected by the non-uniform placement of the fibers along the thickness direction.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020051

Authors: Johan Llamoza Desiderio A. Vasquez

Density gradients across reaction fronts propagating vertically can lead to Rayleigh&ndash;Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele&ndash;Shaw cells or porous media, with the hydrodynamics modeled by Brinkman&rsquo;s equation. The time evolution of the front is described with a Kuramoto&ndash;Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman&rsquo;s equation lead to the same results as Darcy&rsquo;s laws for narrow gap Hele&ndash;Shaw cells. For large gaps, modeling the hydrodynamics using Stokes&rsquo; flow lead to the same results.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020050

Authors: Rodrigo Simile Baroni Ricardo Egydio de Carvalho Bruno Castaldi Bruno Furlanetto

Billiards exhibit rich dynamical behavior, typical of Hamiltonian systems. In the present study, we investigate the classical dynamics of particles in the eccentric annular billiard, which has a mixed phase space, in the limit that the scatterer is point-like. We call this configuration the near singular, in which a single initial condition (IC) densely fills the phase space with straight lines. To characterize the orbits, two techniques were applied: (i) Finite-time Lyapunov exponent (FTLE) and (ii) time recurrence. The largest Lyapunov exponent &lambda; was calculated using the FTLE method, which for conservative systems, &lambda; &gt; 0 indicates chaotic behavior and &lambda; = 0 indicates regularity. The recurrence of orbits in the phase space was investigated through recurrence plots. Chaotic orbits show many different return times and, according to Slater&rsquo;s theorem, quasi-periodic orbits have at most three different return times, the bigger one being the sum of the other two. We show that during the transition to the near singular limit, a typical orbit in the billiard exhibits a sharp drop in the value of &lambda;, suggesting some change in the dynamical behavior of the system. Many different recurrence times are observed in the near singular limit, also indicating that the orbit is chaotic. The patterns in the recurrence plot reveal that this chaotic orbit is composed of quasi-periodic segments. We also conclude that reducing the magnitude of the nonlinear part of the system did not prevent chaotic behavior.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020049

Authors: Feng Qi Xiao-Ting Shi Pietro Cerone

In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss&ndash;Catalan numbers, and the Catalan&ndash;Qi function, and discover some properties of the unified generalization, including a product-ratio expression of the unified generalization in terms of the Catalan&ndash;Qi functions, three integral representations of the unified generalization, and the logarithmically complete monotonicity of the second order for a special case of the unified generalization.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020048

Authors: Brenno Cabella Fernando Meloni Alexandre S. Martinez

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misinterpretations. However, aliasing has been poorly addressed in coupled population dynamics. To illustrate the aliasing effect, the Lotka&ndash;Volterra model oscillatory regime is numerically sampled, creating prey&ndash;predator cycles. We show that inadequate sampling rates may produce inversions in the cause-effect relationship among other artifacts. More generally, slow acquisition rates may distort data interpretation and produce deceptive patterns and eventually leading to misinterpretations, as predators becoming preys. Experiments in coupled population dynamics should be designed that address the eventual aliasing effect.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020047

Authors: Reena Patel Guillermo Riveros David Thompson Edward Perkins Jan Jeffery Hoover John Peters Antoinette Tordesillas

This work presents a transdisciplinary, integrated approach that uses computational mechanics experiments with a flow network strategy to gain fundamental insights into the stress flow of high-performance, lightweight, structured composites by investigating the rostrum of paddlefish. Although computational mechanics experiments give an overall distribution of stress in the structural systems, stress flow patterns formed at nascent stages of loading a biostructure are hard to determine. Computational mechanics experiments on a complex model will involve a high degree of freedom thereby making the extraction of finer details computationally expensive. To address this challenge, the evolution of the stress in the rostrum is formulated as a network flow problem generated by extracting the node and connectivity information from the numerical model of the rostrum. The flow network is weighted based on the parameter of interest, which is stress in the current research. The changing kinematics of the system is provided as input to the mathematical algorithm that computes the minimum cut of the flow network. The flow network approach is verified using two simple classical problems. When applied to the model of the rostrum, the flow network approach identifies strain localization in tensile regions, and buckling/crushing in compressive regions.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020046

Authors: Bruno Rafael Reichert Boaretto Roberto C. Budzinski Thiago L. Prado Sergio Roberto Lopes

The synchronization of neurons is fundamental for the functioning of the brain since its lack or excess may be related to neurological disorders, such as autism, Parkinson&rsquo;s and neuropathies such as epilepsy. In this way, the study of synchronization, as well as its suppression in coupled neurons systems, consists of an important multidisciplinary research field where there are still questions to be answered. Here, through mathematical modeling and numerical approach, we simulated a neural network composed of 5000 bursting neurons in a scale-free connection scheme where non-trivial synchronization phenomenon is observed. We proposed two different protocols to the suppression of phase synchronization, which is related to deep brain stimulation and delayed feedback control. Through an optimization process, it is possible to suppression the abnormal synchronization in the neural network.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020045

Authors: Nissrine Akkari Fabien Casenave Vincent Moureau

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier&ndash;Stokes equations. The lack of stability associated with the order reduction methods of the Navier&ndash;Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2.2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020044

Authors: Gilberto M. Nakamura Ana Carolina P. Monteiro George C. Cardoso Alexandre S. Martinez

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. Agent-based epidemic models mitigate the issue by using a transition matrix which replicates stochastic effects observed in real epidemics. They have met considerable numerical success to simulate small scale epidemics. The problem grows exponentially with population size, reducing the usability of agent-based models for large scale epidemics. Here, we present an algorithm that explores permutation symmetries to enhance the computational performance of agent-based epidemic models. Our findings bound the stochastic process to a single eigenvalue sector, scaling down the dimension of the transition matrix to o ( N 2 ) .

]]>Mathematical and Computational Applications doi: 10.3390/mca24020043

Authors: Patrick Buchfink Ashish Bhatt Bernard Haasdonk

Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g., structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such an ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As a new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020042

Authors: Roberto C. Budzinski Bruno Rafael Reichert Boaretto Thiago L. Prado Sergio Roberto Lopes

The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details of the transition to synchronization in complex networks composed of bursting oscillators under small-world and scale-free topologies using recurrence quantification analysis, specifically the determinism. We demonstrate the existence of non-stationarity states in the transition region. In the small-world network, the transition region denounces the existence of two-state intermittency.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020041

Authors: Fabien Casenave Nissrine Akkari

The industrial application motivating this work is the fatigue computation of aircraft engines&rsquo; high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes the classical unenriched proper orthogonal decomposition method fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the error indicator becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving five million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020040

Authors: Felix Selim Göküzüm Lu Trong Khiem Nguyen Marc-André Keip

The present work addresses a solution algorithm for homogenization problems based on an artificial neural network (ANN) discretization. The core idea is the construction of trial functions through ANNs that fulfill a priori the periodic boundary conditions of the microscopic problem. A global potential serves as an objective function, which by construction of the trial function can be optimized without constraints. The aim of the new approach is to reduce the number of unknowns as ANNs are able to fit complicated functions with a relatively small number of internal parameters. We investigate the viability of the scheme on the basis of one-, two- and three-dimensional microstructure problems. Further, global and piecewise-defined approaches for constructing the trial function are discussed and compared to finite element (FE) and fast Fourier transform (FFT) based simulations.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020039

Authors: Nikabadze Lurie Matevossian Ulukhanyan

The statement of the eigenvalue problem for a tensor&ndash;block matrix of any order and of anyeven rank is formulated. It is known that the eigenvalues of the tensor and the tensor&ndash;block matrixare invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities ofwave propagation of some medias through the eigenvalues of the material objects. In particular, weconsider the classical and micropolar materials with the different anisotropy symbols and for themwe determine the expressions for the velocities of wave propagation through the eigenvalues of thematerial objects.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020038

Authors: Büşra Uzun Ömer Civalek

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen&rsquo;s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler&ndash;Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped&ndash;clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020037

Authors: Santiago Boari Gonzalo Uribarri Ana Amador Gabriel B. Mindlin

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system&rsquo;s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020036

Authors: Samet Gunay Kerem Kaşkaloğlu

In this study, we investigate the existence of chaos in the global cryptocurrency market. Specifically, we analyze parameters of chaotic order, nonlinearity, sensitivity to the initial conditions, monofractality, and multifractality. For this purpose, we conduct a comprehensive series of tests, including Brock–Dechert–Scheinkman (BDS) test, largest Lyapunov exponent, box-counting, and monogram analysis for fractal dimension, and multiple tests for long-range dependence (Aggregated Variances, Peng, Higuchi, R/S Analysis, and Multifractal Detrended Fluctuation Analysis (MFDFA)). All tests are performed over a variety of major cryptocurrencies: Bitcoin, Litecoin, Ethereum, and Ripple. The empirical results support the existence of chaos in the cryptocurrency market. Accordingly, cryptocurrency returns are not random and follow a chaotic order. Therefore, long term predictions are not possible, contrary to most of the discussions ongoing in the media and the public.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020035

Authors: Roy M. Howard

In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series approximation. It is shown that a spline based series approximation to an integral yields, in general, a higher accuracy for a set order of approximation than a dual Taylor series, a Taylor series and an antiderivative series. A spline based series for an integral has many applications and indicative examples are detailed. These include a series for the exponential function, which coincides with a Pad&eacute; series, new series for the logarithm function as well as new series for integral defined functions such as the Fresnel Sine integral function. It is shown that these series are more accurate and have larger regions of convergence than corresponding Taylor series. The spline based series for an integral can be used to define algorithms for highly accurate approximations for the logarithm function, the exponential function, rational numbers to a fractional power and the inverse sine, inverse cosine and inverse tangent functions. These algorithms are used to establish highly accurate approximations for &pi; and Catalan&rsquo;s constant. The use of sub-intervals allows the region of convergence for an integral approximation to be extended.

]]>Mathematical and Computational Applications doi: 10.3390/mca24020034

Authors: Salim Asfirane Sami Hlioui Yacine Amara Mohamed Gabsi

This paper deals with a parallel hybrid excitation synchronous machine (HESM). First, an expanded literature review of hybrid/double excitation machines is provided. Then, the structural topology and principles of operation of the hybrid excitation machine are examined. With the aim of validating the double excitation principle of the topology studied in this paper, the construction of a prototype is presented. In addition, both the 3D finite element method (FEM) and 3D magnetic equivalent circuit (MEC) model are used to model the machine. The flux control capability in the open-circuit condition and results of the developed models are validated by comparison with experimental measurements. The reluctance network model is created from a mesh of the studied domain. The meshing technique aims to combine advantages of finite element modeling, i.e., genericity and expert magnetic equivalent circuit models, i.e., reduced computation time. It also allows taking the non-linear characteristics of ferromagnetic materials into consideration. The machine prototype is tested to validate the predicted results. By confronting results from both modeling techniques and measurements, it is shown that the magnetic equivalent circuit model exhibits fairly accurate results when compared to the 3D finite element method with a gain in computation time.

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