Mathematical and Computational Applications doi: 10.3390/mca23040073

Authors: Silvia Alejandra Seminara María Inés Troparevsky

In this work we obtain approximate solutions for Fredholm integral equations of the second kind by means of Petrov–Galerkin method, choosing “regular pairs” of subspaces, Xn,Yn, which are simply characterized by the positive definitiveness of a correlation matrix. This choice guarantees the solvability and numerical stability of the approximation scheme in an easy way, and the selection of orthogonal basis for the subspaces make the calculations quite simple. Afterwards, we explore an interesting phenomenon called “superconvergence”, observed in the 1970s by Sloan: once the approximations un∈Xn to the solution of the operator equation u-Ku=g are obtained, the convergence can be notably improved by means of an iteration of the method, un*=g+Kun. We illustrate both procedures of approximation by means of two numerical examples: one for a continuous kernel, and the other for a weakly singular one.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040072

Authors: Gabriel A. Mendonça Thales A. C. Maia Braz J. Cardoso Filho

This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell&ndash;Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution is effective to evaluate more realistic magnetic parameters, where measurements of a high-speed permanent-magnet generator prototype indicate saturation in the retaining sleeve due to pole-to-pole leakage flux. The saturation profile is a function of mechanical angle and can be modeled with the aid of a space-varying relative permeability, expressed in terms of a Fourier series. As an example, the presented solution has been applied to a surface-mounted PM machine at no-load condition. Magnetic field calculations show that a simple saturation profile, with low order space-varying permeability in the retaining sleeve significantly affects the magnetic flux density distribution in the air-gap. The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040071

Authors: C. H. H. M. Custers J. W. Jansen E. A. Lomonova

This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040070

Authors: José-Roberto Bermúdez Francisco-Ronay López-Estrada Gildas Besançon Guillermo Valencia-Palomo Lizeth Torres Héctor-Ricardo Hernández

This work presents the modeling and simulation of a hydraulic network with four nodes and two branches that form a two-level water distribution system. It also proposes a distribution of hydraulic valves that allows emulating a leak using a valve and different network configurations, e.g., simple ducts, closed networks and branched networks. The network is modeled in the steady state considering turbulent flow. Numerical experiments are performed, and the results show that the proposed network is useful for the design of leakage diagnosis and control algorithms in different configurations and leakage scenarios.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040069

Authors: Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan

In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condition for a bipolar fuzzy UP-filter to be a bipolar fuzzy UP-ideal. Further, we discuss the relation between bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) and their level cuts.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040068

Authors: Musavarah Sarwar Muhammad Akram Fariha Zafar

A wide variety of human decision-making is based on double-sided or bipolar judgmental thinking on a positive side and a negative side. This paper develops a new method called bipolar fuzzy extended TOPSIS based on entropy weights to address the multi-criteria decision-making problems involving bipolar measurements with positive and negative values. The extended bipolar fuzzy TOPSIS method incorporates the capability of bipolar information into the TOPSIS to address the interactions between criteria and measure the aggregate values on a bipolar scale. In practical problems, this method can be used to measure the benefits and side effects of medical treatments. We also discuss some novel applications of bipolar fuzzy competition graphs in food webs and present certain algorithms to compute the strength of competition between species.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040067

Authors: Silvia Carpitella Fortunato Carpitella Antonella Certa Julio Benítez Joaquín Izquierdo

Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study related to a manufacturing process of a real-world winery is presented, and the proposed approach is applied to rank human factors resulting from a previous organisational risk evaluation from which suitable inference engines may be developed to better support risk management.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040066

Authors: Ray-Ming Chen

Graphs have powerful representations of all kinds of theoretical or experimental mathematical objects. A technique to measure the distance between graphs has become an important issue. In this article, we show how to define distance functions measuring the distance between graphs with directed edges over a fixed set of named and unnamed vertices, respectively. Furthermore, we show how to implement these distance functions via computational matrix operations.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040065

Authors: Kaijun Peng Jieqing Tan Zhiming Li Li Zhang

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan&ndash;Ivrissimtzis&rsquo;s scheme, Siddiqi&ndash;Rehan&rsquo;s scheme, and Siddiqi&ndash;Ahmad&rsquo;s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040064

Authors: Imane Abouelkheir Fadwa El Kihal Mostafa Rachik Ilias Elmouki

In this paper, we attempt to determine the optimal duration of an anti-epidemic control strategy which targets susceptible people, under the isoperimetric condition that we could not control all individuals of this category due to restricted health resources. We state and prove the local and global stability conditions of free and endemic equilibria of a simple epidemic compartmental model devised in the form of four ordinary differential equations which describe the dynamics of susceptible-controlled-infected-removed populations and where it is taken into account that the controlled people cannot acquire long-lived immunity to move towards the removed compartment due to the temporary effect of the control parameter. Thereafter, we characterize the sought optimal control and we show the effectiveness of this limited control policy along with the research of the optimal duration that is needed to reduce the size of the infected population. The isoperimetric constraint is defined over a fixed horizon, while the objective function is defined over a free horizon present under a quadratic form in the payoff term. The complexity of this optimal control problem requires the execution of three numerical methods all combined together at the same time, namely, the forward–backward sweep method to generate the optimal state and control functions, the secant method adapted to the isoperimetric restriction, and, finally, the fixed point method to obtain the optimal final time.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040063

Authors: Le Phuong Quan

A complete MAPLE procedure is designed to effectively implement an algorithm for approximating trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval&ndash;polynomial as its output that we can easily exploit in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both rational and irrational arguments as well as drawing the graph of the piecewise approximate functions are presented. Moreover, from the approximate integration on [ a , b ] with integrands of the form x m sin x , another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best L 2 -approximation of the sine function in the vector space P ℓ of polynomials of degree at most ℓ, a subspace of L 2 ( a , b ) .

]]>Mathematical and Computational Applications doi: 10.3390/mca23040062

Authors: George Oguntala Gbeminiyi Sobamowo Yinusa Ahmed Raed Abd-Alhameed

This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length&ndash;thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge&ndash;Kutta.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040061

Authors: Moin A. Ansari Azeem Haidar Ali N.A. Koam

In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040060

Authors: Joel Guerrero Alberto Cominetti Jan Pralits Diego Villa

Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. These kinds of problems typically involve the interaction of three main applications: a solid modeler, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization work-flow entirely based on open-source tools; it is fault tolerant and software agnostic, allows for asynchronous simulations, and has a high degree of automation. To demonstrate the usability and flexibility of the proposed methodology, we tested it in a practical case related to the naval industry, where we aimed at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. As design variables, we considered the protrusion and immersion of the bulbous bow, and we used surrogate-based optimization. From the results presented, a non-negligible resistance reduction is obtainable using the proposed work-flow and optimization strategy.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040059

Authors: Mohammed Ben Yahia Kamel Boughrara Frédéric Dubas Lazhar Roubache Rachid Ibtiouen

This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell&rsquo;s equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r- and &theta;-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040058

Authors: Anthony Overmars Sitalakshmi Venkatraman

With the increase in the use of electronic transactions in everyday life, secure communications and data storage to withstand any kind of attack is warranted. The golden ratio, being the most irrational among irrational numbers, can be used in elliptic curve cryptosystems, power analysis security, and other applications. However, in such applications, cryptographic operations should take place very quickly before the keys are extracted or decoded by the attackers. This paper proposes an efficient method of golden ratio computation in cryptography to resist information security breaches. We compare our new golden ratio method with the well-known Fibonacci sequence method. The experimental results show that our proposed method is more efficient than the Fibonacci sequence method. Our golden ratio method with infinite precision provides reliable counter measure strategy to address the escalating security attacks.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040057

Authors: Ali Jabbari

Surface-mounted permanent magnet machines are widely used in low and medium speed applications. Pulsating torque components is the most crucial challenge, especially in low-speed applications. Magnet pole shape optimization can be used to mitigate these components. In this research, an analytical model is proposed to calculate the magnetic vector potential in surface-mounted permanent magnet machines. A mathematical expression is also derived for optimal the magnet shape to reduce the cogging torque and electromagnetic torque components. The presented model is based on the resolution of the Laplace&rsquo;s and Poisson&rsquo;s equations in polar coordinates by using the subdomain method and applying hyperbolic functions. The proposed method is applied to the performance computation of a surface-mounted permanent magnet machine, i.e., a 3-phase 12S-10P motor. The analytical results are validated through the finite element analysis (FEA) method.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040056

Authors: Jean Rugamba Yanni Zeng

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040055

Authors: Sasitorn Kaewman Tassin Srivarapongse Chalermchat Theeraviriya Ganokgarn Jirasirilerd

This study aims to solve the real-world multistage assignment problem. The proposed problem is composed of two stages of assignment: (1) different types of trucks are assigned to chicken farms to transport young chickens to egg farms, and (2) chicken farms are assigned to egg farms. Assigning different trucks to the egg farms and different egg farms to the chicken farms generates different costs and consumes different resources. The distance and the idle space in the truck have to be minimized, while constraints such as the minimum number of chickens needed for all egg farms and the longest time that chickens can be in the truck remain. This makes the problem a special case of the multistage assignment (S-MSA) problem. A mathematical model representing the problem was developed and solved to optimality using Lingo v.11 optimization software. Lingo v.11 can solve to optimality only small- and medium-sized test instances. To solve large-sized test instances, the differential evolution (DE) algorithm was designed. An excellent decoding method was developed to increase the search performance of DE. The proposed algorithm was tested with three randomly generated datasets (small, medium, and large test instances) and one real case study. Each dataset is composed of 12 problems, therefore we tested with 37 instances, including the case study. The results show that for small- and medium-sized test instances, DE has 0.03% and 0.05% higher cost than Lingo v.11. For large test instances, DE has 3.52% lower cost than Lingo v.11. Lingo v.11 uses an average computation time of 5.8, 103, and 4320 s for small, medium and large test instances, while DE uses 0.86, 1.68, and 8.79 s, which is, at most, 491 times less than Lingo v.11. Therefore, the proposed heuristics are an effective algorithm that can find a good solution while using less computation time.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040054

Authors: Chahid Kamel Ghaddar

We devise a practical and systematic spreadsheet solution paradigm for general optimal control problems. The paradigm is based on an adaptation of a partial-parametrization direct solution method which preserves the original mathematical optimization statement, but transforms it into a simplified nonlinear programming problem (NLP) suitable for Excel NLP solver. A rapid solution strategy is implemented by a tiered arrangement of pure elementary calculus functions in conjunction with Excel NLP solver. With the aid of the calculus functions, a cost index and constraints are represented by equivalent formulas that fully encapsulate an underlining parametrized dynamical system. Excel NLP solver is then employed to minimize (or maximize) the cost index formula, by varying decision parameters, subject to the constraints formulas. The paradigm is demonstrated for several fixed and free-time nonlinear optimal control problems involving integral and implicit dynamic constraints with direct comparison to published results obtained by fundamentally different methods. Practically, applying the paradigm involves no more than defining a few formulas using basic Excel spreadsheet skills.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040053

Authors: Amaneh Sepahvandzadeh Bahman Ghazanfari Nader Asadian

The present study aimed at solving the stochastic generalized fractional diffusion equation (SGFDE) by means of the random finite difference method (FDM). Moreover, the conditions of mean square convergence of the numerical solution are studied and numerical examples are presented to demonstrate the validity and accuracy of the method.

]]>Mathematical and Computational Applications doi: 10.3390/mca23040052

Authors: Fadwa El Kihal Imane Abouelkheir Mostafa Rachik Ilias Elmouki

We consider a discrete-time susceptible-infected-removed-susceptible &ldquo;again&rdquo; (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030051

Authors: Johan M. Bogoya Andrés Vargas Oliver Cuate Oliver Schütze

The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. As a remedy in the context of evolutionary multi-objective optimization (EMO), the averaged Hausdorff distance &Delta; p has been proposed that is better suited as an indicator for the performance assessment of EMO algorithms since such methods tend to generate outliers. Later on, the two-parameter indicator &Delta; p , q has been proposed for finite sets as an extension to &Delta; p which also averages distances, but which yields some desired metric properties. In this paper, we extend &Delta; p , q to a continuous function between general bounded subsets of finite measure inside a metric measure space. In particular, this extension applies to bounded subsets of R k endowed with the Euclidean metric, which is the natural context for EMO applications. We show that our extension preserves the nice metric properties of the finite case, and finally provide some useful numerical examples that arise in EMO.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030050

Authors: José Sérgio Domingues Ravel Alvarenga Coelho Francielly dos Santos Bento Brenda Cristina Almeida Ayanne Oliveira de Castro

The main objective of this article is to determine the existing linear correlation between the real left ventricular volume (RV) from the heart of bovines and the volumes obtained by Teichholz&rsquo;s mathematical model and the volume of the truncated prolate spheroid (TPS) to identify which model has a higher proximity to the RV. For that, ten silicon rubber molds of the left ventricle (LV) were manufactured, and their real volumes were obtained through Archimedes&rsquo; principle, and their linear dimensions were also obtained. These dimensions were used to feed Teichholz&rsquo;s and the TPS models. It was verified that, for ventricles of lower volume, the models showed relatively close results, and Teichholz&rsquo;s model was the most accurate one. The TPS method shows a grave accuracy mistake for higher volume ventricles. Besides, both methods showed strong linear correlations with the RV, and both with high significance.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030049

Authors: Axel Klein Walter Schumacher

Operations in the Delta-Sigma ( &Delta; &Sigma; ) domain are a broad field of research. In this article the main, focus is on applications in control systems, nevertheless the results are generally applicable for &Delta; &Sigma; -signal processing ( &Delta; &Sigma; SP) in other fields. As the bit-stream does not have an instantaneous value, algebraic operations cannot be executed directly. The first approaches were made in the 1980s based on small-scale integration logic chips by Kouvaras and by Lagoyannis. Further algebraic operations and other implementations were introduced by Zrilic, by Ng, by Bradshaw and by Homann. Other publications utilize complex networks and operations to achieve the desired algebraic operations. These presented operations can be divided into different operation classes by the based implementation idea. In this paper, the known algebraic operation classes are further developed and new operation classes are presented. All implementations are compared and evaluated. For linear operations in control applications, the introduced Bipolar Interpretation is best rated. It compensates for the signal offset of bipolar bit-streams and results in the best signal quality by mapping the logic values true and false of bit-stream to plus and minus one before the algebraic operation. The output of the algebraic operation is a multibit value, to achieve a bit-stream as output value a third step is taken. The result is modulated by a digital &Delta; &Sigma; -modulator ( &Delta; &Sigma; -M). For nonlinear operations the most universal implementation is also based on three steps. In the first stage, the bit-streams are processed with short sinc 3 filters, resulting in multibit values. This signal is processed by digital signal processing (DSP). The output stage is a &Delta; &Sigma; -M. For some nonlinear algebraic operations there can be better solutions than DSP, like shown for limiting. In short, this paper gives a detailed overview about different &Delta; &Sigma; SP classes for linear and nonlinear operations. Newly presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on digital signal processing (DSP), the modified multiplication based on Delta Adder and benchmarks of all presented operations.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030048

Authors: Isabelle Santos Stéphane Puechmorel Guillaume Dufour

Planning conflict-free trajectories is a long-standing problem in Air Traffic Management. Navigation functions designed specifically to produce flyable trajectories have been previously considered, but lack the robustness to uncertain weather conditions needed for use in an operational context. These uncertainties can be taken into account be modifying the boundary of the domain on which the navigation function is computed. In the following work, we present a method for efficiently taking into account boundary variations, using the Hadamard variation.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030047

Authors: Hager A. Ibrahim Mahmoud Riad Mahmoud Fatma A. Khalil Ghada A. El-Kelany

This paper aims to provide an adaptation of the trimmed L (TL)-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. However, our perspective is that we can use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with direct L-moments and maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to compare these methods in terms of estimate average, root of mean square error (RMSE), and relative absolute biases (RABs).

]]>Mathematical and Computational Applications doi: 10.3390/mca23030046

Authors: Juan Carlos Ku-Cauich Guillermo Morales-Luna Horacio Tapia-Recillas

Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities. The second code improves space sizes, but it does not attain optimal probabilities. Additionally, it is conditioned to the existence of a special class of bent maps on Galois rings.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030045

Authors: Ellina Grigorieva Evgenii Khailov

Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are introduced into this system to reflect medication dosages aimed at suppressing interactions between T-lymphocytes and keratinocytes, and between T-lymphocytes and dendritic cells. For such a controlled system, a minimization problem of the concentration of keratinocytes at the terminal time is considered. For its analysis, the Pontryagin maximum principle is applied. As a result of this analysis, the properties of the optimal controls and their possible types are established. It is shown that each of these controls is either a bang-bang type on the entire time interval or (in addition to bang-bang type) contains a singular arc. The obtained analytical results are confirmed by numerical calculations using the software “BOCOP-2.0.5”. Their detailed analysis and the corresponding conclusions are presented.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030044

Authors: Yongsheng Hang Yue Liu Xiaoyang Xu Yan Chen Shu Mo

We, the authors, have requested that the title paper [1] is retracted[...]

]]>Mathematical and Computational Applications doi: 10.3390/mca23030043

Authors: Yansong Li Shougen Chen

A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030042

Authors: Muhammad Akram Amna Habib Farwa Ilyas Jawaria Mohsan Dar

The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n &minus; 1)T is an IFGnT (for n &ge; 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030041

Authors: Somphong Jitman Ekkasit Sangwisut

Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F q , denoted by E ( n , &minus; 1 , q ) , has been investigated. The formula for E ( n , &minus; 1 , q ) has been determined. Some upper and lower bounds of E ( n , &minus; 1 , q ) have been given as well. Asymptotically, it has been shown that either E ( n , &minus; 1 , q ) is zero or it grows the same rate as n.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030040

Authors: Udompong Ketsripongsa Rapeepan Pitakaso Kanchana Sethanan Tassin Srivarapongse

This research aimed to solve the economic crop planning problem, considering transportation logistics to maximize the profit from cultivated activities. Income is derived from the selling price and production rate of the plants; costs are due to operating and transportation expenses. Two solving methods are presented: (1) developing a mathematical model and solving it using Lingo v.11, and (2) using three improved Differential Evolution (DE) Algorithms&mdash;I-DE-SW, I-DE-CY, and I-DE-KV&mdash;which are DE with swap, cyclic moves (CY), and K-variables moves (KV) respectively. The algorithms were tested by 16 test instances, including this case study. The computational results showed that Lingo v.11 and all DE algorithms can find the optimal solution eight out of 16 times. Regarding the remaining test instances, Lingo v.11 was unable to find the optimal solution within 400 h. The results for the DE algorithms were compared with the best solution generated within that time. The DE solutions were 1.196&ndash;1.488% better than the best solution generated by Lingo v.11 and used 200 times less computational time. Comparing the three DE algorithms, MDE-KV was the DE that was the most flexible, with the biggest neighborhood structure, and outperformed the other DE algorithms.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030039

Authors: Chahid Kamel Ghaddar

We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030038

Authors: Dibyendu Biswas Suman Dolai Jahangir Chowdhury Priti K. Roy Ellina V. Grigorieva

Leishmaniasis is a neglected tropical vector-borne epidemic disease, and its transmission is a complex process. Zoonotic transmission to humans or animals occurs through the bites of female Phlebotominae sand flies. Here, reservoir is considered as a major source of endemic pathogen pool for disease outbreak, and the role of more than one reservoir animal becomes indispensable. To study the role of the reservoir animals on disease dynamics, a mathematical model was constructed consisting of susceptible and infected populations of humans and two types of reservoir (animal) and vector populations, respectively. Our aim is to prevent the disease by applying a control theoretic approach, when more than one type of reservoir animal exists in the region. We use drugs like sodium stibogluconate and meglumine antimoniate to control the disease for humans and spray insecticide to control the sand fly population. Similarly, drugs are applied for infected reservoir animals of Types A and B. We calculated the cost-effectiveness of all possible combinations of the intervention and control policies. One of our findings is that the most cost-effective case for Leishmania control is the spray of insecticides for infected sand fly vector. Alternate strategic cases were compared to address the critical shortcomings of single strategic cases, and a range of control strategies were estimated for effective control and economical benefit of the overall control strategy. Our findings provide the most innovative techniques available for application to the successful eradication of cutaneous leishmaniasis in the future.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030037

Authors: Le Phuong Quan Thái Anh Nhan

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor&rsquo;s expansion about a point having a form of k p , k &isin; Z and p = &pi; / 2 , and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating &pi; with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030036

Authors: Hamed Bazgir Bahman Ghazanfari

In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030035

Authors: Joseph Malinzi Paul Amarh Quaye

There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical models that describe natural phenomena. This is because of their high non-linearity and the huge number of parameters of which they consist. In this article we determine, using the hyperbolic tangent (tanh) method, travelling wave solutions to non-linear evolution models of interest in biology and physics. These solutions have recognizable properties expected of other solutions and thus can be used to deduce properties of the general solutions.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030034

Authors: Raknoi Akararungruangkul Sasitorn Kaewman

This research article aims to solve the special case of the location routing problem (SLRP) when the objective function is the fuel consumption. The fuel consumption depends on the distance of travel and the condition of the road. The condition of the road causes the vehicle to use a different speed, which affects fuel usage. This turns the original LRP into a more difficult problem. Moreover, the volume of the goods that are produced in each node could be more or less than the capacity of the vehicle, and as the case study requires the transportation of latex, which is a sensitive good and needs to be carried within a reasonable time so that it does not form solid before being used in the latex process, the maximum time that the latex can be in the truck is limited. All of these attributes are added into the LRP and make it a special case of LRP: a so-called SLRP (a special case of location routing problem). The differential evolution algorithms (DE) are proposed to solve the SLRP. We modified two points in the original DE, which are that (1) the mutation formula is introduced and (2) the new rule of a local search is presented. We call this the modified differential evolution algorithm (MDE). From the computational result, we can see that MDE generates a 13.82% better solution than that of the original version of DE in solving the test instances.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030033

Authors: Babatunde Gbadamosi Mayowa Ojo Segun Oke Maba Matadi

In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0&lt;1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model.

]]>Mathematical and Computational Applications doi: 10.3390/mca23030032

Authors: Dimplekumar N. Chalishajar Avadhesh Kumar

In this manuscript, a stronger concept of exact controllability called Total Controllability has been introduced. Sufficient conditions have been established for the total controllability of the proposed problem. The proposed control problem is a second-order semi-linear differential equation with infinite delay and non-instantaneous impulses. The tools for study include the strongly continuous cosine family and Sadovskii&rsquo;s fixed point theorem. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. In addition, the total controllability of an integrodifferential problem has been investigated. Finally, an example is provided to illustrate the analytical findings.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020031

Authors: Igor Konnov Aleksey Kashuba Erkki Laitinen

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution to this problem, which exploit its special features. We suggest applying first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solving several optimization problems. Our methods differ in approaches for solving these auxiliary problems. We consider three basic methods: Dual Multi Layer (DML), Conditional Gradient Dual Multilayer (CGDM) and Bisection (BS). Besides these methods we consider their modifications adjusted to different kind of cost functions. Our comparison of the performance of the suggested methods on several series of test problems show satisfactory convergence. Nevertheless, proper decomposition techniques enhance the convergence essentially.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020030

Authors: Sebastian Peitz Michael Dellnitz

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020029

Authors: Serge Dumont Franck Jourdan Tarik Madani

In this article, a Space-Time Finite Element Method (STFEM) is proposed for the resolution of mechanical problems involving three dimensions in space and one in time. Special attention will be paid to the non-separation of the space and time variables because this kind of interpolation is well suited to mesh adaptation. For that purpose, we have developed a technique of 4D mesh generation adapted to space-time remeshing. A difficulty arose in the representation of 4D finite elements and meshes. This original technique does not require coarse-to-fine and fine-to-coarse mesh-to-mesh transfer operators and does not increase the size of the linear systems to be solved, compared to traditional finite element methods. Space-time meshes are composed of simplex finite elements. Computations are carried out in the context of the continuous Galerkin method. We have tested the method on a linearized elastodynamics problem. Our technique of mesh adaptation was validated on elementary examples and applied to a problem of mobile loading. The convergence and stability of the method are studied and compared with existing methods. This work is a first implementation of 4D space-time remeshing. A stability criterion for the method is established, as well as a convergence rate of about two. Using simplex elements, it is possible to develop a technique of mesh adaptation able to follow a mobile loading zone.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020028

Authors: Babar Nazir Faiza Ishaq Shahaboddin Shamshirband Anthony T. Chronopoulos

Data Grids deal with geographically-distributed large-scale data-intensive applications. Schemes scheduled for data grids attempt to not only improve data access time, but also aim to improve the ratio of data availability to a node, where the data requests are generated. Data replication techniques manage large data by storing a number of data files efficiently. In this paper, we propose centralized dynamic scheduling strategy-replica placement strategies (CDSS-RPS). CDSS-RPS schedule the data and task so that it minimizes the implementation cost and data transfer time. CDSS-RPS consists of two algorithms, namely (a) centralized dynamic scheduling (CDS) and (b) replica placement strategy (RPS). CDS considers the computing capacity of a node and finds an appropriate location for the job. RPS attempts to improve file access time by using replication on the basis of number of accesses, storage capacity of a computing node, and response time of a requested file. Extensive simulations are carried out to demonstrate the effectiveness of the proposed strategy. Simulation results demonstrate that the replication and scheduling strategies improve the implementation cost and average access time significantly.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020027

Authors: Oluwaseun Egbelowo

The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. &ldquo;Exact&rdquo; finite difference schemes, which are a special NSFD, are provided for the linear models while we apply the NSFD rules, based on Mickens&rsquo; idea of transferring nonlinear models into discrete schemes. The method used was compared with other established methods to verify its efficiency and accuracy. One-compartment pharmacokinetic models are considered for different routes of administration: I.V. bolus injection, I.V. bolus infusion and extravascular administration.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020026

Authors: Terry E. Moschandreou

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves whereas when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020025

Authors: Wanida Limmun Boonorm Chomtee John J. Borkowski

Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of &ldquo;reduced&rdquo; models is also proposed if the original model is misspecified via over-parameterization. In this research, weighted IV-optimality is applied to mixture experiments with a set of prior weights assigned to the potential mixture models of interest. To address the issue of implementation, a genetic algorithm was developed to generate weighted IV-optimal mixture designs that are robust across multiple models. In our examples, we assign models with p parameters to have equal weights, but weights will vary based on varying p. Fraction-of-design-space (FDS) plots are used to compare the performance of an experimental design in terms of the prediction variance properties. An illustrating example is presented. The result shows that the GA-generated designs studied are robust across a set of potential mixture models.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020024

Authors: Herbert Moldenhauer

The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020023

Authors: Lizeth Torres Javier Jiménez-Cabas José Gómez-Aguilar Pablo Pérez-Alcazar

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier Transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020022

Authors: Johanna Pyy Anssi Ahtikoski Alexander Lapin Erkki Laitinen

We solve numerically a forest management optimization problem governed by a nonlinear partial differential equation (PDE), which is a size-structured population model. The formulated problem is supplemented with a natural constraint for a solution to be non-negative. PDE is approximated by an explicit or implicit in time finite difference scheme, whereas the cost function is taken from the very beginning in the finite-dimensional form used in practice. We prove the stability of the constructed nonlinear finite difference schemes on the set of non-negative vectors and the solvability of the formulated discrete optimal control problems. The gradient information is derived by constructing discrete adjoint state equations. The projected gradient method is used for finding the extremal points. The results of numerical testing for several real problems show good agreement with the known results and confirm the theoretical statements.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020021

Authors: Segun Isaac Oke Maba Boniface Matadi Sibusiso Southwell Xulu

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin&rsquo;s maximum principle. Numerical simulations are presented to validate our theoretical results.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020020

Authors: Abdullah Dawar Zahir Shah Muhammad Idrees Waris Khan Saeed Islam Taza Gul

The main intention of this article is to examine the heat transmission of the flow of Eyring–Powell fluid over an unstable oscillatory porous stretching surface. The effect of thermal radiation on the fluid flow is investigated, where the flow is actuated by the unbounded flexible surface which is extended occasionally to and fro on its plane. The rudimentary leading equations are changed to differential equations through the use of applicable similarity variables. An optimal and numerical approach was used to find the solution to the modeled problems. The convergence of the homotopy analysis method (HAM) is shown numerically. The homotopy analysis method predictions of the structures formed are in close agreement with the obtained results from the numerical method. Comparisons between HAM and numerical methods are shown graphically as well as numerically. The convergence of this method is shown numerically. The impacts of the skin friction and heat flux are shown through a table. The influence of the porosity, oscillation, thermal radiation, and heat absorption/generation are the main focus of this work. The consequences of emerging parameters are demonstrated through graphs.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020019

Authors: Roberto López Luis González Gurrola Leonardo Trujillo Olanda Prieto Graciela Ramírez Antonio Posada Perla Juárez-Smith Leticia Méndez

Road traffic injuries are a serious concern in emerging economies. Their death toll and economic impact are shocking, with 9 out of 10 deaths occurring in low or middle-income countries; and road traffic crashes representing 3% of their gross domestic product. One way to mitigate these issues is to develop technology to effectively assist the driver, perhaps making him more aware about how her (his) decisions influence safety. Following this idea, in this paper we evaluate computational models that can score the behavior of a driver based on a risky-safety scale. Potential applications of these models include car rental agencies, insurance companies or transportation service providers. In a previous work, we showed that Genetic Programming (GP) was a successful methodology to evolve mathematical functions with the ability to learn how people subjectively score a road trip. The input to this model was a vector of frequencies of risky maneuvers, which were supposed to be detected in a sensor layer. Moreover, GP was shown, even with statistical significance, to be better than six other Machine Learning strategies, including Neural Networks, Support Vector Regression and a Fuzzy Inference system, among others. A pending task, since then, was to evaluate if a more detailed comparison of different strategies based on GP could improve upon the best GP model. In this work, we evaluate, side by side, scoring functions evolved by three different variants of GP. In the end, the results suggest that two of these strategies are very competitive in terms of accuracy and simplicity, both generating models that could be implemented in current technology that seeks to assist the driver in real-world scenarios.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020018

Authors: Muhammad Aslam

The occurrence of the Gibbs phenomenon near irregular initial data points is a widely known fact in curve generation by interpolating subdivision schemes. In this article, we propose a family of 5-point nonlinear ternary interpolating subdivision schemes. We provide the convergence analysis and prove that this family of subdivision schemes is C 2 continuous. Numerical results are presented to show that nonlinear schemes reduce the Gibbs phenomenon significantly while keeping the same order of smoothness.

]]>Mathematical and Computational Applications doi: 10.3390/mca23020017

Authors: Hamed Bashirpour Saman Bashirpour Shahaboddin Shamshirband Anthony Chronopoulos

In wireless sensor networks (WSNs), users can use broadcast authentication mechanisms to connect to the target network and disseminate their messages within the network. Since data transfer for sensor networks is wireless, as a result, attackers can easily eavesdrop deployed sensor nodes and the data sent between them or modify the content of eavesdropped data and inject false data into the sensor network. Hence, the implementation of the message authentication mechanisms (in order to avoid changes and injecting messages into the network) of wireless sensor networks is essential. In this paper, we present an improved protocol based on elliptic curve cryptography (ECC) to accelerate authentication of multi-user message broadcasting. In comparison with previous ECC-based schemes, complexity and computational overhead of proposed scheme is significantly decreased. Also, the proposed scheme supports user anonymity, which is an important property in broadcast authentication schemes for WSNs to preserve user privacy and user untracking.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010016

Authors: Yousef Barazandeh Bahman Ghazanfari

One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge–Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010015

Authors: Rahma Sadat Magda Kassem

In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM) equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs). Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010014

Authors: Narinder Singh Hanaa Hachimi

The quest for an efficient nature-inspired optimization technique has continued over the last few decades. In this paper, a hybrid nature-inspired optimization technique has been proposed. The hybrid algorithm has been constructed using Mean Grey Wolf Optimizer (MGWO) and Whale Optimizer Algorithm (WOA). We have utilized the spiral equation of Whale Optimizer Algorithm for two procedures in the Hybrid Approach GWO (HAGWO) algorithm: (i) firstly, we used the spiral equation in Grey Wolf Optimizer algorithm for balance between the exploitation and the exploration process in the new hybrid approach; and (ii) secondly, we also applied this equation in the whole population in order to refrain from the premature convergence and trapping in local minima. The feasibility and effectiveness of the hybrid algorithm have been tested by solving some standard benchmarks, XOR, Baloon, Iris, Breast Cancer, Welded Beam Design, Pressure Vessel Design problems and comparing the results with those obtained through other metaheuristics. The solutions prove that the newly existing hybrid variant has higher stronger stability, faster convergence rate and computational accuracy than other nature-inspired metaheuristics on the maximum number of problems and can successfully resolve the function of constrained nonlinear optimization in reality.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010013

Authors: Mahmood Hosseini Imani Mojtaba Jabbari Ghadi Shahaboddin Shamshirband Marius M. Balas

In this paper, the employment of a vehicle-to-grid (V2G) system in the security-constrained unit commitment (SCUC) problem is considered. SCUC has gained remarkable attention from researchers in the field of electric power systems, aiming to determine the generation schedule in which the system operator maximizes the system security and minimizes the generation costs, while satisfying the system and units’ constraints. Tremendous technological advances in recent years have attracted the attention of system operators to utilize novel sources of electricity, accompanied with thermal units. To this end, V2G technology recently drew remarkable consideration as a new energy resource. V2G reduces the dependence of electricity production procedures on small-scale and costly thermal units, and subsequently has a strong impact on the operation costs and ameliorates the management of load vacillations. This paper presents the use of V2G in scheduling and operating power systems. A successful technique for investigating the impacts of V2G on a real power system is running SCUC on power systems in which electric vehicle parking is installed on different buses. In order to assess its applicability, the proposed method has been applied in two case studies: the IEEE 6-bus system and the extended IEEE 30-bus system. This study presents two simulation scenarios: the SCUC problem was first evaluated separately, and then in the presence of some electrical vehicles connected to the grid. The results demonstrate the reduction of the total operation cost. In addition, by using the proposed method, the operator can specify the optimal number of vehicles needed in the parking each hour. The results can help the system operators and designers in designing, planning, and operating such power systems.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010012

Authors: Nkongho Ayuketang Arreyndip Alain Moise Dikande Ebobenow Joseph

A complex nonlinear model for a single-mesh helical gear train is developed by including a time-varying mesh stiffness, axial vibrations, torsional vibrations, shaft and bearing damping, generator back EMF (Electromotive Force) and gear backlashes. With the help of a time series and Fast Fourier Transform (FFT) frequency spectrum, the effects of these nonlinear terms on the wind turbine and generator rotational speeds are studied under different excitation conditions by numerically integrating the associated equations using the RK4 algorithm. Results show that for lightly damped oscillations, an extra harmonic is induced in the generator dynamics due to contributions from internal excitations. However, this extra vibration can be suppressed at higher damping. Big helical angles will generally induce heavy nonlinear vibrations in the turbine and generator; a smaller mesh frequency will induce extra noise in the generator; and the external excitation due to wind gust has a greater influence on the nonlinearity of the wind turbine dynamics as compared to the internal excitations due to static transmission errors, time-varying mesh stiffness and the generator back EMF.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010011

Authors: Ali Hasan Sana Moin Ahmad Karim Shahaboddin Shamshirband

Growth in the area of opinion mining and sentiment analysis has been rapid and aims to explore the opinions or text present on different platforms of social media through machine-learning techniques with sentiment, subjectivity analysis or polarity calculations. Despite the use of various machine-learning techniques and tools for sentiment analysis during elections, there is a dire need for a state-of-the-art approach. To deal with these challenges, the contribution of this paper includes the adoption of a hybrid approach that involves a sentiment analyzer that includes machine learning. Moreover, this paper also provides a comparison of techniques of sentiment analysis in the analysis of political views by applying supervised machine-learning algorithms such as Naïve Bayes and support vector machines (SVM).

]]>Mathematical and Computational Applications doi: 10.3390/mca23010010

Authors: Zhongming Teng Xuansheng Wang

The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems. However, the traditional restarted CMRH method, which completely ignores the history information in the previous cycles, presents a slow speed of convergence. In this paper, we propose a heavy ball restarted CMRH method to remedy the slow convergence by bringing the previous approximation into the current search subspace. Numerical examples illustrate the effectiveness of the heavy ball restarted CMRH method.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010009

Authors: Hossein Karimi Parviz Nasiri

The concept of length-biased distribution is applied in expending proper models for lifetime data. The length-biased distribution is a special case of well-known weighted distribution. In this article, we introduce a length-biased weighted Lomax distribution (LBWLD) with k presence of outliers and estimate the parameter of R = P(Y &lt; X) when the random variables X and Y are independent and have LBWLD in presence of outliers and without outliers, respectively. The bias and mean square error (MSE) of the estimator are examined with simulations of numerical and bootstrap resampling. Analysis of a real data set is considered for illustrative purposes.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010008

Authors: Felix Fritzen Bernard Haasdonk David Ryckelynck Sebastian Schöps

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM). An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (D)EIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010007

Authors: Mohammad Sajid

The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions f λ , n ( x ) = λ x ( e x + 1 ) n , λ &gt; 0 , x ∈ R , n ∈ N \ { 1 } which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of f λ , n ( x ) and their stability are studied analytically and the periodic points of f λ , n ( x ) are computed numerically. The bifurcation diagrams and Lyapunov exponents are simulated; these demonstrate chaotic behaviour in the dynamical system of the function f λ , n ( x ) for certain ranges of parameter λ .

]]>Mathematical and Computational Applications doi: 10.3390/mca23010006

Authors: Chahid Ghaddar

We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP) Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete data integrator, in a direct solution paradigm adapted to the spreadsheet. The technique is tested on several highly nonlinear constrained multivariable control problems with remarkable results in terms of reliability, consistency with pseudo-spectral reported answers, and computing times in the order of seconds. The technique requires no more than defining a few analogous formulas to the problem mathematical equations using basic spreadsheet operations, and no programming skills are needed. It introduces an alternative, simpler tool for solving optimal control problems in social and natural science disciplines.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010005

Authors: Raheleh Jafari Sina Razvarz

The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Significant theorems are suggested in order to explain the properties of FST. The proposed method is validated with three real examples.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010004

Authors: Axel Klein

The fundamental logic operations NOT, OR, AND, and XOR processing bit-streams of Δ Σ -modulators are discussed herein. The resulting bit-streams are evaluated on the basis of their mean values and their standard deviations. Mathematical expressions are presented for their mean values; i.e., the logic function XOR results in the negative multiplication of two bipolar bit-streams, and the logic function AND results in the multiplication of two unipolar bit-streams. As the results are valid for bit-streams with independent high-frequency components, the normed cross-product is utilized for evaluation of the independence of the high-frequency components. In order to achieve a high independence between the input bit-streams, representing the same value, the quantization noise is affected. Multiple strategies are examined and Δ Σ -modulators with different designs are chosen as the best-suited solution. The operations are evaluated on a testbench.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010002

Authors: Chairul Imron Lutfi Mardianto Basuki Widodo Tri Yuwono

One of the many ways to reduce drag force is by adding a small object called passive control. Two passive controls will be placed in front and at the rear of the main object. The main object used is a circular cylinder, and the passive controls used are the Type-I cylinder in the front and an elliptical cylinder at the rear of the main object. The distances between the main object and the passive controls are varied. The Reynolds number used is 1000. The effective distance between the main object and the passive controls is analyzed by using the mathematical model so that the drag coefficient on the main object is compared with the simulated one.

]]>Mathematical and Computational Applications doi: 10.3390/mca23010003

Authors: MCA Editorial Office

Peer review is an essential part in the publication process, ensuring that MCA (Mathematical and Computational Applications) maintains high quality standards for its published papers.[...]

]]>Mathematical and Computational Applications doi: 10.3390/mca23010001

Authors: Hamid Jazayeriy Saghi Mohammadi Shahaboddin Shamshirband

In recent years, recommender systems (RS) provide a considerable progress to users. RSs reduce the cost of a user’s time in order to reach to desired results faster. The main issue of RSs is the presence of cold users which are less active and their preferences are more difficult to detect. The aim of this study is to provide a new way to improve recall and precision in recommender systems for cold users. According to the available categories of items, prioritization of the proposed items is improved and then presented to the cold user. The obtained results show that in addition to increased speed of processing, recall and precision have an acceptable improvement.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040047

Authors: Ali Katebi

The current paper uses data envelopment analysis (DEA) to benchmark the leadership efficiency of civil engineers based on the leadership flexibility space diagram. Since the traditional DEA model does not fit for this problem, a simple modification has been made to enhance the L1-Norm and CCR models to tackle the problem. The engineers are considered to be the decision making unit (DMU). Questionnaires were prepared and responses were received from engineers in an Iranian construction company (MD-2 Corporation) as a case study. The leadership flexibility space diagram uses two basic parameters: (1) a decision-making authority and; (2) data input to a group for decision-making. These parameters are considered as the output, and the model has no input-parameter. The assessment of DEA measures the proximity of the DMUs from the active management. Finally, a correlation among the attributes with leadership efficiency has been considered.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040046

Authors: Fangtao Liu Kwok Tso Yongheng Yang Jingjing Guan

This study analyzes the effects of employee satisfaction and demographic indicators on employee commitment to organizational culture at the enterprise level. With data from a survey of 3029 employees from 27 state-owned enterprises (SOEs), a hierarchical linear model (HLM) is used to identify the influencing factors of employee commitment to organizational culture at the enterprise level. An empirical study indicates that apart from the factors of employee satisfaction and demographic background, four contextual variables of enterprises, namely, comprehensive management, energy intensity, cost-income ratio, and capacity-load ratio, also influence commitment to organizational culture levels. Results show that applying HLM can substantially improve the explanatory power of employee satisfaction factors on commitment to organizational culture using nested enterprise contextual variables. Although measurement scales and satisfaction models have been proposed over the years, only a few studies have addressed the particular nature inherent in Chinese SOEs. HLM, which accounts for the nested data structure and determines the effects of employee satisfaction factors on commitment to organizational culture without bias, is developed in this study. Through an insider view based on empirical work, this research can improve the ability of senior managers to understand the culture and dynamics of organizations, to deliver strong leadership, and to enhance corporate internal management.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040045

Authors: Kimlong Ngin Yen Yat Rufai Hafeez Sijjad Ali Khuhro Mariia Sushchenko

The success of data transaction in a company largely depends on the intelligence system used in its database and application system. The complex and heterogeneous data in the log file make it more difficult for users to manage data effectively. Therefore, this paper creates an application system that can manage data from the log file. A sample was collected from an image editing company in Cambodia by interviewing five customers and seven operators, who worked on the data files for 300 images. This paper found two results: first, the agent script was used for retrieving data from the log file, classifying data, and inserting data into a database; and second, the web interface was used for the viewing of results by the users. The intelligence capabilities of our application, together with a friendly web-based and window-based experience, allow the users to easily acquire, manage, and access the data in an image editing company.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040044

Authors: Adeshina Adegoke Ayo Oyediran

This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040043

Authors: Mehmet Şahin Rızvan Erol

The main purpose of this study was to develop and apply a neural network (NN) approach and an adaptive neuro-fuzzy inference system (ANFIS) model for forecasting the attendance rates at soccer games. The models were designed based on the characteristics of the problem. Past real data was used. Training data was used for training the models, and the testing data was used for evaluating the performance of the forecasting models. The obtained forecasting results were compared to the actual data and to each other. To evaluate the performance of the models, two statistical indicators, Mean Absolute Deviation (MAD) and mean absolute percent error (MAPE), were used. Based on the results, the proposed neural network approach and the ANFIS model were shown to be effective in forecasting attendance at soccer games. The neural network approach performed better than the ANFIS model. The main contribution of this study is to introduce two effective techniques for estimating attendance at sports games. This is the first attempt to use an ANFIS model for that purpose.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040042

Authors: Frédéric Dubas Kamel Boughrara

This paper presents a new scientific contribution to the two-dimensional red(2-D) subdomain technique in polar coordinates taking into account the finite relative permeability of the ferromagnetic material. The constant relative permeability corresponds to the linear part of the nonlinear B ( H ) curve. As in the conventional technique, the separation of variables method and the Fourier series are used for the resolution of magnetostatic Maxwell equations in each region. The general solutions of the magnetic field in subdomains, as well as the boundary conditions (BCs) between regions are different from the conventional method. In the proposed method, the magnetic field solution in each subdomain is a superposition of two magnetic quantities in the two directions (i.e., r- and Θ -axis), and the BCs between two regions are also in both directions. For example, the scientific contribution has been applied to an air- or iron-cored coil supplied by a constant current. The distribution of local quantities (i.e., the magnetic vector potential and flux density) has been validated by a corresponding 2-D finite-element analysis (FEA). The obtained semi-analytical results are in very good agreement with those of the numerical method.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040041

Authors: Donald Boone

This computational research study will analyze the multi-physics of lithium ion insertion into a silicon nanowire in an attempt to explain the electrochemical kinetics at the nanoscale and quantum level. The electron coherent states and a quantum field version of photon density waves will be the joining theories that will explain the electron-photon interaction within the lithium-silicon lattice structure. These two quantum particles will be responsible for the photon absorption rate of silicon atoms that are hypothesized to be the leading cause of breaking diatomic silicon covalent bonds that ultimately leads to volume expansion. It will be demonstrated through the combination of Maxwell stress tensor, optical amplification and path integrals that a stochastic analyze using a variety of Poisson distributions that the anisotropic expansion rates in the &lt;110&gt;, &lt;111&gt; and &lt;112&gt; orthogonal directions confirms the findings ascertained in previous works made by other research groups. The computational findings presented in this work are similar to those which were discovered experimentally using transmission electron microscopy (TEM) and simulation models that used density functional theory (DFT) and molecular dynamics (MD). The refractive index and electric susceptibility parameters of lithiated silicon are interwoven in the first principle theoretical equations and appears frequently throughout this research presentation, which should serve to demonstrate the importance of these parameters in the understanding of this component in lithium ion batteries.

]]>Mathematical and Computational Applications doi: 10.3390/mca22040040

Authors: Yongsheng Hang Yue Liu Xiaoyang Xu Yan Chen Shu Mo

Sensitivity analysis is widely applied in financial risk management and engineering; it describes the variations brought by the changes of parameters. Since the integration by parts technique for Markov chains is well developed in recent years, in this paper we apply it for computation of sensitivity and show the closed-form expressions for two commonly-used time-continuous Markovian models. By comparison, we conclude that our approach outperforms the existing technique of computing sensitivity on Markovian models.

]]>Mathematical and Computational Applications doi: 10.3390/mca22030039

Authors: Hongyan Zhao Lian Zhou

A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of normal, and thus could reflect the approximate performance more properly. The approximation is completely independent of the original curve parameterization, and thus could ensure the stability of the approximation result. Experimental results show that the proposed algorithm is reasonable and effective.

]]>Mathematical and Computational Applications doi: 10.3390/mca22030038

Authors: Sina Razvarz Raheleh Jafari

This paper discusses the elimination of Colour Index Acid Yellow 23 (C.I. AY23) using the ultraviolet (UV)/Ag-TiO2 process. To anticipate the photocatalytic elimination of AY23 with the existence of Ag-TiO2 nanoparticles processed under desired circumstances, two computational techniques, namely artificial neural network (ANN) and imperialist competitive algorithm (ICA) modeling are developed. A sum of 100 datasets are used to establish the models, wherein the introductory concentration of dye, UV light intensity, initial dosage of nano Ag-TiO2, and irradiation time are the four parameters expressed in the form of input variables. Additionally, the elimination of AY23 is considered in the form of the output variable. Out of the 100 datasets, 80 are utilized in order to train the models. The remaining 20 that were not included in the training are used in order to test the models. The comparison of the predicted outcomes extracted from the suggested models and the data obtained from the experimental analysis validates that the performance of the ANN scheme is comparatively sophisticated when compared with the ICA scheme.

]]>Mathematical and Computational Applications doi: 10.3390/mca22030037

Authors: Ali Allahem

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function analytically. A clear example has been studied to illustrate the normal form theory, which can be used as a guide for arbitrary problems.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020036

Authors: Wenling Zhao Ruyu Wang Hongxiang Zhang

We establish the notion of augmented weak sharpness of solution sets for the variational inequality problems which can be abbreviated to VIPs. This notion of augmented weak sharpness is an extension of the weak sharpness of the solution set of monotone variational inequality, and it overcomes the defect of the solution set not satisfying the weak sharpness in many cases. Under the condition of the solution set being augmented weak sharp, we present a necessary and sufficient condition for finite convergence for feasible solution sequence of VIP. The result is an extension of published results, and the augmented weak sharpness also provides weaker sufficient conditions for the finite convergence of many optimization algorithms.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020035

Authors: Xiaolian Liao Guohua Chen Shangzhao Li

The classification of a block-transitive designs is an important subject on algebraic combinatorics. With the aid of MATLAB software, using the classification theorem of 3-homogeneous permutation groups, we look at the classification problem of block-transitive 7–(v, k, 3) design and prove our main theorem: If the automorphism group of a 7–(v, k, 3) design is block-transitive, then it is neither isomorphic to Affine Type Groups nor Almost Simple Type Groups.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020034

Authors: Cheng-ming Liu Ze-kun Wang Hai-bo Pang Jun-xiao Xue

Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF)-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for real time applications. However, fast methods are not able to provide artifacts-free images. In this paper we describe a new image interpolation method by using scanning line algorithm which can generate C - 1 curves or surfaces. The C - 1 interpolation can truncate the interpolation curve at big skipping; hence, the image edge can be kept. Numerical experiments illustrate the efficiency of the novel method.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020033

Authors: A.M.M. Ullah

Dynamical systems play a vital role in studying highly non-linear phenomena. One of the families of the dynamical systems is integer sequences. There is an integer sequence called Q-sequence: Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n − 2)); for n = 3, 4, …; and Q(1) = Q(2) = 1. It exhibits a unique chaotic-order that might help develop approximate models of highly nonlinear phenomena. We explore this possibility and show how to modify a segment of the Q-sequence so that the modified segment becomes an approximate model of surface roughness (a highly non-linear phenomena that results from the material removal processes (e.g., turning, milling, grinding, and so on). The Q-sequence-based models of surface roughness can be used to recreate the surface heights whenever necessary. As such, it is a helpful means for developing simulation systems for virtual manufacturing.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020032

Authors: Taha Öztürk Sadi Bayramov

The concept of soft sets was initiated by Molodtsov. Then, some operations on soft sets were defined by Maji et al. Later on, the concept of soft topological space was introduced. In this paper, we introduce the concept of the pointwise topology of soft topological spaces. Finally, we investigate the properties of soft mapping spaces and the relationships between some soft mapping spaces.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020031

Authors: Touna Yang Nguyen Binh Tran Thang Duong Hoa

In this study, a new smoothing nonlinear penalty function for constrained optimization problems is presented. It is proved that the optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, we develop an algorithm for finding an optimal solution of the optimization problems with inequality constraints. We further discuss the convergence of this algorithm and test this algorithm with three numerical examples. The numerical examples show that the proposed algorithm is feasible and effective for solving some nonlinear constrained optimization problems.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020030

Authors: Danilo Granda , Wilbert G. Aguilar Diego Arcos-Aviles Danny Sotomayor

The importance of early fault detection in electric motors has attracted the attention of research groups, as the detection of incipient faults can prevent damage spreading and increase the lifetime of the motor. At present, studies have focused their attention on optimization procedures used for fault detection in induction machines to achieve a quick and easy-to-interpret assessment at an industrial level. This paper proposes an alternative approach based on the Continuous Wavelet Transform (CWT) for broken bar diagnosis in squirrel cage induction motors. This work uses the Motor Current Signature Analysis (MCSA) method to acquire the current signal of the induction motor. The novelty of this study lies in broken bar detection in electric machines operating at non-load by analyzing variations in the spectrum of the motor’s current signal. This way, the faults are presented as oscillations in the current signal spectrum. Additionally, a quantification of broken bars for the same type of motors operating at fullload is performed in this study. An experimental validation and the comparison with the Fast Fourier Transform (FFT) technique are provided to validate the proposed technique.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020029

Authors: Chunqing Wu

Firstly, an SEIR mathematical model with standard incidence rate is established to describe the transmission of Hand-Foot-Mouth disease (HFMD). The equilibrium of the nondimensionalized model is calculated and the basic reproduction number of the model is defined. In addition, the local stability of the equilibrium is analyzed via the characteristic roots of the Jacobian matrix at the equilibrium, respectively. Numerical simulations are given to confirm the theoretical results. Secondly, a formula aimed to estimate the basic reproduction number of the transmission of HFMD is deduced. As examples to make use of the formula, the basic reproduction number of the HFMD transmission of Singapore of years 2015 and 2016 is estimated based on the newly infected cases notified by the surveillance organizations, respectively. The formula can realize real time estimation for the basic reproduction number and does not need to estimate the transmission efficiency of HFMD between individuals.

]]>Mathematical and Computational Applications doi: 10.3390/mca22020028

Authors: Mohammed Al-Kufi Hayder Hashim Ameer Hussein Hind Mohammed

This paper represents a new image encryption algorithm based on modifying generalized singular value decomposition (GSVD) by decomposing the plain-image into two segments using GSVD with an exchanged key-image to produce the cipher-image. The exchanged key-image is used as an encrypting and decrypting image. Mathematically, this procedure is represented by transforming the plain-image’s matrix into two different matrices and applying the GSVD with the exchanged key-image’s matrix to obtain the cipher-image’s matrix. The two encoded segments can be kept in several places or assigned to a group of authorized persons. No one can obtain the information of the image easily without the knowledge of the decrypting key. This proposed algorithm is represented as one of the digital image encryption techniques used to enhance the security of images that have been sent between recipients.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010027

Authors: Jun Wang Dagang Sun Shizhong Liu Xin Zhang

Temperature has an influence on damping characteristics of the viscoelastic damping structure. The change of the damping characteristics of the structure under the cycle load is a dynamic and coupled process. The hyperelastic-viscoelastic model was used to describe nonlinear deformation and viscoelasticity simultaneously. The temperature distribution and change of the damping characteristics under the coupled condition was analyzed by finite element method (FEM). The maximum value of the simulation results was in agreement with the one calculated by the formula in the literature. Dynamic stiffness and dissipated energy were obtained based on the hysteresis loop. Dynamic stiffness and dissipated energy gradually decreased with the increase of the temperature.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010026

Authors: Yong Zhang Xu Li Tao Zhang

The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) method reduces the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed, to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010025

Authors: Emanuele Dilettoso Santi Rizzo Nunzio Salerno

In multi‐ and many‐objective optimization problems, the optimization target is to obtain a set of non‐dominated solutions close to the Pareto‐optimal front, well‐distributed, maximally extended and fully filled. Comparing solution sets is crucial in evaluating the performance of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. Therefore, an effective performance indicator must encompass these features as a whole and, above all, it must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto‐optimal front.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010024

Authors: Mehrdad Shahmohammadi Beni Kwan Yu

One of the most appealing applications of cold plasmas is medical treatment of the skin. An important concern is the capability to safeguard the non-targeted cells against inactivation temperatures during the plasma treatment. Unfortunately, it is problematic to experimentally determine the highest transient temperatures in these cells during the plasma treatment. In the present work, a complete multiphysics model was built based on finite element analysis using phase field method coupled with heat transfer and fluid dynamics to study the discharge phenomenon of cold plasma with helium carrier gas ejected out of a tube for skin treatment. In such plasmas with carrier gas, the fractions of plasma constituents are small compared to the carrier gas, so thermofluid analysis is needed for the carrier gas as the major contributor to the fluid and heat flow. The phase field method has been used to capture the moving helium gas in air, which has enabled us to compute fluid dynamics parameters for each phase individually. In addition to computational fluid dynamic analyses, we have also considered heat transfer in the fluids and to the skin using the Fourier law of heat conduction, which led to a multiphysics system. In the present paper, various flow velocities and tube-to-target distances (TTDs) have been considered to reveal the dependence of the fluid discharge output parameters on the flow and efficiency of heat transfer to the skin and the surrounding environment. The built model is a useful tool for future development of plasma treatment devices and to safeguard the non-targeted cells against inactivation temperatures.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010023

Authors: Kamonchat Trachoo Wannika Sawangtong Panumart Sawangtong

The Black Scholes model is a well-known and useful mathematical model in ﬁnancial markets. In this paper, the two-dimensional Black Scholes equation with European call option is studied. The explicit solution of this problem is carried out in the form of a Mellin–Ross function by using Laplace transform homotopy perturbation method. The solution example demonstrates that the proposed scheme is effective.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010022

Authors: Jieqing Tan Bo Wang Jun Shi

In order to improve the flexibility of curves, a new five-point binary approximating subdivision scheme with two parameters is presented. The generating polynomial method is used to investigate the uniform convergence and C k -continuity of this scheme. In a special case, the five-point scheme changes into a four-point scheme, which can generate C 3 limit curves. The shape-preserving properties of the four-point scheme are analyzed, and a few examples are given to illustrate the efficiency and the shape-preserving effect of this special case.

]]>Mathematical and Computational Applications doi: 10.3390/mca22010021

Authors: Mahdi Madhi Norizan Mohamed

Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of the GM(1,1) model is an essential issue, and the current study aims to enhance the prediction precision of the GM(1,1) model. Specifically, in order to improve the prediction precision of GM(1,1) model, it is necessary to consider improving the initial condition in the response function of the model. Consequently, the purpose of this paper is to put forward a new method to enhance the performance of the GM(1,1) model by optimizing its initial condition. The minimum sum of squared error was used to optimize the new initial condition of the model. The numerical outcomes show that the improved GM(1,1) model provides considerably better performance than traditional grey model GM(1,1) . The result demonstrates that the improved grey model GM(1,1) achieves the objective of minimizing the forecast errors.

]]>