Mathematics doi: 10.3390/math9151752

Authors: Alexander Zeifman Yacov Satin Alexander Sipin

We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. Such an approach seems very general; the corresponding description and bounds were considered earlier for finite Markov chains with analytical in time intensity functions. Now we generalize this method to locally integrable intensity functions. Special attention is paid to the situation of a countable Markov chain. To obtain these estimates, we investigate the corresponding forward system of Kolmogorov differential equations as a differential equation in the space of sequences l1.

]]>Mathematics doi: 10.3390/math9151751

Authors: Andrés Cacereño David Greiner Blas J. Galván

Maximising profit is an important target for industries in a competitive world and it is possible to achieve this by improving the system availability. Engineers have employed many techniques to improve systems availability, such as adding redundant devices or scheduling maintenance strategies. However, the idea of using such techniques simultaneously has not received enough attention. The authors of the present paper recently studied the simultaneous optimisation of system design and maintenance strategy in order to achieve both maximum availability and minimum cost: the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was coupled with Discrete Event Simulation in a real encoding environment in order to achieve a set of non-dominated solutions. In this work, that study is extended and a thorough exploration using the above-mentioned Multi-objective Evolutionary Algorithm is developed using an industrial case study, paying attention to the possible impact on solutions as a result of different encodings, parameter configurations and chromosome lengths, which affect the accuracy levels when scheduling preventive maintenance. Non-significant differences were observed in the experimental results, which raises interesting conclusions regarding flexibility in the preventive maintenance strategy.

]]>Mathematics doi: 10.3390/math9151750

Authors: Zhenghui Li Zhiming Ao Bin Mo

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment horizons and quantiles. We find that in most cases, the correlation between global financial assets and stock indexes is not significant or is weakly positive. From the perspective of investment horizons (frequency domain), the correlation in the short term is mostly manifested in Bitcoin, while in the medium and long term it is shifted to dollar assets. At the same time, the relationships are significantly higher in the medium and long term than in the short term. From the point of view of quantiles, it shows a weak positive correlation at the lower quantile. However, the correlation between the two is not significant at the median quantile. At the high quantiles, there is a weak negative linkage. According to the causality-in-quantiles approach results, in most cases global financial assets have different degrees of predictive capacity for the selected stock markets. Especially around the median quantile, the predictive ability was strongest.

]]>Mathematics doi: 10.3390/math9151749

Authors: Thomas J. X. Li Christian M. Reidys

In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure and that the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex.

]]>Mathematics doi: 10.3390/math9151748

Authors: Gregor Bánó Jana Kubacková Andrej Hovan Alena Strejčková Gergely T. Iványi Gaszton Vizsnyiczai Lóránd Kelemen Gabriel Žoldák Zoltán Tomori Denis Horvath

In this work, we investigate the properties of a stochastic model, in which two coupled degrees of freedom are subordinated to viscous, elastic, and also additive random forces. Our model, which builds on previous progress in Brownian motion theory, is designed to describe waterimmersed microparticles connected to a cantilever nanowire prepared by polymerization using two-photon direct laser writing (TPP-DLW). The model focuses on insights into nanowires exhibiting viscoelastic behavior, which defines the specific conditions of the microbead. The nanowire bending is described by a three-parameter linear model. The theoretical model is studied from the pointof view of the power spectrum density of Brownian fluctuations. Our approach also focuses on the potential energy equipartition, which determines random forcing parametrization. Analytical calculations are provided that result in a double-Lorentzian power density spectrum with two corner frequencies. The proposed model explained our preliminary experimental findings as aresult of the use of regression analysis. Furthermore, an a posteriori form of regression efficiency evaluation was designed and applied to three typical spectral regions. The agreement of respective moments obtained by integration of regressed dependences as well as by summing experimentaldata was confirmed.

]]>Mathematics doi: 10.3390/math9151747

Authors: Martina Bukač

We present an extension of a non-iterative, partitioned method previously designed and used to model the interaction between an incompressible, viscous fluid and a thick elastic structure. The original method is based on the Robin boundary conditions and it features easy implementation and unconditional stability. However, it is sub-optimally accurate in time, yielding only O(Δt12) rate of convergence. In this work, we propose an extension of the method designed to improve the sub-optimal accuracy. We analyze the stability properties of the proposed method, showing that the method is stable under certain conditions. The accuracy and stability of the method are computationally investigated, showing a significant improvement in the accuracy when compared to the original scheme, and excellent stability properties. Furthermore, since the method depends on a combination parameter used in the Robin boundary conditions, whose values are problem specific, we suggest and investigate formulas according to which this parameter can be determined.

]]>Mathematics doi: 10.3390/math9151746

Authors: Iñigo Calderon-Uriszar-Aldaca Sergio Perez Ravi Sinha Maria Camara-Torres Sara Villanueva Carlos Mota Alessandro Patelli Amaia Matanza Lorenzo Moroni Alberto Sanchez

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume &gt; 1 cm3). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm3, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios.

]]>Mathematics doi: 10.3390/math9151745

Authors: Andreas C. Georgiou Alexandra Papadopoulou Pavlos Kolias Haris Palikrousis Evanthia Farmakioti

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

]]>Mathematics doi: 10.3390/math9151744

Authors: Abdelmejid Bayad Yilmaz Simsek

The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and the Bernoulli functions involving the Bernoulli polynomials, we derive reciprocity laws of these sums. Further developments and observations on these new Dedekind type sums are given.

]]>Mathematics doi: 10.3390/math9151743

Authors: Messaoud Aloui Faiçal Hamidi Houssem Jerbi Mohamed Omri Dumitru Popescu Rabeh Abbassi

Nowadays, solving constrained engineering problems related to optimization approaches is an attractive research topic. The chaotic krill herd approach is considered as one of most advanced optimization techniques. An advanced hybrid technique is exploited in this paper to solve the challenging problem of estimating the largest domain of attraction for nonlinear systems. Indeed, an intelligent methodology for the estimation of the largest stable equilibrium domain of attraction established on quadratic Lyapunov functions is developed. The designed technique aims at computing and characterizing a largest level set of a Lyapunov function that is included in a particular region, satisfying some hard and delicate algebraic constraints. The formulated optimization problem searches to solve a tangency constraint between the LF derivative sign and constraints on the level sets. Such formulation avoids possible dummy solutions for the nonlinear optimization solver. The analytical development of the solution exploits the Chebyshev chaotic map function that ensures high search space capabilities. The accuracy and efficiency of the chaotic krill herd technique has been evaluated by benchmark models of nonlinear systems. The optimization solution shows that the chaotic krill herd approach is effective in determining the largest estimate of the attraction domain. Moreover, since global optimality is needed for proper estimation, a bound type meta-heuristic optimization solver is implemented. In contrast to existing strategies, the synthesized technique can be exploited for both rational and polynomial Lyapunov functions. Moreover, it permits the exploitation of a chaotic operative optimization algorithm which guarantees converging to an expanded domain of attraction in an essentially restricted running time. The synthesized methodology is discussed, with several examples to illustrate the advantageous aspects of the designed approach.

]]>Mathematics doi: 10.3390/math9151742

Authors: Hugo Barros Teresa Pereira António G. Ramos Fernanda A. Ferreira

This paper presents a study on the complexity of cargo arrangements in the pallet loading problem. Due to the diversity of perspectives that have been presented in the literature, complexity is one of the least studied practical constraints. In this work, we aim to refine and propose a new set of metrics to measure the complexity of an arrangement of cargo in a pallet. The parameters are validated using statistical methods, such as principal component analysis and multiple linear regression, using data retrieved from the company logistics. Our tests show that the number of boxes was the main variable responsible for explaining complexity in the pallet loading problem.

]]>Mathematics doi: 10.3390/math9151741

Authors: Yuri Morales-López Yerlin Chacón-Camacho Wilbert Vargas-Delgado

The objective of this work is to present the results of an investigation on the technological, pedagogical and content knowledge evidenced by mathematics teachers in the second year of initial training (preservice) at the Universidad Nacional, from the TPACK model perspective, on the subject of functions. The research has a qualitative approach with an interpretive hermeneutical stance. A sample of 27 teachers in training who were enrolled in courses related to the three base domains of the TPACK model (pedagogical, technological and content of quadratic function) during the first semester (I cycle) of 2020 was used. Three instruments with situations involving the quadratic function were created to determine students’ knowledge. They were also asked to design their own situation to teach an element linked to this topic, which was then shared and evaluated by their peers. The results show that participants possess instrumental dominance over the basic forms of knowledge underlying the model. It is concluded that, although participants have already experimented in courses related to these forms of knowledge, there is insufficient evidence to ascertain that their current knowledge would allow them to integrate technologies as a didactic resource within the teaching of the subject of quadratic function.

]]>Mathematics doi: 10.3390/math9151740

Authors: Elizabeth Martinez-Villarraga Isabel Lopez-Cobo David Becerra-Alonso Francisco Fernández-Navarro

The aim of this work is to characterize the process of constructing mathematical knowledge by higher education students in a distance learning course. This was done as part of an algebra course within engineering degrees in a Colombian university. The study used a Transformative Sequential Design in mixed methods research. The analysis also determined the kinds of mathematical knowledge attained by the students and its relationship to the Colombian social and cultural context. The students acquired declarative, procedural, and conditional knowledge, while the learning strategies were often superficial. In a context where power is distant, students take on a passive approach to learning despite being highly respectful towards the educator. Thus, the educational system has the educator at the center.

]]>Mathematics doi: 10.3390/math9151739

Authors: Syed Sabir Hussain Bukhari Ali Asghar Memon Sadjad Madanzadeh Ghulam Jawad Sirewal Jesús Doval-Gandoy Jong-Suk Ro

This paper proposes a novel brushless excitation topology for a three-phase synchronous machine based on a customary current-controlled voltage source inverter (VSI). The inverter employs a simple hysteresis-controller-based current control scheme that enables it to inject a three-phase armature current to the stator winding which contains a dc offset. This dc offset generates an additional air gap magneto-motive force (MMF). On the rotor side, an additional harmonic winding is mounted to harness the harmonic power from the air gap flux. Since a third harmonic flux is generated in this type of topology, the machine structure is also modified to accommodate the third harmonic rotor winding to have a voltage induced as the rotor rotates at synchronous speed. Specifically, four-pole armature and field winding patterns are used, whereas the harmonic winding is configured for a twelve-pole pattern. A diode rectifier is also mounted on the rotor between the harmonic and field windings. Therefore, the generated voltage on the harmonic winding feeds the current to the field winding for excitation. A 2D-finite element analysis (FEA) in JMAG-Designer was carried out for performance evaluation and verification of the topology. The simulation results are consistent with the proposed theory. The topology could reduce the cost and stator winding volume compared to a conventional brushless machine, with good potential for various applications.

]]>Mathematics doi: 10.3390/math9151738

Authors: Hina Usman Junaid Ikram Khurram Saleem Alimgeer Muhammad Yousuf Syed Sabir Hussain Bukhari Jong-Suk Ro

In this paper, a hexagonal magnet shape is proposed to have an arc profile capable of reducing torque ripples resulting from cogging torque in a single-sided axial flux permanent magnet (AFPM) machine. The arc-shaped permanent magnet increases the air-gap length effectively and makes the flux of the air-gap more sinusoidal, which decreases air-gap flux density and hence causes a reduction in cogging torque. Cogging torque is the basic source of vibration, along with the noise in PM machines, since it is the main cause of torque ripples. Cogging torque is independent of the load current and is proportional to the air-gap flux and the reluctance variation. Three-dimensional finite element analysis (FEA) is used in the JMAG-Designer to analyze the performance of the conventional and proposed hexagonal-shaped PM AFPM machines. The proposed shape is designed to reduce cogging torque, and the voltage remains the same as compared to the conventional hexagonal-shaped PM machine. Further, optimization is performed by utilizing an asymmetric overhang. Latin hypercube sampling (LHS) is used to create samples, the kriging method is applied to approximate the model, and a genetic algorithm is applied to obtain the optimum parameters of the machine.

]]>Mathematics doi: 10.3390/math9151737

Authors: Sónia Rolland Sobral

Introductory programming courses in science, technology, engineering, and mathematics (STEM) degrees are critical to student success throughout the students’ academic and professional route but have traditional failure and dropout rates. The number of publications and reviews on the subject is growing, so we realize the need to prepare an umbrella review, or review of reviews, to group previous studies and extract more comprehensive and ambitious results. Based on the databases ACM, Google Scholar, IEEE, SCOPUS and Web of Science libraries, a formal search was created that resulted in 21 reviews on programming fundamentals in higher education context. Results include bibliometric information on the CS1 reviews, in the context of higher education (namely annual evolution, number and information on authors, types and sources of information, countries of affiliation, languages, keywords and most cited articles), the purpose of the reviews and research questions, methods (namely search strategy, databases used, eligibility criteria) and results (number of records and tables or divisions were made to catalog the articles). We present a taxonomy with four different types of purpose: general, specific, student group and teacher directed. We found very interesting catalogs that can serve as a tool for future work, whether by researchers in the field or by authors who intend to carry out reviews related to introduction to programming, especially in the context of higher education.

]]>Mathematics doi: 10.3390/math9151734

Authors: Jiří Fürst Tomáš Halada Milan Sedlář Tomáš Krátký Pavel Procházka Martin Komárek

This article presents numerical simulation of flow in the discharge object with the welded siphon and the free water level. The main numerical tool used in this study is the lattice Boltzmann method combined with the Volume-of-Fluid approach and the Smagorinski LES model. Some aspects of the numerical method are discussed, especially the formulation of the outlet boundary condition. The simulations are carried out with in-house software based on the open-source Palabos framework. Presented results are compared with the CFD simulations, based on the ANSYS CFX software applying the SST and SAS turbulence models and the free-surface flow modeling by means of the Volume-of-Fluid method. The evolution and interactions of main flow structures are analyzed using visualizations and the spectral analysis. All numerical simulations are verified by the experimental data obtained in the hydraulic laboratory with water circuit. A stationary flow regime has been visualized by means of PIV. Both the vertical planes and horizontal planes have been examined, focused mainly on the regions below and behind the siphon outlet. The results show a good agreement of calculated and measured complex flow structures, including time-averaged and instantaneous flow fields.

]]>Mathematics doi: 10.3390/math9151736

Authors: Sergei Rogosin Maryna Dubatovskaya

In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov. Some of the discussed results are either unknown or inaccessible.

]]>Mathematics doi: 10.3390/math9151735

Authors: Shuang-Shuang Zhou Nehad Ali Shah Ioannis Dassios S. Saleem Kamsing Nonlaopon

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

]]>Mathematics doi: 10.3390/math9151733

Authors: Hao Wang Yanping Zheng Yang Yu

In order to improve the estimation accuracy of the battery state of charge (SOC) based on the equivalent circuit model, a lithium-ion battery SOC estimation method based on adaptive forgetting factor least squares and unscented Kalman filtering is proposed. The Thevenin equivalent circuit model of the battery is established. Through the simulated annealing optimization algorithm, the forgetting factor is adaptively changed in real-time according to the model demand, and the SOC estimation is realized by combining the least-squares online identification of the adaptive forgetting factor and the unscented Kalman filter. The results show that the terminal voltage error identified by the adaptive forgetting factor least-squares online identification is extremely small; that is, the model parameter identification accuracy is high, and the joint algorithm with the unscented Kalman filter can also achieve a high-precision estimation of SOC.

]]>Mathematics doi: 10.3390/math9151732

Authors: Vitaly Promyslov Kirill Semenkov

The paper discusses the problem of performance and timing parameters with respect to the validation of digital instrumentation and control systems (I&amp;C). Statistical methods often implicitly assume that the probability distribution law of the estimated parameters is close to normal. Thus, the confidence intervals for the parameter are determined on the grounds of this assumption. However, we encountered cases when the delay distribution law in I&amp;C is not normal. In these cases, we used the non-statistical network calculus method for time parameters estimation. The network calculus method is well elaborated for lossless digital system models with seamless processing algorithm depending only on data volume. We consider the extension of the method to the case of I&amp;C systems with considerable changes in the data flow and content-dependent processing disciplines. The model is restricted to systems with cyclic processing algorithms and fast network connections. Network calculus describes the data flow and system parameters in terms of flow envelopes and service curves that are generally unknown in advance. In this paper, we define equations that allow the calculation of these characteristics from experimental data. The correspondence of the Network Calculus and classical statistical estimation methods is discussed. Additionally, we give an example of model application to a real I&amp;C system.

]]>Mathematics doi: 10.3390/math9151730

Authors: Mohammad Reza Komari Alaei Mehmet Soysal Atabak Elmi Audrius Banaitis Nerija Banaitiene Reza Rostamzadeh Shima Javanmard

The present research addresses the single transportation robot used to alleviate problems of robotic cell scheduling of the machines. For the purpose of minimizing the make-span, a model of mixed-integer linear programming (MILP) has been suggested. Since the inefficiency exists in NP-hard, a decomposition algorithm posed by Bender was utilized to alleviate the problem in real life situations. The proposed algorithm can be regarded as an efficient attempt to apply optimality Bender’s cuts regarding the problem of parallel machine robotic cell scheduling in order to reach precise resolutions for medium and big sized examples. The numerical analyses have demonstrated the efficiency of the proposed solving approach.

]]>Mathematics doi: 10.3390/math9151731

Authors: Mikel Brun Fernando Cortés María Jesús Elejabarrieta

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction.

]]>Mathematics doi: 10.3390/math9151728

Authors: Yury Khokhlov Victor Korolev

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of “anisotropic” random summation where sums of independent random vectors with multivariate random index having a special multivariate geometric distribution are considered. Anisotropic-geometric stable distributions are introduced. It is demonstrated that these distributions are coordinate-wise scale mixtures of elliptically contoured stable distributions with the Marshall–Olkin mixing distributions. The corresponding “anisotropic” analogs of multivariate Laplace, Linnik and Mittag–Leffler distributions are introduced. Some relations between these distributions are presented.

]]>Mathematics doi: 10.3390/math9151727

Authors: Konstantin Mikhailovich Fedorov Alexander Yanovich Gilmanov Alexander Pavlovich Shevelev Alexander Vyacheslavovich Kobyashev Denis Alekseevich Anuriev

This study is focused on a solution for the problem of suspension penetration in a porous formation. Such a solution forms the basis of injection profile diversion technology for oil reservoir sweep improvement. A conventional model of deep-bed suspension flow was used to describe the suspension injection process. The suspension slug was followed by water injection, and the inflow injection profile before and after treatment was investigated. For the first time, the criteria that determine the effectiveness of the inflow profile improvement process are introduced. The effect of the suspension filtration coefficient on the particle penetration depth was studied. A specific filtration coefficient value for the maximum penetration depth was achieved. The obtained analytical solution was generalized on multi-reservoir strata with poor interlayer crosslinking. The efficiency of profile conformance improvement was described by the differences in the root-mean-square deviations of the inflow velocities in interlayers from mean values before and after the treatment. It was shown that the complex criterion of suspension treatment efficiency should include a reduction in total injectivity. An increase in suspension slug volume improves the injectivity profile but decreases the total injectivity of an injector.

]]>Mathematics doi: 10.3390/math9151729

Authors: Georgios Katsouleas Vasiliki Panagakou Panayiotis Psarrakos

In this note, given a matrix A∈Cn×n (or a general matrix polynomial P(z), z∈C) and an arbitrary scalar λ0∈C, we show how to define a sequence μkk∈N which converges to some element of its spectrum. The scalar λ0 serves as initial term (μ0=λ0), while additional terms are constructed through a recursive procedure, exploiting the fact that each term μk of this sequence is in fact a point lying on the boundary curve of some pseudospectral set of A (or P(z)). Then, the next term in the sequence is detected in the direction which is normal to this curve at the point μk. Repeating the construction for additional initial points, it is possible to approximate peripheral eigenvalues, localize the spectrum and even obtain spectral enclosures. Hence, as a by-product of our method, a computationally cheap procedure for approximate pseudospectra computations emerges. An advantage of the proposed approach is that it does not make any assumptions on the location of the spectrum. The fact that all computations are performed on some dynamically chosen locations on the complex plane which converge to the eigenvalues, rather than on a large number of predefined points on a rigid grid, can be used to accelerate conventional grid algorithms. Parallel implementation of the method or use in conjunction with randomization techniques can lead to further computational savings when applied to large-scale matrices.

]]>Mathematics doi: 10.3390/math9151726

Authors: Simo Sun Hui Yang Guanghui Yang Jinxiu Pi

Based on a tripartite game model among suppliers of public goods, consumers, and the government, a tripartite repeated game model is constructed to analyze the evolution mechanism of which suppliers supply at low prices, consumers purchase, and the government provides incentives, and to establish the dynamics system of a repeated game. The equilibrium points of the evolutionary game are solved, and among them, the equilibrium points are found to satisfy the parameter conditions of ESS. The numerical simulation is employed to verify the impact of penalty coefficients and discount factors on the stability of strategies, which are adopted by the three players in a tripartite repeated game on public goods, and scenario analyses are conducted. The research results of this paper could provide a reference for the government, suppliers, and consumers to make rapid decisions, who are in the supply chain of public goods, especially quasi-public goods, such as coal, water, electricity, and gas, and help them to obtain stable incomes and then ensure the stable operation of the market.

]]>Mathematics doi: 10.3390/math9151725

Authors: Beatriz Abdul-Jalbar Roberto Dorta-Guerra José M. Gutiérrez Joaquín Sicilia

Trade credit is a crucial source of capital particularly for small businesses with limited financing opportunities. Inventory models considering trade credit financing have been widely studied. However, while there is extensive research on the single-vendor single-buyer inventory model allowing delays in payments, the systems where the vendor supplies to more than one buyer have received less attention. In this paper, we analyze a two-echelon inventory system where a single vendor supplies an item to two buyers who face a constant deterministic demand. The vendor produces the items at a finite rate and offers the buyers a delay payment period. That is, the buyers can delay the payment for the purchased items until the end of the credit period. Therefore, during such a period, the buyers sell the items and use the sales revenue to earn interest. At the end of the credit period, the buyers should pay the purchasing cost to the vendor for which external funding may be necessary. It is widely accepted that, in general, centralized policies reduce the total cost of the supply chain. Therefore, we first deal with an integrated model assuming that the vendor and the buyers make decisions jointly. However, in some cases, the buyers are not willing to collaborate, and the management of the supply chain has to be carried out in a decentralized manner. Hence, we also address the problem under a non-cooperative setting. Numerical examples are presented to illustrate both models. Additionally, we perform a computational experiment to compare both strategies, and a sensitivity analysis of the parameters is also carried out. From the results, we derived that, in general, it was more profitable to follow the integrated policy excepting when the replenishment costs for the buyers were high. Finally, in order to validate the computational results, a statistical analysis is performed.

]]>Mathematics doi: 10.3390/math9151724

Authors: Kristina Krulić Himmelreich Josip Pečarić Dora Pokaz Marjan Praljak

In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications.

]]>Mathematics doi: 10.3390/math9151723

Authors: Nieves Atienza Maria-Jose Jimenez Manuel Soriano-Trigueros

We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial complexes) that are built from the regions representing the cells in the tissue. We use a complete and well-grounded set of numerical variables over those persistence barcodes, also known as topological summaries. A novel combination of normalization methods for both the set of input segmented images and the produced barcodes allows for the proven stability results for those variables with respect to small changes in the input, as well as invariance to image scale. Our study provides new insights to this problem, such as a possible novel indicator for the development of the drosophila wing disc tissue or the importance of centroids’ distribution to differentiate some tissues from their CVT-path counterpart (a mathematical model of epithelia based on Voronoi diagrams). We also show how the use of topological summaries may improve the classification accuracy of epithelial images using a Random Forest algorithm.

]]>Mathematics doi: 10.3390/math9151722

Authors: Ruba Abu Khurma Hamad Alsawalqah Ibrahim Aljarah Mohamed Abd Elaziz Robertas Damaševičius

Software defect prediction (SDP) is crucial in the early stages of defect-free software development before testing operations take place. Effective SDP can help test managers locate defects and defect-prone software modules. This facilitates the allocation of limited software quality assurance resources optimally and economically. Feature selection (FS) is a complicated problem with a polynomial time complexity. For a dataset with N features, the complete search space has 2N feature subsets, which means that the algorithm needs an exponential running time to traverse all these feature subsets. Swarm intelligence algorithms have shown impressive performance in mitigating the FS problem and reducing the running time. The moth flame optimization (MFO) algorithm is a well-known swarm intelligence algorithm that has been used widely and proven its capability in solving various optimization problems. An efficient binary variant of MFO (BMFO) is proposed in this paper by using the island BMFO (IsBMFO) model. IsBMFO divides the solutions in the population into a set of sub-populations named islands. Each island is treated independently using a variant of BMFO. To increase the diversification capability of the algorithm, a migration step is performed after a specific number of iterations to exchange the solutions between islands. Twenty-one public software datasets are used for evaluating the proposed method. The results of the experiments show that FS using IsBMFO improves the classification results. IsBMFO followed by support vector machine (SVM) classification is the best model for the SDP problem over other compared models, with an average G-mean of 78%.

]]>Mathematics doi: 10.3390/math9151721

Authors: Syed Sabir Hussain Bukhari Fareed Hussain Mangi Irfan Sami Qasim Ali Jong-Suk Ro

This paper discusses the design and analysis of a high-harmonic injection-based field excitation scheme for the brushless operation of wound field synchronous machines (WFSMs) in order to achieve a higher efficiency. The proposed scheme involves two inverters. One of these inverters provides the three-phase fundamental-harmonic current to the armature winding, whereas the second inverter injects the single-phase high-harmonic i.e., 6th harmonic current in this case, to the neutral-point of the Y-connected armature winding. The injection of the high-harmonic current in the armature winding develops the high-harmonic magnetomotive force (MMF) in the air gap of the machine beside the fundamental. The high-harmonic MMF induces the harmonic current in the excitation winding of the rotor, whereas the fundamental MMF develops the main armature field. The harmonic current is rectified to inject the direct current (DC) into the main rotor field winding. The main armature and rotor fields, when interacting with each other, produce torque. Finite element analysis (FEA) is carried out in order to develop a 4-pole 24-slot machine and investigate it using a 6th harmonic current injection for the rotor field excitation to both attain a brushless operation and analyze its electromagnetic performance. Later on, the performance of the proposed topology is compared with the typical brushless WFSM topology employing the 3rd harmonic current injection-based field excitation scheme.

]]>Mathematics doi: 10.3390/math9151720

Authors: Mihaela Ribičić Penava

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind.

]]>Mathematics doi: 10.3390/math9151719

Authors: Marco A. Martínez Bocanegra Javier Bayod López Agustín Vidal-Lesso Andrés Mena Tobar Ricardo Becerro de Bengoa Vallejo

Penetration and shared nodes between muscles, tendons and the plantar aponeurosis mesh elements in finite element models of the foot may cause inappropriate structural behavior of the tissues. Penetration between tissues caused using separate mesh without motion constraints or contacts can change the loading direction because of an inadequate mesh displacement. Shared nodes between mesh elements create bonded areas in the model, causing progressive or complete loss of load transmitted by tissue. This paper compares by the finite element method the structural behavior of the foot model in cases where a shared mesh has been used versus a separated mesh with sliding contacts between some important tissues. A very detailed finite element model of the foot and ankle that simulates the muscles, tendons and plantar aponeurosis with real geometry has been used for the research. The analysis showed that the use of a separate mesh with sliding contacts and a better characterization of the mechanical behavior of the soft tissues increased the mean of the absolute values of stress by 83.3% and displacement by 17.4% compared with a shared mesh. These increases mean an improvement of muscle and tendon behavior in the foot model. Additionally, a better quantitative and qualitative distribution of plantar pressure was also observed.

]]>Mathematics doi: 10.3390/math9151717

Authors: Liang Shen Xiaodi Wang Qinqin Liu Yuyan Wang Lingxue Lv Rongyun Tang

Considering the carbon trading mechanism and consumers’ preference for low-carbon products, a game decision-making model for the low-carbon e-commerce supply chain (LCE-SC) is constructed. The influences of commission and carbon trading on the optimal decisions of LCE-SC are discussed and then verified through numerical analysis. On this basis, the influence of carbon trading on regional sustainable development is empirically analyzed. The results show that the establishment of carbon trading pilots alleviates the negative impact of unfair profit distribution. Increasing the commission rate in a reasonable range improves the profitability of LCE-SC. Nevertheless, with the enhancement of consumers’ low-carbon preference, a lower commission rate is more beneficial to carbon emission reduction. The total carbon emission is positively related to the commission rate. However, the unit carbon emission decreases first and then increases with the commission rate. The influence of the carbon price sensitivity coefficient on the service level is first positive and then negative, while the influence on the manufacturer’s profit goes the opposite. The empirical analysis confirms that the implementation of carbon trading is conducive to regional sustainable development and controlling environmental governance intensity promotes carbon productivity.

]]>Mathematics doi: 10.3390/math9151718

Authors: Huiliang Liu Yao Chu Yulong Zhang Weiguo Hou Yinqiao Li Yuan Yao Yaxing Cai

With the booming development of satellite applications, the giant constellations of low Earth orbit (LEO) satellites have introduced challenges for the data relay service. The multi-beam satellite not only offers concurrent access to a large number of objects, but can also meet the high data requirements toward specific coverage of the LEO constellation. However, the multi-beam satellite often faces the mismatch problem of spot allocation and data requirements, which can cause an overload traffic jam or a waste of resources. An optimization algorithm on spot beam allocation is necessary to automatically place the spot centers with appropriate beam widths in line with the density of the traffic demands and to realize the uniformity of the beam occupation. Compared with the conventional K-means algorithm, two adjustable parameters α and β are introduced: one for tuning the ratio of two components making up the distance matrix, and the other for setting the obligatory minimum number of objects per beam. In this paper, the whole process of the proposed method is demonstrated, including the establishment of the low-orbit satellite constellation model, the extraction of the distribution features, and the implementation and evaluation of the modified K-means algorithm. The results prove the validity of the proposed algorithm. A larger value of β with a relative smaller value of α tends to obtain the uniformity of beam occupation; the minimum standard deviation of objects per beam is achieved when α is 0.2 and β is 0.8. This demonstrates that the uniformity of objects per beam can be realized by adjusting the parameters of the distance determination matrix and the obligatory minimal number of objects in each beam. The impact of parameter range on the results is also analyzed.

]]>Mathematics doi: 10.3390/math9151716

Authors: Adrian Marius Deaconu Delia Spridon

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

]]>Mathematics doi: 10.3390/math9151715

Authors: Shih-Chia Chang Ming-Tsang Lu Mei-Jen Chen Li-Hua Huang

Since its conception, corporate social responsibility (CSR) has seen continuous growth and become a highly discussed issue. In this paper, we propose an evaluation of how the COVID-19 pandemic could impact CSR applications. The pandemic has provided an opportunity for commerce to move on to being more authentic, to offer genuine CSR applications and to contribute toward dealing with pressing environmental and social issues. Hence, this purpose of the research is to obtain a better understanding of whether the integration of environment, social, corporate governance and economic (ESGE) aspects into CSR strategies can support sustainable development toward more sustainable growth during the COVID-19 pandemic. To meet this challenge, we offer a mixture multiple-criteria decision making (MCDM) model. Very few empirical studies have discussed CSR in the high-tech industry and proposed strategies and planning for ESGE efficiency. Using interviews with experts and a literature review, we identify the elements related to actual practices of the high-tech industry’s appraisal and the integrated MCDM techniques to suggest efficient enhancement models. The best worst method (BWM) and modified VIKOR are implemented to estimate the strategic weights and the gaps of the aspiration value. The results are valuable for classifying the priorities of CSR and are therefore helpful for those who are associated with high-tech industry management, practices and implementation.

]]>Mathematics doi: 10.3390/math9151714

Authors: Gemma Sala Sebastià Berta Barquero Vicenç Font

International research has pointed out the importance of integrating mathematical modeling and inquiry processes into the teaching and learning of mathematics. This paper aims to present an integrative model that enables analyzing the characteristics inquiry and modeling processes share in the same model with a view to using them when designing and implementing interdisciplinary teaching sequences. After presenting a synthesis of the literature review, our theoretical approach to inquiry and modeling for the analysis of an interdisciplinary teaching sequence will be introduced. We focus here on the case of an inquiry situation in an archaeological context where mathematics and history are interrelated. It was implemented at secondary school level with students aged 13–14. We use this particular case study to analyze the appearance of both processes, in order to look for coincidences, concatenations and synergies. The main result is an integrative model for the joint analysis of both processes.

]]>Mathematics doi: 10.3390/math9151713

Authors: Tianbao Zhou Xinghao Li Peng Wang

Despite the future price of individual stocks has long been proved to be unpredictable and irregular according to the EMH, the turning points (or the reversal) of the stock indices trend still remain the rules to follow. Therefore, this study mainly aimed to provide investors with new strategies in buying ETFs of the indices, which not only avoided the instability of individual stocks, but were also able to get a high profit within weeks. Famous theories like Gann theory and the Elliott wave theory suggest that as part of the nature, market regulations and economic activities of human beings shall conform to the laws of nature and the operation of the universe. They further refined only the rules related to specific timepoints and the time cycle rather than the traditional analysis of the complex economic and social factors, which is, to some extent, similar to what the Chinese traditional culture proposes: that every impact on and change in the human society is always attributable to changes in the nature. The study found that the turns of the stock indices trend were inevitable at specific timepoints while the strength and intensity of the turns were uncertain, affected by various factors by then, which meant the market was intertwined with both certainty and uncertainty at the same time. The analysis was based on the data of the Shanghai Index, the Second Board Index and the Shenzhen Index, the three major indices that represent almost all aspects of the Chinese stock market, for the past decades. It could effectively reduce the heteroscedasticity, instability and irregularity of time series models by replacing 250 daily high-frequency data with the extreme points near every twenty-four solar terms per year. The forecasts focusing on the future stock trend of the all-solar-terms group and the eight-solar-terms group were proved accurate. What is more, the indices trend was at a high probability to turn in a range of four days at each solar term. The alert period also provided the readers with a practical example of how it works in the real investment environment.

]]>Mathematics doi: 10.3390/math9151712

Authors: Jožef Ritonja

The basic characteristic of batch bioreactors is their inability to inflow or outflow the substances during the fermentation process. This follows in the simple construction and maintenance, which is the significant advantage of batch bioreactors. Unfortunately, this characteristic also results in the inability of the current industrial and laboratory batch bioreactors to control fermentation production during the process duration. In some recent studies, it was shown that changing the temperature could influence the execution of the fermentation process. The presented paper shows that this phenomenon could be used to develop the closed-loop control system for the fermentation production control in batch bioreactors. First, based on theoretical work, experiments, and numerical methods, the appropriate structure of the mathematical model was determined and parameters were identified. Next, the closed-loop control system structure for batch bioreactor was proposed, and the linear and adaptive control system based on this structure and the derived and identified model were developed. Both modeling and adaptive control system design are new and represent original contributions. As expected, due to the non-linearity of the controlled plant, the adaptive control represents a more successful approach. The simulation and experimental results were used to confirm the applicability of the proposed solution.

]]>Mathematics doi: 10.3390/math9151711

Authors: Xing Wan Xing-Quan Zuo Xin-Chao Zhao

The double row layout problem is to arrange a number of machines on both sides of a straight aisle so as to minimize the total material handling cost. Aiming at the random distribution of product demands, we study a stochastic robust double row layout problem (SR-DRLP). A mixed integer programming (MIP) model is established for SR-DRLP. A surrogate model is used to linearize the nonlinear term in the MIP to achieve a mixed integer linear programming model, which can be readily solved by an exact method to yield high-quality solutions (layouts) for small-scale SR-DRLPs. Furthermore, we propose a hybrid approach combining a local search and an exact approach (LS-EA) to solve large-scale SR-DRLPs. Firstly, a local search is designed to optimize the machine sequences on two rows and the clearance from the most left machine on row 1 to the left boundary. Then, the exact location of each machine is further optimized by an exact approach. The LS-EA is applied to six problem instances ranging from 8 to 50 machines. Experimental results show that the surrogate model is effective and LS-EA outperforms the comparison approaches.

]]>Mathematics doi: 10.3390/math9151710

Authors: Nicuşor Minculete Diana Savin

In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.

]]>Mathematics doi: 10.3390/math9141709

Authors: Freek Verdonck Herwig Bruneel Sabine Wittevrongel

In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

]]>Mathematics doi: 10.3390/math9141708

Authors: Melike Bildirici Nilgun Guler Bayazit Yasemen Ucan

In this paper, we propose hybrid models for modelling the daily oil price during the period from 2 January 1986 to 5 April 2021. The models on S2 manifolds that we consider, including the reference ones, employ matrix representations rather than differential operator representations of Lie algebras. Firstly, the performance of LieNLS model is examined in comparison to the Lie-OLS model. Then, both of these reference models are improved by integrating them with a recurrent neural network model used in deep learning. Thirdly, the forecasting performance of these two proposed hybrid models on the S2 manifold, namely Lie-LSTMOLS and Lie-LSTMNLS, are compared with those of the reference LieOLS and LieNLS models. The in-sample and out-of-sample results show that our proposed methods can achieve improved performance over LieOLS and LieNLS models in terms of RMSE and MAE metrics and hence can be more reliably used to assess volatility of time-series data.

]]>Mathematics doi: 10.3390/math9141707

Authors: Tomaž Kos Damir Vrančić

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides a good model and requires a relatively simple experiment. This is the advantage of the method of moments. In this paper, an analytical method based on the measurement of the process moments (characteristic areas) is proposed, to identify the five-parameter model (second-order process with zero plus time delay) from either the closed-loop or open-loop time responses of the process (in the time-domain), or the general-order transfer function with time delay (in the frequency-domain). The only parameter required by the user is the type of process (minimum phase or non-minimum phase process), which in practice can be easily determined from the time response of the process. The method can also be used to reduce the higher-order process model. The proposed identification method was tested on several illustrative examples, and compared to other identification methods. The comparison with existing methods showed the superiority of the proposed method. Moreover, the tests confirmed that the algorithm of the proposed method works properly for a wide family of process models, even in the presence of moderate process noise.

]]>Mathematics doi: 10.3390/math9141706

Authors: Bo Wang Rekha Srivastava Jin-Lin Liu

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper.

]]>Mathematics doi: 10.3390/math9141705

Authors: Khaled Alhamad Rym M’Hallah Cormac Lucas

This paper considers the scheduling of preventive maintenance for the boilers, turbines, and distillers of power plants that produce electricity and desalinated water. It models the problem as a mathematical program (MP) that maximizes the sum of the minimal ratios of production to the demand of electricity and water during a planning time horizon. This objective encourages the plants’ production and enhances the chances of meeting consumers’ needs. It reduces the chance of power cuts and water shortages that may be caused by emergency disruptions of equipment on the network. To assess its performance and effectiveness, we test the MP on a real system consisting of 32 units and generate a preventive maintenance schedule for a time horizon of 52 weeks (one year). The generated schedule outperforms the schedule established by experts of the water plant; it induces, respectively, 16% and 12% increases in the surpluses while either matching or surpassing the total production. The sensitivity analysis further indicates that the generated schedule can handle unforeseen longer maintenance periods as well as a 120% increase in demand—a sizable realization in a country that heavily relies on electricity to acclimate to the harsh weather conditions. In addition, it suggests the robustness of the schedules with respect to increased demand. In summary, the MP model yields optimal systematic sustainable schedules.

]]>Mathematics doi: 10.3390/math9141704

Authors: Hristo Manev Mancho Manev

We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements.

]]>Mathematics doi: 10.3390/math9141703

Authors: Heng-Xiao Chi Ji-Hwei Horng Chin-Chen Chang

Pixel value ordering and prediction error expansion (PVO+PEE) is a very successful reversible data hiding (RDH) scheme. A series of studies were proposed to improve the performance of the PVO-based scheme. However, the embedding capacity of those schemes is quite limited. We propose a two-step prediction-error-triplet expansion RDH scheme based on PVO. A three-dimensional state transition map for the prediction-error triplet is also proposed to guide the embedding of the two-step scheme. By properly designing the state transitions, the proposed scheme can embed secret data or expand without embedding by modifying just a single entry of the triplet. The experimental results show that the proposed scheme significantly enlarges the embedding capacity of the PVO-based scheme and further reduces the distortion due to embedding.

]]>Mathematics doi: 10.3390/math9141702

Authors: Fernando Castelló-Sirvent Pablo Pinazo-Dallenbach

Entrepreneurship is the basis of the production network, and thus a key to territorial development. In this line, entrepreneurial intention has been pointed out as an indicator of latent entrepreneurship. In this article, the entrepreneurial intention of university students is studied from a configurational approach, allowing the study of the combined effect of corruption perception, corruption normalization, gender, university career area, and family entrepreneurial background to explain high levels of entrepreneurial intention. The model was tested with the fsQCA methodology according to two samples of students grouped according to their household income (medium and high level: N = 180; low level: N = 200). Stress tests were run to confirm the robustness of the results. This study highlights the negative impact produced by corruption among university students’ entrepreneurial intention. Furthermore, the importance of family entrepreneurial background for specific archetypes like female, STEM, and low household income students is pointed out, as well as the importance of implementing education programs for entrepreneurship in higher education, and more specifically in STEM areas. Policies focused on facilitating the access to financial resources for female students and low household income students, and specific programs to foster female entrepreneurship, are also recommended.

]]>Mathematics doi: 10.3390/math9141701

Authors: Simona Dzitac Sorin Nădăban

This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a special reverential volume, dedicated to the Centenary of the Birth of Lotfi A. Zadeh, whom Ioan Dzitac considered to be is his mentor, and to whom he showed his gratitude many times and in innumerable ways, including by being the Guest Editor of this Special Issue. Professor Ioan Dzitac had many important achievements throughout his career: he was co-founder and Editor-in-Chief of an ISI Expanded quoted journal, International Journal of Computers Communications &amp; Control; together with L.A. Zadeh, D. Tufis and F.G. Filip he edited the volume “From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence”; his scientific interest focused on different sub-fields: fuzzy logic applications, soft computing in a fuzzy environment, artificial intelligence, learning platform, distributed systems in internet. He had the most important contributions in soft computing in a fuzzy environment. Some of them will be presented in this paper. Finally, some future trends are discussed.

]]>Mathematics doi: 10.3390/math9141700

Authors: Yi-Chieh Chen Lin-Huan Hu Wan Chen Lu Jei-Zheng Wu Jiun-Jen Yang

Background: This study aims to develop an efficient future game participation strategy for teenaged athletes based on an analysis of the 2019 International Table Tennis Federation (ITTF) World Tour game expenditure efficiency and prize-winning efficiency. Methods: In this research, Chinese Taipei (TPE) players served as the main research subjects. The input and output categories were determined through a literature analysis. A two-stage efficiency process of data envelopment analysis (DEA) and Boston consulting group (BCG) matrix were applied in this study to facilitate the calculation. Results: Based on a slack variable analysis, local travel expenses are the key elements impacting efficiency. The game recommendation order was based on a BCG matrix. The top seven recommended games were the Japan Open, Czech Open, Australian Open, Bulgarian Open, Austrian Open, China Open, and German Open. Conclusion: The results of this current study provide efficient game participation recommendations for teenaged athletes. Long-term follow-up records of game participation information should be developed to provide teenaged athletes with a precise efficiency analysis.

]]>Mathematics doi: 10.3390/math9141699

Authors: Young Seop Son Wonhee Kim

In this paper, a nonlinear differential braking control method is developed to avoid collision during lane change under driver torque. The lateral dynamics consist of lateral offset error and yaw error dynamics and can be interpreted as a semi-strict feedback form. In the differential braking control problem under the driver torque, a matching condition does not satisfy, and the system is not in the form of, the strict feedback form. Thus, a general backstepping control method cannot be applied. To overcome this problem, the proposed method is designed via the combination of the sliding mode control and backstepping. Two sliding surfaces are designed for differential braking control. One of the surfaces is designed considering the lateral offset error, and the other sliding surface is designed using the combination of the yaw and yaw rate errors as the virtual input of the lateral offset error dynamics. A brake steer force input is developed to regulate the two sliding surfaces using a backstepping procedure under the driver torque. Integral action and a super twisting algorithm are used in the lateral controller to ensure the robustness of the system. The proposed method, which is designed via the combination of the sliding mode control and backstepping, can improve the lateral control performance using differential braking. The proposed method is validated through simulations.

]]>Mathematics doi: 10.3390/math9141698

Authors: Vladimir Kodnyanko Stanislav Shatokhin Andrey Kurzakov Yuri Pikalov Lilia Strok Iakov Pikalov Olga Grigorieva Maxim Brungardt

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance and an increased tendency for instability. In radial bearings, it is possible to use longitudinal microgrooves, which practically exclude circumferential air leakage, and contributes to a significant increase in load-bearing capacity. To reduce compliance to zero and negative values, inlet diaphragm and elastic airflow regulators are used. Active flow compensation is inextricably linked to the problem of ensuring the stability of bearings due to the presence of relatively large volumes of gas in the regulator, which have a destabilizing effect. This problem was solved by using an external combined throttling system. Bearings with input flow regulators have a number of disadvantages-they are very energy-intensive and have an insufficiently stable load capacity. A more promising way to reduce compliance is the use of displacement compensators for the movable element. Such bearings also allow for a decrease in compliance to zero and negative values, which makes it possible to use them not only as supports, but also as active deformation compensators of the technological system of machine tools in order to reduce the time and increase the accuracy of metalworking. The new idea of using active flow compensators is to regulate the flow rate not at the inlet, but at the outlet of the air flow. This design has the energy efficiency that is inherent to a conventional bearing, but the regulation of the lubricant output flow allows the compliance to be reduced to zero and negative values. This article discusses the results of a theoretical study of the static and dynamic characteristics of a two-row radial aerostatic bearing with longitudinal microgrooves and an output flow regulator. Mathematical modeling and theoretical study of stationary modes have been carried out. Formulas for determining static compliance and load capacity are obtained. Iterative finite-difference methods for determining the dynamic characteristics of a structure are proposed. The calculation of dynamic quality criteria was carried out on the basis of the method of rational interpolation of the bearing transfer function, as a system with distributed parameters, developed by the authors. It was found that the volumes of the microgrooves do not have a noticeable effect on the bearing dynamics. It is shown that, in this design, the external combined throttling system is an effective means of maintaining stability and high dynamic quality of the design operating in the modes of low, zero and negative compliance.

]]>Mathematics doi: 10.3390/math9141695

Authors: Tzitlali Gasca-Ortiz Francisco J. Domínguez-Mota Diego A. Pantoja

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated by an ellipse, finding the optimal major and minor axes. The inverse problem was implemented by comparing these observational data with the concentration obtained numerically from the 2D advection–diffusion equation, varying the diffusion tensor. When the tensor was isotropic, values of K11=K22≈0.003&nbsp;m2/s were found; when nonequal coefficients were considered, it was found that K11≈0.005&nbsp;m2/s and K22≈0.002&nbsp;m2/s, and the cross-term K12 influenced the results of the orientation of the ellipse. It is important to mention that, with this simple technique, the parameter estimation had consequences of great importance as the value for the diffusion coefficient was bounded significantly under particular conditions for this site of study.

]]>Mathematics doi: 10.3390/math9141697

Authors: María Jesús Caurcel Cara Emilio Crisol Moya Carmen del Pilar Gallardo-Montes

Research on teachers’ perceptions about diversity is key to understanding the different approaches to be implemented to build inclusive education. Within this framework, the perceptions and attitudes of 73 students in the Mathematics specialization of the University Master’s Degree in Teacher Training for Secondary Education, Bachillerato, Vocational Training and Language Teaching (Máster Universitario en Profesorado de Educación Secundaria Obligatoria, Formación Profesional y Enseñanza de Idiomas (MAES) at the University of Granada (Spain) were analyzed to determine their views about the initial training they received on attention to diversity during the Master’s program. The study is a descriptive and correlational-predictive transversal examination of the responses obtained from the “Questionnaire for preservice secondary education teachers on perceptions about attention to diversity” (Colmenero Ruiz and Pegalajar Palomino, 2015). The findings demonstrate that the students—preservice secondary education teachers—held favorable attitudes toward diversity and the principle of inclusion. The findings also show that contact with persons with disability influences perception of this population. The authors conclude that better training and knowledge of the elements that condition the teaching–learning process for high-quality attention to diversity predict better pedagogical preparation in matters of attention to diversity.

]]>Mathematics doi: 10.3390/math9141696

Authors: Piyush Dhawankar Prashant Agrawal Bilal Abderezzak Omprakash Kaiwartya Krishna Busawon Maria Simona Raboacă

This paper is concerned with designing and numerically implementing a V2X (Vehicle-to-Vehicle and Vehicle-to-Infrastructure) control system architecture for a platoon of autonomous vehicles. The V2X control architecture integrates the well-known Intelligent Driver Model (IDM) for a platoon of Autonomous Driving Vehicles (ADVs) with Vehicle-to-Infrastructure (V2I) Communication. The main aim is to address practical implementation issues of such a system as well as the safety and security concerns for traffic environments. To this end, we first investigated a channel estimation model for V2I communication. We employed the IEEE 802.11p vehicular standard and calculated path loss, Packet Error Rate (PER), Signal-to-Noise Ratio (SNR), and throughput between transmitter and receiver end. Next, we carried out several case studies to evaluate the performance of the proposed control system with respect to its response to: (i) the communication infrastructure; (ii) its sensitivity to an emergency, inter-vehicular gap, and significant perturbation; and (iii) its performance under the loss of communication and changing driving environment. Simulation results show the effectiveness of the proposed control model. The model is collision-free for an infinite length of platoon string on a single lane road-driving environment. It also shows that it can work during a lack of communication, where the platoon vehicles can make their decision with the help of their own sensors. V2X Enabled Intelligent Driver Model (VX-IDM) performance is assessed and compared with the state-of-the-art models considering standard parameter settings and metrics.

]]>Mathematics doi: 10.3390/math9141694

Authors: José Antonio Roldán-Nofuentes Saad Bouh Regad

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In this manuscript the estimation of the average kappa coefficient of a diagnostic test in the presence of verification bias is studied. Confidence intervals for the average kappa coefficient are studied applying the methods of maximum likelihood and multiple imputation by chained equations. Simulation experiments have been carried out to study the asymptotic behaviors of the proposed intervals, given some application rules. The results obtained in our simulation experiments have shown that the multiple imputation by chained equations method provides better results than the maximum likelihood method. A function has been written in R to estimate the average kappa coefficient by applying multiple imputation. The results have been applied to the diagnosis of liver disease.

]]>Mathematics doi: 10.3390/math9141693

Authors: Mohammed K. A. Kaabar Ahmed Refice Mohammed Said Souid Francisco Martínez Sina Etemad Zailan Siri Shahram Rezapour

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.

]]>Mathematics doi: 10.3390/math9141691

Authors: Shaohong Wang Zhan Zhou

Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.

]]>Mathematics doi: 10.3390/math9141692

Authors: Izhar Uddin Sajan Aggarwal Afrah A. N. Abdou

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

]]>Mathematics doi: 10.3390/math9141690

Authors: Youngkyu Kim Karen Wang Youngsoo Choi

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than 10−5 for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve O(10−3) to O(10−4) relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve O(10) online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.

]]>Mathematics doi: 10.3390/math9141689

Authors: Odysseas Kosmas Pieter Boom Andrey P. Jivkov

The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential (elastic) energy, a function of the deformation gradient invariants. Based on this, in the present work we built a “discrete energy model” that uses maps between nodal positions of a discrete mesh linked with the invariants of the deformation gradient via standard barycentric coordinates. A special derivation is provided for domains tessellated by tetrahedrons, where the energy functionals are constrained by prescribed boundary conditions via Lagrange multipliers. The analysis of these domains is performed via energy minimisation, where the constraints are eliminated via pre-multiplication of the discrete equations by a discrete null-space matrix of the constraint gradients. Numerical examples are provided to verify the accuracy of the proposed technique. The standard barycentric coordinate system in this work is restricted to three-dimensional (3-D) convex polytopes. We show that for an explicit energy expression, applicable also to non-convex polytopes, the general barycentric coordinates constitute fundamental tools. We define, in addition, the discrete energy via a gradient for general polytopes, which is a natural extension of the definition for discrete domains tessellated by tetrahedra. We, finally, prove that the resulting expressions can consistently describe the deformation of solids.

]]>Mathematics doi: 10.3390/math9141688

Authors: Guangyu Dan Weiguo Li Zheng Zhong Kaibao Sun Qingfei Luo Richard L. Magin Xiaohong Joe Zhou M. Muge Karaman

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time random-walk (CTRW) model, which introduces two new parameters: a fractional order time derivative α and a fractional order spatial derivative β. These new parameters have been linked to intravoxel diffusion heterogeneities in time and space, respectively, and are believed to depend on diffusion times. Studies on this time dependency are limited, largely because the diffusion time cannot vary over a board range in a conventional spin-echo echo-planar imaging sequence due to the accompanying T2 decays. In this study, we investigated the time-dependency of the CTRW model in Sephadex gel phantoms across a broad diffusion time range by employing oscillating-gradient spin-echo, pulsed-gradient spin-echo, and pulsed-gradient stimulated echo sequences. We also performed Monte Carlo simulations to help understand our experimental results. It was observed that the diffusion process fell into the Gaussian regime at extremely short diffusion times whereas it exhibited a strong time dependency in the CTRW parameters at longer diffusion times.

]]>Mathematics doi: 10.3390/math9141687

Authors: Slobodan Filipovski Robert Jajcay

Let G be a graph on n vertices and m edges, with maximum degree Δ(G) and minimum degree δ(G). Let A be the adjacency matrix of G, and let λ1≥λ2≥…≥λn be the eigenvalues of G. The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G, that is E(G)=|λ1|+…+|λn|. The energy of G is known to be at least twice the minimum degree of G, E(G)≥2δ(G). Akbari and Hosseinzadeh conjectured that the energy of a graph G whose adjacency matrix is nonsingular is in fact greater than or equal to the sum of the maximum and the minimum degrees of G, i.e., E(G)≥Δ(G)+δ(G). In this paper, we present a proof of this conjecture for hyperenergetic graphs, and we prove an inequality that appears to support the conjectured inequality. Additionally, we derive various lower and upper bounds for E(G). The results rely on elementary inequalities and their application.

]]>Mathematics doi: 10.3390/math9141686

Authors: Jordan Elliott Maria Kristina Belen Luca Mainardi Josè Felix Rodriguez Matas

(1) Background: in silico models are increasingly relied upon to study the mechanisms of atrial fibrillation. Due to the complexity associated with atrial models, cellular variability is often ignored. Recent studies have shown that cellular variability may have a larger impact on electrophysiological behaviour than previously expected. This paper compares two methods for AF remodelling using regional populations. (2) Methods: using 200,000 action potentials, experimental data was used to calibrate healthy atrial regional populations with two cellular models. AF remodelling was applied by directly adjusting maximum channel conductances. AF remodelling was also applied through adjusting biomarkers. The methods were compared upon replication of experimental data. (3) Results: compared to the percentage method, the biomarker approach resulted in smaller changes. RMP, APD20, APD50, and APD90 were changed in the percentage method by up to 11%, 500%, 50%, and 60%, respectively. In the biomarker approach, RMP, APD20, APD50, and APD90 were changed by up to 4.5%, 132%, 50%, and 35%, respectively. (4) Conclusion: applying AF remodelling through biomarker-based clustering resulted in channel conductance changes that were consistent with experimental data, while maintaining the highly non-linear relationships between channel conductances and biomarkers. Directly changing conductances in the healthy regional populations impacted the non-linear relationships and resulted in non-physiological APD20 and APD50 values.

]]>Mathematics doi: 10.3390/math9141685

Authors: Julian Miller Lukas Trümper Christian Terboven Matthias S. Müller

With the quickly evolving hardware landscape of high-performance computing (HPC) and its increasing specialization, the implementation of efficient software applications becomes more challenging. This is especially prevalent for domain scientists and may hinder the advances in large-scale simulation software. One idea to overcome these challenges is through software abstraction. We present a parallel algorithm model that allows for global optimization of their synchronization and dataflow and optimal mapping to complex and heterogeneous architectures. The presented model strictly separates the structure of an algorithm from its executed functions. It utilizes a hierarchical decomposition of parallel design patterns as well-established building blocks for algorithmic structures and captures them in an abstract pattern tree (APT). A data-centric flow graph is constructed based on the APT, which acts as an intermediate representation for rich and automated structural transformations. We demonstrate the applicability of this model to three representative algorithms and show runtime speedups between 1.83 and 2.45 on a typical heterogeneous CPU/GPU architecture.

]]>Mathematics doi: 10.3390/math9141684

Authors: Yuexia Wang Zhihuo Xu

Contract cheating refers to students using third-party online resources to complete their coursework. It is not only a unilateral result of the student, but also has a relationship with educators, as well as social resources. However, little work has been performed to analyze the complex behavioral aspects behind contract cheating in Chinese universities. To this end, this article presents a statistical analysis of contract cheating in Chinese universities. First, a unique parallel survey of educators and students was conducted to collect data from August 2018 to August 2020. Next, statistical analyses were performed to explore students’ experiences and attitudes toward contract cheating and the contextual factors that relate to these behaviors. Additionally, Pearson correlation tests were conducted on the survey data to find potential factors for contract cheating. Finally, a multivariate statistical technique, partial-least-squares regression (PLSR), was applied to interpret the results. The results of the statistical analysis showed that the main motivation for contract cheating is to receive good grades (the correlation coefficient ρ is 0.1309) from the perspective of students’ personal learning; from the side of university management, clear regulations (ρ=−0.1378), penalties for cheating (ρ=−0.1275), and the use of cheating-detection software (ρ=−0.1186) can directly reduce cheating; from the perspective of teachers’ teaching, lecturers’ feedback on cheating on assignments (ρ=−0.1510) can effectively reduce students’ cheating behavior; in addition, increasing students’ sense of achievement in course learning (ρ=−0.2619) also helps to reduce the probability of cheating.

]]>Mathematics doi: 10.3390/math9141683

Authors: Sergei Dotsenko Vladimir Mazalov

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and its form is obtained. For several particular graphs, the explicit form of the core is presented.

]]>Mathematics doi: 10.3390/math9141682

Authors: Jianfeng Liu Liguo Zhou Yuyan Wang

With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research on the irrational behavior of the e-platform altruistic preference. Therefore, aiming at the LCECSC composed of a single e-platform and a single manufacturer, this paper establishes two basic models with or without altruistic preference. Additionally, this paper combines the characteristics of online sales and assumes that altruistic preference is a proportional function of commission, then establishes a commission-based extended model with altruistic preference to further explore the influence of commission on its altruistic preference. The current literature does not consider this point, nor does it analyze the influence of other parameters on the degree of altruism preference. By comparing the optimal decisions and numerical analysis among the models, the following conclusions can be drawn that: (1) different from the traditional offline supply chain, the profit of the dominator e-platform is lower than the profit of the follower manufacturer; (2) when the consumers’ carbon emission reduction elasticity coefficient increases, service level, sales price, carbon emission reduction, sales, supply chain members profits, and system profit increase, ultimately improving economic and environmental performances; (3) the altruistic preference behavior of the e-platform is a behavior of ‘profit transferring’. The moderate altruistic preference is conducive to the stable operation and long-term development of LCECSC.

]]>Mathematics doi: 10.3390/math9141681

Authors: Brecht Verbeken Marie-Anne Guerry

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria.

]]>Mathematics doi: 10.3390/math9141680

Authors: Hui Chen Kunpeng Xu Lifei Chen Qingshan Jiang

Kernel clustering of categorical data is a useful tool to process the separable datasets and has been employed in many disciplines. Despite recent efforts, existing methods for kernel clustering remain a significant challenge due to the assumption of feature independence and equal weights. In this study, we propose a self-expressive kernel subspace clustering algorithm for categorical data (SKSCC) using the self-expressive kernel density estimation (SKDE) scheme, as well as a new feature-weighted non-linear similarity measurement. In the SKSCC algorithm, we propose an effective non-linear optimization method to solve the clustering algorithm’s objective function, which not only considers the relationship between attributes in a non-linear space but also assigns a weight to each attribute in the algorithm to measure the degree of correlation. A series of experiments on some widely used synthetic and real-world datasets demonstrated the better effectiveness and efficiency of the proposed algorithm compared with other state-of-the-art methods, in terms of non-linear relationship exploration among attributes.

]]>Mathematics doi: 10.3390/math9141679

Authors: Jacopo Giacomelli Luca Passalacqua

The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

]]>Mathematics doi: 10.3390/math9141675

Authors: Irena Jadlovská George E. Chatzarakis Jozef Džurina Said R. Grace

In this paper, effective oscillation criteria for third-order delay differential equations of the form, r2r1y′′′(t)+q(t)y(τ(t))=0 ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when applied to a Euler-type delay differential equation and, to the best of our knowledge, improve all existing results from the literature. Examples are provided to illustrate the importance of the main results.

]]>Mathematics doi: 10.3390/math9141678

Authors: Mariano González-Sánchez Eva M. Ibáñez Jiménez Ana I. Segovia San Juan

The usual measures of market risk are based on the axiom of positive homogeneity while neglecting an important element of market information—liquidity. To analyze the effects of this omission, in the present study, we define the behavior of prices and volume via stochastic processes subordinated to the time elapsing between two consecutive transactions in the market. Using simulated data and market data from companies of different sizes and capitalization levels, we compare the results of measuring risk using prices compared to using both prices and volumes. The results indicate that traditional measures of market risk behave inversely to the degree of liquidity of the asset, thereby underestimating the risk of liquid assets and overestimating the risk of less liquid assets.

]]>Mathematics doi: 10.3390/math9141677

Authors: Zdravka Aljinović Branka Marasović Tea Šestanović

This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naïve portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process.

]]>Mathematics doi: 10.3390/math9141676

Authors: Chao Liu Kexin Li Peng Jiang Ding Li Liping Su Shuting Lu Anni Li

With the dawn of economic globalization and the knowledge economy, intellectual capital has become the most important factor to determine economic growth. However, due to resource endowment, location conditions, policy differences, and other factors, provinces in China show sizeable differences in regional intellectual capital (RIC), which affects the coordinated development of the regional economy. Evaluating RIC is a typical multiple-criteria decision-making (MCDM) problem. Therefore, this study employs a set of MCDM techniques to solve this problem. First, the Delphi method is used to determine the formal decision structure based on a systematic literature review. A novel hybrid method, namely, the Grey-based Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Network Process (ANP), i.e., GDANP, is employed to obtain the relative weight of each criterion. Finally, based on the data of 31 provinces in China, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to evaluate the RIC. According to the questionnaires filled out by an expert panel, we establish an evaluation index of RIC with 21 criteria. Based on the results of empirical study, the level of RIC in different regions in China is quite different. Furthermore, the RIC ranking is largely consistent with the provincial gross domestic product (GDP) ranking, in line with the current status of development in the regions. Indeed, this paper shows that the proposed hybrid method can effectively measure the level of RIC.

]]>Mathematics doi: 10.3390/math9141674

Authors: Hesham Alhumade Hegazy Rezk Abdulrahim A. Al-Zahrani Sharif F. Zaman Ahmed Askalany

The main target of this research work is to model the output performance of adsorption water desalination system (AWDS) in terms of switching and cycle time using artificial intelligence. The output performance of the ADC system is expressed by the specific daily water production (SDWP), the coefficient of performance (COP), and specific cooling power (SCP). A robust Adaptive Network-based Fuzzy Inference System (ANFIS) model of SDWP, COP, and SCP was built using the measured data. To demonstrate the superiority of the suggested ANFIS model, the model results were compared with those achieved by Analysis of Variance (ANOVA) based on the maximum coefficient of determination and minimum error between measured and estimated data in addition to the mean square error (MSE). Applying ANOVA, the average coefficient-of-determination values were 0.8872 and 0.8223, respectively, for training and testing. These values are increased to 1.0 and 0.9673, respectively, for training and testing thanks to ANFIS based modeling. In addition, ANFIS modelling decreased the RMSE value of all datasets by 83% compared with ANOVA. In sum, the main findings confirmed the superiority of ANFIS modeling of the output performance of adsorption water desalination system compared with ANOVA.

]]>Mathematics doi: 10.3390/math9141673

Authors: Kiki Ariyanti Sugeng Denny Riama Silaban Martin Bača Andrea Semaničová-Feňovčíková

Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights are distinct, where the weight of a vertex x∈V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d=1 and determine the precise values of the corresponding graph invariant for certain families of graphs.

]]>Mathematics doi: 10.3390/math9141672

Authors: Juhaina Awawdeh Shahbari

This study was conducted among 28 seventh-grade students. They worked in groups in an activity with modeling features; the activity consisted of three tasks dealing with an intuitive error, namely, same A–same B. The data source was nine video recordings of three groups across the three activities. The results obtained from analyses of students’ discussions and interactions indicate that they moved through three central stages: the intuitive error stage, the revealing of the intuitive error connected with cognitive conflict and the stage of overcoming the intuitive errors. In each of the three stages in the three tasks, we identified similar emotion features among the three groups across the three tasks. In the intuitive error stage, the participants were characterized by confidence, comfort and enjoyment. In revealing the intuitive errors, we identified several indicators and signs of non-comfortable situations by revealing the errors in the three tasks, such as a high sound or sad tone of voice, physical movements such as moving closer to the computer screen and other physical indicators such as opening the mouth and putting a hand on the head or the face. After overcoming and understanding the sources of the errors, the participants showed confidence that was clear in their facial signs, joy and smiles, loud tone and eye contact between students and the teacher, or between students.

]]>Mathematics doi: 10.3390/math9141671

Authors: Javier De la Hoz-M Mª José Fernández-Gómez Susana Mendes

In this paper we propose an open source application called LDAShiny, which provides a graphical user interface to perform a review of scientific literature using the latent Dirichlet allocation algorithm and machine learning tools in an interactive and easy-to-use way. The procedures implemented are based on familiar approaches to modeling topics such as preprocessing, modeling, and postprocessing. The tool can be used by researchers or analysts who are not familiar with the R environment. We demonstrated the application by reviewing the literature published in the last three decades on the species Oreochromis niloticus. In total we reviewed 6196 abstracts of articles recorded in Scopus. LDAShiny allowed us to create the matrix of terms and documents. In the preprocessing phase it went from 530,143 unique terms to 3268. Thus, with the implemented options the number of unique terms was reduced, as well as the computational needs. The results showed that 14 topics were sufficient to describe the corpus of the example used in the demonstration. We also found that the general research topics on this species were related to growth performance, body weight, heavy metals, genetics and water quality, among others.

]]>Mathematics doi: 10.3390/math9141670

Authors: Ali Enayat Vladimir Kanovei Vassily Lyubetsky

Examples of effectively indiscernible projective sets of real numbers in various models of set theory are presented. We prove that it is true, in Miller and Laver generic extensions of the constructible universe, that there exists a lightface Π21 equivalence relation on the set of all nonconstructible reals, having exactly two equivalence classes, neither one of which is ordinal definable, and therefore the classes are OD-indiscernible. A similar but somewhat weaker result is obtained for Silver extensions. The other main result is that for any n, starting with 2, the existence of a pair of countable disjoint OD-indiscernible sets, whose associated equivalence relation belongs to lightface Πn1, does not imply the existence of such a pair with the associated relation in Σn1 or in a lower class.

]]>Mathematics doi: 10.3390/math9141668

Authors: Chi-Lu Peng Wen-Kuei Chen An-Pin Wei

Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mathematics and science, but they may not have studied financial theory. To facilitate the classroom teaching of the Capital Asset Pricing Model (CAPM) for STEM students, this paper seeks to expound on the essence of the theory starting at a two-asset framework. Adopting the concepts proposed by Merton (1972), this paper accomplishes the derivation by virtue of basic mathematical tools such as linear algebra, geometry, and statistics except for calculus. We show that the major aspects of Merton’s derivation of the CAPM for a universe of N assets may also be obtained in a two-asset world. Through the methods of this article, students will learn the in-depth theory of CAPM and its hands-on empirical tool. For example, students will realize that even if investors specify different threshold rewards, their different CAPMs will yield identical pricing for assets and portfolios.

]]>Mathematics doi: 10.3390/math9141669

Authors: Marie Billaud-Friess Antonio Falcó Anthony Nouy

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension r&lt;k in Rk, which avoids the use of equivalence classes. The set Gr(Rk) is equipped with an atlas, which provides it with the structure of an analytic manifold modeled on R(k−r)×r. Then, we define an atlas for the set Mr(Rk×r) of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rk) and typical fibre GLr, the general linear group of invertible matrices in Rk×k. Finally, we define an atlas for the set Mr(Rn×m) of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rn)×Gr(Rm) and typical fibre GLr. The atlas of Mr(Rn×m) is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the set Mr(Rn×m) equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space Rn×m equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space Rn×m, seen as the union of manifolds Mr(Rn×m), as an analytic manifold equipped with a topology for which the matrix rank is a continuous map.

]]>Mathematics doi: 10.3390/math9141667

Authors: Mikhail I. Gomoyunov

The paper deals with a two-person zero-sum differential game for a dynamical system described by differential equations with the Caputo fractional derivatives of an order α∈(0,1) and a Bolza-type cost functional. A relationship between the differential game and the Cauchy problem for the corresponding Hamilton–Jacobi–Bellman–Isaacs equation with fractional coinvariant derivatives of the order α and the natural boundary condition is established. An emphasis is given to construction of optimal positional (feedback) strategies of the players. First, a smooth case is studied when the considered Cauchy problem is assumed to have a sufficiently smooth solution. After that, to cope with a general non-smooth case, a generalized minimax solution of this problem is involved.

]]>Mathematics doi: 10.3390/math9141663

Authors: Yiqing Xue Ping Zhao

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results.

]]>Mathematics doi: 10.3390/math9141664

Authors: Chun-Tang Chao Ding-Horng Chen Juing-Shian Chiou

This paper proves that the controller design for switched singularly perturbed systems can be synthesized from the controllers of individual slow–fast subsystems. Under the switching rules of individual slow–fast subsystems, switched singularly perturbed systems can be stabilized under a small value of ε. The switching rule is designed on the basis of state transformation of the individual subsystems.

]]>Mathematics doi: 10.3390/math9141665

Authors: Fátima Cruz Ricardo Almeida Natália Martins

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

]]>Mathematics doi: 10.3390/math9141666

Authors: Surang Sitho Muhammad Aamir Ali Hüseyin Budak Sotiris K. Ntouyas Jessada Tariboon

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the qϰ2-quantum integral to show midpoint and trapezoidal inequalities for qϰ2-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite–Hadamard-type inequality for preinvex functions via qϰ1-quantum integral is not valid for preinvex functions, and we present its proper form. We use qϰ1-quantum integrals to show midpoint inequalities for qϰ1-differentiable preinvex functions. It is also demonstrated that by considering the limit q→1− and ηϰ2,ϰ1=−ηϰ1,ϰ2=ϰ2−ϰ1 in the newly derived results, the newly proved findings can be turned into certain known results.

]]>Mathematics doi: 10.3390/math9141662

Authors: Jacques Lobry

A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is eliminated at the discrete level by using the finite element approximation of the fundamental solutions (Green’s functions) at every node of the related mesh. This “FEM-Green” approach replaces the standard boundary element method. It is simpler to implement because no integration on the boundary of the domain is required. Then, the method leads to a substantially reduced computational burden. Moreover, the coupling with finite elements is more natural since it is based on the same Galerkin approximation. Some examples with open boundary and nonlinear materials are presented and compared with the standard finite element method.

]]>Mathematics doi: 10.3390/math9141661

Authors: Mohamed Abdel-Basset Reda Mohamed Safaa Saber S. S. Askar Mohamed Abouhawwash

In this paper, a modified flower pollination algorithm (MFPA) is proposed to improve the performance of the classical algorithm and to tackle the nonlinear equation systems widely used in engineering and science fields. In addition, the differential evolution (DE) is integrated with MFPA to strengthen its exploration operator in a new variant called HFPA. Those two algorithms were assessed using 23 well-known mathematical unimodal and multimodal test functions and 27 well-known nonlinear equation systems, and the obtained outcomes were extensively compared with those of eight well-known metaheuristic algorithms under various statistical analyses and the convergence curve. The experimental findings show that both MFPA and HFPA are competitive together and, compared to the others, they could be superior and competitive for most test cases.

]]>Mathematics doi: 10.3390/math9141660

Authors: Pau Fonseca i Casas Joan Garcia i Subirana Víctor García i Carrasco Xavier Pi i Palomés

The spread of the SARS-CoV-2 modeling is a challenging problem because of its complex nature and lack of information regarding certain aspects. In this paper, we explore a Digital Twin approach to model the pandemic situation in Catalonia. The Digital Twin is composed of three different dynamic models used to perform the validations by a Model Comparison approach. We detail how we use this approach to obtain knowledge regarding the effects of the nonpharmaceutical interventions and the problems we faced during the modeling process. We use Specification and Description Language (SDL) to represent the compartmental forecasting model for the SARS-CoV-2. Its graphical notation simplifies the different specialists’ understanding of the model hypotheses, which must be validated continuously following a Solution Validation approach. This model allows the successful forecasting of different scenarios for Catalonia. We present some formalization details, discuss the validation process and present some results obtained from the validation model discussion, which becomes a digital twin of the pandemic in Catalonia.

]]>Mathematics doi: 10.3390/math9141657

Authors: Jochen Merker Benjamin Kunsch Gregor Schuldt

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

]]>Mathematics doi: 10.3390/math9141659

Authors: Ahmed AlGhamdi Omar Bazighifan Rami Ahmad El-Nabulsi

In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than one practical example.

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Authors: Shipra Singh Aviv Gibali Simeon Reich

We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized Nash equilibrium problem can be applied to solving traffic network problems, the aim of which is to minimize the traffic cost of each route and to solving a river basin pollution problem. Moreover, we also study the proposed multi-time generalized Nash equilibrium problem as a projected dynamical system and numerically illustrate our theoretical results.

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Authors: José Carlos R. Alcantud

This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit and amenable to mathematical manipulations. Various consequences demonstrate that our theory has far-reaching implications for the development of soft topology and its extensions.

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Authors: Zdenek Smutny Zdenek Sulc Jan Lansky

The cryptocurrency market is very young, volatile, and highly risky. By the end of 2020, a new bull run started, and the prices of several cryptocurrencies reached record-breaking highs. The factors affecting this rise of cryptocurrencies include the impacts of the COVID-19 pandemic, the economic crisis and the global increase in the inflation rate, as well as the gradual acceptance and adoption of cryptocurrencies by people worldwide. This exploratory research is focused on this last factor, i.e., using cryptocurrency and with it, the associated support of its ecosystem (e.g., mining, staking). A survey was carried out investigating the motivational factors and barriers to investment in cryptocurrency for Czech representatives of Generations Y and Z (18–42 years; n = 468). The geographic scope was nationwide, and quota sampling was used. Notably, this survey was carried out prior to the global COVID-19 pandemic outbreak, and it is thus not affected by the pandemic and its related economic impacts. The article investigates the dependency between the individual motivational factors and barriers from the perspective of the tendency to take risks (using the risk propensity scale), according to gender and representation of Generations Y and Z. The lack of information on this form of investment is considered as the main barrier to investment in cryptocurrency, with respect to sex and generations. Compared to that, a negative experience with investment in cryptocurrency constitutes the most minor barrier. Respondents that have a tendency to take risks are mostly put off by their lack of experience with investment in general. The main motivational factor for investment in cryptocurrency, with respect to sex and generations, is considered to be the speed of increase in cryptocurrency value. On the other hand, the least encouraging factor is the opportunity to use the high volatility of cryptocurrency for speculative trading. Interestingly, this factor mostly encourages respondents that do not have a tendency to take risks. The findings are discussed, along with the presentation of their implications for practice and the directions of further explanatory research.

]]>Mathematics doi: 10.3390/math9141654

Authors: Iulia-Elena Hirica Cristina-Liliana Pripoae Gabriel-Teodor Pripoae Vasile Preda

The paper generalizes and extends the notions of dual connections and of statistical manifold, with and without torsion. Links with the deformation algebras and with the Riemannian Rinehart algebras are established. The semi-Riemannian manifolds admitting flat dual connections with torsion are characterized, thus solving a problem suggested in 2000 by S. Amari and H. Nagaoka. New examples of statistical manifolds are constructed, within and beyond the classical setting. The invariant statistical structures on Lie groups are characterized and the dimension of their set is determined. Examples for the new defined geometrical objects are found in the theory of Information Geometry.

]]>Mathematics doi: 10.3390/math9141653

Authors: Gabriela Czibula Andrei Mihai Alexandra-Ioana Albu Istvan-Gergely Czibula Sorin Burcea Abdelkader Mezghani

Short-term quantitative precipitation forecast is a challenging topic in meteorology, as the number of severe meteorological phenomena is increasing in most regions of the world. Weather radar data is of utmost importance to meteorologists for issuing short-term weather forecast and warnings of severe weather phenomena. We are proposing AutoNowP, a binary classification model intended for precipitation nowcasting based on weather radar reflectivity prediction. Specifically, AutoNowP uses two convolutional autoencoders, being trained on radar data collected on both stratiform and convective weather conditions for learning to predict whether the radar reflectivity values will be above or below a certain threshold. AutoNowP is intended to be a proof of concept that autoencoders are useful in distinguishing between convective and stratiform precipitation. Real radar data provided by the Romanian National Meteorological Administration and the Norwegian Meteorological Institute is used for evaluating the effectiveness of AutoNowP. Results showed that AutoNowP surpassed other binary classifiers used in the supervised learning literature in terms of probability of detection and negative predictive value, highlighting its predictive performance.

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