Mathematics doi: 10.3390/math9050572

Authors: Samuele Antonini Giulia Lisarelli

In this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment and having the semiotic potential for embedding mathematical meanings of covariation of independent and dependent variables. After laying down the theoretical grounds, we formulate the design principles that emerged as the result of bringing the theory into a dialogue with the didactical aims. Finally, we present a teaching sequence, designed and implemented on the basis of the design principles and we show how students’ efforts in describing and manipulating the different graphs of functions can promote their production of specific signs that can progressively evolve towards mathematical meanings.

]]>Mathematics doi: 10.3390/math9050571

Authors: Marat Akhmet Duygu Aruğaslan Çinçin Madina Tleubergenova Zakhira Nugayeva

This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches.

]]>Mathematics doi: 10.3390/math9050570

Authors: Jin Hee Bae Minwoo Kim J.S. Lim Zong Woo Geem

This paper proposes a feature selection method that is effective in distinguishing colorectal cancer patients from normal individuals using K-means clustering and the modified harmony search algorithm. As the genetic cause of colorectal cancer originates from mutations in genes, it is important to classify the presence or absence of colorectal cancer through gene information. The proposed methodology consists of four steps. First, the original data are Z-normalized by data preprocessing. Candidate genes are then selected using the Fisher score. Next, one representative gene is selected from each cluster after candidate genes are clustered using K-means clustering. Finally, feature selection is carried out using the modified harmony search algorithm. The gene combination created by feature selection is then applied to the classification model and verified using 5-fold cross-validation. The proposed model obtained a classification accuracy of up to 94.36%. Furthermore, on comparing the proposed method with other methods, we prove that the proposed method performs well in classifying colorectal cancer. Moreover, we believe that the proposed model can be applied not only to colorectal cancer but also to other gene-related diseases.

]]>Mathematics doi: 10.3390/math9050569

Authors: Kai Zhang Yicheng Yu

Recently, the differential evolution (DE) algorithm has been widely used to solve many practical problems. However, DE may suffer from stagnation problems in the iteration process. Thus, we propose an enhancing differential evolution with a rank-up selection, named RUSDE. First, the rank-up individuals in the current population are selected and stored into a new archive; second, a debating mutation strategy is adopted in terms of the updating status of the current population to decide the parent’s selection. Both of the two methods can improve the performance of DE. We conducted numerical experiments based on various functions from CEC 2014, where the results demonstrated excellent performance of this algorithm. Furthermore, this algorithm is applied to the real-world optimization problem of the four-bar linkages, where the results show that the performance of RUSDE is better than other algorithms.

]]>Mathematics doi: 10.3390/math9050568

Authors: Huthaifa AL-Khazraji Colin Cole William Guo

The production–inventory system is a problem of multivariable input and multivariant output in mathematics. Selecting the best system control parameters is a crucial managerial decision to achieve and dynamically maintain an optimal performance in terms of balancing the order rate and stock level under dynamic influence of many factors affecting the system operations. The dynamic performance of the popular APIOBPCS model and the newly modified 2APIOBPCS model for optimal control of production–inventory systems is examined in the study. This examination is based on the leveled ground with a new simulation scheme that incorporates a designated multi-objective particle swarm optimization (MOPSO) algorithm into the simulation, which enables the optimal set of system control parameters to be selected for achieving the situational best possible performance of the production–inventory system under study. The dynamic performance is measured by the variance ratio between the order rate and the sales rate related to the bullwhip effect, and the integral of absolute error related to the inventory responsiveness in response to a random customer demand. Our simulation indicates that the 2APIOBPCS model performed better than or at least no worse than, and more robust than the APIOBPCS model under different conditions.

]]>Mathematics doi: 10.3390/math9050567

Authors: Giovanni Tocci Monaco Nicholas Fantuzzi Francesco Fabbrocino Raimondo Luciano

Nanoplates have been extensively utilized in the recent years for applications in nanoengineering as sensors and actuators. Due to their operative nanoscale, the mechanical behavior of such structures might also be influenced by inter-atomic material interactions. For these reasons, nonlocal models are usually introduced for studying their mechanical behavior. Sensor technology of plate structures should be formulated with coupled mechanics where elastic, magnetic and electric fields interact among themselves. In addition, the effect of hygro-thermal environments are also considered since their presence might effect the nanoplate behavior. In this work a trigonometric approach is developed for investigating smart composite nanoplates using a strain gradient nonlocal procedure. Convergence of the present method is also reported in terms of displacements and electro-magnetic potentials. Results agree well with the literature and open novel applications in this field for further developments.

]]>Mathematics doi: 10.3390/math9050566

Authors: Julio Emilio Marco-Franco Pedro Pita-Barros Silvia González-de-Julián Iryna Sabat David Vivas-Consuelo

When exceptional situations, such as the COVID-19 pandemic, arise and reliable data is not available at decision-making times, estimation using mathematical models can provide a reasonable reckoning for health planning. We present a simplified model (static but with two-time references) for estimating the cost-effectiveness of the COVID-19 vaccine. A simplified model provides a quick assessment of the upper bound of cost-effectiveness, as we illustrate with data from Spain, and allows for easy comparisons between countries. It may also provide useful comparisons among different vaccines at the marketplace, from the perspective of the buyer. From the analysis of this information, key epidemiological figures, and costs of the disease for Spain have been estimated, based on mortality. The fatality rate is robust data that can alternatively be obtained from death registers, funeral homes, cemeteries, and crematoria. Our model estimates the incremental cost-effectiveness ratio (ICER) to be 5132 € (4926–5276) as of 17 February 2021, based on the following assumptions/inputs: An estimated cost of 30 euros per dose (plus transport, storing, and administration), two doses per person, efficacy of 70% and coverage of 70% of the population. Even considering the possibility of some bias, this simplified model provides confirmation that vaccination against COVID-19 is highly cost-effective.

]]>Mathematics doi: 10.3390/math9050555

Authors: Chénangnon Frédéric Tovissodé Sèwanou Hermann Honfo Jonas Têlé Doumatè Romain Glèlè Kakaï

Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

]]>Mathematics doi: 10.3390/math9050565

Authors: Roberto G. Aragón Jesús Medina Eloísa Ramírez-Poussa

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA’s unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences.

]]>Mathematics doi: 10.3390/math9050564

Authors: Pilar Ester Isabel Morales Álvaro Moraleda Vicente Bermejo

The main aim of the present study is to analyze the differences that may exist when students address the resolution of verbal problems in their mother tongue and in the language of instruction when these are different. We understand that knowing the type of verbal problems and their semantic structure can be helpful for students’ contextual and mathematical understanding and will allow teachers to improve instruction during the first years of elementary education in bilingual schools specialized in the area of second language acquisition as well as in CLIL (Content and Language Integrated Learning). This study shows how children, as they are acquiring a greater command of the second language, show similar effectiveness to those students who work on mathematics in their mother tongue. This transversal study was conducted on 169 bilinguals studying in international schools. The sample was made up of 80 1st grade students (39 girls, mean age of 7.1 years and 41 boys, mean age of 7.3 years); and 89 2nd grade students (38 girls, mean age 8.2 years, and 51 boys, mean age 8.2 years). The exploratory analyses let us show how 1st grade students demonstrate lower effectiveness in solving problems when they do it in a second language, compared to 2nd grade students whose effectiveness is higher in carrying them out. It is also relevant that in first graders, the largest number of errors are found in the simplest tasks as students’ effectiveness is less when they are taught in a second language, since it takes them longer to create effective resolution models. This fact will allow us to reconsider appropriate strategies and interventions when teaching mathematics in bilingual contexts.

]]>Mathematics doi: 10.3390/math9050563

Authors: Mahmoud H. DarAssi Mohammad A. Safi Morad Ahmad

In this paper, we have investigated the global dynamics of a discrete-time middle east respiratory syndrome (MERS-Cov) model. The proposed discrete model was analyzed and the threshold conditions for the global attractivity of the disease-free equilibrium (DFE) and the endemic equilibrium are established. We proved that the DFE is globally asymptotically stable when R0≤1. Whenever R˜0&gt;1, the proposed model has a unique endemic equilibrium that is globally asymptotically stable. The theoretical results are illustrated by a numerical simulation.

]]>Mathematics doi: 10.3390/math9050562

Authors: Siarka

This paper addresses the problem of modeling credit risk for multi-product and global loan portfolios. The authors presented an improved version of the Basel Committee’s one-factor model for capital requirements calculation. They examined whether latent market factors corresponding to distinct portfolios are always highly correlated within the global portfolio and how this correlation impacts total losses distribution function. Historical losses of top-tier banks (JPMorgan Chace, Bank of America, Citigroup, Wells Fargo, US Bancorp) were analyzed. Furthermore, the estimation of the correlations between latent market factors was conducted, and its impact on the total loss distribution function was assessed. The research was performed based on consolidated financial statements for holding companies - FR Y-9C reports provided by the Federal Reserve Bank of Chicago. To verify the improved model, the authors analyzed two distinct loan portfolios for each bank, i.e., credit cards and commercial and industrial loans. They showed that the correlation between latent market factors could be significantly lower than one and disregarding this conclusion may lead to overestimating total unexpected losses. Hence, capital requirements calculated according to the IRB (Internal Ratings Based Approach) formula as a sum of individual VaR999 estimates may be biased. According to this finding, the enhanced one-factor model seems to be more accurate while calculating unexpected total loss for global portfolios. The authors proved that the active credit risk management process aiming to lower market factors’ correlation results in less volatile total losses. Therefore, financial institutions could be more resistant to macroeconomic downturns.

]]>Mathematics doi: 10.3390/math9050561

Authors: Pierluigi Benevieri Alessandro Calamai Massimo Furi Maria Patrizia Pera

We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.

]]>Mathematics doi: 10.3390/math9050560

Authors: Luboš Brim Samuel Pastva David Šafránek Eva Šmijáková

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

]]>Mathematics doi: 10.3390/math9050559

Authors: Achyutha Krishnamoorthy Anu Nuthan Joshua Vladimir Vishnevsky

In most of the service systems considered so far in queuing theory, no fresh customer is admitted to a batch undergoing service when the number in the batch is less than a threshold. However, a few researchers considered the case of customers accessing ongoing service batch, irrespective of how long service was provided to that batch. A queuing system with a different kind of accessibility that relates to a real situation is studied in the paper. Consider a single server queuing system in which the service process comprises of k stages. Customers can enter the system for service from a node at the beginning of any of these stages (provided the pre-determined maximum service batch size is not reached) but cannot leave the system after completion of service in any of the intermediate stages. The customer arrivals to the first node occur according to a Markovian Arrival Process (MAP). An infinite waiting room is provided at this node. At all other nodes, with finite waiting rooms (waiting capacity cj,2≤j≤k), customer arrivals occur according to distinct Poisson processes with rates λj,2≤j≤k. The service is provided according to a general bulk service rule, i.e., the service process is initiated only if at least a customers are present in the queue at node 1 and the maximum service batch size is b. Customers can join for service from any of the subsequent nodes, provided the number undergoing service is less than b. The service time distribution in each phase is exponential with service rate μjm, which depends on the service stage j,1≤j≤k, and the size of the batch m,a≤m≤b. The behavior of the system in steady-state is analyzed and some important system characteristics are derived. A numerical example is presented to illustrate the applicability of the results obtained.

]]>Mathematics doi: 10.3390/math9050558

Authors: David Valiente Héctor Campello-Vicente Emilio Velasco-Sánchez Fernando Rodríguez-Mas Nuria Campillo-Davo

University education approaches related to the field of science, technology, engineering and mathematics (STEM), have generally particularized on teaching activity and learning programs which are commonly understood as reoriented lessons that fuse theoretic concepts interweaved with practical activities. In this context, team work has been widely acknowledged as a means to conduct practical and hands-on lessons, and has been revealed to be successful in the achievement of exercise resolution and design tasks. Besides this, methodologies sustained by ICT resources such as online or blended approaches, have also reported numerous benefits for students’ active learning. However, such benefits have to be fully validated within the particular teaching context, which may facilitate student achievement to a greater or lesser extent. In this work, we analyze the impact of attendance modalities on the learning performance of a STEM-related course on “Machines and Mechanisms Theory”, in which practical lessons are tackled through a team work approach. The validity of the results is reinforced by group testing and statistical tests with a sample of 128 participants. Students were arranged in a test group (online attendance) and in a control group (face-to-face attendance) to proceed with team work during the practical lessons. Thus, the efficacy of distance and in situ methodologies is compared. Moreover, additional variables have also been compared according to the historical record of the course, in regards to previous academic years. Finally, students’ insights about the collaborative side of this program, self-knowledge and satisfaction with the proposal have also been reported by a custom questionnaire. The results demonstrate greater performance and satisfaction amongst participants in the face-to-face modality. Such a modality is prooven to be statistically significant for the final achievement of students in detriment to online attendance.

]]>Mathematics doi: 10.3390/math9050557

Authors: Morten Elkjær Uffe Thomas Jankvist

Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic online environments for mathematics teaching and learning that are emerging today, we are presented with a perhaps unique opportunity to do something about this. This study sets out to apply the research on lower secondary school students’ difficulties with equation solving, in order to eventually inform students’ personalised learning through a specific task design in a particular dynamic online environment (matematikfessor.dk). In doing so, task design theory is applied, particularly variation theory. The final design we present consists of eleven general equation types—ten types of arithmetical equations and one type of algebraic equation—and a broad range of variations of these, embedded in a potential learning-trajectory-tree structure. Besides establishing this tree structure, the main theoretical contribution of the study and the task design we present is the detailed treatment of the category of arithmetical equations, which also involves a new distinction between simplified and non-simplified arithmetical equations.

]]>Mathematics doi: 10.3390/math9050556

Authors: Guillermo Cotrina Alberto Peinado Andrés Ortiz

A new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field GF(2n) of the one using cyclic rotations of linear feedback shift registers (LFSRs) originally defined in GF(2). The rotations applied to LFSRs in the binary case are no longer needed in the extended field due to the implicit rotations found in the binary equivalent model of LFSRs in GF(2n). The new proposal is aligned with the current trend in cryptography of using extended fields as a way to speed up the bitrate of the pseudorandom generators. This proposal allows the use of LFSRs in cryptography to be taken further, from the generation of the classical uniformly distributed sequences to other areas, such as quantum key distribution schemes, in which sequences with Gaussian distribution are needed. The paper contains the statistical analysis of the numbers produced and a comparison with other Gaussian generators.

]]>Mathematics doi: 10.3390/math9050554

Authors: Jiří Mazurek Radomír Perzina Jaroslav Ramík David Bartl

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

]]>Mathematics doi: 10.3390/math9050549

Authors: Nurul Amira Zainal Roslinda Nazar Kohilavani Naganthran Ioan Pop

There has been significant interest in exploring a stagnation point flow due to its numerous potential uses in engineering applications such as cooling of nuclear reactors. Hence, this study proposed a numerical analysis on the unsteady magnetohydrodynamic (MHD) mixed convection at three-dimensional stagnation point flow in Al2O3–Cu/H2O hybrid nanofluid over a permeable sheet. The ordinary differential equations are accomplished by simplifying the governing partial differential equations through suitable similarity transformation. The numerical computation is established by the MATLAB system software using the bvp4c technique. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The influence of certain functioning parameters is inspected, and notable results exposed that the rate of heat transfer is exaggerated along with the skin friction coefficient while the suction/injection and magnetic parameters are intensified. The results also signified that the rise in the volume fraction of the nanoparticle and the decline of the unsteadiness parameter demonstrates a downward attribution towards the heat transfer performance and skin friction coefficient. Conclusively, the observations are confirmed to have multiple solutions, which eventually contribute to an investigation of the analysis of the solution stability, thereby justifying the viability of the first solution.

]]>Mathematics doi: 10.3390/math9050553

Authors: Anak Nongmanee Sorasak Leeratanavalee

Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

]]>Mathematics doi: 10.3390/math9050551

Authors: Trung Duc Tran Vinh Ngoc Tran Jongho Kim

Accurate and reliable dam inflow prediction models are essential for effective reservoir operation and management. This study presents a data-driven model that couples a long short-term memory (LSTM) network with robust input predictor selection, input reconstruction by wavelet transformation, and efficient hyper-parameter optimization by K-fold cross-validation and the random search. First, a robust analysis using a “correlation threshold” for partial autocorrelation and cross-correlation functions is proposed, and only variables greater than this threshold are selected as input predictors and their time lags. This analysis indicates that a model trained on a threshold of 0.4 returns the highest Nash–Sutcliffe efficiency value; as a result, six principal inputs are selected. Second, using additional subseries reconstructed by the wavelet transform improves predictability, particularly for flow peak. The peak error values of LSTM with the transform are approximately one-half to one-quarter the size of those without the transform. Third, for a K of 5 as determined by the Silhouette coefficients and the distortion score, the wavelet-transformed LSTMs require a larger number of hidden units, epochs, dropout, and batch size. This complex configuration is needed because the amount of inputs used by these LSTMs is five times greater than that of other models. Last, an evaluation of accuracy performance reveals that the model proposed in this study, called SWLSTM, provides superior predictions of the daily inflow of the Hwacheon dam in South Korea compared with three other LSTM models by 84%, 78%, and 65%. These results strengthen the potential of data-driven models for efficient and effective reservoir inflow predictions, and should help policy-makers and operators better manage their reservoir operations.

]]>Mathematics doi: 10.3390/math9050552

Authors: Zhiyu Zhang Ruihua Feng Irena Jadlovská Qingmin Liu

Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.

]]>Mathematics doi: 10.3390/math9050550

Authors: Vilém Novák Soheyla Mirshahi

In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies than a given threshold and reduce the random noise significantly. The F-transform also provides an estimation of the slope of time series in a given imprecisely delineated time. We prove some of the suggested index properties and show its ability to measure similarity (and thus the interrelation) on a selection of several real financial time series. The method is well interpretable and easy to adjust.

]]>Mathematics doi: 10.3390/math9050548

Authors: Yuri S. Popkov

The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

]]>Mathematics doi: 10.3390/math9050547

Authors: Silvia Curteanu Florin Leon Andra-Maria Mircea-Vicoveanu Doina Logofătu

Empirical models based on sampled data can be useful for complex chemical engineering processes such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. In this case, the goal is to predict the monomer conversion, the numerical average molecular weight and the gravimetrical average molecular weight. This process is characterized by non-linear gel and glass effects caused by the sharp increase in the viscosity as the reaction progresses. To increase accuracy, one needs more samples in the areas with higher variation and this is achieved with adaptive sampling. An extensive comparative study is performed between three regression algorithms for this chemical process. The first two are based on the concept of a large margin, typical of support vector machines, but used for regression, in conjunction with an instance-based method. The learning of problem-specific distance metrics can be performed by means of either an evolutionary algorithm or an approximate differential approach. Having a set of prototypes with different distance metrics is especially useful when a large number of instances should be handled. Another original regression method is based on the idea of denoising autoencoders, i.e., the prototype weights and positions are set in such a way as to minimize the mean square error on a slightly corrupted version of the training set, where the instances inputs are slightly changed with a small random quantity. Several combinations of parameters and ways of splitting the data into training and testing sets are used in order to assess the performance of the algorithms in different scenarios.

]]>Mathematics doi: 10.3390/math9050546

Authors: Ramandeep Behl Sonia Bhalla Ángel Alberto Magreñán Alejandro Moysi

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

]]>Mathematics doi: 10.3390/math9050545

Authors: Jin Hee Yoon Zong Woo Geem

The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud detection, law enforcement, disease spread modeling, cancer detection, astronomical observation, music composition, fine art appreciation, and sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach to show how HS converges on an optimal solution under specific conditions. Here, we introduce a distance concept and prove the convergence based on the empirical probability. Moreover, a numerical example is provided to easily explain the theorem.

]]>Mathematics doi: 10.3390/math9050544

Authors: Alexander Bulinski Denis Dimitrov

Asymptotic unbiasedness and L2-consistency are established, under mild conditions, for the estimates of the Kullback–Leibler divergence between two probability measures in Rd, absolutely continuous with respect to (w.r.t.) the Lebesgue measure. These estimates are based on certain k-nearest neighbor statistics for pair of independent identically distributed (i.i.d.) due vector samples. The novelty of results is also in treating mixture models. In particular, they cover mixtures of nondegenerate Gaussian measures. The mentioned asymptotic properties of related estimators for the Shannon entropy and cross-entropy are strengthened. Some applications are indicated.

]]>Mathematics doi: 10.3390/math9050543

Authors: Alejandra Ríos Eusebio E. Hernández S. Ivvan Valdez

This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.

]]>Mathematics doi: 10.3390/math9050542

Authors: Gheorghe Grigoraș Bogdan-Constantin Neagu Florina Scarlatache Livia Noroc Ecaterina Chelaru

In the last years, the distribution network operators (DNOs) assumed transition strategies of the electric distribution networks (EDNs) towards the active areas of the microgrids where, regardless of the operating regimes, flexibility, economic efficiency, low power losses, and high power quality are ensured. Artificial intelligence techniques, combined with the smart devices and real-time remote communication solutions of the enormous data amounts, can represent the starting point in establishing decision-making strategies to solve one of the most important challenges related to phase load balancing (PLB). In this context, the purpose of the paper is to prove that a decision-making strategy based on a limited number of PLB devices installed at the consumers (small implementation degree) leads to similar technical benefits as in the case of full implementation in the EDNs. Thus, an original bi-level PLB methodology, considering a clustering-based selection criterion of the consumers for placement of the switching devices, was proposed. A real EDN from a rural area belonging to a Romanian DNO has been considered in testing the proposed methodology. An implementation degree of the PLB devices in the EDN by 17.5% represented the optimal solution, leading to a faster computational time with 43% and reducing the number of switching operations by 92%, compared to a full implementation degree (100%). The performance indicators related to the unbalance factor and energy-saving highlighted the efficiency of the proposed methodology.

]]>Mathematics doi: 10.3390/math9050540

Authors: Soodabeh Asadi Janez Povh

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

]]>Mathematics doi: 10.3390/math9050541

Authors: Shamoona Jabeen Zhiming Zheng Mutti-Ur Rehman Wei Wei Jehad Alzabut

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.

]]>Mathematics doi: 10.3390/math9050539

Authors: Seda Yamaç Akbiyik Mücahit Akbiyik Fatih Yilmaz

The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell numbers and its Hadamard exponential matrix. We investigate some linear algebraic properties and obtain inequalities by using matrix norms. Furthermore, some summation identities for harmonic Pell numbers are obtained. Finally, we give a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix.

]]>Mathematics doi: 10.3390/math9050537

Authors: Iulia Hirica Constantin Udriste Gabriel Pripoae Ionel Tevy

In this paper the following three goals are addressed. The first goal is to study some strong partial differential equations (PDEs) that imply curvature-flatness, in the cases of both symmetric and non-symmetric connection. Although the curvature-flatness idea is classic for symmetric connection, our main theorems about flatness solutions are completely new, leaving for a while the point of view of differential geometry and entering that of PDEs. The second goal is to introduce and study some strong partial differential relations associated to curvature-flatness. The third goal is to introduce and analyze some vector spaces of exotic objects that change the meaning of a generalized Kronecker delta projection operator, in order to discover new PDEs implying curvature-flatness. Significant examples clarify some ideas.

]]>Mathematics doi: 10.3390/math9050538

Authors: Iskandar Waini Anuar Ishak Ioan Pop

In this paper, we examine the influence of hybrid nanoparticles on flow and heat transfer over a permeable non-isothermal shrinking surface and we also consider the radiation and the magnetohydrodynamic (MHD) effects. A hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water. The similarity equations are obtained using a similarity transformation and numerical results are obtained via bvp4c in MATLAB. The results show that dual solutions are dependent on the suction strength of the shrinking surface; in addition, the heat transfer rate is intensified with an increase in the magnetic parameter and the hybrid nanoparticles volume fractions for higher values of the radiation parameter. Furthermore, the heat transfer rate is higher for isothermal surfaces as compared with non-isothermal surfaces. Further analysis proves that the first solution is physically reliable and stable.

]]>Mathematics doi: 10.3390/math9050536

Authors: Junjun Shi Jingfang Shen Yaohui Li

Finding new valuable sampling points and making these points better distributed in the design space is the key to determining the approximate effect of Kriging. To this end, a high-precision Kriging modeling method based on hybrid sampling criteria (HKM-HS) is proposed to solve this problem. In the HKM-HS method, two infilling sampling strategies based on MSE (Mean Square Error) are optimized to obtain new candidate points. By maximizing MSE (MMSE) of Kriging model, it can generate the first candidate point that is likely to appear in a sparse area. To avoid the ill-conditioned correlation matrix caused by the too close distance between any two sampling points, the MC (MSE and Correlation function) criterion formed by combining the MSE and the correlation function through multiplication and division is minimized to generate the second candidate point. Furthermore, a new screening method is used to select the final expensive evaluation point from the two candidate points. Finally, the test results of sixteen benchmark functions and a house heating case show that the HKM-HS method can effectively enhance the modeling accuracy and stability of Kriging in contrast with other approximate modeling methods.

]]>Mathematics doi: 10.3390/math9050535

Authors: Aleksandra Wójcicka-Wójtowicz Krzysztof Piasecki

Over the years, banks have faced many difficulties, related mainly to lax credit standards for borrowers and counterparties. The goal of credit risk management is to maintain the volume of credit risk at acceptable level as it is a vital feature in risk management. Credit analysts take into consideration factors of a wider spectrum, e.g., the prospects of the line of business, the experience of board members, credibility of suppliers, etc. Those factors are often considered on the linguistic scale, which includes such imprecise and inaccurate phrases, for instance, such as: more/less experienced, better/worse prospects, etc., which, for the experts and decision makers, are justified and result from their personal experience, preferences and human nature. The paper presents the approach of supporting methods in the credit risk decision-making process. It presents evaluation scales of imprecise phrases commonly used during the process of credit risk assessment based on experts’ preferences. Due to the imprecision, the oriented fuzzy numbers are a useful tool. For such described evaluation scales, we use a scoring function determined with the use of an adapted Simple Additive Weighting (SAW) method.

]]>Mathematics doi: 10.3390/math9050534

Authors: F. Thomas Bruss

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

]]>Mathematics doi: 10.3390/math9050533

Authors: Sergio Amat Alberto Magreñan Juan Ruiz Juan Carlos Trillo Dionisio F. Yañez

Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence of discontinuities, and having the maximum possible order of approximation in smooth areas. Once we have these nonlinear reconstruction operators defined, we can build the related nonlinear subdivision and multiresolution schemes and prove more accurate inequalities regarding the contractivity of the scheme for the first differences and in turn the results about stability. In this paper, we also define a new nonlinear two-dimensional multiresolution scheme as non-separable, i.e., not based on tensor product. We then present the study of the stability issues for the scheme and numerical experiments reinforcing the proven theoretical results and showing the usefulness of the algorithm.

]]>Mathematics doi: 10.3390/math9050532

Authors: María de los Ángeles Pérez-Sánchez Zhuowei Tian Almudena Barrientos-Báez José Gómez-Galán Hanliang Li

Remarkable changes have taken in social operation mode and consumers’ behavior mode because of the foot ban during the pandemic spread of COVID-19. Digital technologies such as Blockchain have shown potential in gaining competitive advantages for enterprises in such situations. This study aims to provide an insight into how to gain consumer loyalty through the use of modern and efficient Blockchain technology. In contrast to the current literature, this study combined the technology acceptance model of planned behavior theory, social exchange theory to explain the loyalty of an online travel agency (OTA) consumer. A self-administered questionnaire was used to collect data from citizens in Hangzhou, a city full of technological innovation atmosphere. Using structural equation modeling with SmartPLS©, responses from 1403 citizens were analyzed. Social norm was discovered to have a positive and significant association with the consumers’ attitude toward technology and thus enhancing the perceived usability and hedonism of OTA application, which can increase consumer loyalty. The findings suggested OTAs may gain consumers’ loyalty through adopting Blockchain technology, and local governments have played a key role in creating such an environment. New technologies have become essential professional and social tools for society. The technological environment and Blockchain within the tourism sector are fundamental elements of China’s economic engine.

]]>Mathematics doi: 10.3390/math9050531

Authors: Pedro Pablo Ortega Palencia Ruben Dario Ortiz Ortiz Ana Magnolia Marin Ramirez

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

]]>Mathematics doi: 10.3390/math9050530

Authors: Lvyang Qiu Shuyu Li Yunsick Sung

Music is a type of time-series data. As the size of the data increases, it is a challenge to build robust music genre classification systems from massive amounts of music data. Robust systems require large amounts of labeled music data, which necessitates time- and labor-intensive data-labeling efforts and expert knowledge. This paper proposes a musical instrument digital interface (MIDI) preprocessing method, Pitch to Vector (Pitch2vec), and a deep bidirectional transformers-based masked predictive encoder (MPE) method for music genre classification. The MIDI files are considered as input. MIDI files are converted to the vector sequence by Pitch2vec before being input into the MPE. By unsupervised learning, the MPE based on deep bidirectional transformers is designed to extract bidirectional representations automatically, which are musicological insight. In contrast to other deep-learning models, such as recurrent neural network (RNN)-based models, the MPE method enables parallelization over time-steps, leading to faster training. To evaluate the performance of the proposed method, experiments were conducted on the Lakh MIDI music dataset. During MPE training, approximately 400,000 MIDI segments were utilized for the MPE, for which the recovery accuracy rate reached 97%. In the music genre classification task, the accuracy rate and other indicators of the proposed method were more than 94%. The experimental results indicate that the proposed method improves classification performance compared with state-of-the-art models.

]]>Mathematics doi: 10.3390/math9050529

Authors: Eudald Romo Luis Ortiz-Gracia

In the present work, the SWIFT method for pricing European options is extended to Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiple strikes, outperforming the state-of-the-art method we compare it with. Further, the a priori knowledge of SWIFT parameters makes a reliable and practical implementation of the presented calibration method possible. A wide range of stress, speed and convergence numerical experiments is carried out, with deep in-the-money, at-the-money and deep out-of-the-money options for very short and very long maturities.

]]>Mathematics doi: 10.3390/math9050528

Authors: Qinwen Zhu Grégoire Loeper Wen Chen Nicolas Langrené

The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate a more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be well-approximated by the forward-variance Bergomi model with wisely chosen weights and mean-reversion speed parameters (aBergomi), which has the Markovian property. We establish an explicit bound on the L2-error between the respective kernels of these two models, which is explicitly controlled by the number of terms in the aBergomi model. We establish and describe the affine structure of the rBergomi model, and show the convergence of the affine structure of the aBergomi model to the one of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a classical Markovian Monte Carlo simulation scheme for the aBergomi model, which we compare to the hybrid scheme of the rBergomi model.

]]>Mathematics doi: 10.3390/math9050527

Authors: Manoj Kumar Singh Arvind K. Singh

In this paper, we have obtained three optimal order Newton’s like methods of order four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis of all the optimal order methods is discussed separately. We have discussed the corresponding conjugacy maps for quadratic polynomials and also obtained the extraneous fixed points. We have considered several test functions to examine the convergence order and to explain the dynamics of our proposed methods. Theoretical results, numerical results, and fractal patterns are in support of the efficiency of the optimal order methods.

]]>Mathematics doi: 10.3390/math9050526

Authors: Salvador López-Alfonso Manuel López-Pellicer Santiago Moll-López

A subset B of an algebra A of subsets of a set Ω has property (N) if each B-pointwise bounded sequence of the Banach space ba(A) is bounded in ba(A), where ba(A) is the Banach space of real or complex bounded finitely additive measures defined on A endowed with the variation norm. B has property (G) [(VHS)] if for each bounded sequence [if for each sequence] in ba(A) the B-pointwise convergence implies its weak convergence. B has property (sN) [(sG) or (sVHS)] if every increasing covering {Bn:n∈N} of B contains a set Bp with property (N) [(G) or (VHS)], and B has property (wN) [(wG) or (wVHS)] if every increasing web {Bn1n2⋯nm:ni∈N,1≤i≤m,m∈N} of B contains a strand {Bp1p2⋯pm:m∈N} formed by elements Bp1p2⋯pm with property (N) [(G) or (VHS)] for every m∈N. The classical theorems of Nikodým–Grothendieck, Valdivia, Grothendieck and Vitali–Hahn–Saks say, respectively, that every σ-algebra has properties (N), (sN), (G) and (VHS). Valdivia’s theorem was obtained through theorems of barrelled spaces. Recently, it has been proved that every σ-algebra has property (wN) and several applications of this strong Nikodým type property have been provided. In this survey paper we obtain a proof of the property (wN) of a σ-algebra independent of the theory of locally convex barrelled spaces which depends on elementary basic results of Measure theory and Banach space theory. Moreover we prove that a subset B of an algebra A has property (wWHS) if and only if B has property (wN) and A has property (G).

]]>Mathematics doi: 10.3390/math9050525

Authors: Javier Rodrigo Susana Merchán Danilo Magistrali Mariló López

In this paper, we improve the lower bound on the minimum number of &nbsp;≤k-edges in sets of n points in general position in the plane when k is close to n2. As a consequence, we improve the current best lower bound of the rectilinear crossing number of the complete graph Kn for some values of n.

]]>Mathematics doi: 10.3390/math9050524

Authors: Walguen Oscar Jean Vaillant

Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.

]]>Mathematics doi: 10.3390/math9050523

Authors: Krzysztof Piasecki Anna Łyczkowska-Hanćkowiak

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

]]>Mathematics doi: 10.3390/math9050522

Authors: Jaime Navarro-Fuentes Salvador Arellano-Balderas Oscar Herrera-Alcántara

The smoothness of functions f in the space Lp(R) with 1&lt;p&lt;∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.

]]>Mathematics doi: 10.3390/math9050521

Authors: Angela L. Riffo-Campos Guillermo Ayala Francisco Montes

Gene differential expression consists of the study of the possible association between the gene expression, evaluated using different types of data as DNA microarray or RNA-Seq technologies, and the phenotype. This can be performed marginally for each gene (differential gene expression) or using a gene set collection (gene set analysis). A previous (marginal) per-gene analysis of differential expression is usually performed in order to obtain a set of significant genes or marginal p-values used later in the study of association between phenotype and gene expression. This paper proposes the use of methods of spatial statistics for testing gene set differential expression analysis using paired samples of RNA-Seq counts. This approach is not based on a previous per-gene differential expression analysis. Instead, we compare the paired counts within each sample/control using a binomial test. Each pair per gene will produce a p-value so gene expression profile is transformed into a vector of p-values which will be considered as an event belonging to a point pattern. This would be the first component of a bivariate point pattern. The second component is generated by applying two different randomization distributions to the correspondence between samples and treatment. The self-contained null hypothesis considered in gene set analysis can be formulated in terms of the associated point pattern as a random labeling of the considered bivariate point pattern. The gene sets were defined by the Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. The proposed methodology was tested in four RNA-Seq datasets of colorectal cancer (CRC) patients and the results were contrasted with those obtained using the edgeR-GOseq pipeline. The proposed methodology has proved to be consistent at the biological and statistical level, in particular using Cuzick and Edwards test with one realization of the second component and between-pair distribution.

]]>Mathematics doi: 10.3390/math9050520

Authors: Manuel De la Sen Santiago Alonso-Quesada Asier Ibeas

A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.

]]>Mathematics doi: 10.3390/math9050519

Authors: Ruiheng Li Lei Gao Nian Yu Jianhua Li Yang Liu Enci Wang Xiao Feng

The heuristic algorithm represented by particle swarm optimization (PSO) is an effective tool for addressing serious nonlinearity in one-dimensional magnetotelluric (MT) inversions. PSO has the shortcomings of insufficient population diversity and a lack of coordination between individual cognition and social cognition in the process of optimization. Based on PSO, we propose a new memetic strategy, which firstly selectively enhances the diversity of the population in evolutionary iterations through reverse learning and gene mutation mechanisms. Then, dynamic inertia weights and cognitive attraction coefficients are designed through sine-cosine mapping to balance individual cognition and social cognition in the optimization process and to integrate previous experience into the evolutionary process. This improves convergence and the ability to escape from local extremes in the optimization process. The memetic strategy passes the noise resistance test and an actual MT data test. The results show that the memetic strategy increases the convergence speed in the PSO optimization process, and the inversion accuracy is also greatly improved.

]]>Mathematics doi: 10.3390/math9050518

Authors: Natividad Adamuz-Povedano Elvira Fernández-Ahumada M. Teresa García-Pérez Jesús Montejo-Gámez

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

]]>Mathematics doi: 10.3390/math9050517

Authors: Blanca Viviana Martínez Javier Sanchis Sergio García-Nieto Miguel Martínez

A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.

]]>Mathematics doi: 10.3390/math9050516

Authors: Mohsen Dlala Adarey Saud Almutairi

This paper investigates the problem of rapid exponential stabilization for damped wave equations. Based on a new event-triggered impulsive control (ETIC) method, impulsive control was designed to solve the rapid exponential stabilization of a class of damped wave equations derived from brain activity. The effectiveness of our control was verified through a numerical example.

]]>Mathematics doi: 10.3390/math9050515

Authors: Woraphon Yamaka Xuefeng Zhang Paravee Maneejuk

This study investigates the nonlinear impact of various modes of transportation (air, road, railway, and maritime) on the number of foreign visitors to China originating from major source countries. Our nonlinear tourism demand equations are determined through the Markov-switching regression (MSR) model, thereby, capturing the possible structural changes in Chinese tourism demand. Due to many variables and the limitations from the small number of observations confronted in this empirical study, we may face multicollinearity and endogeneity bias. Therefore, we introduce the two penalized maximum likelihoods, namely Ridge and Lasso, to estimate the high dimensional parameters in the MSR model. This investigation found the structural changes in all tourist arrival series with significant coefficient shifts in transportation variables. We observe that the coefficients are relatively more significant in regime 1 (low tourist arrival regime). The coefficients in regime 1 are all positive (except railway length in operation), while the estimated coefficients in regime 2 are positive in fewer numbers and weak. This study shows that, in the process of transportation, development and changing inbound tourism demand from ten countries, some variables with the originally strong positive effect will have a weak positive effect when tourist arrivals are classified in the high tourist arrival regime.

]]>Mathematics doi: 10.3390/math9050514

Authors: María del Carmen Valls Martínez Pedro Antonio Martín Cervantes

Investors and practitioners are increasingly concerned with financial assets within the scope of corporate social responsibility (CSR) meaning that, in recent times, such assets have become enshrined in the preferences of the new generations of investors and consumers. Just when the interest of investors was at its highest, SARS-CoV-2 (COVID-19) affected all international financial markets, so that, at first sight, it might seem that the financial assets assigned to CSR should have suffered collapses that were identical to the rest; however, our work shows the opposite, providing a comparative analysis of how the pandemic has affected the financial markets of each continent to demonstrate its outstanding resilience through the use of the Wavelets methodology. We analyzed the global impact of the registered cases of COVID-19 on the Dow Jones Sustainability World Index (DJSWI), the world’s leading indicator of sustainable companies, in addition to six other financial indices selected from each continent. The empirical results of this research show that the worldwide repercussions of the sudden outbreak of SARS-CoV-2 has had a substantially smaller effect on sustainability-related indices compared to the other considered indices. Similarly, the methodology employed allowed the establishment of a chronogram with details of the dating of COVID-19 expansion through the considered countries, a certain gradation in terms of the impact of the pandemic on these stock indices, and certain common guidelines describing their devastating effects on each of the financial markets represented by the indices in this research.

]]>Mathematics doi: 10.3390/math9050513

Authors: Olga Fullana Mariano González David Toscano

In this paper, we test whether the short-run econometric conditions for the basic assumptions of the Ohlson valuation model hold, and then we relate these results with the fulfillment of the short-run econometric conditions for this model to be effective. Better future modeling motivated us to analyze to what extent the assumptions involved in this seminal model are not good enough approximations to solve the firm valuation problem, causing poor model performance. The model is based on the well-known dividend discount model and the residual income valuation model, and it adds a linear information model, which is a time series model by nature. Therefore, we adopt the time series approach. In the presence of non-stationary variables, we focus our research on US-listed firms for which more than forty years of data with the required cointegration properties to use error correction models are available. The results show that the clean surplus relation assumption has no impact on model performance, while the unbiased accounting property assumption has an important effect on it. The results also emphasize the uselessness of forcing valuation models to match the value displacement property of dividends.

]]>Mathematics doi: 10.3390/math9050512

Authors: Maryam Baghipur Modjtaba Ghorbani Hilal A. Ganie Yilun Shang

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

]]>Mathematics doi: 10.3390/math9050511

Authors: Andrei D. Polyanin Vsevolod G. Sorokin

We study nonlinear pantograph-type reaction–diffusion PDEs, which, in addition to the unknown u=u(x,t), also contain the same functions with dilated or contracted arguments of the form w=u(px,t), w=u(x,qt), and w=u(px,qt), where p and q are the free scaling parameters (for equations with proportional delay we have 0&lt;p&lt;1, 0&lt;q&lt;1). A brief review of publications on pantograph-type ODEs and PDEs and their applications is given. Exact solutions of various types of such nonlinear partial functional differential equations are described for the first time. We present examples of nonlinear pantograph-type PDEs with proportional delay, which admit traveling-wave and self-similar solutions (note that PDEs with constant delay do not have self-similar solutions). Additive, multiplicative and functional separable solutions, as well as some other exact solutions are also obtained. Special attention is paid to nonlinear pantograph-type PDEs of a rather general form, which contain one or two arbitrary functions. In total, more than forty nonlinear pantograph-type reaction–diffusion PDEs with dilated or contracted arguments, admitting exact solutions, have been considered. Multi-pantograph nonlinear PDEs are also discussed. The principle of analogy is formulated, which makes it possible to efficiently construct exact solutions of nonlinear pantograph-type PDEs. A number of exact solutions of more complex nonlinear functional differential equations with varying delay, which arbitrarily depends on time or spatial coordinate, are also described. The presented equations and their exact solutions can be used to formulate test problems designed to evaluate the accuracy of numerical and approximate analytical methods for solving the corresponding nonlinear initial-boundary value problems for PDEs with varying delay. The principle of analogy allows finding solutions to other nonlinear pantograph-type PDEs (including nonlinear wave-type PDEs and higher-order equations).

]]>Mathematics doi: 10.3390/math9050510

Authors: Yan-Ran Li Xin-Hui Shao Shi-Yu Li

In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We propose the three-block splitting (TBS) iterative method and proved that it is unconditionally convergent. At the same time, the corresponding TBS preconditioner is derived from the TBS iteration method, and we studied the spectral properties of the preconditioned matrix. Finally, numerical examples in two-dimensions is applied to demonstrate the advantages of the TBS iterative method and TBS preconditioner with the Krylov subspace method.

]]>Mathematics doi: 10.3390/math9050507

Authors: Khadija Yakoubi Soufiane Montassir Hassane Moustabchir Ahmed Elkhalfi Catalin Iulian Pruncu Jamal Arbaoui Muhammad Umar Farooq

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

]]>Mathematics doi: 10.3390/math9050508

Authors: Alaa Omran Almagrabi Rashid Ali Daniyal Alghazzawi Abdullah AlBarakati Tahir Khurshaid

The 5th generation (5G) wireless networks propose to address a variety of usage scenarios, such as enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable low-latency communications (URLLC). Due to the exponential increase in the user equipment (UE) devices of wireless communication technologies, 5G and beyond networks (B5G) expect to support far higher user density and far lower latency than currently deployed cellular technologies, like long-term evolution-Advanced (LTE-A). However, one of the critical challenges for B5G is finding a clever way for various channel access mechanisms to maintain dense UE deployments. Random access channel (RACH) is a mandatory procedure for the UEs to connect with the evolved node B (eNB). The performance of the RACH directly affects the performance of the entire network. Currently, RACH uses a uniform distribution-based (UD) random access to prevent a possible network collision among multiple UEs attempting to access channel resources. However, in a UD-based channel access, every UE has an equal chance to choose a similar contention preamble close to the expected value, which causes an increase in the collision among the UEs. Therefore, in this paper, we propose a Poisson process-based RACH (2PRACH) alternative to a UD-based RACH. A Poisson process-based distribution, such as exponential distribution, disperses the random preambles between two bounds in a Poisson point method, where random variables occur continuously and independently with a constant parametric rate. In this way, our proposed 2PRACH approach distributes the UEs in a probability distribution of a parametric collection. Simulation results show that the shift of RACH from UD-based channel access to a Poisson process-based distribution enhances the reliability and lowers the network’s latency.

]]>Mathematics doi: 10.3390/math9050509

Authors: Raúl Martín-Santamaría Ana D. López-Sánchez María Luisa Delgado-Jalón J. Manuel Colmenar

Crowd logistics is a recent trend that proposes the participation of ordinary people in the distribution process of products and goods. This idea is becoming increasingly important to both delivery and retail companies, because it allows them to reduce their delivery costs and, hence, to increase the sustainability of the company. One way to obtain these reductions is to hire external drivers who use their own vehicles to make deliveries to destinations which are close to their daily trips from work to home, for instance. This situation is modelled as the Vehicle Routing Problem with Occasional Drivers (VRPOD), which seeks to minimize the total cost incurred to perform the deliveries using vehicles belonging to the company and occasionally hiring regular citizens to make just one delivery. However, the integration of this features into the distribution system of a company requires a fast and efficient algorithm. In this paper, we propose three different implementations based on the Iterated Local Search algorithm that are able to outperform the state-of-art of this problem with regard to the quality performance. Besides, our proposal is a light-weight algorithm which can produce results in small computation times, allowing its integration into corporate information systems.

]]>Mathematics doi: 10.3390/math9050506

Authors: Jorge Daniel Mello-Román Adolfo Hernández Julio César Mello-Román

Kernel partial least squares regression (KPLS) is a non-linear method for predicting one or more dependent variables from a set of predictors, which transforms the original datasets into a feature space where it is possible to generate a linear model and extract orthogonal factors also called components. A difficulty in implementing KPLS regression is determining the number of components and the kernel function parameters that maximize its performance. In this work, a method is proposed to improve the predictive ability of the KPLS regression by means of memetic algorithms. A metaheuristic tuning procedure is carried out to select the number of components and the kernel function parameters that maximize the cumulative predictive squared correlation coefficient, an overall indicator of the predictive ability of KPLS. The proposed methodology led to estimate optimal parameters of the KPLS regression for the improvement of its predictive ability.

]]>Mathematics doi: 10.3390/math9050505

Authors: Lluís Bermúdez Dimitris Karlis

A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.

]]>Mathematics doi: 10.3390/math9050504

Authors: Marcos Albuquerque Junior José António Filipe Paulo de Melo Jorge Neto Cristiano da Costa da Silva

Diversification in a portfolio is an important tool for the systematic risk management that is inherent to different asset classes. The composition of a portfolio with domestic and international assets is seen as one of the main alternatives for building a diversified portfolio, as this approach tends to reduce portfolio return exposure depending on country factors. However, in scenarios where industry factors are predominant, international diversification can increase systematic risk in a portfolio centered on a single asset class. This study is a pioneer in using wavelet-based methods to identify intersectoral co-movements, based on a portfolio of shares of the world’s top five consulting engineering companies, providing an innovative way to be applied to this phenomenon. Our evidence indicates that companies share a strong pattern of co-movements among themselves, especially in cycles of 32 to 64 days, suggesting a higher exposure to risk for portfolios with an investment horizon in long-term cycles.

]]>Mathematics doi: 10.3390/math9050503

Authors: Ru Guo Xiaodong Qiu Yiyi He

Central and East European (CEE) countries are attractive among emerging markets due to a combination of factors such as economic growth and market potential. Although the CEE countries as a whole have a very high degree of connectivity, each country has different market opportunities and external environment, so agricultural enterprises wanting to enter the CEE market must take into account the diverse and complex resource base of CEE countries. In the light of economic globalization, China and CEE countries face mutual opportunities and challenges, and it is necessary to strengthen agricultural cooperation. The potential of agricultural investment cooperation between China and CEE countries is the basis for multinational enterprises to allocate resources and implement internationalization strategies rationally. The purpose of this paper is to analyze theagricultural cooperation potential between China and CEE countries in the perspective of resource complementarity, with a selection of macro data related to agricultural capacity from 2009–2018. In particular, this study examines the differences and complementarities between China and CEE countries in terms of agricultural resource conditions and product output and trade; by constructing an agricultural cooperation potential evaluation model, the entropy value method is applied to predict and evaluate the potential characteristics of agricultural cooperation between China and CEE countries in 2021–2025. The research results show that the current intermittent and episodic nature of agricultural cooperation between China and CEE countries does not match the high or medium-high level of complementarity between agricultural production factors. Thus, agricultural enterprises can utiliza such considerable cooperation potential based on the resource complementarity to develop internationalization strategies and overseas investment.

]]>Mathematics doi: 10.3390/math9050502

Authors: Zuzana Pátíková

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).

]]>Mathematics doi: 10.3390/math9050501

Authors: Ruslan Gabdullin Vladimir Makarenko Irina Shevtsova

Following (Shevtsova, 2013) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen’s, Rozovskii’s, and Wang–Ahmad’s inequalities and their structural improvements obtained in our previous works. The above inequalities involve algebraic truncated third-order moments and the classical Lindeberg fraction and assume finiteness only the second-order moments of random summands. We present lower bounds for the introduced asymptotically exact constants as well as for the universal and for the most optimistic constants which turn to be not far from the upper ones.

]]>Mathematics doi: 10.3390/math9050500

Authors: E. Laxmi Lydia A. Arokiaraj Jovith A. Francis Saviour Devaraj Changho Seo Gyanendra Prasad Joshi

Presently, a green Internet of Things (IoT) based energy aware network plays a significant part in the sensing technology. The development of IoT has a major impact on several application areas such as healthcare, smart city, transportation, etc. The exponential rise in the sensor nodes might result in enhanced energy dissipation. So, the minimization of environmental impact in green media networks is a challenging issue for both researchers and business people. Energy efficiency and security remain crucial in the design of IoT applications. This paper presents a new green energy-efficient routing with DL based anomaly detection (GEER-DLAD) technique for IoT applications. The presented model enables IoT devices to utilize energy effectively in such a way as to increase the network span. The GEER-DLAD technique performs error lossy compression (ELC) technique to lessen the quantity of data communication over the network. In addition, the moth flame swarm optimization (MSO) algorithm is applied for the optimal selection of routes in the network. Besides, DLAD process takes place via the recurrent neural network-long short term memory (RNN-LSTM) model to detect anomalies in the IoT communication networks. A detailed experimental validation process is carried out and the results ensured the betterment of the GEER-DLAD model in terms of energy efficiency and detection performance.

]]>Mathematics doi: 10.3390/math9050499

Authors: Feliz Minhós Infeliz Coxe

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ∞. In the last section, an example illustrates the applicability of our main result.

]]>Mathematics doi: 10.3390/math9050498

Authors: Muhammad Zainul Abidin Jiecheng Chen

In this paper, we consider the generalized porous medium equation. For small initial data u0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution.

]]>Mathematics doi: 10.3390/math9050497

Authors: Liang Wang Chunguang Xiong Xinpeng Yuan Huibin Wu

The objective of this work is to study finite element methods for approximating the solution of convection equations on surfaces embedded in R3. We propose the discontinuous Galerkin (DG) isogeometric analysis (IgA) formulation to solve convection problems on implicitly defined surfaces. Three numerical experiments shows that the numerical scheme converges with the optimal convergence order.

]]>Mathematics doi: 10.3390/math9050496

Authors: Ignacio J. Navarro José V. Martí Víctor Yepes

After the recent establishment of the Sustainable Development Goals and the Agenda 2030, the sustainable design of products in general and infrastructures in particular emerge as a challenging field for the development and application of multicriteria decision-making tools. Sustainability-related decision problems usually involve, by definition, a wide variety in number and nature of conflicting criteria, thus pushing the limits of conventional multicriteria decision-making tools practices. The greater the number of criteria and the more complex the relations existing between them in a decisional problem, the less accurate and certain are the judgments required by usual methods, such as the analytic hierarchy process (AHP). The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%.

]]>Mathematics doi: 10.3390/math9050495

Authors: Umakanta Mishra Abu Hashan Md Mashud Ming-Lang Tseng Jei-Zheng Wu

This study investigated how greenhouse managers should invest in preservation and green technologies and introduce trade credit to increase their profits. We propose a supply chain inventory model with controllable deterioration and emission rates under payment schemes for shortage and surplus, where demand depends on price and trade credit. Carbon emissions and deterioration are factors affecting global warming, and many greenhouse managers have focused on reducing carbon emissions. Carbon caps and tax-based incentives have been used in many greenhouses to achieve such reduction. Because of the importance of reducing carbon emissions for developing a green supply chain, various studies have investigated how firms deal with carbon emission constraints. In this continuation, we have used green technology to curb the excessive emissions from the environment or make it clean from CO2. In a seller–buyer relationship, the seller can offer a trade credit period to the buyer to manage stock and stimulate demand. Deterioration may become a challenge for most firms as they are under time constraints control, and preservation technology could help. This study proposes three novel inventory strategies for a sustainable supply chain (full backorder, partial backorder, and no backorder), linking all these important issues. The solution optimizes total annual profit for inventory shortage or surplus. We conducted a numerical study with three examples to evaluate the model’s authenticity and effectiveness and demonstrate the solution technique. The deterioration and emission rates can be included in a trade credit policy to increase greenhouse profits. The results suggest that greenhouse managers could apply the proposed model to manage real-world situations.

]]>Mathematics doi: 10.3390/math9050494

Authors: Sarka Hoskova-Mayerova Madeline Al Tahan

Recently, fuzzy multisets have come to the forefront of scientists’ interest and have been used for algebraic structures such as groups, rings, and near rings. In this paper, we first summarize the knowledge about algebraic structure of fuzzy multisets such as fuzzy multi-subnear rings and fuzzy multi-ideals of near rings. Then we recall the results from our related previous work, where we defined different operations on fuzzy multi-ideals of near rings and we generalized some known results for fuzzy ideals of near rings to fuzzy multi-ideals of near rings. Finally, we define anti-fuzzy multi-subnear rings (multi-ideals) of near rings and study their properties.

]]>Mathematics doi: 10.3390/math9050493

Authors: Malik Bataineh Rashid Abu-Dawwas

The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different. Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different. Several properties of graded 2-prime ideals are investigated. We study graded rings in which every graded 2-prime ideal is graded prime, we call such a graded ring a graded 2-P-ring. Moreover, we introduce the concept of graded semi-primary ideals, and show that graded 2-prime ideals and graded semi-primary ideals are different concepts. In fact, we show that graded semi-primary, graded 2-prime and graded primary ideals are equivalent over Z-graded principal ideal domain.

]]>Mathematics doi: 10.3390/math9050492

Authors: Enrique Soriano-Heras Higinio Rubio Alejandro Bustos Cristina Castejon

Chuck holders are widely used for jobs with high precision. A chuck holder consists of a nut with a tapered surface and a thin-slotted clamping sleeve typically made of hardened steel and named a collet. Chuck holders are, essentially, wedge mechanisms. In this paper, we investigated the reactions and strains due to the forces during the chip removal process in the contact elements or jaws of the collet by means of mathematical analysis. Deflections in the jaws of the collet arise with a high influence from the precision of the workpieces. The cutting or process forces cause an axial force, a radial force, a torsional moment, and a bending moment on the chuck collet, and, consequently, displacements and inclinations of the clamping system are caused. Therefore, the proposed analytical models are based on elasticity and contact theories. The mathematical model for determining the deflections of the clamping system force was developed and implemented using MATLAB. The results showed that the variation in the clamping force during rotation in a collet chuck holder mainly depends on the stiffness of the collet chuck holder and the stiffness of the workpiece. The results indicated that the collet should be vulcanized to minimize the deformations that affect the final product. The deflections of a collet chuck holder due to process forces depend strongly on the clearances, wedge angle, and stiffness of the collet.

]]>Mathematics doi: 10.3390/math9050491

Authors: Patchara Pornsurat Pakorn Palakawong na Ayutthaya Bundit Pibaljommee

We study the concept of i-ideal of an ordered n-ary semigroup and give a construction of the i-ideal of an ordered n-ary semigroup generated by its nonempty subset. Moreover, we study the notions of prime, weakly prime, semiprime and weakly semiprime ideals of an ordered n-ary semigroup.

]]>Mathematics doi: 10.3390/math9050490

Authors: Sorin Vlase Marin Marin Maria Luminita Scutaru Catalin Pruncu

The paper studies the vibration behavior of a concrete structure, currently used in civil engineering. The truss structure considered has symmetries that can be used to facilitate both the design and construction of the building. Moreover, the symmetries encountered can be used to simplify the calculation of vibrations of the system. Based on the mechanical model built, eigenvalues and eigenvectors of such mechanical system are determined, and properties, specific to these symmetries, are identified. In this way, the dynamic analysis of the structure can be simplified and also, the design as well as the costs related to this stage.

]]>Mathematics doi: 10.3390/math9050489

Authors: Zeng Lian Jie Zheng

This paper studies firms’ dynamic interaction in a Cournot market. In each period of the game, the firm decides whether to make a stochastic positioning investment (establishing or maintaining its position in market competition). The market demand is also stochastic (high or low). By adopting symmetric Market perfect Nash equilibrium, firms choose strategies to maximize the discounted present value of cash flow. By considering the cases with one, two, and three active firms in the market, respectively, we present the stage game market outcome, show the transition probabilities, find the steady state of the system, and discuss the speed of convergence. Our work allows for two types of uncertainty in firms’ interactions, which contribute to the dynamic oligopoly literature.

]]>Mathematics doi: 10.3390/math9050488

Authors: Stephanie Yang Hsueh-Chih Chen Chih-Hsien Wu Meng-Ni Wu Cheng-Hong Yang

The World Health Organization has urged countries to prioritize dementia in their public health policies. Dementia poses a tremendous socioeconomic burden, and the accurate prediction of the annual increase in prevalence is essential for establishing strategies to cope with its effects. The present study established a model based on the architecture of the long short-term memory (LSTM) neural network for predicting the number of dementia cases in Taiwan, which considers the effects of age and sex on the prevalence of dementia. The LSTM network is a variant of recurrent neural networks (RNNs), which possesses a special gate structure and avoids the problems in RNNs of gradient explosion, gradient vanishing, and long-term memory failure. A number of patients diagnosed as having dementia from 1997 to 2017 was collected in annual units from a data set extracted from the Health Insurance Database of the Ministry of Health and Welfare in Taiwan. To further verify the validity of the proposed model, the LSTM network was compared with three types of models: statistical models (exponential smoothing (ETS), autoregressive integrated moving average model (ARIMA), trigonometric seasonality, Box–Cox transformation, autoregressive moving average errors, and trend seasonal components model (TBATS)), hybrid models (support vector regression (SVR), particle swarm optimization–based support vector regression (PSOSVR)), and deep learning model (artificial neural networks (ANN)). The mean absolute percentage error (MAPE), root-mean-square error (RMSE), mean absolute error (MAE), and R-squared (R2) were used to evaluate the model performances. The results indicated that the LSTM network has higher prediction accuracy than the three types of models for forecasting the prevalence of dementia in Taiwan.

]]>Mathematics doi: 10.3390/math9050487

Authors: Carlos Roncero-Clemente Eugenio Roanes-Lozano Fermín Barrero-González

The electric system scenario has been changing during the last years moving to a distributed system with a high penetration of renewables. Due to the unpredictable behavior of some renewables sources, the development of the energy management system is considered crucial to guarantee the reliability and stability of the system. At the same time, increasing the lifespan of the energy storage system is one of the most important points to take into account. In this sense, a software package implemented in the computer algebra system Maple is proposed in this work to control a grid-connected nanogrid with hybrid energy storage system (composed by batteries and supercapacitors). The energy management system considers several rules as the state of charge of the energy storage system, the photovoltaic power generation and the load profile, the nanogrid power trend and the energy prices. The improved performance of the nanogrid is proven by simulations in MATLAB/Simulink.

]]>Mathematics doi: 10.3390/math9050486

Authors: Stefano Innamorati Mauro Zannetti

Marcugini et al. proved, by computer-based proof, the unicity of the maximum (k,3)-arc in PG(2,7). In this paper, we show how the (15,3)-arc in PG(2,7) may be described using only geometrical properties. The description we provide, believing it is novel, relies on the union of a conic and a complete external quadrangle.

]]>Mathematics doi: 10.3390/math9050485

Authors: Marco Gribaudo Mauro Iacono Daniele Manini

We applied a flexible modeling technique capable of representing dynamics of large populations interacting in space and time, namely Markovian Agents, to study the evolution of COVID-19 in Italy. Our purpose was to show that this modeling approach, that is based on mean field analysis models, provides good performances in describing the diffusion of phenomena, like COVID-19. The paper describes the application of this modeling approach to the Italian scenario and results are validated against real data available about the Italian official documentation of the diffusion of COVID-19. The model of each agent is organized similarly to what largely established in literature in the Susceptible-Infected-Recovered (SIR) family of approaches. Results match the main events taken by the Italian government and their effects.

]]>Mathematics doi: 10.3390/math9050484

Authors: Anita Keszler Zsolt Tuza

In this paper, we consider the problem of constructing hypercycle systems of 5-cycles in complete 3-uniform hypergraphs. A hypercycle system C(r,k,v) of order v is a collection of r-uniform k-cycles on a v-element vertex set, such that each r-element subset is an edge in precisely one of those k-cycles. We present cyclic hypercycle systems C(3,5,v) of orders v=25,26,31,35,37,41,46,47,55,56, a highly symmetric construction for v=40, and cyclic 2-split constructions of orders 32,40,50,52. As a consequence, all orders v≤60 permitted by the divisibility conditions admit a C(3,5,v) system. New recursive constructions are also introduced.

]]>Mathematics doi: 10.3390/math9050483

Authors: Chia-Nan Wang Nhat-Luong Nhieu Trang Thi Thu Tran

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies.

]]>Mathematics doi: 10.3390/math9050482

Authors: Bilal A. Rather Shariefuddin Pirzada Tariq A. Naikoo Yilun Shang

Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p&lt;q are primes and N1,N2 are positive integers.

]]>Mathematics doi: 10.3390/math9050481

Authors: Enriqueta Mancilla-Rendón Carmen Lozano Enrique Torres-Esteva

This article aims to analyze the functions of corporate governance agents as a key part of the study and evaluation of the internal control by the independent auditor to propose a governance fuzzy model based on legality. This is a descriptive–hermeneutical study based on mercantile-securities law, the code of best practice of corporate governance, and auditing standards. The research design is cross-sectional and uses fuzzy logic theory as an alternative tool in contrast to classical mathematical models. The results suggest that corporate governance agents strongly influence the application of a management system. Evidence is given regarding the positive relationship between the functions of corporate governance agents as a management system. Additionally, the importance of an internal control management system as an inherent mechanism for governance is proven. The scientific value of this work lies in showing how the interaction between the application of mathematical models based on fuzzy set theory and the qualitative attributes of internal control policies and practices. It is a tool to evaluate governance as a management system for decision making. This work emphasizes that a model based on fuzzy sets is useful to evaluate a management system of internal control policies and procedures necessary to improve corporate governance.

]]>Mathematics doi: 10.3390/math9050480

Authors: Frank A. Hernández Mira Ernesto Parra Inza José M. Sigarreta Almira Nodari Vakhania

A nonempty subset D⊂V of vertices of a graph G=(V,E) is a dominating set if every vertex of this graph is adjacent to at least one vertex from this set except the vertices which belong to this set itself. D⊆V is a total k-dominating set if there are at least k vertices in set D adjacent to every vertex v∈V, and it is a global total k-dominating set if D is a total k-dominating set of both G and G¯. The global total k-domination number of G, denoted by γktg(G), is the minimum cardinality of a global total k-dominating set of G, GTkD-set. Here we derive upper and lower bounds of γktg(G), and develop a method that generates a GTkD-set from a GT(k−1)D-set for the successively increasing values of k. Based on this method, we establish a relationship between γ(k−1)tg(G) and γktg(G), which, in turn, provides another upper bound on γktg(G).

]]>Mathematics doi: 10.3390/math9050479

Authors: Aníbal Coronel Fernando Huancas Esperanza Lozada Marko Rojas-Medar

We research a control problem for an ecological model given by a reaction–diffusion system. The ecological model is given by a nonlinear parabolic PDE system of three equations modelling the interaction of three species by considering the standard Lotka-Volterra assumptions. The optimal control problem consists of the determination of a coefficient such that the population density of predator decreases. We reformulate the control problem as an optimal control problem by introducing an appropriate cost function. Then, we introduce and prove three types of results. A first contribution of the paper is the well-posedness framework of the mathematical model by considering that the interaction of the species is given by a general functional responses. Second, we study the differentiability properties of a cost function. The third result is the existence of optimal solutions, the existence of an adjoint state, and a characterization of the control function. The first result is proved by the application of semigroup theory and the second and third result are proved by the application of Dubovitskii and Milyutin formalism.

]]>Mathematics doi: 10.3390/math9050478

Authors: Jose Luis Martin-Navarro Amparo Fúster-Sabater

The ubiquity of smart devices and IoT are the main forces behind the development of cryptographic primitives that preserve the security of this devices, with the resources constraints they face. In this sense, the development of lightweight cryptographic algorithms, where PRNGs are an essential part of them, provides security to all these interconnected devices. In this work, a family of sequence generators with hard characteristics to be analyzed by standard methods is described. Moreover, we introduce an innovative technique for sequence decomposition that allows one to extract useful information on the sequences under study. In addition, diverse algorithms to evaluate the strength of such binary sequences have been introduced and analyzed to show which performs better.

]]>Mathematics doi: 10.3390/math9050477

Authors: Katarzyna Górska Andrzej Horzela

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.

]]>Mathematics doi: 10.3390/math9050476

Authors: Mingming Zhang Shurong Hao Anping Hou

In order to obtain the aerodynamic loads of the vibrating blades efficiently, the eXterme Gradient Boosting (XGBoost) algorithm in machine learning was adopted to establish a three-dimensional unsteady aerodynamic force reduction model. First, the database for the unsteady aerodynamic response during the blade vibration was acquired through the numerical simulation of flow field. Then the obtained data set was trained by the XGBoost algorithm to set up the intelligent model of unsteady aerodynamic force for the three-dimensional blade. Afterwards, the aerodynamic load could be gained at any spatial location during blade vibration. To evaluate and verify the reliability of the intelligent model for the blade aerodynamic load, the prediction results of the machine learning model were compared with the results of Computation Fluid Dynamics (CFD). The determination coefficient R2 and the Root Mean Square Error (RMSE) were introduced as the model evaluation indicators. The results show that the prediction results based on the machine learning model are in good agreement with the CFD results, and the calculation efficiency is significantly improved. The results also indicate that the aerodynamic intelligent model based on the machine learning method is worthy of further study in evaluating the blade vibration stability.

]]>Mathematics doi: 10.3390/math9050475

Authors: Payam Aboutalebi Fares M’zoughi Izaskun Garrido Aitor J. Garrido

Undesired motions in Floating Offshore Wind Turbines (FOWT) lead to reduction of system efficiency, the system’s lifespan, wind and wave energy mitigation and increment of stress on the system and maintenance costs. In this article, a new barge platform structure for a FOWT has been proposed with the objective of reducing these undesired platform motions. The newly proposed barge structure aims to reduce the tower displacements and platform’s oscillations, particularly in rotational movements. This is achieved by installing Oscillating Water Columns (OWC) within the barge to oppose the oscillatory motion of the waves. Response Amplitude Operator (RAO) is used to predict the motions of the system exposed to different wave frequencies. From the RAOs analysis, the system’s performance has been evaluated for representative regular wave periods. Simulations using numerical tools show the positive impact of the added OWCs on the system’s stability. The results prove that the proposed platform presents better performance by decreasing the oscillations for the given range of wave frequencies, compared to the traditional barge platform.

]]>Mathematics doi: 10.3390/math9050474

Authors: Luciano Abadias Edgardo Alvarez Rogelio Grau

We investigate the semi-linear, non-autonomous, first-order abstract differential equation x′(t)=A(t)x(t)+f(t,x(t),φ[α(t,x(t))]),t∈R. We obtain results on existence and uniqueness of (ω,c)-periodic (second-kind periodic) mild solutions, assuming that A(t) satisfies the so-called Acquistapace–Terreni conditions and the homogeneous associated problem has an integrable dichotomy. A new composition theorem and further regularity theorems are given.

]]>Mathematics doi: 10.3390/math9050472

Authors: Ana M. Ferreiro Enrico Ferri José A. García Carlos Vázquez

Starting from an original portfolio of life insurance policies, in this article we propose a methodology to select model points portfolios that reproduce the original one, preserving its market risk under a certain measure. In order to achieve this goal, we first define an appropriate risk functional that measures the market risk associated to the interest rates evolution. Although other alternative interest rate models could be considered, we have chosen the LIBOR (London Interbank Offered Rate) market model. Once we have selected the proper risk functional, the problem of finding the model points of the replicating portfolio is formulated as a problem of minimizing the distance between the original and the target model points portfolios, under the measure given by the proposed risk functional. In this way, a high-dimensional global optimization problem arises and a suitable hybrid global optimization algorithm is proposed for the efficient solution of this problem. Some examples illustrate the performance of a parallel multi-CPU implementation for the evaluation of the risk functional, as well as the efficiency of the hybrid Basin Hopping optimization algorithm to obtain the model points portfolio.

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