Mathematics doi: 10.3390/math8101670

Authors: Marek Lampart Alžběta Lampartová

The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory.

]]>Mathematics doi: 10.3390/math8101669

Authors: Jun Moon Wonhee Kim

We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD). Specifically, there are two players in the I-LQ-MF-SZSDG-JD, where Player 1 minimizes the objective functional, while Player 2 maximizes the same objective functional. In the I-LQ-MF-SZSDG-JD, the jump-diffusion-type state dynamics controlled by the two players and the objective functional include the mean-field variables, i.e., the expected values of state and control variables, and the parameters of the objective functional do not need to be (positive) definite matrices. These general settings of the I-LQ-MF-SZSDG-JD make the problem challenging, compared with the existing literature. By considering the interaction between two players and using the completion of the squares approach, we obtain the explicit feedback Nash equilibrium, which is linear in state and its expected value, and expressed as the coupled integro-Riccati differential equations (CIRDEs). Note that the interaction between the players is analyzed via a class of nonanticipative strategies and the &ldquo;ordered interchangeability&rdquo; property of multiple Nash equilibria in zero-sum games. We obtain explicit conditions to obtain the Nash equilibrium in terms of the CIRDEs. We also discuss the different solvability conditions of the CIRDEs, which lead to characterization of the Nash equilibrium for the I-LQ-MF-SZSDG-JD. Finally, our results are applied to the mean-field-type stochastic mean-variance differential game, for which the explicit Nash equilibrium is obtained and the simulation results are provided.

]]>Mathematics doi: 10.3390/math8101667

Authors: Laura Ballester Ana González-Urteaga

This study complements the current literature, providing a thorough investigation of the lead&ndash;lag connection between stock indices and sovereign credit default swap (CDS) returns for 14 European countries and the US over the period 2004&ndash;2016. We use a rolling VAR framework that enables us to analyse the connection process over time covering both crisis and non-crisis periods. In addition, we analyse the relationship between stock market volatility and CDS returns. We find that the connection between the credit and equity markets does exist and that it is time variable and seems to be related to financial crises. We also observe that stock market returns anticipate sovereign CDS returns, and sovereign CDSs anticipate the conditional volatility of equity returns, closing a connectedness circle between markets. Contribution percentages in terms of returns are more intense in the US than in Europe and the opposite result is found with respect to volatilities. Within Europe, a greater impact in Eurozone countries compared to non-Eurozone countries is observed. Finally, an additional analysis is also carried out for the financial sector, obtaining results largely consistent with those found using sovereign data.

]]>Mathematics doi: 10.3390/math8101668

Authors: Eber Lenes Exequiel Mallea-Zepeda Jonnathan Rodríguez

Let G be a graph, for any real 0&le;&alpha;&le;1, Nikiforov defines the matrix A&alpha;(G) as A&alpha;(G)=&alpha;D(G)+(1&minus;&alpha;)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G. This paper presents some extremal results about the spectral radius &rho;&alpha;(G) of the matrix A&alpha;(G). In particular, we give a lower bound on the spectral radius &rho;&alpha;(G) in terms of order and independence number. In addition, we obtain an upper bound for the spectral radius &rho;&alpha;(G) in terms of order and minimal degree. Furthermore, for n&gt;l&gt;0 and 1&le;p&le;&lfloor;n&minus;l2&rfloor;, let Gp&cong;Kl&or;(Kp&cup;Kn&minus;p&minus;l) be the graph obtained from the graphs Kl and Kp&cup;Kn&minus;p&minus;l and edges connecting each vertex of Kl with every vertex of Kp&cup;Kn&minus;p&minus;l. We prove that &rho;&alpha;(Gp+1)&lt;&rho;&alpha;(Gp) for 1&le;p&le;&lfloor;n&minus;l2&rfloor;&minus;1.

]]>Mathematics doi: 10.3390/math8101666

Authors: Young Sik Kim

We prove that the Wiener integral, the analytic Wiener integral and the analytic Feynman integral of the first variation of F(x)=exp{&int;0T&theta;(t,x(t))dt} successfully exist under the certain condition, where &theta;(t,u)=&int;Rexp{iuv}d&sigma;t(v) is a Fourier&ndash;Stieltjes transform of a complex Borel measure &sigma;t&isin;M(R) and M(R) is a set of complex Borel measures defined on R. We will find this condition. Moreover, we prove that the change of scale formula for Wiener integrals about the first variation of F(x) sucessfully holds on the Wiener space.

]]>Mathematics doi: 10.3390/math8101665

Authors: Yabing Gao Yongxiang Li

We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the sectorial operator theory and the imbedding theory in the interpolation spaces, where the nonlinear term satisfies more general conditions, we obtain the existence and uniqueness of the saturated classical solutions. The results obtained generalize the recent conclusions on this topic. Finally, an example is given to illustrate the feasibility of our main results.

]]>Mathematics doi: 10.3390/math8101664

Authors: Sergey Grachev Petr Skobelev Igor Mayorov Elena Simonova

The paper is devoted to an overview of multi-agent principles, methods, and technologies intended to adaptive real-time data clustering. The proposed methods provide new principles of self-organization of records and clusters, represented by software agents, making it possible to increase the adaptability of different clustering processes significantly. The paper also presents a comparative review of the methods and results recently developed in this area and their industrial applications. An ability of self-organization of items and clusters suggests a new perspective to form groups in a bottom-up online fashion together with continuous adaption previously obtained decisions. Multi-agent technology allows implementing this methodology in a parallel and asynchronous multi-thread manner, providing highly flexible, scalable, and reliable solutions. Industrial applications of the intended for solving too complex engineering problems are discussed together with several practical examples of data clustering in manufacturing applications, such as the pre-analysis of customer datasets in the sales process, pattern discovery, and ongoing forecasting and consolidation of orders and resources in logistics, clustering semantic networks in insurance document processing. Future research is outlined in the areas such as capturing the semantics of problem domains and guided self-organization on the virtual market.

]]>Mathematics doi: 10.3390/math8101663

Authors: Sharief Deshmukh Josef Mikeš Nasser Bin Turki Gabriel-Eduard Vîlcu

The concircularity property of vector fields implies the geodesicity property, while the converse of this statement is not true. The main objective of this note is to find conditions under which the concircularity and geodesicity properties of vector fields are equivalent. Moreover, it is shown that the geodesicity property of vector fields is also useful in characterizing not only spheres, but also Euclidean spaces.

]]>Mathematics doi: 10.3390/math8101662

Authors: Hans Nina Hector Flores Callisaya H. Pickmann-Soto Jonnathan Rodriguez

In this paper, sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors for a list of complex numbers with nonnegative real part are obtained, and the corresponding nonnegative matrices are constructed. In addition, results of how to perturb complex eigenvalues of a nonnegative matrix while keeping its elementary divisors and its nonnegativity are derived.

]]>Mathematics doi: 10.3390/math8101661

Authors: Dayong Han Qiuhua Tang Zikai Zhang Zixiang Li

Steelmaking and the continuous-casting (SCC) scheduling problem is a realistic hybrid flow shop scheduling problem with continuous-casting production at the last stage. This study considers the SCC scheduling problem with diverse products, which is a vital and difficult problem in steel plants. To tackle this problem, this study first presents the mixed-integer linear programming (MILP) model to minimize the objective of makespan. Then, an improved migrating birds optimization algorithm (IMBO) is proposed to tackle this considered NP-hard problem. In the proposed IMBO, several improvements are employed to achieve the proper balance between exploration and exploitation. Specifically, a two-level decoding procedure is designed to achieve feasible solutions; the simulated annealing-based acceptance criterion is employed to ensure the diversity of the population and help the algorithm to escape from being trapped in local optima; a competitive mechanism is developed to emphasize exploitation capacity by searching around the most promising solution space. The computational experiments demonstrate that the proposed IMBO obtains competing performance and it outperforms seven other implemented algorithms in the comparative study.

]]>Mathematics doi: 10.3390/math8101660

Authors: Rubén Trigueros José M. Aguilar-Parra Isabel Mercader Juan M. Fernández-Campoy José Carrión

According to the latest PISA report, the level of mathematical competence of Spanish students is far behind the rest of the OECD countries. One of the main reasons for this is the animosity that students feel towards this subject. Therefore, this study aims to analyze the processes of overcoming the vicissitudes of mathematical anxiety with respect to motivation, metacognitive strategies and academic performance. This study involved 1742 high school students with an average age of 14.87. To analyze the variables of the study, descriptive statistical analyses and a model of structural equations were carried out. The results revealed a negative correlation between resilience and anxiety. In turn, resilience was positively related to motivation and metacognitive strategies, while anxiety was negatively related to motivation and metacognitive strategies. Motivation was positively related to metacognitive strategies and academic performance; finally, metacognitive strategies were positively related to academic performance.

]]>Mathematics doi: 10.3390/math8101659

Authors: Shin Hee Baek Jong Soo Kim

This paper considers a multi-period supplier selection and order allocation problem for a green supply chain system that consists of a single buyer and multiple heterogeneous suppliers. The buyer sells multiple products to end customers and periodically replenishes each item&rsquo;s inventory using a periodic inventory control policy. The periodic inventory control policy used by the buyer starts every period with an order size determination of each item and the subsequent supplier selection to fulfill the orders. Because each supplier in the system is different from other suppliers in the types of carrying items, delivery distance, item price, and quantity discount schedule, the buyer&rsquo;s problem becomes a complicated optimization problem. For the described order size and supplier selection problem of the buyer, we propose a nonlinear integer programming model and develop two different algorithms to enhance the usability of the model in a real business environment with a large amount of data. The algorithms are developed to considerably cut computational time and at the same time to generate a good feasible solution to a given supplier selection and order allocation problem. Computational experiments that were conducted to test the efficiency of the algorithms showed that they can cut as much as 99% of the computational time and successfully find feasible solutions, deviating not more than 3.4% from the optimal solutions.

]]>Mathematics doi: 10.3390/math8101658

Authors: Ilona Nagy Valery G. Romanovski János Tóth

We search for limit cycles in the dynamical model of two-species chemical reactions that contain seven reaction rate coefficients as parameters and at least one third-order reaction step, that is, the induced kinetic differential equation of the reaction is a planar cubic differential system. Symbolic calculations were carried out using the Mathematica computer algebra system, and it was also used for the numerical verifications to show the following facts: the kinetic differential equations of these reactions each have two limit cycles surrounding the stationary point of focus type in the positive quadrant. In the case of Model 1, the outer limit cycle is stable and the inner one is unstable, which appears in a supercritical Hopf bifurcation. Moreover, the oscillations in a neighborhood of the outer limit cycle are slow-fast oscillations. In the case of Model 2, the outer limit cycle is unstable and the inner one is stable. With another set of parameters, the outer limit cycle can be made stable and the inner one unstable.

]]>Mathematics doi: 10.3390/math8101655

Authors: Dening Luo Jianwei Zhang

Anti-aliasing plays a decisive role in enhancing immersion experience in games and 3D visualization fields. In general, hardware anti-aliasing is not directly compatible with deferred shading. It is challenging to detect geometry edges accurately from sub-pixel to alleviate artifacts. In this paper, we propose an anti-aliasing algorithm of the #-filter anti-aliasing based on sub-pixel continuous edges. It can solve the geometry edges aliasing and the flicker problem in deferred shading. First, the geometry scene with multi-sampling anti-aliasing (MSAA) is rendered to a G-Buffer designed elaborately. Second, the geometry edges are detected on the sub-pixel-level. We mainly take advantage of the Chebyshev inequality to adaptively determine the edges from the probability statistic and the view frustum location. Third, the continuous geometry edges are reconstructed by a #-filter method. Finally, the edge pixels are shaded adaptively. The implementation demonstrates that our algorithm is efficient and scalable for generating high-quality anti-aliasing geometry and reducing shading calculation overhead.

]]>Mathematics doi: 10.3390/math8101657

Authors: Yasutaka Chiba

In some clinical studies, assessing covariate effect types indicating whether a covariate is predictive and/or prognostic is of interest, in addition to the study endpoint. Recently, for a case with a binary outcome, Chiba (Clinical Trials, 2019; 16: 237&ndash;245) proposed the new concept of covariate effect type, which is assessed in terms of four response types, and showed that standard subgroup or regression analysis is applicable only in certain cases. Although this concept could be useful for supplementing conventional standard analysis, its application is limited to cases with a binary outcome. In this article, we aim to generalize Chiba&rsquo;s concept to continuous and time-to-event outcomes. We define covariate effect types based on four response types. It is difficult to estimate the response types from the observed data without making certain assumptions, so we propose a simple method to estimate them under the assumption of independent potential outcomes. Our approach is illustrated using data from a clinical study with a time-to-event outcome.

]]>Mathematics doi: 10.3390/math8101656

Authors: Jukkrit Daengsaen Sorasak Leeratanavalee Bijan Davvaz

The concept of j-hyperideals, for all positive integers 1&le;j&le;n and n&ge;2, in n-ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j-(0-)simple n-ary semihypergroups and discuss their related properties through terms of j-hyperideals. Furthermore, we characterize the minimality and maximality of j-hyperideals in n-ary semihypergroups and establish the relationships between the (0-)minimal, maximal j-hyperideals and the j-(0-)simple n-ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

]]>Mathematics doi: 10.3390/math8101654

Authors: Octav Olteanu

This paper starts by recalling the author&rsquo;s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ℝn, n&ge;2, which are not sums of squares.

]]>Mathematics doi: 10.3390/math8101653

Authors: Muhammad Naeem Muhammad Qiyas Mohammed M. Al-Shomrani Saleem Abdullah

The fractional orthotriple fuzzy set (FOFS) is more generalized than the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to cope with awkward and complex information in fuzzy set (FS) theory. The FOFS is a more powerful technique with respect to the existing drawbacks because of its conditions, i.e., the sum of the f powers of positive, neutral, and negative grades is bounded to [0,1]. With the advantages of the FOFS, in this paper, we study the basic definitions and some existing similarity measures (SMs) of intuitionistic fuzzy sets (IFSs), PFSs, Pythagorean fuzzy sets (PyFSs) and SFSs. The existing approaches have certain limitations and cannot be applied to problems that are in the form of FOFSs. The goal of this paper is to propose the idea of some new SMs including cosine SMs for FOFSs, SMs for FOFSs based on the cosine function, and SMs for FOFSs based on the cotangent function. Further, some weighted SMs (WSMs) are also proposed for which the weight of the attributes is considered. Then, we apply these SMs and WSMs to the pattern recognition problem. Finally, the comparative study of the new SMs for FOFSs is established with existing SMs, and also, some advantages of the proposed work are discussed.

]]>Mathematics doi: 10.3390/math8101652

Authors: Jaeyong Kang Jeonghwan Gwak

In recent years, deep learning models have been used successfully in almost every field including both industry and academia, especially for computer vision tasks. However, these models are huge in size, with millions (and billions) of parameters, and thus cannot be deployed on the systems and devices with limited resources (e.g., embedded systems and mobile phones). To tackle this, several techniques on model compression and acceleration have been proposed. As a representative type of them, knowledge distillation suggests a way to effectively learn a small student model from large teacher model(s). It has attracted increasing attention since it showed its promising performance. In the work, we propose an ensemble model that combines feature-based, response-based, and relation-based lightweight knowledge distillation models for simple image classification tasks. In our knowledge distillation framework, we use ResNet&minus;20 as a student network and ResNet&minus;110 as a teacher network. Experimental results demonstrate that our proposed ensemble model outperforms other knowledge distillation models as well as the large teacher model for image classification tasks, with less computational power than the teacher model.

]]>Mathematics doi: 10.3390/math8101651

Authors: Oliver Cuate Oliver Schütze

Optimization problems where several objectives have to be considered concurrently arise in many applications. Since decision-making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known as many objective optimization problems (MaOPs). For such problems, it is not possible any more to compute finite size approximations that suitably represent the entire solution set. If no users preferences are at hand, so-called knee points are promising candidates since they represent at least locally the best trade-off solutions among the considered objective values. In this paper, we extend the global/local exploration tool Pareto Explorer (PE) for the detection of such solutions. More precisely, starting from an initial solution, the goal of the modified PE is to compute a path of evenly spread solutions from this point along the Pareto front leading to a knee of the MaOP. The knee solution, as well as all other points from this path, are of potential interest for the underlying decision-making process. The benefit of the approach is demonstrated in several examples.

]]>Mathematics doi: 10.3390/math8101650

Authors: Zhaojun Zhang Zhaoxiong Xu Shengyang Luan Xuanyu Li Yifei Sun

Opposition-based learning (OBL) has been widely used to improve many swarm intelligent optimization (SI) algorithms for continuous problems during the past few decades. When the SI optimization algorithms apply OBL to solve discrete problems, the construction and utilization of the opposite solution is the key issue. Ant colony optimization (ACO) generally used to solve combinatorial optimization problems is a kind of classical SI optimization algorithm. Opposition-based ACO which is combined in OBL is proposed to solve the symmetric traveling salesman problem (TSP) in this paper. Two strategies for constructing opposite path by OBL based on solution characteristics of TSP are also proposed. Then, in order to use information of opposite path to improve the performance of ACO, three different strategies, direction, indirection, and random methods, mentioned for pheromone update rules are discussed individually. According to the construction of the inverse solution and the way of using it in pheromone updating, three kinds of improved ant colony algorithms are proposed. To verify the feasibility and effectiveness of strategies, two kinds of ACO algorithms are employed to solve TSP instances. The results demonstrate that the performance of opposition-based ACO is better than that of ACO without OBL.

]]>Mathematics doi: 10.3390/math8101649

Authors: Nurul Amira Zainal Roslinda Nazar Kohilavani Naganthran Ioan Pop

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

]]>Mathematics doi: 10.3390/math8101648

Authors: Mohamed Aboraya Haitham M. Yousof G.G. Hamedani Mohamed Ibrahim

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be &ldquo;decreasing&rdquo;, &ldquo;upside down&rdquo;, &ldquo;increasing&rdquo;, and &ldquo;decreasing-constant-increasing (U-shape)&rdquo;. Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis&ndash;Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications.

]]>Mathematics doi: 10.3390/math8101647

Authors: Yongsheng Rao Saeed Kosari Zehui Shao

Fuzzy graph models enjoy the ubiquity of being present in nature and man-made structures, such as the dynamic processes in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems that are often uncertain, for an expert, it is highly difficult to demonstrate those problems through a fuzzy graph. Resolving the uncertainty associated with the inconsistent and indeterminate information of any real-world problem can be done using a vague graph (VG), with which the fuzzy graphs may not generate satisfactory results. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGs. The objective of this paper is to present certain types of vague graphs (VGs), including strongly irregular (SI), strongly totally irregular (STI), neighborly edge irregular (NEI), and neighborly edge totally irregular vague graphs (NETIVGs), which are introduced for the first time here. Some remarkable properties associated with these new VGs were investigated, and necessary and sufficient conditions under which strongly irregular vague graphs (SIVGs) and highly irregular vague graphs (HIVGs) are equivalent were obtained. The relation among strongly, highly, and neighborly irregular vague graphs was established. A comparative study between NEI and NETIVGs was performed. Different examples are provided to evaluate the validity of the new definitions. A new definition of energy called the Laplacian energy (LE) is presented, and its calculation is shown with some examples. Likewise, we introduce the notions of the adjacency matrix (AM), degree matrix (DM), and Laplacian matrix (LM) of VGs. The lower and upper bounds for the Laplacian energy of a VG are derived. Furthermore, this study discusses the VG energy concept by providing a real-time example. Finally, an application of the proposed concepts is presented to find the most effective person in a hospital.

]]>Mathematics doi: 10.3390/math8101646

Authors: Dorina Răducanu

In this note, we consider a subclass H3/2(p) of starlike functions f with f&Prime;(0)=p for a prescribed p&isin;[0,2]. Usually, in the study of univalent functions, estimates on the Taylor coefficients, Fekete&ndash;Szeg&ouml; functional or Hankel determinats are given. Another coefficient problem which has attracted considerable attention is to estimate the moduli of successive coefficients |an+1|&minus;|an|. Recently, the related functional |an+1&minus;an| for the initial successive coefficients has been investigated for several classes of univalent functions. We continue this study and for functions f(z)=z+&sum;n=2&infin;anzn&isin;H3/2(p), we investigate upper bounds of initial coefficients and the difference of moduli of successive coefficients |a3&minus;a2| and |a4&minus;a3|. Estimates of the functionals |a2a4&minus;a32| and |a4&minus;a2a3| are also derived. The obtained results expand the scope of the theoretical results related with the functional |an+1&minus;an| for various subclasses of univalent functions.

]]>Mathematics doi: 10.3390/math8101645

Authors: Massimiliano Sala Domenica Sogiorno Daniele Taufer

We show how a small subgroup confinement-like attack may be mounted on the Bitcoin addresses generation protocol, by inspecting a special subgroup of the group associated to point multiplication. This approach does not undermine the system security but highlights the importance of using fair random sources during the private key selection.

]]>Mathematics doi: 10.3390/math8101644

Authors: Selda Çalkavur Patrick Solé

A (t,n)-secret sharing scheme is a method of distribution of information among n participants such that any t&gt;1 of them can reconstruct the secret but any t&minus;1 cannot. A ramp secret sharing scheme is a relaxation of that protocol that allows that some (t&minus;1)-coalitions could reconstruct the secret. In this work, we explore some ramp secret sharing schemes based on quotients of polynomial rings. The security analysis depends on the distribution of zero-sum sets in abelian groups. We characterize all finite commutative rings for which the sum of all elements is zero, a result of independent interest. When the quotient is a finite field, we are led to study the weight distribution of a coset of shortened Hamming codes.

]]>Mathematics doi: 10.3390/math8101643

Authors: S. Chatterjee T. Bag Jeong-Gon Lee

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t-norm is left-continuous at (1,1). In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo&rsquo;s generalization of the Schauder-type fixed point theorem is developed for the class of &psi;-set contractions. This theorem is proven by using the idea of the measure of non-compactness.

]]>Mathematics doi: 10.3390/math8101642

Authors: Song-Kyoo (Amang) Kim

This paper deals with the explicit design of strategy formulations to make the best strategic choices from a conventional matrix form of representing strategic choices. The explicit strategy formulation is an analytical model that is targeted to provide a mathematical strategy framework to find the best moment for strategy shifting to prepare rapid market changes. This theoretical model could be adapted into practically any strategic decision making situation when a strategic formulation is described as a matrix form with quantitative measured decision parameters. Analytically tractable results are obtained by using the fluctuation theory and these results are able to predict the best moments for changing strategies in a matrix form. This research can help strategy decision makers who want to find the optimal moments of shifting present strategies.

]]>Mathematics doi: 10.3390/math8101641

Authors: Melchor Gómez-García Hossein Hossein-Mohand Juan Manuel Trujillo-Torres Hassan Hossein-Mohand

Currently, information and communication technology (ICT) has acquired an important role in education. The incorporation of ICT by mathematics teachers has been a challenge as it requires an improvement in their knowledge of the use of new technologies. We aimed to examine the most relevant items of the indicators related to teaching mathematics and ICT, to estimate the relationships between teachers individually and by clusters, and to analyze the incidence of age variables, teaching experience, and gender in this study. A total of 73 high school teachers were included in this cross-sectional study. A validated questionnaire was used to assess mathematics and teaching practice, use, resources, and domain of ICT. Principal component analysis (PCA) was applied to determine the associations among variables of the present study. The application of ICT to teaching was associated with the use of ICT resources in the classroom and indicated that teachers made more choice in selecting a variety of software than electing different hardware devices. Teachers combined technology with educational platforms to improve student learning in mathematics. The general perception of mathematics teachers about their digital competence does not match with models employed in the classroom. Gender was not an influencing factor.

]]>Mathematics doi: 10.3390/math8101640

Authors: Amirhosein Mosavi Yaser Faghan Pedram Ghamisi Puhong Duan Sina Faizollahzadeh Ardabili Ely Salwana Shahab S. Band

The popularity of deep reinforcement learning (DRL) applications in economics has increased exponentially. DRL, through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL), offers vast opportunities for handling sophisticated dynamic economics systems. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this paper, we initially consider a brief review of DL, RL, and deep RL methods in diverse applications in economics, providing an in-depth insight into the state-of-the-art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher efficiency as compared to the traditional algorithms while facing real economic problems in the presence of risk parameters and the ever-increasing uncertainties.

]]>Mathematics doi: 10.3390/math8101639

Authors: Marek Skarupski

The classical secretary problem models a situation in which the decision maker can select or reject in the sequential observation objects numbered by the relative ranks. In theoretical studies, it is known that the strategy is to reject the first 37% of objects and select the next relative best one. However, an empirical result for the problem is that people do not apply the optimal rule. In this article, we propose modeling doubts of decision maker by considering a modification of the secretary problem. We assume that the decision maker can not observe the relative ranks in a proper way. We calculate the optimal strategy in such a problem and the value of the problem. In special cases, we also combine this problem with the no-information best choice problem and a no-information second-best choice problem.

]]>Mathematics doi: 10.3390/math8101638

Authors: Wen Su Wenguang Yu

Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim sizes of sample. However, whether the estimators are asymptotically normal or not is unknown. In this paper, we give the details to verify the asymptotic normality of these estimators and present some simulation examples to support our result.

]]>Mathematics doi: 10.3390/math8091637

Authors: Kenzu Abdella Glen Ross

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well.

]]>Mathematics doi: 10.3390/math8091636

Authors: Noé Ortega-Sánchez Diego Oliva Erik Cuevas Marco Pérez-Cisneros Angel A. Juan

The techniques of halftoning are widely used in marketing because they reduce the cost of impression and maintain the quality of graphics. Halftoning converts a digital image into a binary image conformed by dots. The output of the halftoning contains less visual information; a possible benefit of this task is the reduction of ink when graphics are printed. The human eye is not able to detect the absence of information, but the printed image stills have good quality. The most used method for halftoning is called Floyd-Steinberger, and it defines a specific matrix for the halftoning conversion. However, most of the proposed techniques in halftoning use predefined kernels that do not permit adaptation to different images. This article introduces the use of the harmony search algorithm (HSA) for halftoning. The HSA is a popular evolutionary algorithm inspired by the musical improvisation. The different operators of the HSA permit an efficient exploration of the search space. The HSA is applied to find the best configuration of the kernel in halftoning; meanwhile, as an objective function, the use of the structural similarity index (SSIM) is proposed. A set of rules are also introduced to reduce the regular patterns that could be created by non-appropriate kernels. The SSIM is used due to the fact that it is a perception model used as a metric that permits comparing images to interpret the differences between them numerically. The aim of combining the HSA with the SSIM for halftoning is to generate an adaptive method that permits estimating the best kernel for each image based on its intrinsic attributes. The graphical quality of the proposed algorithm has been compared with classical halftoning methodologies. Experimental results and comparisons provide evidence regarding the quality of the images obtained by the proposed optimization-based approach. In this context, classical algorithms have a lower graphical quality in comparison with our proposal. The results have been validated by a statistical analysis based on independent experiments over the set of benchmark images by using the mean and standard deviation.

]]>Mathematics doi: 10.3390/math8091635

Authors: Li-Ting Yeh

The socioeconomic costs of occupational accidents represent an important factor in the safety and healthy development of a country&rsquo;s economy. Insurance payments (which cover workplace incidents, such as wounds or illness, disability and fatality) can be considered a proxy for the socioeconomic cost of occupational accidents. Occupational accidents in different industries cause important variations in these three socioeconomic costs&mdash;for example, in their frequency and severity. One of the most commonly used mathematical programming approaches that analyze the performance of inputs, economic outputs and occupational accidents is data envelopment analysis (DEA), which has also been used in recent years to estimate the relative performance related to occupational injuries. This study measures the safety and healthy economic performance of Taiwan&rsquo;s 17 industrial sectors by incorporating the varying importance of the three socioeconomic costs of occupational accidents into a weighted DEA Model. The empirical results demonstrate that integrating the varying importance of the three socioeconomic costs of occupational accidents in the evaluation of safety and healthy economic performance is very important. To improve the occupational safety and healthy economic performance of Taiwan&rsquo;s main industrial sectors, efforts should focus on reducing fatalities, which are very costly. These findings could help Taiwan&rsquo;s policy makers effectively improve their safety and healthy economic performance, based on the specific context of each industry, especially the mining and quarrying industry.

]]>Mathematics doi: 10.3390/math8091634

Authors: Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid

In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results.

]]>Mathematics doi: 10.3390/math8091633

Authors: Wonhee Kim Sangmin Suh

In this paper, a stability-driven optimal disturbance observer (DO) is proposed. The proposed method does not require any plant inverse dynamics to detect introduced disturbances or a stabilizing Q filter. It does not require additional compensators to resolve causality problems, due to the relative degree, or filters to solve instability problems of non-minimum phase plants. Using this method enables wideband and narrowband disturbances to be attenuated by simply multiplying the corresponding peak filters by the baseline weight function. Furthermore, the proposed DO guarantees the stability of closed-loop systems because the already designed outer-loop systems are considered as a target plant to be stabilized and because of the Lyapunov stability-based H&infin; control. In the application example, it was confirmed that the proposed method is effective, and the position error signals were improved by 20.9% in commercial hard disk drives and 36.6% in optical image stabilization systems.

]]>Mathematics doi: 10.3390/math8091632

Authors: Khaled Zennir Mohamad Biomy

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love&rsquo;s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory &piv; in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

]]>Mathematics doi: 10.3390/math8091631

Authors: Daewoo Pak Klaus Langohr Jing Ning Jordi Cortés Martínez Guadalupe Gómez Melis Yu Shen

The incubation period of coronavirus disease 2019 (COVID-19) is not always observed exactly due to uncertain onset times of infection and disease symptoms. In this paper, we demonstrate how to estimate the distribution of incubation and its association with patient demographic factors when the exact dates of infection and symptoms&rsquo; onset may not be observed. The findings from analysis of the confirmed COVID-19 cases indicate that age could be associated with the incubation period, and an age-specific quarantine policy might be more efficient than a unified one in confining COVID-19.

]]>Mathematics doi: 10.3390/math8091630

Authors: Hark-Mahn Kim Hwan-Yong Shin

In this paper, we find the solution of the following quadratic functional equation n&sum;1&le;i&lt;j&le;nQxi&minus;xj=&sum;i=1nQ&sum;j&ne;ixj&minus;(n&minus;1)xi, which is derived from the gravity of the n distinct vectors x1,⋯,xn in an inner product space, and prove that the stability results of the A-quadratic mappings in &mu;-complete convex fuzzy modular &lowast;-algebras without using lower semicontinuity and &beta;-homogeneous property.

]]>Mathematics doi: 10.3390/math8091629

Authors: Jelena Vujaković Slobodanka Mitrović Zoran Mitrović Stojan Radenović

In the paper, we consider some fixed point results of F-contractions for triangular α-admissible and triangular weak α-admissible mappings in metric-like spaces. The results on F-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property (F1) of the strictly increasing mapping F:0,+∞→−∞,+∞. Our approach gives a proper generalization of several results given in current literature.

]]>Mathematics doi: 10.3390/math8091628

Authors: Hoang Pham

COVID-19, known as Coronavirus disease 2019, is caused by a coronavirus called SARS-CoV-2. As coronavirus restrictions ease and cause changes to social and business activities around the world, and in the United States in particular, including social distancing, reopening states, reopening schools, and the face mask mandates, COVID-19 outbreaks are on the rise in many states across the United States and several other countries around the world. The United States recorded more than 1.9 million new infections in July, which is nearly 36 percent of the more than 5.4 million cases reported nationwide since the pandemic began, including more than 170,000 deaths from the disease, according to data from Johns Hopkins University as of 16 August 2020. In April 2020, the author of this paper presented a model to estimate the number of deaths related to COVID-19, which assumed that there would be no significant change in the COVID-19 restrictions and guidelines in the coming days. This paper, which presents the evolved version of the previous model published in April, discusses a new explicit mathematical model that considers the time-dependent effects of various pandemic restrictions and changes related to COVID-19, such as reopening states, social distancing, reopening schools, and face mask mandates in communities, along with a set of selected indicators, including the COVID-19 recovered cases and daily new cases. We analyzed and compared the modeling results to two recent models based on several model selection criteria. The model could predict the death toll related to the COVID-19 virus in the United States and worldwide based on the data available from Worldometer. The results show the proposed model fit the data significantly better for the United States and worldwide COVID-19 data that were available on 16 August 2020. The results show very encouraging predictability that reflected the time-dependent effects of various pandemic restrictions for the proposed model. The proposed model predicted that the total number of U.S. deaths could reach 208,375 by 1 October 2020, with a possible range of approximately 199,265 to 217,480 deaths based on data available on 16 August 2020. The model also projected that the death toll could reach 233,840 by 1 November 2020, with a possible range of 220,170 to 247,500 American deaths. The modeling result could serve as a baseline to help decision-makers to create a scientific framework to quantify their guidelines related to COVID-19 affairs. The model predicted that the death toll worldwide related to COVID-19 virus could reach 977,625 by 1 October 2020, with a possible range of approximately 910,820 to 1,044,430 deaths worldwide based on data available on 16 August 2020. It also predicted that the global death toll would reach nearly 1,131,000 by 1 November 2020, with a possible range of 1,030,765 to 1,231,175 deaths. The proposed model also predicted that the global death toll could reach 1.47 million deaths worldwide as a result of the SARS CoV-2 coronavirus that causes COVID-19. We plan to apply or refine the proposed model in the near future to further study the COVID-19 death tolls for India and Brazil, where the two countries currently have the second and third highest total COVID-19 cases after the United States.

]]>Mathematics doi: 10.3390/math8091627

Authors: Lucas Schneider Johannes Stübinger

This paper develops a dispersion trading strategy based on a statistical index subsetting procedure and applies it to the S&amp;P 500 constituents from January 2000 to December 2017. In particular, our selection process determines appropriate subset weights by exploiting a principal component analysis to specify the individual index explanatory power of each stock. In the following out-of-sample trading period, we trade the most suitable stocks using a hedged and unhedged approach. Within the large-scale back-testing study, the trading frameworks achieve statistically and economically significant returns of 14.52 and 26.51 percent p.a. after transaction costs, as well as a Sharpe ratio of 0.40 and 0.34, respectively. Furthermore, the trading performance is robust across varying market conditions. By benchmarking our strategies against a naive subsetting scheme and a buy-and-hold approach, we find that our statistical trading systems possess superior risk-return characteristics. Finally, a deep dive analysis shows synchronous developments between the chosen number of principal components and the S&amp;P 500 index.

]]>Mathematics doi: 10.3390/math8091626

Authors: Jin Hee Yoon Taechang Byun Ji Eun Lee Keun Young Lee

The paper is concerned with complex fuzzy numbers and complex fuzzy inner product spaces. In the classical complex number set, a complex number can be expressed using the Cartesian form or polar form. Both expressions are needed because one expression is better than the other depending on the situation. Likewise, the Cartesian form and the polar form can be defined in a complex fuzzy number set. First, the complex fuzzy numbers (CFNs) are categorized into two types, the polar form and the Cartesian form, as type I and type II. The properties of the complex fuzzy number set of those two expressions are discussed, and how the expressions can be used practically is shown through an example. Second, we study the complex fuzzy inner product structure in each category and find the non-existence of an inner product on CFNs of type I. Several properties of the fuzzy inner product space for type II are proposed from the modulus that is newly defined. Specfically, the Cauchy-Schwartz inequality for type II is proven in a compact way, not only the one for fuzzy real numbers. In fact, it was already discussed by Hasanhani et al; however, they proved every case in a very complicated way. In this paper, we prove the Cauchy-Schwartz inequality in a much simpler way from a general point of view. Finally, we introduce a complex fuzzy scalar product for the generalization of a complex fuzzy inner product and propose to study the condition for its existence on CFNs of type I.

]]>Mathematics doi: 10.3390/math8091625

Authors: Jie Wei Wenxian Xie Yufeng Nie

Bayesian Network is one of the famous network models, and the loop cutset is one of the crucial structures for Bayesian Inference. In the Bayesian Network and its inference, how to measure the relationship between nodes is very important, because the relationship between different nodes has significant influence on the node-probability of the loop cutset. To analyse the relationship between two nodes in a graph, we define the shared node, prove the upper and lower bounds of the shared nodes number, and affirm that the shared node influences the node-probability of the loop cutset according to the theorems and experiments. These results can explain the problems that we found in studying on the statistical node-probability belonging to the loop cutset. The shared nodes are performed not only to improve the theoretical analysis on the loop cutset, but also to the loop cutset solving algorithms, especially the heuristic algorithms, in which the heuristic strategy can be optimized by a shared node. Our results provide a new tool to gauge the relationship between different nodes, a new perspective to estimate the loop cutset, and it is helpful to the loop cutset algorithm and network analysis.

]]>Mathematics doi: 10.3390/math8091624

Authors: Daniel Mejia-Parra Oscar Ruiz-Salguero Carlos Cadavid Aitor Moreno Jorge Posada

In the context of CAD CAM CAE (Computer-Aided Design, Manufacturing and Engineering) and Additive Manufacturing, the computation of level sets of closed 2-manifold triangular meshes (mesh slicing) is relevant for the generation of 3D printing patterns. Current slicing methods rely on the assumption that the function used to compute the level sets satisfies strong Morse conditions, rendering incorrect results when such a function is not a Morse one. To overcome this limitation, this manuscript presents an algorithm for the computation of mesh level sets under the presence of non-Morse degeneracies. To accomplish this, our method defines weak-Morse conditions, and presents a characterization of the possible types of degeneracies. This classification relies on the position of vertices, edges and faces in the neighborhood outside of the slicing plane. Finally, our algorithm produces oriented 1-manifold contours. Each contour orientation defines whether it belongs to a hole or to an external border. This definition is central for Additive Manufacturing purposes. We set up tests encompassing all known non-Morse degeneracies. Our algorithm successfully processes every generated case. Ongoing work addresses (a) a theoretical proof of completeness for our algorithm, (b) implementation of interval trees to improve the algorithm efficiency and, (c) integration into an Additive Manufacturing framework for industry applications.

]]>Mathematics doi: 10.3390/math8091623

Authors: Chanjuan Liu Junming Yan Yuanye Ma Tianhao Zhao Qiang Zhang Xiaopeng Wei

A deeper game-tree search can yield a higher decision quality in a heuristic minimax algorithm. However, exceptions can occur as a result of pathological nodes, which are considered to exist in all game trees and can cause a deeper game-tree search, resulting in worse play. To reduce the impact of pathological nodes on the search quality, we propose an iterative optimal minimax (IOM) algorithm by optimizing the backup rule of the classic minimax algorithm. The main idea is that calculating the state values of the intermediate nodes involves not only the static evaluation function involved but also a search into the future, where the latter is given a higher weight. We experimentally demonstrated that the proposed IOM algorithm improved game-playing performance compared to the existing algorithms.

]]>Mathematics doi: 10.3390/math8091622

Authors: Siraj Uddin M. Z. Ullah

In the early 20th century, B.-Y. Chen introduced the concept of CR-warped products and obtained several fundamental results, such as inequality for the length of second fundamental form. In this paper, we obtain B.-Y. Chen&rsquo;s inequality for CR-slant warped products in nearly cosymplectic manifolds, which are the more general classes of manifolds. The equality case of this inequality is also investigated. Furthermore, the inequality is discussed for some important subclasses of CR-slant warped products.

]]>Mathematics doi: 10.3390/math8091621

Authors: Irfan Ali Armin Fügenschuh Srikant Gupta Umar Muhammad Modibbo

Vendor selection is an established problem in supply chain management. It is regarded as a strategic resource by manufacturers, which must be managed efficiently. Any inappropriate selection of the vendors may lead to severe issues in the supply chain network. Hence, the desire to develop a model that minimizes the combination of transportation, deliveries, and ordering costs under uncertainty situation. In this paper, a multi-objective vendor selection problem under fuzzy environment is solved using a fuzzy goal programming approach. The vendor selection problem was modeled as a multi-objective problem, including three primary objectives of minimizing the transportation cost; the late deliveries; and the net ordering cost subject to constraints related to aggregate demand; vendor capacity; budget allocation; purchasing value; vendors&rsquo; quota; and quantity rejected. The proposed model input parameters are considered to be LR fuzzy numbers. The effectiveness of the model is illustrated with simulated data using R statistical package based on a real-life case study which was analyzed using LINGO 16.0 optimization software. The decision on the vendor&rsquo;s quota allocation and selection under different degree of vagueness in the information was provided. The proposed model can address realistic vendor selection problem in the fuzzy environment and can serve as a useful tool for multi-criteria decision-making in supply chain management.

]]>Mathematics doi: 10.3390/math8091620

Authors: Ganjar Alfian Muhammad Syafrudin Norma Latif Fitriyani Muhammad Anshari Pavel Stasa Jiri Svub Jongtae Rhee

Extracting information from individual risk factors provides an effective way to identify diabetes risk and associated complications, such as retinopathy, at an early stage. Deep learning and machine learning algorithms are being utilized to extract information from individual risk factors to improve early-stage diagnosis. This study proposes a deep neural network (DNN) combined with recursive feature elimination (RFE) to provide early prediction of diabetic retinopathy (DR) based on individual risk factors. The proposed model uses RFE to remove irrelevant features and DNN to classify the diseases. A publicly available dataset was utilized to predict DR during initial stages, for the proposed and several current best-practice models. The proposed model achieved 82.033% prediction accuracy, which was a significantly better performance than the current models. Thus, important risk factors for retinopathy can be successfully extracted using RFE. In addition, to evaluate the proposed prediction model robustness and generalization, we compared it with other machine learning models and datasets (nephropathy and hypertension&ndash;diabetes). The proposed prediction model will help improve early-stage retinopathy diagnosis based on individual risk factors.

]]>Mathematics doi: 10.3390/math8091619

Authors: Cheng-Shu You Ming-Jyh Chern Dedy Zulhidayat Noor Tzyy-Leng Horng

The fluid-structure interaction of solid objects freely falling in a Newtonian fluid was investigated numerically by direct-forcing immersed boundary (DFIB) method. The Navier&ndash;Stokes equations are coupled with equations of motion through virtual force to describe the motion of solid objects. Here, we rigorously derived the equations of motion by taking control-volume integration of momentum equation. The method was validated by a popular numerical test example describing the 2D flow caused by the free fall of a circular disk inside a tank of fluid, as well as 3D experimental measurements in the sedimentation of a sphere. Then, we demonstrated the method by a few more 2D sedimentation examples: (1) free fall of two tandem circular disks showing drafting, kissing and tumbling phenomena; (2) sedimentation of multiple circular disks; (3) free fall of a regular triangle, in which the rotation of solid object is significant; (4) free fall of a dropping ellipse to mimic the falling of a leaf. In the last example, we found rich falling patterns exhibiting fluttering, tumbling, and chaotic falling.

]]>Mathematics doi: 10.3390/math8091618

Authors: Iñigo Querejeta-Azurmendi David Arroyo Guardeño Jorge L. Hernández-Ardieta Luis Hernández Encinas

This paper proposes NetVote, an internet voting protocol where usability and ease in deployment are a priority. We introduce the notion of strict coercion resistance, to distinguish between vote-buying and coercion resistance. We propose a protocol with ballot secrecy, practical everlasting privacy, verifiability and strict coercion resistance in the re-voting setting. Coercion is mitigated via a random dummy vote padding strategy to hide voting patterns and make re-voting deniable. This allows us to build a filtering phase with linear complexity, based on zero knowledge proofs to ensure correctness while maintaining privacy of the process. Voting tokens are formed by anonymous credentials and pseudorandom identifiers, achieving practical everlasting privacy, where even if dealing with a future computationally unbounded adversary, vote intention is still hidden. It is not assumed for voters to own cryptographic keys prior to the election, nor store cryptographic material during the election. This property allows voters not only to vote multiple times, but also from different devices each time, granting the voter a vote-from-anywhere experience. This paper builds on top of the paper published in CISIS&rsquo;19. In this version, we modify the filtering. Moreover, we formally define the padding technique, which allows us to perform the linear filtering scheme. Similarly we provide more details on the protocol itself and include a section of the security analysis, where we include the formal definitions of strict coercion resistance and a game based definition of practical everlasting privacy. Finally, we prove that NetVote satisfies them all.

]]>Mathematics doi: 10.3390/math8091617

Authors: Sang-Eon Han

Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,l&or;⋯&or;Ckn,l︷m-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(&ge;7) is an odd natural number and k&ne;2n. Secondly, given a digital image (X,k) with X♯=n, we find a certain condition that supports n&minus;1,n&minus;2&isin;F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X♯&ge;2.

]]>Mathematics doi: 10.3390/math8091616

Authors: Seher Sultan Yeşilkaya Cafer Aydın

In this study, we introduce set-valued Pre&scaron;ić type almost contractive mapping, Pre&scaron;ić type almost F-contractive mapping and set-valued Pre&scaron;ić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Pre&scaron;ić type almost F-contractive operators is not included in Pre&scaron;ić type class of set-valued Pre&scaron;ić type almost contractive operators.

]]>Mathematics doi: 10.3390/math8091615

Authors: Akio Matsumoto Ferenc Szidarovszky

The dynamic behavior of n-firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings.

]]>Mathematics doi: 10.3390/math8091614

Authors: Hsien-Chung Wu

The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the &alpha;-level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications.

]]>Mathematics doi: 10.3390/math8091613

Authors: Chin-Lin Li Yangcong Su Ran-Zan Wang

A photomosaic is an image with two layers of visual information, including an overarching image that can be seen from a distance and a matrix of individual tile images when examined closely. This paper presents a method for generating photomosaics with an additional layer of quick response code (QR code) information that can be accessed by typical QR code scanners in cell phones. The basic idea is to carefully classify the tile images in different categories and generate the photomosaic patches by referring to the properties of QR code modules. Three levels of construction methods for generating the proposed photomosaics in different image resolutions are proposed. The results show that the generated photomosaics have good visual quality and high robustness for decoding the QR code. The proposed method endows conventional photomosaics with the QR code capability. It extends photomosaics from exhibiting purely visual information to the linkage of multimedia data. Furthermore, it increases the feasibility and potential of applying photomosaics in diverse applications, such as activity promotions or commercial product advertisements.

]]>Mathematics doi: 10.3390/math8091612

Authors: Giphil Cho Daewook Kim Sukgeun Jung Il Hyo Jung Sangil Kim

To estimate age-specific natural mortality, we proposed an age-structured biomass model with an impulsive dynamical system. In the estimation of natural mortality, we considered growth rate and also reproduction rate, growth, and catch of sandfish, Arctoscopus japonicus. Assuming a linear relationship between observed values of the catch per unit effort (CPUE) and total biomass estimated by the age-structured biomass model, we estimated the age-specific natural mortality using the CPUE and catch data, from 1994 to 2009, for varying values of the assumed initial total biomass in 1994, by selecting the largest coefficient of determination (R2). We suggested the following empirical formula: Mi=qKL&infin;ln(eK(i+1&minus;t0)&nbsp;&minus;&nbsp;1eK(i&minus;t0)&nbsp;&minus;&nbsp;1), which estimated natural mortality of sandfish, and the derived age-specific natural mortality was significantly related to fecundity and growth. The parameters of von Bertalanffy growth equation and a logistic equation of maturity with total length were derived from the data of otolith and gonad analysis of female sandfish collected from 2005 to 2008 and from 2005 to 2006, respectively. We also conducted sensitivity analysis by varying the exponent in the inverse function of total length.

]]>Mathematics doi: 10.3390/math8091611

Authors: Mauro Mezzini Fernando L. Pelayo

In this paper we present an algorithm which counts the number of fixed point orbits of an AND-OR dynamical system. We further extend the algorithm in order to list all its fixed point orbits (FPOs) in polynomial time on the number of FPOs of the system.

]]>Mathematics doi: 10.3390/math8091609

Authors: Samah Horrigue Ibrahim A. Abbas

The present work is aimed at studying the effect of fractional order and thermal relaxation time on an unbounded fiber-reinforced medium. In the context of generalized thermoelasticity theory, the fractional time derivative and the thermal relaxation times are employed to study the thermophysical quantities. The techniques of Fourier and Laplace transformations are used to present the problem exact solutions in the transformed domain by the eigenvalue approach. The inversions of the Fourier-Laplace transforms hold analytical and numerically. The numerical outcomes for the fiber-reinforced material are presented and graphically depicted. A comparison of the results for different theories under the fractional time derivative is presented. The properties of the fiber-reinforced material with the fractional derivative act to reduce the magnitudes of the variables considered, which can be significant in some practical applications and can be easily considered and accurately evaluated.

]]>Mathematics doi: 10.3390/math8091610

Authors: Chenyu Lu Yang Zhang Hengji Li Zilong Zhang Wei Cheng Shulei Jin Wei Liu

Since the 1990s, the notion of a circular economy has been developing globally; countries all over the world have been considering the development of a circular economy as an important means of achieving sustainable development. As the development of an industrial circular economy can help promote the efficient recycling of resources, it is an important starting point for industrial transformation and upgrading, and represents a key factor that will lead to the development of a circular economy in China. China&rsquo;s varying provinces (municipalities and autonomous regions) have successively implemented circular economy practices in the industrial field. The research object of the present study is 30 provinces, autonomous regions, and municipalities directly under the control of central government (Hong Kong, Macao, Taiwan, and Tibet were not included owing to lack of data). Through the integration of geographic information systems (GIS) technology and the spatial analysis model, data envelopment analysis (DEA) model, and Tobit regression model, a measure model and index system are constructed, in order to carry out a multi-angle comprehensive study integrating the efficiency evaluation, spatial analysis, and influencing factors analysis of China&rsquo;s industrial circular economy. It is an important innovation, and an important contribution to the existing research system. The conclusions are as follows: (1) In general, the overall level of China&rsquo;s industrial circular economy&rsquo;s efficiency was not high, and there was still a lot of room for improvement. The integrated efficiency of the industrial circular economy in the eastern region was relatively high, followed by that in the western region, and the lowest level in the middle region. (2) The efficiency of China&rsquo;s industrial circular economy displayed obvious spatial aggregation characteristics at the provincial level, including clear spatial dependence and spatial heterogeneity. High-value aggregation areas were mainly distributed in the eastern coastal areas, and low-value aggregation areas were concentrated and contiguously distributed in the middle and western inland areas. (3) The four elements of economic level, openness to the outside, government regulation, and industrialization aggregation each impose a significant positive impact on the efficiency of China&rsquo;s industrial circular economy, which can promote its efficiency. The level of industrialization exerts a significant negative impact on the efficiency of the industrial circular economy, which hampers its improvement. The impact of technological innovation on the efficiency of the industrial circular economy is not statistically significant.

]]>Mathematics doi: 10.3390/math8091608

Authors: J. Ignacio Tello Lourdes Tello María Luisa Vilar

The aim of this article is to fill part of the existing gap between the mathematical modeling of a green roof and its computational treatment, focusing on the mathematical analysis. We first introduce a two-dimensional mathematical model of the thermal behavior of an extensive green roof based on previous models and secondly we analyze such a system of partial differential equations. The model is based on an energy balance for buildings with vegetation cover and it is presented for general shapes of roofs. The model considers a vegetable layer and the substratum and the energy exchange between them. The unknowns of the problem are the temperature of each layer described by a coupled system of two partial differential equations of parabolic type. The equation modeling the evolution of the temperature of the substratum also considers the change of phase of water described by a maximal monotone graph. The main result of the article is the proof of the existence of solutions of the system which is given in detail by using a regularization of the maximal monotone graph. Appropriate estimates are obtained to pass to the limit in a weak formulation of the problem. The result goes one step further from modeling to validate future numerical results.

]]>Mathematics doi: 10.3390/math8091607

Authors: Baocheng Wang Wentao Cai

Session-based recommendation, which aims to match user needs with rich resources based on anonymous sessions, nowadays plays a critical role in various online platforms (e.g., media streaming sites, search and e-commerce). Existing recommendation algorithms usually model a session as a sequence or a session graph to model transitions between items. Despite their effectiveness, we would argue that the performance of these methods is still flawed: (1) Using only fixed session item embedding without considering the diversity of users&rsquo; interests and target items. (2) For user&rsquo;s long-term interest, the difficulty of capturing the different priorities for different items accurately. To tackle these defects, we propose a novel model which leverages both the target attentive network and self-attention network to improve the graph-neural-network (GNN)-based recommender. In our model, we first model user&rsquo;s interaction sequences as session graphs which serves as the input of the GNN, and each node vector involved in session graph can be obtained via the GNN. Next, target attentive network can activates different user interests corresponding to varied target items (i.e., the session embedding learned varies with different target items), which can reveal the relevance between users&rsquo; interests and target items. At last, after applying the self-attention mechanism, the different priorities for different items can be captured to improve the precision of the long-term session representation. By using a hybrid of long-term and short-term session representation, we can capture users&rsquo; comprehensive interests at multiple levels. Extensive experiments demonstrate the effectiveness of our algorithm on two real-world datasets for session-based recommendation.

]]>Mathematics doi: 10.3390/math8091606

Authors: Daniela Onita Adriana Birlutiu Liviu P. Dinu

Images and text represent types of content that are used together for conveying a message. The process of mapping images to text can provide very useful information and can be included in many applications from the medical domain, applications for blind people, social networking, etc. In this paper, we investigate an approach for mapping images to text using a Kernel Ridge Regression model. We considered two types of features: simple RGB pixel-value features and image features extracted with deep-learning approaches. We investigated several neural network architectures for image feature extraction: VGG16, Inception V3, ResNet50, Xception. The experimental evaluation was performed on three data sets from different domains. The texts associated with images represent objective descriptions for two of the three data sets and subjective descriptions for the other data set. The experimental results show that the more complex deep-learning approaches that were used for feature extraction perform better than simple RGB pixel-value approaches. Moreover, the ResNet50 network architecture performs best in comparison to the other three deep network architectures considered for extracting image features. The model error obtained using the ResNet50 network is less by approx. 0.30 than other neural network architectures. We extracted natural language descriptors of images and we made a comparison between original and generated descriptive words. Furthermore, we investigated if there is a difference in performance between the type of text associated with the images: subjective or objective. The proposed model generated more similar descriptions to the original ones for the data set containing objective descriptions whose vocabulary is simpler, bigger and clearer.

]]>Mathematics doi: 10.3390/math8091605

Authors: Fernando Reche María Morales Antonio Salmerón

In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures.

]]>Mathematics doi: 10.3390/math8091602

Authors: Jan Andres Jerzy Jezierski

The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics.

]]>Mathematics doi: 10.3390/math8091604

Authors: Jing-Nan Li San-Hua Wang Yu-Ping Xu

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

]]>Mathematics doi: 10.3390/math8091603

Authors: Yun Ho Choi Sung Jin Yoo

A quantized-feedback-based adaptive event-triggered tracking problem is investigated for strict-feedback nonlinear systems with unknown nonlinearities and external disturbances. All state variables are quantized through a uniform quantizer and the quantized states are only measurable for the control design. An approximation-based adaptive event-triggered control strategy using quantized states is presented. Compared with the existing recursive quantized feedback control results, the primary contributions of the proposed strategy are (1) to derive a quantized-states-based function approximation mechanism for compensating for unknown and unmatched nonlinearities and (2) to design a quantized-states-based event triggering law for the intermittent update of the control signal. A Lyapunov-based stability analysis is provided to conclude that closed-loop signals are uniformly ultimately bounded and there exists a minimum inter-event time for excluding Zeno behavior. In simulation results, it is shown that the proposed quantized-feedback-based event-triggered control law can be implemented with less than 10% of the total sample data of the existing quantized-feedback continuous control law.

]]>Mathematics doi: 10.3390/math8091601

Authors: Zakieh Avazzadeh Omid Nikan José A. Tenreiro Machado

This paper investigates the solitary wave solutions of the generalized Rosenau&ndash;Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau&ndash;Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.

]]>Mathematics doi: 10.3390/math8091600

Authors: Francisco José Navarro-González Yolanda Villacampa Mónica Cortés-Molina Salvador Ivorra

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.

]]>Mathematics doi: 10.3390/math8091599

Authors: Stoil I. Ivanov

In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros.

]]>Mathematics doi: 10.3390/math8091598

Authors: Vishnu Narayan Mishra Luis Manuel Sánchez Ruiz Pragati Gautam Swapnil Verma

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich&ndash;Rus&ndash;Ćirić type contraction and Hardy&ndash;Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

]]>Mathematics doi: 10.3390/math8091597

Authors: Umair Khan Anum Shafiq Aurang Zaib El-Sayed M. Sherif Dumitru Baleanu

Cancer remains one of the world&rsquo;s leading healthcare issues, and attempts continue not only to find new medicines but also to find better ways of distributing medications. It is harmful and lethal to most of its patients. The need to selectively deliver cytotoxic agents to cancer cells, to enhance protection and efficacy, has prompted the implementation of nanotechnology in medicine. The latest findings have found that gold nanomaterials can heal and conquer it because the material is studied such as gold (atomic number 79) which produces a large amount of heat and contribute to the therapy of malignant tumors. The purpose of the present study is to research the consequence of heat transport through blood flow (Casson model) that contains gold particles in a slippery shrinking/stretching curved surface. The mathematical modeling of Casson nanofluid containing gold nanomaterials towards the slippery curved shrinking/stretching surface is simplified by utilizing suitable transformation. Numerical dual solutions for the temperature and velocity fields are calculated by using bvp4c methodology in MATLAB. Impacts of related parameters are investigated in the temperature and velocity distribution. The results indicate that the suction parameter accelerates the velocity in the upper branch solution and decelerates it in the lower branch solution, while the temperature diminishes in both solutions. In addition, the Casson parameter shrinks the thickness of the velocity boundary-layer owing to rapid enhancement in the plastic dynamics&rsquo; viscosity. Moreover, the nanoparticle volume fraction accelerates the viscosity of blood as well as the thermal conductivity. Thus, findings suggested that gold nanomaterials are useful for drug moving and delivery mechanisms since the velocity boundary is regulated by the volume fraction parameter. Gold nanomaterials also raise the temperature field, so that cancer cells can be destroyed.

]]>Mathematics doi: 10.3390/math8091596

Authors: Raquel Sanchis Alfonso Duran-Heras Raul Poler

In today&rsquo;s volatile business arena, companies need to be resilient to deal with the unexpected. One of the main pillars of enterprise resilience is the capacity to anticipate, prevent and prepare in advance for disruptions. From this perspective, the paper proposes a mixed-integer linear programming (MILP) model for optimising preparedness capacity. Based on the proposed reference framework for enterprise resilience enhancement, the MILP optimises the activation of preventive actions to reduce proneness to disruption. To do so, the objective function minimizes the sum of the annual expected cost of disruptive events after implementing preventive actions and the annual cost of such actions. Moreover, the algorithm includes a constraint capping the investment in preventive actions and an attenuation formula to deal with the joint savings produced by the activation of two or more preventive actions on the same disruptive event. The management and business rationale for proposing the MILP approach is to keep it as simple and comprehensible as possible so that it does not require highly mathematically skilled personnel, thus allowing top managers at enterprises of any size to apply it effortlessly. Finally, a real pilot case study was performed to validate the mathematical formulation.

]]>Mathematics doi: 10.3390/math8091594

Authors: Nour Abed Alhaleem Abd Ghafur Ahmad

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.

]]>Mathematics doi: 10.3390/math8091595

Authors: Aura Hernández-Sabaté Lluís Albarracín F. Javier Sánchez

In this article, we present a sequence of activities in the form of a project in order to promote learning on design and analysis of algorithms. The project is based on the resolution of a real problem, the salesperson problem, and it is theoretically grounded on the fundamentals of mathematical modelling. In order to support the students&rsquo; work, a multimedia tool, called Graph-based Problem Explorer (GbPExplorer), has been designed and refined to promote the development of computer literacy in engineering and science university students. This tool incorporates several modules to allow coding different algorithmic techniques solving the salesman problem. Based on an educational design research along five years, we observe that working with GbPExplorer during the project provides students with the possibility of representing the situation to be studied in the form of graphs and analyze them from a computational point of view.

]]>Mathematics doi: 10.3390/math8091593

Authors: Daniele Mortari David Arnas

This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains.

]]>Mathematics doi: 10.3390/math8091592

Authors: İnan Ünal

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)&times;S1.

]]>Mathematics doi: 10.3390/math8091591

Authors: Jie Zhao Zhichao Fang Hong Li Yang Liu

In this paper, a finite volume element (FVE) method is proposed for the time fractional Sobolev equations with the Caputo time fractional derivative. Based on the L1-formula and the Crank&ndash;Nicolson scheme, a fully discrete Crank&ndash;Nicolson FVE scheme is established by using an interpolation operator Ih*. The unconditional stability result and the optimal a priori error estimate in the L2(&Omega;)-norm for the Crank&ndash;Nicolson FVE scheme are obtained by using the direct recursive method. Finally, some numerical results are given to verify the time and space convergence accuracy, and to examine the feasibility and effectiveness for the proposed scheme.

]]>Mathematics doi: 10.3390/math8091590

Authors: Muhammad Syafrudin Ganjar Alfian Norma Latif Fitriyani Muhammad Anshari Tony Hadibarata Agung Fatwanto Jongtae Rhee

Detecting self-care problems is one of important and challenging issues for occupational therapists, since it requires a complex and time-consuming process. Machine learning algorithms have been recently applied to overcome this issue. In this study, we propose a self-care prediction model called GA-XGBoost, which combines genetic algorithms (GAs) with extreme gradient boosting (XGBoost) for predicting self-care problems of children with disability. Selecting the feature subset affects the model performance; thus, we utilize GA to optimize finding the optimum feature subsets toward improving the model&rsquo;s performance. To validate the effectiveness of GA-XGBoost, we present six experiments: comparing GA-XGBoost with other machine learning models and previous study results, a statistical significant test, impact analysis of feature selection and comparison with other feature selection methods, and sensitivity analysis of GA parameters. During the experiments, we use accuracy, precision, recall, and f1-score to measure the performance of the prediction models. The results show that GA-XGBoost obtains better performance than other prediction models and the previous study results. In addition, we design and develop a web-based self-care prediction to help therapist diagnose the self-care problems of children with disabilities. Therefore, appropriate treatment/therapy could be performed for each child to improve their therapeutic outcome.

]]>Mathematics doi: 10.3390/math8091589

Authors: Emilio Abad-Segura Mariana-Daniela González-Zamar

The technological transformation has directly affected the functional areas of companies. This circumstance has been a challenge for corporate accounting, since the emerging technology allows handling a large volume of data, and providing valuable information for operational management, managerial control, and strategic planning. The aim of this study is to analyze current and future lines of research globally, during the period 1961&ndash;2019, on emerging technologies in corporate accounting. For this, bibliometric techniques were applied to 1126 articles on this subject to obtain findings on scientific production and the main subject areas. Scientific production has increased annually, so that in the last decade de 60.66% of all articles have been published. The main subject areas in which more articles were linked were business, management and accounting, social sciences, and economics, econometrics, and finance. Six lines of research have been identified that generate contributions on this topic. Furthermore, the analysis of the relevance of the keywords has detected the main future directions of research. The increasing worldwide trend of scientific production shows interest in developing aspects of this field of study. This study contributes to the academic, scientific, and professional discussion to improve decision-making based on the available information.

]]>Mathematics doi: 10.3390/math8091588

Authors: Hua Xin Wan-Ju Hsieh Yuhlong Lio Tzong-Ru Tsai

In this study, two new integrated control charts, named T2-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be specified. The T2-MAE chart is composed of two memoryless-type control charts and the MS-MAE chart is composed of one memory-type and one memoryless-type control charts. The normality assumption of error terms in the nonlinear profile model for both proposed control charts are extended to a generalized model. An intensive simulation study is conducted to evaluate the performance of the T2-MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the T2-MAE chart with less false alarms during the Phase I monitoring. Moreover, the MS-MAE chart is sensitive to different shifts on the model parameters and profile shape during the Phase II monitoring. An example about the vertical density profile is used for illustration.

]]>Mathematics doi: 10.3390/math8091587

Authors: Alejandra Tapia Viviana Giampaoli Víctor Leiva Yuhlong Lio

Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence analytics based on mixed-effects logistic regression models is proposed for detecting potentially influential observations which can affect the quality of these models. Global and local influence diagnostic techniques are used simultaneously in this detection, which are often used separately. In addition, predictive performance measures are considered for this analytics. A study with children and adolescent asthma real data, collected from a public hospital of S&atilde;o Paulo, Brazil, is conducted to illustrate the proposed methodology. The results show that the influence diagnostic methodology is helpful for obtaining an accurate predictive model that provides scientific evidence when data-driven medical decision-making.

]]>Mathematics doi: 10.3390/math8091586

Authors: Arturo Fuentes-Cabrera María Elena Parra-González Jesús López-Belmonte Adrián Segura-Robles

Nowadays, different methodologies are booming in the field of education, and active gamification-based methodologies such as the Escape Room are an example of these methodologies, which is the base of this research. The purpose of this research is to analyze the effectiveness of the use of an Escape Room as an active methodology to learn mathematics. A quantitative research method was performed through an experimental design. Two study groups were set up. With the control group, a traditional training methodology was used, and with the experimental group, an innovative one was used through an Escape room experience. A total of 62 students of the 3rd level of Secondary Education from an educational center in Ceuta (Spain) participated. Results show how the experience developed through the escape room improved achievement, motivation and autonomy in a significant way. It has also reduced learning anxiety significantly. It is concluded that the use of the Escape room in Mathematics improves learning achievement, anxiety, motivation and autonomy, with gender being a variable to be taken into account, especially in motivation and autonomy. Therefore, the escape room has a greater potential than a traditional methodology in Mathematics.

]]>Mathematics doi: 10.3390/math8091585

Authors: Manman Wang Shuai Lian Shi Yin Hengmin Dong

Taking the rational use of environmental regulations to promote the diffusion of green technology innovation in China&rsquo;s manufacturing enterprises as the starting point, this study analyzed the benefits to the government, innovation-supplying enterprises, and potential demand-oriented enterprises. In addition, a tripartite evolutionary model was constructed to examine the impact of command-and-control environmental regulation and market-driven environmental regulation on the diffusion of green technology innovation in manufacturing enterprises. Finally, the study compared and analyzed the heterogeneous effects of different types of environmental regulation tools on the diffusion of green technology innovation in manufacturing enterprises using local stability analysis and numerical simulation. The results are as follows: (i) When the government does not implement environmental regulation tools or the regulation intensity is relatively small, the diffusion depth of green technology innovation in manufacturing enterprises is zero. (ii) When government regulation reaches a certain level, the system of manufacturing enterprises, innovation-supplying enterprises, and potential demand-oriented enterprises will choose to actively promote the diffusion of green technology innovation following a long evolution process. (iii) Increasing the punishment intensity and subsidy rate of green technology innovation can stimulate the diffusion of green technology innovation in manufacturing enterprises. (iv) The comprehensive use of the two kinds of environmental regulation tools has a heterogeneous influence on the strategic choice of green technology innovation diffusion subjects of manufacturing enterprises, and its incentive effect on potential demand-oriented enterprises is relatively poor.

]]>Mathematics doi: 10.3390/math8091584

Authors: Abdullah Al-Mazrooei Abdullah Shoaib Jamshaid Ahmad

This paper is designed to display some results which generalize the recent results that cannot be established from the corresponding results in other spaces and do not satisfy the remarks of Jleli et al. (Fixed Point Theor Appl. 210, 2012) and Samet et al. (Int. J. Anal. Article ID 917158, 2013). We obtain unique fixed-point for mapping satisfying β-ψˇ contraction only on a closed Gd ball in complete dislocated Gd-metric space. An example is also discussed to shed light on the main result.

]]>Mathematics doi: 10.3390/math8091583

Authors: Jong Taek Cho

We prove that a contact strongly pseudo-convex CR (Cauchy&ndash;Riemann) manifold M2n+1, n&ge;2, is locally pseudo-Hermitian symmetric and satisfies &nabla;&xi;h=&mu;hϕ, &mu;&isin;R, if and only if M is either a Sasakian locally ϕ-symmetric space or a non-Sasakian (k,&mu;)-space. When n=1, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry.

]]>Mathematics doi: 10.3390/math8091582

Authors: Hongliang Cai Dan Tang

A Multi Secret Image sharing scheme can share several secret images among certain participators securely. Boolean-based secret sharing schemes are one kind of secret sharing method with light-weighted computation compared to the previous complex algebraic-based methods, which can realize the sharing of multi secret images. However, the existing Boolean-based multi secret sharing schemes are mostly restricted to the particular case of (2, n) and (n, n), only few Boolean-based multi secret sharing schemes study the general access structure, and the shares are mostly meaningless. In this paper, a new Boolean-based multi secret sharing scheme with the general access structure is proposed. All the shares are meaningful, which can avoid attracting the attention of adversaries, and the secret images can be recovered in a lossless manner. The feasibility of the scheme is proven, the performance is validated by the experiments on the gray images, and the analysis of the comparison with other methods is also given out.

]]>Mathematics doi: 10.3390/math8091581

Authors: Sebastián Fuentes Josué Trejo-Alonso Antonio Quevedo Carlos Fuentes Carlos Chávez

Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation.

]]>Mathematics doi: 10.3390/math8091580

Authors: Francisco Javier Garcia-Pacheco

The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functional Analysis results towards the scope of topological modules is a relatively new trend that has enriched the literature of Functional Analysis with deeper classical results as well as with pathological phenomena. Following this trend, it has been recently proved that every real or complex Hausdorff locally convex topological vector space with dimension greater than or equal to 2 has a balanced and absorbing subset with empty interior. Here we propose an extension of this result to topological modules over topological rings. A sufficient condition is provided to accomplish this extension. This sufficient condition is a new property in topological module theory called strong open property. On the other hand, topological regularity of closed balls and open balls in real or complex normed spaces is a trivial fact. Sufficient conditions, related to the strong open property, are provided on seminormed modules over an absolutely semivalued ring for closed balls to be regular closed and open balls to be regular open. These sufficient conditions are in fact characterizations when the seminormed module is the absolutely semivalued ring. These characterizations allow the provision of more examples of closed-unit neighborhoods of zero. Consequently, the closed-unit ball of any unital real Banach algebra is proved to be a closed-unit zero-neighborhood. We finally transport all these results to topological modules over topological rings to obtain nontrivial regular closed and regular open neighborhoods of zero. In particular, if M is a topological R-module and m&lowast;&isin;M&lowast; is a continuous linear functional on M which is open as a map between topological spaces, then m&lowast;&minus;1(int(B)) is regular open and m&lowast;&minus;1(B) is regular closed, for B any closed-unit zero-neighborhood in R.

]]>Mathematics doi: 10.3390/math8091579

Authors: Jinkyu Lee

In real-time distributed systems, it is important to provide offline guarantee for an upper-bound of each real-time task&rsquo;s end-to-end delay, which has been achieved by assigning proper intermediate deadlines of individual real-time tasks at each node. Although existing studies have succeeded to utilize mathematical theories of distributed computation/control for intermediate deadline assignment, they have assumed that every task operates in a cooperative manner, which does not always hold for real-worlds. In addition, existing studies have not addressed how to exploit a trade-off between end-to-end delay fairness among real-time tasks and performance for minimizing aggregate end-to-end delays. In this paper, we recapitulate an existing cooperative distributed framework, and propose a non-cooperate distributed framework that can operate even with selfish tasks, each of which is only interested in minimizing its own end-to-end delay regardless of achieving the system goal. We then propose how to design utility functions that allow the real-time distributed system to exploit the trade-off. Finally, we demonstrate the validity of the cooperative and non-cooperative frameworks along with the designed utility functions, via simulations.

]]>Mathematics doi: 10.3390/math8091577

Authors: Francisco Valverde-Albacete Carmen Peláez-Moreno

In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.

]]>Mathematics doi: 10.3390/math8091578

Authors: Hazem Al-Mofleh Ahmed Z. Afify Noor Akma Ibrahim

In this paper, a new two-parameter generalized Ramos&ndash;Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall&ndash;Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson&ndash;Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

]]>Mathematics doi: 10.3390/math8091576

Authors: Jingyi Liu Guoqiang Liu Longjiang Qu

The ACE algorithm is a candidate of the Lightweight Cryptography standardization process started by the National Institute of Standards and Technology (NIST) of the USA that passed the first round and successfully entered the second round. It is designed to achieve a balance between hardware cost and software efficiency for both authenticated encryption with associated data (AEAD) and hashing functionalities. This paper focuses on the impossible differential attack against the ACE permutation, which is the core component of the ACE algorithm. Based on the method of characteristic matrix, we build an automatic searching algorithm that can be used to search for structural impossible differentials and give the optimal permutation for ACE permutation and other SPN ciphers. We prove that there is no impossible differential of ACE permutation longer than 9 steps and construct two 8-step impossible differentials. In the end, we give the optimal word permutation against impossible differential cryptanalysis, which is &pi;&prime;=(2,4,1,0,3), and a safer word XOR structure of ACE permutation.

]]>Mathematics doi: 10.3390/math8091575

Authors: Valentín Gregori Juan-José Miñana David Miravet

In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm &lowast;. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm &lowast; is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship.

]]>Mathematics doi: 10.3390/math8091574

Authors: Li Li Hegong Lei Jun Wang

The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis.

]]>Mathematics doi: 10.3390/math8091573

Authors: Angel Zúñiga Gemma Bel-Enguix

(Coinductive) natural semantics is presented as a unifying framework for the verification of total correctness of compilers in Coq (with the feature that a verified compiler can be obtained). In this way, we have a simple, easy, and intuitive framework; to carry out the verification of a compiler, using a proof assistant in which both cases are considered: terminating and non-terminating computations (total correctness).

]]>Mathematics doi: 10.3390/math8091572

Authors: Hyoshin Kim Hye-Young Jung

This paper proposes an &alpha;-level estimation algorithm for ridge fuzzy regression modeling, addressing the multicollinearity phenomenon in the fuzzy linear regression setting. By incorporating &alpha;-levels in the estimation procedure, we are able to construct a fuzzy ridge estimator which does not depend on the distance between fuzzy numbers. An optimized &alpha;-level estimation algorithm is selected which minimizes the root mean squares for fuzzy data. Simulation experiments and an empirical study comparing the proposed ridge fuzzy regression with fuzzy linear regression is presented. Results show that the proposed model can control the effect of multicollinearity from moderate to extreme levels of correlation between covariates, across a wide spectrum of spreads for the fuzzy response.

]]>Mathematics doi: 10.3390/math8091571

Authors: Francisco J. Fernández F. Adrián F. Tojo

This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue&ndash;Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based on Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence, and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation and use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based on a Stieltjes differential equation and a system of Stieltjes differential equations with several derivators.

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