Mathematics, Volume 8, Issue 5 (May 2020) – 206 articles

Mathematics education for sustainable development is perceived as a core keystone, although its concept is related to its typical issue of ecology and economy in the educational realm. Thus, through current information and communication technology (ICT) impacts, altering pedagogy is highly conflicted in teaching/learning mathematics. This research attempted to classify and investigate criteria for mathematics education with a multi-criteria decision analysis/fuzzy-decision-making trial and evaluation laboratory (MCDA/F-DEMATEL) method in the context of the system of flipped e-learning. In particular, the sustainable development of this research focus is in mathematics education in view of pre-service teachers (PSTs) adapting to their pedagogical changes. With the MCDA/F-DEMATEL, the main criteria and sub-criteria were selected after the consultation of a group of experts as follows: mathematics education, sustainable development, and flipped-e-learning technology criteria. Then, with fifteen sub-criteria, the definitive analyses results were gauged with simple additive weighting (SAW) along with their weight coefficients’ calculation, sensitivity analysis (i–v scenarios), and a professional survey. The results described as the most important criteria for adapting to PSTs pedagogical changes in sustainable mathematical education through a flipped e-learning system were the flipped e-learning technology criteria (scenario i), with an 83% positive perception by professionals’ survey; among its sub-criteria, information technology usage contents (0.43) was the most affected variable, with a 42% very likely perception. Scenario iii, which was the slightly more preferred criteria than mathematics education, got a 78% positive perception from professionals’ survey. Therefore, this proposed methodology could be employed to validate the most important sustainable mathematics with flipped e-learning criteria for adapting to PSTs’ pedagogical changes with corresponding education contexts in more long-term learning. Full article

Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence of outlying errors in phase-I. The unnecessary variation, due to outlying errors, disturbs the control limits implying a less efficient control chart in phase-II. In this study, we propose models based on Tukey and median absolute deviation outlier detectors for detecting the errors in phase-I. These two outlier detection models are as efficient and robust as they are distribution free. Using the Monte-Carlo simulation method, we study the estimation effect via the proposed outlier detection models on the Shewhart chart in the normal as well as non-normal environments. The performance evaluation is done through studying the run length properties namely average run length and standard deviation run length. The findings of the study show that the proposed design structures are more stable in the presence of outlier detectors and require less phase-I observation to stabilize the run-length properties. Finally, we implement the findings of the current study in the semiconductor manufacturing industry, where a real dataset is extracted from a photolithography process. Full article

In this study, a semantic segmentation network is presented to develop an indoor navigation system for a mobile robot. Semantic segmentation can be applied by adopting different techniques, such as a convolutional neural network (CNN). However, in the present work, a residual neural network is implemented by engaging in ResNet-18 transfer learning to distinguish between the floor, which is the navigation free space, and the walls, which are the obstacles. After the learning process, the semantic segmentation floor mask is used to implement indoor navigation and motion calculations for the autonomous mobile robot. This motion calculations are based on how much the estimated path differs from the center vertical line. The highest point is used to move the motors toward that direction. In this way, the robot can move in a real scenario by avoiding different obstacles. Finally, the results are collected by analyzing the motor duty cycle and the neural network execution time to review the robot’s performance. Moreover, a different net comparison is made to determine other architectures’ reaction times and accuracy values. Full article

A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector $N(\eta )$ . Full article

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered. Full article

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on $\mu$ having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration. Full article

Text classification is an essential aspect in many applications, such as spam detection and sentiment analysis. With the growing number of textual documents and datasets generated through social media and news articles, an increasing number of machine learning methods are required for accurate textual classification. For this paper, a comprehensive evaluation of the performance of multiple supervised learning models, such as logistic regression (LR), decision trees (DT), support vector machine (SVM), AdaBoost (AB), random forest (RF), multinomial naive Bayes (NB), multilayer perceptrons (MLP), and gradient boosting (GB), was conducted to assess the efficiency and robustness, as well as limitations, of these models on the classification of textual data. SVM, LR, and MLP had better performance in general, with SVM being the best, while DT and AB had much lower accuracies amongst all the tested models. Further exploration on the use of different SVM kernels was performed, demonstrating the advantage of using linear kernels over polynomial, sigmoid, and radial basis function kernels for text classification. The effects of removing stop words on model performance was also investigated; DT performed better with stop words removed, while all other models were relatively unaffected by the presence or absence of stop words. Full article

The aim of this research is to apply a novel technique based on the embedding method to solve the $n\times n$ fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created $n\times n$ crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created $n\times n$ crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors. Full article

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results. Full article

In this work, we consider a multilayer shallow water model with variable density. It consists of a system of hyperbolic equations with non-conservative products that takes into account the pressure variations due to density fluctuations in a stratified fluid. A second-order finite volume method that combines a hydrostatic reconstruction technique with a MUSCL second order reconstruction operator is developed. The scheme is well-balanced for the lake-at-rest steady state solutions. Additionally, hints on how to preserve a general class of stationary solutions corresponding to a stratified density profile are also provided. Some numerical results are presented, including validation with laboratory data that show the efficiency and accuracy of the approach introduced here. Finally, a comparison between two different parallelization strategies on GPU is presented. Full article

The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order $\alpha$ and strongly close-to-convexity of order $\alpha$ . Furthermore, the main results presented here are compared with the previous outcomes obtained in this area. Full article

In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes $\xi$ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions. Full article

We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy. Full article

In this paper, by using the Banach contraction principle and the Schauder’s fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results. Full article

In this article, by using the concept of the quantum (or q-) calculus and a general conic domain ${\Omega }_{k,q}$ , we study a new subclass of normalized analytic functions with respect to symmetrical points in an open unit disk. We solve the Fekete-Szegö type problems for this newly-defined subclass of analytic functions. We also discuss some applications of the main results by using a q-Bernardi integral operator. Full article

Solar energy is an alternative source of energy that can be used to replace fossil fuels. Various types of solar cells have been developed to harvest this seemingly endless supply of energy, leading to the construction of solar cell devices, such as dye-sensitized solar cells. An important factor that affects energy conversion efficiency of dye-sensitized solar cells is the distribution of dye molecules within the porous semiconductor (TiO ${}_2$ ). In this paper, we formulate a continuum model for the interaction between the dye molecule Tris(2,2 ${}^{\prime }$ -bipyridyl)ruthenium(II) (Ru(bpy) ${}_3^{2+}$ ) and titanium dioxide (TiO ${}_2$ ) semiconductor. We obtain the equilibrium position at the minimum energy position between the dye molecules and between the dye and TiO ${}_2$ nanoporous structure. Our main outcome is an analytical expression for the energy of the two molecules as a function of their sizes. We also show that the interaction energy obtained using the continuum model is in close agreement with molecular dynamics simulations. Full article

Currently, the e-learning method, due to the period of confinement that is occurring due to COVID-19, has increased its use and application in the teaching and learning processes. The main objective of this research is to identify the effectiveness of the e-learning method in the teaching of mathematics with adults who are in high school, in contrast to the traditional expository method. The study developed is quantitative, descriptive and correlational. The research design is quasi-experimental, with a control group and an experimental group. The results show that the use of the e-learning method has a positive influence on motivation, autonomy, participation, mathematical concepts, results and grades. It can be concluded that the e-learning method leads to improvement in adult students who are studying the mathematical subject in the educational stage of high school, provided that it is compared with the expository method. Therefore, this method is considered effective for its implementation in adults. Full article

By performing data analysis, statistical approaches are highly welcome to explore the data. Nowadays with the increases in computational power and the availability of big data in different domains, it is not enough to perform exploratory data analysis (descriptive statistics) to obtain some prior insights from the data, but it is a requirement to apply higher-level statistics that also require much greater knowledge from the user to properly apply them. One research area where proper usage of statistics is important is multi-objective optimization, where the performance of a newly developed algorithm should be compared with the performances of state-of-the-art algorithms. In multi-objective optimization, we are dealing with two or more usually conflicting objectives, which result in high dimensional data that needs to be analyzed. In this paper, we present a web-service-based e-Learning tool called DSCTool that can be used for performing a proper statistical analysis for multi-objective optimization. The tool does not require any special statistics knowledge from the user. Its usage and the influence of a proper statistical analysis is shown using data taken from a benchmarking study performed at the 2018 IEEE CEC (The IEEE Congress on Evolutionary Computation) is appropriate. Competition on Evolutionary Many-Objective Optimization. Full article

Visual cryptography scheme (VCS) shares a binary secret image into multiple shadows printed on transparencies. Stacking shadows can visually decode the secret image without computational resources. Specifically, a (k, n) threshold VCS ((k, n)-VCS) shares a secret image into n shadows, stacking any k shadows can reveal the secret image by human visual system, while any less than k shadows cannot decode any information regarding the secret image. In practice, some participants (essentials) play more important roles than others (non-essentials). In this paper, we propose a (t, s, k, n) VCS with essential participants (so called (t, s, k, n)-EVCS). The secret image is shared into n shadows with s essentials and n-s non-essentials. Any k shadows, including at least t essentials, can reveal the secret image. The proposed scheme is constructed from a monotonic (K, N)-VCS. The condition and optimal choice of (K, N)-VCS to construct (t, s, k, n)-EVCS are given by solving integer programming model. The experimental results are conducted to verify the feasibility of our scheme. Full article

The concepts of b-metric spaces and $\omega t$ -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, $\mathcal{H}$ -simulation function which is used in this manuscript together with the notion of $\omega t$ -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work. Full article

Core competency is the basis of promoting a competitive advantage for any organization; this study aims to establish an objective and systematic assessment model for companies to identify their capabilities. This model will not only assist companies in understanding their own capabilities but will also allow them to compare their performance with that of main competitors to strengthen their competitiveness. The analysis process involved a combination of the fuzzy analytic hierarchy process, fuzzy linguistic value, and the ideal and anti-ideal concept. An objective and systematic model was first developed, which underwent empirical analysis using data from the top three home delivery companies in Taiwan. It was found that “Basic organizational competencies” and “Special competitive competencies” were the two key categories for the home delivery industry. Moreover, “Service price”, “On-time delivery”, and “Secure delivery” were found to be the three most important capabilities needed for home delivery companies. The results showed that the model is able to effectively assist organizations in constructing or assessing their organizational capabilities; in addition, organizations can adjust their service profiles to adapt to today’s turbulent business environment and rapidly changing consumer demands. Full article

In this paper, which is based on a real-life motivation, we present an algebraic theory of automata and multi-automata. We combine these (multi-)automata using the products introduced by W. Dörfler, where we work with the cartesian composition and we define the internal links among multiautomata by means of the internal links’ matrix. We used the obtained product of n-ary multi-automata as a system that models and controls certain traffic situations (lane shifting) for autonomous vehicles. Full article

This paper analyzes the volatility dynamics in the financial markets of the (three) most powerful countries from a military perspective, namely, the U.S., Russia, and China, during the period 2015–2018 that corresponds to their intervention in the Syrian war. As far as we know, there is no literature studying this topic during such an important distress period, which has had very serious economic, social, and humanitarian consequences. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH (1, 1)) model yielded the best volatility results for the in-sample period. The weighted historical simulation produced an accurate value at risk (VaR) for a period of one month at the three considered confidence levels. For the out-of-sample period, the Monte Carlo simulation method, based on student t-copula and peaks-over-threshold (POT) extreme value theory (EVT) under the Gaussian kernel and the generalized Pareto (GP) distribution, overstated the risk for the three countries. The comparison of the POT-EVT VaR of the three countries to a portfolio of stock indices pertaining to non-military countries, namely Finland, Sweden, and Ecuador, for the same out-of-sample period, revealed that the intervention in the Syrian war may be one of the pertinent reasons that significantly affected the volatility of the stock markets of the three most powerful military countries. This paper is of great interest for policy makers, central bank leaders, participants involved in these markets, and all practitioners given the economic and financial consequences derived from such dynamics. Full article

This paper formulates the problem of determining all reducts of an information system as a graph search problem. The search space is represented in the form of a rooted graph. The proposed algorithm uses a breadth-first search strategy to search for all reducts starting from the graph root. It expands nodes in breadth-first order and uses a pruning rule to decrease the search space. It is mathematically shown that the proposed algorithm is both time and space efficient. Full article

Low-carbon tourism plays the increasingly significant role in carbon emission reduction and natural environmental protection. The choice of low-carbon tourist destination (LCTD) often involves the multiple attributes or criteria and can be regarded as the corresponding multiple attribute group decision making (MAGDM) issues. Since the Pythagorean fuzzy sets (PFSs) could well depict uncertain information or fuzzy information and cope with the LCTD selection, thus this essay develops a framework to tackle such MAGDM issues under the Pythagorean fuzzy environment. In this essay, due to few methods can compare with different alternatives along with their advantages from designed attributes, therefore, to overcome this challenge, the taxonomy method is utilized to integrate with PFSs. What’s more, the entropy method is also utilized to determine the attribute weights. Eventually, an application related to LCTD selection and some comparative analysis have been given to demonstrate the superiority of the designed method. The results illustrate that the designed framework is useful for identifying optimal tourist destination among the potential tourist destinations. Full article

Locating arrays (LAs) can be used to detect and identify interaction faults among factors in a component-based system. The optimality and constructions of LAs with a single fault have been investigated extensively under the assumption that all the factors have the same values. However, in real life, different factors in a system have different numbers of possible values. Thus, it is necessary for LAs to satisfy such requirements. We herein establish a general lower bound on the size of mixed-level $(\overline{1},t)$ -locating arrays. Some methods for constructing LAs including direct and recursive constructions are provided. In particular, constructions that produce optimal LAs satisfying the lower bound are described. Additionally, some series of optimal LAs satisfying the lower bound are presented. Full article

Let A be an n-by-n matrix. The numerical range of A is defined as $W\left(A\right)=\{x^{*}Ax:x\in {\mathbb{C}}^n,x^{*}x=1\}$ . The Moore–Penrose inverse $A^{+}$ of A is the unique matrix satisfying $A{A}^{+}A=A,A^{+}A{A}^{+}=A^{+},{\left(A{A}^{+}\right)}^{*}=A{A}^{+}$ , and ${\left(A^{+}A\right)}^{*}=A^{+}A$ . This paper investigates the numerical range of the Moore–Penrose inverse $A^{+}$ of a matrix A, and examines the relation between the numerical ranges $W\left(A^{+}\right)$ and $W\left(A\right)$ . Full article

While integrated circuit technologies keep scaling aggressively, analog, mixed-signal, and radio-frequency (RF) circuits encounter challenges by creating robust designs in advanced complementary metal–oxide–semiconductor (CMOS) processes with the diminishing voltage headroom. The increasing random mismatch of smaller feature sizes in leading-edge technology nodes severely limit the benefits of scaling for (RF)/analog circuits. This paper describes the details of the combinatorial randomness by statistically selecting device elements that relies on the significant growth in subsets number of combinations. The randomness can be utilized to provide post-manufacturing reconfiguration of the selectable circuit elements to achieve required specifications for ultra-low-power systems. The calibration methodology is demonstrated with an ultra-low-voltage chaos-based true random number generator (TRNG) for energy-constrained Internet of things (IoT) devices in the secure communications. Full article