Mathematics, Volume 9, Issue 2 (January-2 2021) – 93 articles

Project selection is a common problem for many companies. Specifically, it consists in identifying which projects should be selected with regard to their economic efficiency, i.e., the projects that maximise the profit they bring in while minimising the cost of the resources consumed. In this paper, we have focused our interest on energy service companies because of the importance of a convenient selection of their projects. In these types of companies, the attractiveness of a project depends on both the profit estimations obtained in simulations of the energy systems to be improved, as well as the probability that the project will be awarded (e.g., in local government bids, where typically several energy service companies compete to win the bid). We propose a new project selection method, especially tailored to energy service companies and based on centralised data envelopment analysis models with limited availability of the resources. This contrasts with all existing project selection methods and allows the proposed approach to make more efficient use of the limited resources. We have applied the model to a real-world case by selecting projects in a Spanish energy service company, showing the benefits of applying this approach, and comparing the results obtained with other data envelopment analysis project selection approaches. Full article

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments. Full article

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed. Full article

Recently, different recommendation techniques in e-learning have been designed that are helpful to both the learners and the educators in a wide variety of e-learning systems. Customized learning, which requires e-learning systems designed based on educational experience that suit the interests, goals, abilities, and willingness of both the learners and the educators, is required in some situations. In this research, we develop an intelligent recommender using split and conquer strategy-based clustering that can adapt automatically to the requirements, interests, and levels of knowledge of the learners. The recommender analyzes and learns the styles and characteristics of learners automatically. The different styles of learning are processed through the split and conquer strategy-based clustering. The proposed cluster-based linear pattern mining algorithm is applied to extract the functional patterns of the learners. Then, the system provides intelligent recommendations by evaluating the ratings of frequent sequences. Experiments were conducted on different groups of learners and datasets, and the proposed model suggested essential learning activities to learners based on their style of learning, interest classification, and talent features. It was experimentally found that the proposed cluster-based recommender improves the recommendation performance by resulting in more lessons completed when compared to learners present in the no-recommender cluster category. It was found that more than 65% of the learners considered all criteria to evaluate the proposed recommender. The simulation of the proposed recommender showed that for learner size values of <1000, better metric values were produced. When the learner size exceeded 1000, significant differences were obtained in the evaluated metrics. The significant differences were analyzed in terms of a computational structure depending on $\left|L\right|$, the recommendation list size, and the attributes of learners. The learners were also satisfied with the accuracy and speed of the recommender. For the sample dataset considered, a significant difference was observed in the standard deviation σ and mean μ of parameters, in terms of the Recall (List, User) and Ranking Score (User) measures, compared to other methods. The devised method performed well concerning all the considered metrics when compared to other methods. The simulation results signify that this recommender minimized the mean absolute error metric for the different clusters in comparison with some well-known methods. Full article

The human face holds a privileged position in multi-disciplinary research as it conveys much information—demographical attributes (age, race, gender, ethnicity), social signals, emotion expression, and so forth. Studies have shown that due to the distribution of ethnicity/race in training datasets, biometric algorithms suffer from “cross race effect”—their performance is better on subjects closer to the “country of origin” of the algorithm. The contributions of this paper are two-fold: (a) first, we gathered, annotated and made public a large-scale database of (over 175,000) facial images by automatically crawling the Internet for celebrities’ images belonging to various ethnicity/races, and (b) we trained and compared four state of the art convolutional neural networks on the problem of race and ethnicity classification. To the best of our knowledge, this is the largest, data-balanced, publicly-available face database annotated with race and ethnicity information. We also studied the impact of various face traits and image characteristics on the race/ethnicity deep learning classification methods and compared the obtained results with the ones extracted from psychological studies and anthropomorphic studies. Extensive tests were performed in order to determine the facial features to which the networks are sensitive to. These tests and a recognition rate of 96.64% on the problem of human race classification demonstrate the effectiveness of the proposed solution. Full article

Let $\left(X_n\right)$ be a sequence of real random variables, $\left(T_n\right)$ a sequence of random indices, and $\left({\tau }_n\right)$ a sequence of constants such that ${\tau }_n\to \infty$. The asymptotic behavior of $L_n=(1/{\tau }_n){\sum }_{i=1}^{T_n}{X}_i$, as $n\to \infty$, is investigated when $\left(X_n\right)$ is exchangeable and independent of $\left(T_n\right)$. We give conditions for $M_n=\sqrt{{\tau }_n}(L_n-L)⟶M$ in distribution, where L and M are suitable random variables. Moreover, when $\left(X_n\right)$ is i.i.d., we find constants $a_n$ and $b_n$ such that ${sup}_{A\in \mathcal{B}\left(\mathbb{R}\right)}\left|P(L_n\in A)-P(L\in A)\right|\le a_n$ and ${sup}_{A\in \mathcal{B}\left(\mathbb{R}\right)}\left|P(M_n\in A)-P(M\in A)\right|\le b_n$ for every n. In particular, $L_n\to L$ or $M_n\to M$ in total variation distance provided $a_n\to 0$ or $b_n\to 0$, as it happens in some situations. Full article

Herein we study the problem of recovering a density operator from a set of compatible marginals, motivated by limitations of physical observations. Given that the set of compatible density operators is not singular, we adopt Jaynes’ principle and wish to characterize a compatible density operator with maximum entropy. We first show that comparing the entropy of compatible density operators is complete for the quantum computational complexity class QSZK, even for the simplest case of 3-chains. Then, we focus on the particular case of quantum Markov chains and trees and establish that for these cases, there exists a procedure polynomial in the number of subsystems that constructs the maximum entropy compatible density operator. Moreover, we extend the Chow–Liu algorithm to the same subclass of quantum states. Full article

Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity. Full article

Two sufficiency theorems for parametric and a nonparametric problems of Bolza in optimal control are derived. The dynamics of the problems are nonlinear, the initial and final states are free, and the main results can be applied when nonlinear mixed time-state-control inequality and equality constraints are presented. The deviation between admissible costs and optimal costs around the optimal control is estimated by functionals playing the role of the square of some norms. Full article

In this paper, we propose a family of indistinguishability operators, that we have called Yager Possibilitic Response Functions (YPRFs for short), as an appropriate tool for allocating tasks to a collective of agents. In order to select the best agent to carry out each task, we have used the so-called response threshold method, where each agent decides the next task to perform following a probabilistic Markov process and, in addition, involves a response function which models how appropriate the task is for the agent. In previous works, we developed a new response threshold method which incorporates the use of indistinguishability operators as response functions and possibility theory instead of probability, for task allocation from a very general perspective without taking into account the specific characteristics of the agents except their limitations to carry out a task. Such an allocation is modelled by means of possibilistic, instead of probabilisitic, Markov chains. We show that possibilistic Markov chains outperform its probabilistic counterparts for the aforementioned propose. All the indistinguishability operators considered in previous papers were not able to take into account the agents’ restrictions for moving from a task to another one, or equivalently to carry out a task instead of another one. In order to avoid this handicap, we introduce a new kind of response functions, YPRFs, which are modelled by means of indistinguishability operators obtained via Yager t-norms. This new type of response functions drops to zero when an agent, due to its limitations, is not able to execute a task and, therefore, is able to model a generic multi-agent system with restrictions. The performed simulation, under Matlab, allows us to compare the results obtained using the new YPRFs with those obtained applying celebrated response functions also generated via indistinguishability operators (that we call Original Possibilitic Response Functions, OPRFs for short). Moreover, the results confirm that the YPRFs are able to take into account agent’s restrictions while the OPRFs are not able. Finally, in the light of the experimental results, we can confirm that those systems modelled. Full article

Steganalysis is a method to detect whether the objects contain secret messages. With the popularity of deep learning, using convolutional neural networks (CNNs), steganalytic schemes have become the chief method of combating steganography in recent years. However, the diversity of filters has not been fully utilized in the current research. This paper constructs a new effective network with diverse filter modules (DFMs) and squeeze-and-excitation modules (SEMs), which can better capture the embedding artifacts. As the essential parts, combining three different scale convolution filters, DFMs can process information diversely, and the SEMs can enhance the effective channels out from DFMs. The experiments presented that our CNN is effective against content-adaptive steganographic schemes with different payloads, such as S-UNIWARD and WOW algorithms. Moreover, some state-of-the-art methods are compared with our approach to demonstrate the outstanding performance. Full article

The credit risk management process is a critical element that allows financial institutions to withstand economic downturns. Unlike the methods regarding the probability of default, which have been deeply addressed after the financial crisis in 2008, recovery rate models still need further development. As there are no industry standards, leading banks are modeling recovery rates using internal models developed with different assumptions. Therefore, the outcomes are often incomparable and may lead to confusion. The author presents the concept of a unified recovery rate analysis for US banks. He uses data derived from FR Y-9C reports disclosed by the Federal Reserve Bank of Chicago. Based on the historical recoveries and credit portfolio book values, the author examines the distribution function of recoveries. The research refers to a credit card portfolio and covers nine leading US banks. The author leveraged Vasicek’s one-factor model with the asset correlation parameter and implemented it for recovery rate analysis. This experiment revealed that the estimated latent correlation ranges from 0.2% to 1.5% within the examined portfolios. They are large enough to impact the recovery rate volatility and cannot be treated as negligible. It was shown that the presented method could be applied under US Comprehensive Capital Analysis and Review exercise. Full article

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense. Full article

There is an increasing concentration in the influences of nonconventional power sources on power system process and management, as the application of these sources upsurges worldwide. Renewable energy technologies are one of the best technologies for generating electrical power with zero fuel cost, a clean environment, and are available almost throughout the year. Some of the widespread renewable energy sources are tidal energy, geothermal energy, wind energy, and solar energy. Among many renewable energy sources, wind and solar energy sources are more popular because they are easy to install and operate. Due to their high flexibility, wind and solar power generation units are easily integrated with conventional power generation systems. Traditional generating units primarily use synchronous generators that enable them to ensure the process during significant transient errors. If massive wind generation is faltered due to error, it may harm the power system’s operation and lead to the load frequency control issue. This work proposes binary moth flame optimizer (MFO) variants to mitigate the frequency constraint issue. Two different binary variants are implemented for improving the performance of MFO for discrete optimization problems. The proposed model was evaluated and compared with existing algorithms in terms of standard testing benchmarks and showed improved results in terms of average and standard deviation. Full article

In the present paper, we test the use of Markov-Switching (MS) models with time-fixed or Generalized Autoregressive Conditional Heteroskedasticity (GARCH) variances. This, to enhance the performance of a U.S. dollar-based portfolio that invest in the S&P 500 (SP500) stock index, the 3-month U.S. Treasury-bill (T-BILL) or the 1-month volatility index (VIX) futures. For the investment algorithm, we propose the use of two and three-regime, Gaussian and t-Student, MS and MS-GARCH models. This is done to forecast the probability of high volatility episodes in the SP500 and to determine the investment level in each asset. To test the algorithm, we simulated 8 portfolios that invested in these three assets, in a weekly basis from 23 December 2005 to 14 August 2020. Our results suggest that the use of MS and MS-GARCH models and VIX futures leads the simulated portfolio to outperform a buy and hold strategy in the SP500. Also, we found that this result holds only in high and extreme volatility periods. As a recommendation for practitioners, we found that our investment algorithm must be used only by institutional investors, given the impact of stock trading fees. Full article

At present it is claimed that all electrical energy systems operate with high values of efficiency and reliability. In electric power systems (EPS), electrical power and distribution transformers are responsible for transferring the electrical energy from power stations up to the load centers. Consequently, it is mandatory to design transformers that possess the highest efficiency and reliability possible. Considerable power losses and hotspots may exist in the bushing region of a transformer, where conductors pass through the tank. Most transformer tanks are made of low-carbon steel, for economical reasons, causing the induction of high eddy currents in the bushing regions. Using a non-magnetic insert in the transformer tank can reduce the eddy currents in the region and as a consequence avoid overheating. In this work, analytical formulations were developed to calculate the magnetic field distribution and the stray losses in the transformer region where bushings are mounted, considering a stainless steel insert (SSI) in the transformer tank. Previously, this problem had only been tackled with numerical models. Several cases were analyzed considering different non-magnetic insert sizes. Additionally, a numerical study using a two dimensional (2D) finite element (FE) axisymmetric model was carried out in order to validate the analytical results. The solved cases show a great concordance between models, obtaining relative errors between the solutions of less than two percent. Full article

A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed and analyzed. The Alikhanov $L2$-$1_{\sigma }$ difference formula is utilized to discretize the time Caputo fractional derivative, while the Legendre-Galerkin spectral approximation is used to approximate the Riesz spatial fractional operator. The scheme is shown efficiently applicable with spectral accuracy in space and second-order in time. A discrete form of the fractional Grönwall inequality is applied to establish the error estimates of the approximate solution based on the discrete energy estimates technique. The key aspects of the implementation of the numerical continuation are complemented with some numerical experiments to confirm the theoretical claims. Full article

A graph is even (resp. odd) if all its vertex degrees are even (resp. odd). We consider edge coverings by prescribed number of even and/or odd subgraphs. In view of the 8-Flow Theorem, a graph admits a covering by three even subgraphs if and only if it is bridgeless. Coverability by three odd subgraphs has been characterized recently [Petruševski, M.; Škrekovski, R. Coverability of graph by three odd subgraphs. J. Graph Theory 2019, 92, 304–321]. It is not hard to argue that every acyclic graph can be decomposed into two odd subgraphs, which implies that every graph admits a decomposition into two odd subgraphs and one even subgraph. Here, we prove that every 3-edge-connected graph is coverable by two even subgraphs and one odd subgraph. The result is sharp in terms of edge-connectivity. We also discuss coverability by more than three parity regular subgraphs, and prove that it can be efficiently decided whether a given instance of such covering exists. Moreover, we deduce here a polynomial time algorithm which determines whether a given set of edges extends to an odd subgraph. Finally, we share some thoughts on coverability by two subgraphs and conclude with two conjectures. Full article

For a graph G with no isolated vertex, let ${\gamma }_{pr}\left(G\right)$ and ${\mathrm{sd}}_{{\gamma }_{pr}}\left(G\right)$ denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order $n\ge 4$ different from a healthy spider (subdivided star), then ${\mathrm{sd}}_{{\gamma }_{pr}}\left(T\right)\le min\{\frac{{\gamma }_{pr}\left(T\right)}{2}+1,\frac{n}{2}\},$ improving the $(n-1)$-upper bound that was recently proven. Full article

The spread of the COVID-19 epidemic worldwide has led to investigations in various aspects, including the estimation of expected cases. As it helps in identifying the need to deal with cases caused by the pandemic. In this study, we have used artificial neural networks (ANNs) to predict the number of cases of COVID-19 in Brazil and Mexico in the upcoming days. Prey predator algorithm (PPA), as a type of metaheuristic algorithm, is used to train the models. The proposed ANN models’ performance has been analyzed by the root mean squared error (RMSE) function and correlation coefficient (R). It is demonstrated that the ANN models have the highest performance in predicting the number of infections (active cases), recoveries, and deaths in Brazil and Mexico. The simulation results of the ANN models show very well predicted values. Percentages of the ANN’s prediction errors with metaheuristic algorithms are significantly lower than traditional monolithic neural networks. The study shows the expected numbers of infections, recoveries, and deaths that Brazil and Mexico will reach daily at the beginning of 2021. Full article

In this paper, we use a statistical arbitrage method in different developed and emerging countries to show that the profitability of the strategy is based on the degree of market efficiency. We will show that our strategy is more profitable in emerging ones and in periods with greater uncertainty. Our method consists of a Pairs Trading strategy based on the concept of mean reversion by selecting pair series that have the lower Hurst exponent. We also show that the pair selection with the lowest Hurst exponent has sense, and the lower the Hurst exponent of the pair series, the better the profitability that is obtained. The sample is composed by the 50 largest capitalized companies of 39 countries, and the performance of the strategy is analyzed during the period from 1 January 2000 to 10 April 2020. For a deeper analysis, this period is divided into three different subperiods and different portfolios are also considered. Full article

This paper concerns the properties of the generalized bi-periodic Fibonacci numbers $\left\{G_n\right\}$ generated from the recurrence relation: $G_n=a{G}_{n-1}+G_{n-2}$ (n is even) or $G_n=b{G}_{n-1}+G_{n-2}$ (n is odd). We derive general identities for the reciprocal sums of products of two generalized bi-periodic Fibonacci numbers. More precisely, we obtain formulas for the integer parts of the numbers ${\left({\sum }_{k=n}^{\infty }\frac{{(a/b)}^{\xi (k+1)}}{G_k{G}_{k+m}}\right)}^{-1},m=0,2,4,\cdots ,$ and ${\left({\sum }_{k=n}^{\infty }\frac{1}{G_k{G}_{k+m}}\right)}^{-1},m=1,3,5,\cdots .$ Full article

One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that this formula over Sylvester Hadamard matrices of order $2^m$, $H_m$, can be carried out by enumerating m-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient $per\left(H_m\right)/2^{2^m}$ might be a measure of the “density” of m-variable Boolean functions with high nonlinearity. Full article

This study is concerned with robust synchronization for master–slave chaotic systems with matched/mismatched disturbances and uncertainty in the control input. A robust sliding mode control (SMC) is presented to achieve chaos synchronization even under the influence of matched/mismatched disturbances and uncertainty of inputs. A proportional-integral (PI) switching surface is introduced to make the controlled error dynamics in the sliding manifold easy to analyze. Furthermore, by using the proposed SMC scheme even subjected to input uncertainty, we can force the trajectories of the error dynamics to enter the sliding manifold and fully synchronize the master–slave systems in spite of matched uncertainties and input nonlinearity. As for the mismatched disturbances, the bounds of synchronization errors can be well estimated by introducing the limit of the Riemann sum, which is not well addressed in previous works. Simulation experiments including matched and mismatched cases are presented to illustrate the robustness and synchronization performance with the proposed SMC synchronization controller. Full article

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures. Full article

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature. Full article

Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is $\overline{\mathcal{K}}$-four-fold Formal Concept Analysis ($\overline{\mathcal{K}}$-4FCA) where $\overline{\mathcal{K}}$ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in dually-ordered pairs—e.g., the complete max-plus and min-plus semirings—the basic construction shows dual-order-, row–column- and Galois-connection-induced dualities that appear simultaneously a number of times to provide the full spectrum of variability. Our results lead to a fundamental theorem of $\overline{\mathcal{K}}$-four-fold Formal Concept Analysis that properly defines quadrilattices as 4-tuples of (order-dually) isomorphic lattices of vectors and discuss its relevance vis-à-vis previous formal conceptual analyses and some affordances of their results. Full article

A novel integrated guidance and control (IGC) scheme for a Re-entry Hypersonic Vehicle (RHV) is proposed with the capabilities of online aerodynamic coefficient estimation based on an Unscented Kalman Filter and online trajectory generation based on the Gaussian pseudospectral method. A linear quadratic regulator is adopted for trajectory tracking guidance and a second-layer sliding mode controller is designed for attitude control. The variation of lift and drag coefficients are modeled and estimated online, based on which a new trajectory can be generated. The commands of trajectory generation are set as moments of actuators and their extremums pose more constraints on the rate and acceleration of flow angles. Comprehensive simulations are conducted and comparable IGC performances with normal conditions are obtained under large aerodynamic coefficient errors according to online generated trajectory, which proves the effectiveness and advantages of the proposed IGC scheme. Full article

Path-planning for uninhabited combat air vehicles (UCAV) is a typically complicated global optimization problem. It seeks a superior flight path in a complex battlefield environment, taking into various constraints. Many swarm intelligence (SI) algorithms have recently gained remarkable attention due to their capability to address complex optimization problems. However, different SI algorithms present various performances for UCAV path-planning since each algorithm has its own strengths and weaknesses. Therefore, this study provides an overview of different SI algorithms for UCAV path-planning research. In the experiment, twelve algorithms that published in major journals and conference proceedings are surveyed and then applied to UCAV path-planning. Moreover, to demonstrate the performance of different algorithms in further, we design different scales of problem cases for those comparative algorithms. The experimental results show that UCAV can find the safe path to avoid the threats efficiently based on most SI algorithms. In particular, the Spider Monkey Optimization is more effective and robust than other algorithms in handling the UCAV path-planning problem. The analysis from different perspectives contributes to highlight trends and open issues in the field of UCAVs. Full article