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Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios.

In the paper, we consider a new approach to the comparison of the distributions of sums of random variables. Unlike preceding works, for this purpose we use the notion of deficiency that is well known in mathematical statistics. This approach is used, first, to determine the distribution of a separate random variable in the sum that provides the least possible number of summands guaranteeing the prescribed value of the (1−α)-quantile of the normalized sum for a given α∈(0,1), and second, to determine the distribution of a separate random variable in the sum that provides the least possible number of summands guaranteeing the prescribed value of the probability for the normalized sum to fall into a given interval. Both problems are solved under the condition that possible distributions of random summands possess coinciding three first moments. In both settings the best distribution delivers the smallest number of summands. Along with distributions of a non-random number of summands, we consider the case of random summation and introduce an analog of deficiency which can be used to compare the distributions of sums with random and non-random number of summands. The main mathematical tools used in the paper are asymptotic expansions for the distributions of R-valued functions of random vectors, in particular, normalized sums of independent identically distributed r.v.s and their quantiles. Along with the general case, main attention is paid to the situation where the summarized random variables are independent and identically distributed. The approach under consideration is applied to determination of the distribution of insurance payments providing the least insurance portfolio size under prescribed Value-at-Risk or non-ruin probability.

The order-of-addition generalization simplex-centroid designs play a key role in mixture experiments, for example, the mixture experiments with process variables. The paper formally combines order-of-addition (OofA) with mixture components in the same experiment. This paper proposes a new algorithm which generates full OofA mth-degree generalization simplex-centroid designs for q components by a class of the direction graphs, and a series of examples also confirms the value of the proposed algorithm.

The paper promotes the notion of computational experiment supported by a multi-tool digital environment as a means of the development of new mathematical knowledge in the context of education. The main study of the paper deals with the issues of teaching this knowledge to secondary teacher candidates within a graduate capstone mathematics education course. The interplay of mathematics and education is considered through the lens of using technology to enhance one’s mathematical background by advancing ideas from mostly known to genuinely unknown. In this paper, the knowns consist of Fibonacci numbers, Pascal’s triangle, and continued fractions; among the unknowns are Fibonacci-like polynomials and generalized golden ratios in the form of cycles of various lengths. The paper discusses the interplay of pragmatic and epistemic uses of digital tools by the learners of mathematics. The data for the study were collected over the years through solicited comments by teacher candidates enrolled in the capstone course. The main results indicate the candidates’ appreciation of the need for deep mathematical knowledge as an instrument of the modern-day pedagogy aimed at making high schoolers interested in the subject matter.

This study contributes to the debate on accessibility of higher education in Chile, with a special focus on the geospatial dimension of access to university studies. This paper addresses the central question of whether geography (physical distance and neighborhood effects) plays a significant role in determining the accessibility of higher education to students in Chile. We use Heckman probit-type (Heckit) models to adjust for selection during application for higher education-that is, pre-selection among applications to study at university and, ultimately, admission (or denial) to a higher educational institution. Of all high school graduates who took the university selection test (PSU), only 37.9% were able to attend higher education. The results show that the geospatial elements-neighborhood characteristics and distance from the city of Santiago-have a significant local effect on the student's application and access to Chilean universities. Specifically, the most significant local range for each candidate is 300 neighbors. We also find that, when distance to the capital city increases, the probability of applying to university increases to a threshold of 1400 km, at which point probability begins to decrease. We are grateful to the participants at the 9th Seminar of Spatial Econometric Jean Paelinck|6–7 October 2017, Cartagena, Spain and at the 2021 RSAI World Conference|25–28 May 2021, Virtual Conference for their valuable comments on several versions of this paper. We also acknowledge Andrés Vallone’s contribution of the postal address geocoding process and Carmen Pérez Esparrells, Mónica Navarrete, and Dusan Paredes for their invaluable comments during Juan Luis Quiroz’s dissertation defense.

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

The purpose of this paper is to provide evidence of the insertion of Romanian students of economic cybernetics on the labor market by connecting business environment expectations with the goals of a competitive digital economy. The research is organized around three hypotheses to address the issues of both non-employed and employed economic cybernetics students. A rank-ordered probit choice model was estimated to compute the probability that a certain skill requires improvement. The empirical results showed that the COVID-19 pandemic stimulated more cybernetics students to get a job in this period. Moreover, these students present the necessary level of digital skills to be employed, but other skills need improvement: skills of analysis and synthesis, adaptability in handling crisis situations and creativity. This research reveals the lack of working experience as the main cause for rejection after an interview and the students’ tendency to overestimate their salary. This study also identified barriers of the insertion on the labor market for these students with digital skills that were not the subject of previous studies. Moreover, the impact of the COVID-19 pandemic on their decision to get a job in this period is assessed and a few recommendations of skills improvements are provided. These results present practical implications for educational policies and the business environment in the context of achieving a competitive European digital economy. The limit of this research is given by the sample representativeness for cybernetics students only for Bucharest, but a future paper will ensure a representative sample at the national level.

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1+ϵ)-approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j−1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O((1891ekϵ2)8k/ϵnd), and outputs a collection of size O((1891ekϵ2)8k/ϵn) of candidate sets including approximation centers.

Using simple fuzzy numbers to approximate general fuzzy numbers is an important research aspect of fuzzy number theory and application. The existing results in this field are basically based on the unweighted metric to establish the best approximation method for solving general fuzzy numbers. In order to obtain more objective and reasonable best approximation, in this paper, we use the weighted distance as the evaluation standard to establish a method to solve the best approximation of general fuzzy numbers. Firstly, the conceptions of I-nearest r-s piecewise linear approximation (in short, PLA) and the II-nearest r-s piecewise linear approximation (in short, PLA) are introduced for a general fuzzy number. Then, most importantly, taking weighted metric as a criterion, we obtain a group of formulas to get the I-nearest r-s PLA and the II-nearest r-s PLA. Finally, we also present specific examples to show the effectiveness and usability of the methods proposed in this paper.

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1/t1−1/γ scaling law, where γ>0" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">γ>0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values.

The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix.

The theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has been introduced. The construction was done in the framework of iterated function systems and fractal theory. In this article we extract the main features of this association, and consider binary operations in metric spaces satisfying properties as idempotency and inequalities related to the distance between operated elements with the same right or left factor (side inequalities). Important examples are the logical disjunction and conjunction in the set of integers modulo 2 and the union of compact sets, besides the aforementioned fractal convolution. The operations described are called in the present paper convolutions of two elements of a metric space E. We deduce several properties of these associations, coming from the considered initial conditions. Thereafter, we define self-operators (maps) on E by using the convolution with a fixed component. When E is a Banach or Hilbert space, we add some hypotheses inspired in the fractal convolution of maps, and construct in this way convolved Schauder and Riesz bases, Bessel sequences and frames for the space.

This review paper combs through reports that have enhanced antenna gain for ultra-wideband (UWB) frequencies using frequency-selective surface (FSS) techniques. The FSS techniques found across the research landscape were mapped onto a taxonomy in order to determine the most effective method for improving antenna gain. Additionally, this study looked into the motivation behind using FSS as a reflector in UWB frequencies to obtain directional radiation. The FSS suits multiple applications due to its exceptional ability to minimize power loss in undesired transmission areas in the antenna, as well as to hinder the interference that may occur from undesirable and wasted radiation. An efficient way to obtain constant gain over a wide range of frequencies is also elaborated in this paper. Essentially, this paper offers viable prescription to enhance antenna gain for UWB applications. Methods: A comprehensive study was performed using several imminent keywords, such as “high gain using FSS”, “gain enhancement using FSS”, “high gain UWB antennas”, and “gain enhancement of UWB antennas”, in different modifications to retrieve all related articles from three primary engines: Web of Science (WoS), IEEE Xplore, and Science Direct. Results: The 41 papers identified after a comprehensive literature review were classified into two categories. The FSS single- and multi-layer reflectors were reported in 25 and 16 papers, respectively. New direction: An effective method is proposed for FSS miniaturization and for obtaining constant gain over UWB frequencies while maintaining the return loss at −10 dB. Conclusion: The use of FSS is indeed effective and viable for gain enhancement in UWB antennas. This systematic review unravels a vast range of opportunities for researchers to bridge the identified gaps.

This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

Waves of electrical excitation rotating around an obstacle is one of the important mechanisms of dangerous cardiac arrhythmias occurring in the heart damaged by a post-infarction scar. Such a scar is also surrounded by the region of heterogeneity called a gray zone. In this paper, we perform the first comprehensive numerical study of various regimes of wave rotation around an obstacle surrounded by a gray zone. We use the TP06 cellular ionic model for human cardiomyocytes and study how the period and the pattern of wave rotation depend on the radius of a circular obstacle and the width of a circular gray zone. Our main conclusions are the following. The wave rotation regimes can be subdivided into three main classes: (1) functional rotation, (2) scar rotation and the newly found (3) gray zone rotation regimes. In the scar rotation regime, the wave rotates around the obstacle, while in the gray zone regime, the wave rotates around the gray zone. As a result, the period of rotation is determined by the perimeter of the scar, or gray zone perimeter correspondingly. The transition from the scar to the gray rotation regimes can be determined from the minimal period principle, formulated in this paper. We have also observed additional regimes associated with two types of dynamical instabilities which may affect or not affect the period of rota-tion. The results of this study can help to identify the factors determining the period of arrhythmias in post-infarction patients. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. A.V.P., P.K., D.M., A.D. and O.S. were funded by the Russian Foundation for Basic Research (№ 18-29-13008). The work of P.K., D.M., A.D. and O.S. was carried out within the framework of the IIF UrB RAS theme No AAAA-A21-121012090093-0.

Today, artificial intelligence (AI) and machine learning (ML) have dramatically advanced in various industries, especially medicine. AI describes computational programs that mimic and simulate human intelligence, for example, a person’s behavior in solving problems or his ability for learning. Furthermore, ML is a subset of artificial intelligence. It extracts patterns from raw data automatically. The purpose of this paper is to help researchers gain a proper understanding of machine learning and its applications in healthcare. In this paper, we first present a classification of machine learning-based schemes in healthcare. According to our proposed taxonomy, machine learning-based schemes in healthcare are categorized based on data pre-processing methods (data cleaning methods, data reduction methods), learning methods (unsupervised learning, supervised learning, semi-supervised learning, and reinforcement learning), evaluation methods (simulation-based evaluation and practical implementation-based evaluation in real environment) and applications (diagnosis, treatment). According to our proposed classification, we review some studies presented in machine learning applications for healthcare. We believe that this review paper helps researchers to familiarize themselves with the newest research on ML applications in medicine, recognize their challenges and limitations in this area, and identify future research directions.

The main purpose of this paper is to study the influence of game players’ behavior preferences on the strategy choice and equilibrium results in the game process of large-scale engineering projects’ extreme disputes. In contrast to the self-interested preference and completely rational assumptions of traditional economics, this paper focuses on the discussion of loss aversion preference and fairness preference against the background of incomplete information about the game subject. Considering the influence of the decision-makers’ multidimensional preferences, this paper establishes a three-party game model for the government, the project construction units, and the public. Furthermore, the equilibrium results of four different types of extreme disputes are deduced using the game method. We deduce the evolutionary paths and equilibrium characteristics and discuss them in combination with actual cases in China in an attempt to provide theoretical support and scientific analysis tools to avoid serious disputes and conflict decision results. Through research, this paper finds that the transformation of prior beliefs, the role of multidimensional preference sets, and a lack of information between the game players in the game process are key to the evolution of project disputes into extreme dispute decisions.

In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed, and the equivalent forms and the operator expressions are also considered. As applications, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

Positive linear electrical circuits systems described by generalized fractional derivatives are studied in this paper. We mainly focus on the reachability and observability of linear electrical circuits systems. Firstly, generalized fractional derivatives and ρ-Laplace transform of f is presented and some preliminary results are provided. Secondly, the positivity of linear electrical circuits systems described by generalized fractional derivatives is investigated and conditions for checking positivity of the systems are derived. Thirdly, reachability and observability of the generalized fractional derivatives systems are studied, in which the ρ-Laplace transform of a Mittag-Leffler function plays an important role. At the end of the paper, illustrative electrical circuits systems are presented, and conclusions of the paper are presented.

Since the first fully homomorphic encryption scheme was published in 2009, many papers have been published on fully homomorphic encryption and its applications. Machine learning is one of the most interesting applications and has drawn a lot of attention from researchers. To better represent and understand the field of Homomorphic Encryption in Machine Learning (HEML), this paper utilizes automated citation and topic analysis to characterize the HEML research literature over the years and provide the bibliometrics assessments for this burgeoning field. This is conducted by using a bibliometric statistical analysis approach. We make use of web-based literature databases and automated tools to present the development of HEML. This allows us to target several popular topics for in-depth discussion. To achieve these goals, we have chosen the well-established Scopus literature database and analyzed them through keyword counts and Scopus relevance searches. The results show a relative increase in the number of papers published each year that involve both homomorphic cryptography and machine learning. Using text mining of articles titles, we have found that cloud computing is a popular topic in this field, which also includes neural networks, big data, and the Internet of Things. The analysis results show that China, the US, and India have generated almost half of all the research contributions in HEML. The citation statistics, keyword statistics, and topic analyses give us a quick overview of the development of the field, which can be of great help to new researchers. It is also possible to apply our methodology to other research areas, and we see great value in this approach.

The efficient control of permanent magnet synchronous motors (PMSM) requires the development of a technique for loss optimization. The best approach is the implementation of power loss minimization algorithms, which are hard to model and design. Therefore, the developers typically involve maximum torque per ampere (MTPA) control, which optimizes Joule loss only. The conventional MTPA control requires knowledge of motor parameters and can only properly operate when these parameters are constant. However, motor parameters vary depending on operating conditions, thus, conventional techniques cannot be used. Furthermore, many industrial drives are designed for self-commissioning, and they do not have prior information on motor parameters. In order to solve this problem, various MTPA-seeking techniques, which track the minimum of motor current, have been developed. The dynamic performance between these seeking algorithms and maximum deviation from the true MTPA trajectory are defined by the constraints in most cases, in which proper design improves the dynamic behavior of MTPA-seeking algorithms. This paper considers a PMSM, which was designed to operate in the saturation area and whose MTPA trajectory significantly deviates from the same curve constructed for the initial unsaturated parameters. This paper considers existing approaches, explains their pros and cons, and demonstrates that these methods do not utilize full potential of the motor. A new constraint design was proposed and explained step by step. The experiment verifies the proposed technique and demonstrates improvements in efficiency and dynamic behavior of the seeking algorithm.

As the environment of the Internet of Things (IoT) gradually becomes common and mature, various smart application (APP) platforms have sprung up, making what we are doing more convenient, more economical and more efficient. Then, this paper used a bank APP as the research background to discuss issues related to smart APPs. Obviously, through the bank APPs, customers can complete their transfer and payment for various expenses at home, eliminating the inconvenience of going out, which not only can alleviate traffic congestion as well as reduce carbon emissions but also can save the manpower expenditure costs for banks. Consequently, improving APP performance and increasing the number of users of an APP is a very important issue. Therefore, this paper proposed an APP performance index to evaluate the performance of a bank APP. This APP performance index is to evaluate the performance of the APP through the time interval of customers’ access to the APP. The shorter the time interval is, the greater the number of users within a unit time is. In addition, based on cost considerations and effectiveness, the sample size n is usually not too large in practice, in order to make decisions quickly and accurately in a short time. Since the fuzzy testing model based on the confidence interval can be integrated with the past accumulated experience of data experts, the testing accuracy can be leveled up under the condition of small-sized samples. Accordingly, a fuzzy evaluation model was proposed to evaluate whether the performance of the bank APP can reach the required level, and this model was also regarded as a basis for decision-making to determine whether to improve the bank APP. At the same time, we can grasp the opportunities for improvement, achieve the effect of cost reduction, energy saving and carbon reduction, and further move towards the goal of innovative and intelligent management.

The spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the first author’s papers written in 1997 and 2000, as well as Lemarié-Rieusset’s 2013 paper. As a corollary, the main result in the present paper shows that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the present paper is to provide a complete picture of the pointwise multiplier spaces.

Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inversion formula, and the Parseval relation for the Wiener transform. But, they do not establish homomorphism properties for the Wiener transform. In this paper, the author establishes some basic fundamental formulas for the Wiener transform via some concepts and motivations introduced by Segal and used by Hayker et al. We then state the usefulness of basic fundamental formulas as some applications.

This paper estimates the technical efficiency of Olympic disciplines in which Spanish athletes participate, taking into account the results obtained in the last three Olympic Games. A stochastic production frontier model (normal-exponential), using two control variables linked to economic factors such as budget and sports scholarships, is estimated in order to obtain different Olympic sports’ efficiencies distinguished by gender, using data from 2005 to 2016. The results detect some differences among the considered disciplines. In all the cases, athletics, canoeing, cycling, swimming, and tennis, depending on the gender, reach better values. This paper’s novelty lies in the efficiency analysis carried out on the Olympic disciplines and athletes of a country and not on the country’s efficiency, which allows managers and stakeholders to decide about investments concerning disciplines and athletes. Ministerio Ciencia e Innovación | Ref. PID2019-105428RB-I00 Ministerio de Economía, Industria y Competitividad | Ref. ECO2017-85577-P

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of unified chaotic systems. Then, the secret message embedded in the master chaotic system can be transmitted from transmitter to receiver. Different from previous works using discontinuous SMC, the undesired chattering phenomenon can be fully eliminated, and it becomes possible to precisely recover the embedded secret message at the receiver. Last, an example is given to illustrate the success of secure data transmission with the continuous SMC developed in this paper.

This paper aims at studying the Bi-Objective Insular Traveling Salesman Problem (BO-InTSP), which searches for a set of efficient, single visit sequences to collect (or distribute) freight from a set of islands. In this problem, the selection of ports (nodes) to be visited at each island, along with the associated port visit sequence, are optimized simultaneously, while the maritime transportation costs and the ground transportation costs inside the islands are minimized with a bi-objective perspective. This approach is employed since these costs are of a conflictive nature. A previous Approximated Formulation of the BO-InTSP relies on aggregating the actual demand locations within each island in a certain number of centroids for computing the ground transportation costs. Conversely, this paper proposes and develops a novel Exact Formulation for the problem based on the actual demand locations, instead of aggregating the demand inside the islands. Additionally, a systematic evaluation approach is developed to compare the two alternative formulations with different levels of demand aggregation inside the islands, considering the bi-objective nature of the problem. The results reveal that the novel Exact Formulation significantly outperforms the previous aggregated approach in terms of the solutions quality and computational resources.

The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market.

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.

The registration of point clouds in a three-dimensional space is an important task in many areas of computer vision, including robotics and autonomous driving. The purpose of registration is to find a rigid geometric transformation to align two point clouds. The registration problem can be affected by noise and partiality (two point clouds only have a partial overlap). The Iterative Closed Point (ICP) algorithm is a common method for solving the registration problem. Recently, artificial neural networks have begun to be used in the registration of point clouds. The drawback of ICP and other registration algorithms is the possible convergence to a local minimum. Thus, an important characteristic of a registration algorithm is the ability to avoid local minima. In this paper, we propose an ICP-type registration algorithm (λ-ICP) that uses a multiparameter functional (λ-functional). The proposed λ-ICP algorithm generalizes the NICP algorithm (normal ICP). The application of the λ-functional requires a consistent choice of the eigenvectors of the covariance matrix of two point clouds. The paper also proposes an algorithm for choosing the directions of eigenvectors. The performance of the proposed λ-ICP algorithm is compared with that of a standard point-to-point ICP and neural network Deep Closest Points (DCP).

In this paper, two new integral operators are defined using the operator DRλm,n, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator DRλm,n are also obtained.

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets.

In this paper, the normal form and central manifold theories are used to discuss the influence of two-degree-of-freedom coupled van der Pol oscillators with time delay feedback. Compared with the single-degree-of-freedom time delay van der Pol oscillator, the system studied in this paper has richer dynamical behavior. The results obtained include: the change of time delay causing the stability switching of the system, and the greater the time delay, the more complicated the stability switching. Near the double Hopf bifurcation point, the system is simplified by using the normal form and central manifold theories. The system is divided into six regions with different dynamical properties. With the above results, for practical engineering problems, we can perform time delay feedback adjustment to make the system show amplitude death, limit loop, and so on. It is worth noting that because of the existence of unstable limit cycles in the system, the limit cycle cannot be obtained by numerical solution. Therefore, we derive the approximate analytical solution of the system and simulate the time history of the interaction between two frequencies in Region IV.

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', at [https://doi.org/10.3390/math9192355]. Cite this paper as: F. Nda\"{\i}rou and D.F.M. Torres, Optimal control problems involving combined fractional operators with general analytic kernels, Mathematics 9 (2021), no. 19, Art. 2355, 17 pp

Feature selection is a well-known prepossessing procedure, and it is considered a challenging problem in many domains, such as data mining, text mining, medicine, biology, public health, image processing, data clustering, and others. This paper proposes a novel feature selection method, called AOAGA, using an improved metaheuristic optimization method that combines the conventional Arithmetic Optimization Algorithm (AOA) with the Genetic Algorithm (GA) operators. The AOA is a recently proposed optimizer, it has been employed to solve several benchmark and engineering problems and has shown a promising performance. The main aim behind the modification of the AOA is to enhance its search strategies. The conventional version suffers from weaknesses, the local search strategy, and the trade-off between the search strategies. Therefore, the operators of the GA can overcome the shortcomings of the conventional AOA. The proposed AOAGA was evaluated with several well-known benchmark datasets, using several standard evaluation criteria, namely accuracy, number of selected features, and fitness function. Finally, the results were compared with the state-of-the-art techniques to prove the performance of the proposed AOAGA method. Moreover, to further assess the performance of the proposed AOAGA method, two real-world problems containing gene datasets were used. The findings of this paper illustrated that the proposed AOAGA method finds new best solutions for several test cases, and it got promising results compared to other comparative methods published in the literature.

The accurate localization of the rolling element failure is very important to ensure the reliability of rotating machinery. This paper proposes an efficient and anti-noise fault diagnosis model for rolling elements. The proposed model is composed of feature extraction, feature selection and fault classification. Feature extraction is composed of signal processing and signal noise reduction. Signal processing is carried out by local mean decomposition (LMD), and signal noise reduction is performed by product function (PF) selection and wavelet packet decomposition (WPD). Through the steps of signal noise reduction, high-frequency noise can be effectively removed, and the fault information hidden under the noise can be extracted. To further improve the effectiveness of the diagnostic model, an improved binary particle swarm optimization (IBPSO) is proposed to find the most important features from the feature space. In IBPSO, cycling time-varying inertia weight is introduced to balance exploitation and exploration and improve the capability to escape from local solutions, and crossover and mutation operations are also introduced to improve exploration and exploitation capabilities, respectively. The main contributions of this research are briefly described as follows: (1) The feature extraction process applied in this research can effectively remove noise and establish a high-accuracy feature set. (2) The proposed feature selection algorithm has higher accuracy than the other state-of-the-art feature selection algorithms. (3) In a strong noise environment, the proposed rolling element fault diagnosis model is compared with the state-of-the-art fault diagnosis model in terms of classification accuracy. Experimental results show that the model can maintain high classification accuracy in a strong noise environment. Therefore, it can be proved that the fault diagnosis model proposed in this paper can be effectively applied to the fault diagnosis of rotating machinery.

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base, that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

The present research paper explains the influence of Marangoni convection on magnetohydrodynamic viscous dissipation and heat transfer on hybrid nanofluids in a rotating system among two surfaces. Then, the properties of heat and mass transfer are analysed. With the similarity transformation, the governing equations of the defined flow problem are converted into nonlinear ordinary differential equations. These compact equations are solved approximately and analytically using the optimal homotopy analysis method. The impact of different parameters is interpreted through graphs in the form of velocity and temperature profiles. The influence of the skin friction coefficient and Nusselt number are presented in the form of tables. The comparison of the present research paper and published works is also presented table.

In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.

Since December 2019, the novel coronavirus (SARS-CoV-2) and its associated illness COVID-19 have rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, we used statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national levels in Mexico. In this paper, we propose two types of models. First, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model used to estimate the middle and the end of the outbreak. Model selection was performed using Vuong’s test. The proposed models showed overall fit similar to predictive models (e.g., time series and machine learning), however, the interpretation of parameters is simpler for decisionmakers, and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.

This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie's symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning., The support of the Plan Propio de Investigacion de la Universidad de Cadiz is gratefully acknowledged. The authors also thank the referees for their suggestions to improve the quality of the paper.

In this paper, we study the single machine vector scheduling problem (SMVS) with general penalties, in which each job is characterized by a d-dimensional vector and can be accepted and processed on the machine or rejected. The objective is to minimize the sum of the maximum load over all dimensions of the total vector of all accepted jobs and the rejection penalty of the rejected jobs, which is determined by a set function. We perform the following work in this paper. First, we prove that the lower bound for SMVS with general penalties is α(n), where α(n) is any positive polynomial function of n. Then, we consider a special case in which both the diminishing-return ratio of the set function and the minimum load over all dimensions of any job are larger than zero, and we design an approximation algorithm based on the projected subgradient method. Second, we consider another special case in which the penalty set function is submodular. We propose a noncombinatorial ee−1-approximation algorithm and a combinatorial min{r,d}-approximation algorithm, where r is the maximum ratio of the maximum load to the minimum load on the d-dimensional vector.

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Variance, as a measurement of dispersion, is a basic component of decision-making processes. Recent advances in intelligent systems have included the concept of variance in information fusion techniques for decision-making under uncertainty. These dispersion measures broaden the spectrum of decision makers by extending the toolset for the analysis and modeling of problems. This paper introduces some variance logarithmic averaging operators, including the variance generalized ordered weighted averaging (Var-GOWLA) operator and the induced variance generalized ordered weighted averaging (Var-IGOWLA) operator. Moreover, this paper analyzes some properties, families and particular cases of the proposed operators. Finally, an illustrative example of the characteristic design of the operators is proposed using real-world information retrieved from financial markets. The objective of this paper is to analyze the performance of some equities based on the expected payoff and the dispersion of its elements. Results show that the equity payoff results present diverse rankings combined with the proposed operators, and the introduced variance measures aid decision-making by offering new tools for information analysis. These results are particularly interesting when selecting logarithmic averaging operators for decision-making processes. The approach presented in this paper extends the available tools for decision-making under ignorance, uncertainty, and subjective environments.

Events such as the Financial Crisis of 2007–2008 or the COVID-19 pandemic caused significant losses to banks and insurance entities. They also demonstrated the importance of using accurate equity risk models and having a risk management function able to implement effective hedging strategies. Stock volatility forecasts play a key role in the estimation of equity risk and, thus, in the management actions carried out by financial institutions. Therefore, this paper has the aim of proposing more accurate stock volatility models based on novel machine and deep learning techniques. This paper introduces a neural network-based architecture, called Multi-Transformer. Multi-Transformer is a variant of Transformer models, which have already been successfully applied in the field of natural language processing. Indeed, this paper also adapts traditional Transformer layers in order to be used in volatility forecasting models. The empirical results obtained in this paper suggest that the hybrid models based on Multi-Transformer and Transformer layers are more accurate and, hence, they lead to more appropriate risk measures than other autoregressive algorithms or hybrid models based on feed forward layers or long short term memory cells.

This paper analyzes the co-movements of prices of fossil fuels, energy stock markets and EU allowances. This analysis is conducted in order to identify the spillover effect of volatility and correlation among these financial markets, and to provide a scientific basis that shows the interest of incorporating sustainable assets in the design of minimum risk strategies of investment. To achieve this goal, we have used a Vector Autoregressive-Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroscedasticity (VAR-DCC-GARCH) model that also incorporates a stock index of industrial companies as a leading indicator of the level of economic activity. In addition, the paper conducts an impulse response analysis to determine how unexpected shocks to prices are propagated along time, and, in particular, how they affect prices of the others, both in mean, variance and correlation. Therefore, the results of this one- and two-dimensional analysis allow for the study of short and long run dynamics of the relationship among those prices, thus, providing greater meaning and information for investors, which has implications for building their portfolios. The analyzed period was from January 2010 to February 2021, so that the data include half of phase II, full phase III and the onset of phase IV of the EU ETS, as well as the COVID-19 outbreak in the European context. We also analyzed whether the EUA price impulses the demand of clean energy stocks, which has important implications for the objective of triggering the investment in clean energy. Our results show the transmission mechanism of all of those prices, which are relevant not only for investors but also for policymakers to construct an early-warning system, revealing the most important transmission channels. Moreover, from an investment viewpoint, we observe a decline in dirty energies and a rise in the clean energy market, which might be an indication of the progress towards the energy transition to renewables sources within a circular economy perspective. Therefore, this shows that the EU ETS is achieving its goals, and that clean energy companies, aligned with their role towards socially responsible initiatives, are also gaining acceptance in terms of investments, which would be beneficial for the environment.

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