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A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

In this paper, by employing matched spaces for time scales, we introduce a &delta, almost periodic function and obtain some related properties. Also the hull equation for homogeneous dynamic equation is introduced and results of the existence are presented. In the sense of admitting exponential dichotomy for the homogeneous equation, the expression of a &delta, almost periodic solution for a type of nonhomogeneous dynamic equation is obtained and the existence of &delta, almost periodic solutions for new delay dynamic equations is considered. The results in this paper are valid for delay q-difference equations and delay dynamic equations whose delays may be completely separated from the time scale T .

This paper constructs the generalized viscosity implicit midpoint rule for nonexpansive mappings in Banach space. It obtains strong convergence conclusions for the proposed algorithm and promotes the related results in this field. Moreover, this paper gives some applications. Finally, the paper gives six numerical examples to support the main results.

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.

This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a special reverential volume, dedicated to the Centenary of the Birth of Lotfi A. Zadeh, whom Ioan Dzitac considered to be is his mentor, and to whom he showed his gratitude many times and in innumerable ways, including by being the Guest Editor of this Special Issue. Professor Ioan Dzitac had many important achievements throughout his career: he was co-founder and Editor-in-Chief of an ISI Expanded quoted journal, International Journal of Computers Communications & Control; together with L.A. Zadeh, D. Tufis and F.G. Filip he edited the volume “From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence”; his scientific interest focused on different sub-fields: fuzzy logic applications, soft computing in a fuzzy environment, artificial intelligence, learning platform, distributed systems in internet. He had the most important contributions in soft computing in a fuzzy environment. Some of them will be presented in this paper. Finally, some future trends are discussed.

The emerging sixth-generation networks have to provide effective support to a wide plethora of novel disruptive heterogeneous applications. This paper models the probabilistic end-to-end delay bound for the virtual reality services in the presence of heterogeneous traffic flows by resorting to the stochastic network calculus principles and exploiting the martingale envelopes. The paper presents the network performance analysis under the assumption of different scheduling policies, considering both the earliest deadline first and the first-in-first-out queue discipline. Furthermore, differently from previous literature, the probabilistic per-flow bounds have been formulated taking into account a number of traffic flows greater than two, which results in a theoretical analysis that is remarkably more complex than the case in which only two concurrent flows are considered. Finally, the validity of the theoretical bounds have been confirmed by the evident closeness between the analytical predictions and the actual simulation results considering, for the sake of argument, four concurrent traffic flows with heterogeneous quality-of-service constraints. That closeness exhibits the ability of the proposed analysis in fitting the actual behavior of the system, representing a suitable theoretical tool to support resource allocation strategies, without violating service constraints.

Battle casualties are the subject of study in military operations research, which applies mathematical models to quantify the probability of victory vs. loss. In particular, different approaches have been proposed to model the course of battles. However, none of them provide adequate decision-making support for high-level command. To overcome this situation, this paper presents an innovative high-level decision-making model, which uses an adaptive and predictive control architecture. The paper reports empirical evidence supporting our model by considering one of the greatest battles of World War II: the Battle of Crete.

This paper studies the economically significant problem of the optimization of customs fraud control, which is a critical issue for many countries. The European Union (EU) alone handles 4693 tons of goods every minute (2018 figures). Even though 70% of goods are imported at zero tariff, the EU raised EUR 25.4 billions in 2018, and customs-related income transferred by member states to the EU accounts for nearly 13% of its overall budget. In this field, (a) the conflicting objectives are qualitative and cannot be reduced to a common measure (security and terrorism, health, drug market access control, taxes, etc.); (b) each submitted item has dozens of characteristics; (c) there are constraints; and (d) risk analysis systems have to make decisions in real time. Although the World Customs Organization has promoted the use of artificial intelligence to increase the precision of controls, the problem is very complex due to the data characteristics and interpretability, which is a requirement established by customs officers. In this paper, we propose a new Bayesian-based hybrid approach combining machine learning and multi-objective linear programming (MOLP), called multi-objective Bayesian with dynamic optimization (MOBADO). We demonstrate that it is possible to more than double (with a 237% increase) the precision of current inspection systems, freeing up almost 50% of human resources, and outperform past results with respect to each of the above objectives. MOBADO is an optimization technique that could be combined with any artificial intelligence approach capable of optimizing the quality of multi-objective risk analysis in real time.

This paper considers a variant of the relocation problem, which is formulated from an urban renewal project. There is a set of jobs to be processed in a two-machine flow shop subject to a given initial resource level. Each job consumes some units of the resource to start its processing on machine 1 and will return some amount of the resource when it is completed on machine 2. The amount of resource released by a job is not necessarily equal to the amount of resource acquired by the job for starting the process. Subject to the resource constraint, the problem is to find a feasible schedule whose makespan is minimum. In this paper, we first prove the NP-hardness of two special cases. Two heuristic algorithms with different processing characteristics, permutation and non-permutation, are designed to construct feasible schedules. Ant colony optimization (ACO) algorithms are also proposed to produce approximate solutions. We design and conduct computational experiments to appraise the performances of the proposed algorithms.

The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples.

Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is often uncertain, modeling these problems based on FG is highly demanding for an expert. A vague graph (VG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems in which fuzzy graphs may not succeed in bringing about satisfactory results. Domination in FGs theory is one of the most widely used concepts in various sciences, including psychology, computer sciences, nervous systems, artificial intelligence, decision-making theory, etc. Many research studies today are trying to find other applications for domination in their field of interest. Hence, in this paper, we introduce different kinds of domination sets, such as the edge dominating set (EDS), the total edge dominating set (TEDS), the global dominating set (GDS), and the restrained dominating set (RDS), in product vague graphs (PVGs) and try to represent the properties of each by giving some examples. The relation between independent edge sets (IESs) and edge covering sets (ECSs) are established. Moreover, we derive the necessary and sufficient conditions for an edge dominating set to be minimal and show when a dominance set can be a global dominance set. Finally, we try to explain the relationship between a restrained dominating set and a restrained independent set with an example. Today, we see that there are still diseases that can only be treated in certain countries because they require a long treatment period with special medical devices. One of these diseases is leukemia, which severely affects the immune system and the body’s defenses, making it impossible for the patient to continue living a normal life. Therefore, in this paper, using a dominating set, we try to categorize countries that are in a more favorable position in terms of medical facilities, so that we can transfer the patients to a suitable hospital in the countries better suited in terms of both cost and distance.

This paper focuses on the dynamic effects of flexible propellers on F2 class aircraft models. An oscillating propeller affects an engine’s mechanical performance, and this combination has a huge influence on the model’s flight dynamic performance. In the first and second sections of this paper, two physical tests that were performed according to the test results obtained using a CFX numerical model are discussed. The studies on flexible propellers for class F2 aircraft models performed in this paper show that, when the first resonant frequencies of the propeller are within the operating range of the aircraft, better flight parameters are achieved. This study helps to explain the effect of a glass composite’s Young’s modulus on the mechanical behavior of a physical propeller in operating conditions and the effect of propeller stiffness on flapping propeller dynamics and unsteady aerodynamics.

In this paper, we prove some new Ostrowski-type integral inequalities for q-differentiable bounded functions. It is also shown that the results presented in this paper are a generalization of know results in the literarure. Applications to special means are also discussed.

Oscillatory systems arise in the different biological and medical fields. Mathematical and statistical approaches are fundamental to deal with these processes. The Frequency Modulated Mobiüs approach (FMM), reviewed in this paper, is one of these approaches. Little known as it has been recently developed, it solves a variety of exciting questions with real data; some of them, such as the decomposition of the signal into components and their multiple uses, are of general application, others are specific. Among the exciting specific applications is the automatic interpretation of the electrocardiogram signal. In this paper, a summary of the theoretical, statistical and computational properties of the FMM approach are revised. Additionally, as a novelty, the FMM approach’s usefulness for the analysis of blood pressure signals is shown. For the latter, a new robust estimation algorithm is proposed using FMM models with restrictions. The paper ends with a view about challenges for the future.

This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and its possible extensions. In this paper, it is shown that the PQ penny flip game can be associated, in a precise way, with the dihedral group D8 and that within D8 there exist precisely two classes of equivalent winning strategies for Q. This is achieved by proving that there are exactly two different sequences of states that can guarantee Q’s win with probability 1.0. It is demonstrated that the game can be played in every dihedral group D8n, where n≥1, without any significant change. A formal examination of what happens when Q can draw their moves from the entire U(2), leads to the conclusion that, again, there are exactly two classes of winning strategies for Q, each class containing an infinite number of equivalent strategies, but all of them sending the coin through the same sequence of states as before. Finally, when general extensions of the game, with the quantum player having U(2) at their disposal, are considered, a necessary and sufficient condition for Q to surely win against Picard is established: Q must make both the first and the last move in the game.

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

This paper examines the positive aspects of aging. Some items, such as valuable and rare stamps, old coins, works of art, and antiques, become more expensive over time. More popular examples demonstrating the positive effect of aging that influences price are the aging of boutique wine and artisan cheese. The present paper examines the wine aging process that brings about quality improvement. This process also leads to determining (i) optimal aging periods for different wines, (ii) optimal grape juice inventory allocations and prices for different wines, (iii) optimal quantities of different kinds of wine, and (iv) the time durations of wine production and consumption from each vintage. These aspects are considered in an environment in which the demand increases over time due to the aging and rarity of the product.

[EN] Including designer preferences in every phase of the resolution of a multi-objective optimization problem is a fundamental issue to achieve a good quality in the final solution. To consider preferences, the proposal of this paper is based on the definition of what we call a preference basis that shows the preferred optimization directions in the objective space. Associated to this preference basis a new basis in the objective space-dominance basis-is computed. With this new basis the meaning of dominance is reinterpreted to include the designer's preferences. In this paper, we show the effect of changing the geometric properties of the underlying structure of the Euclidean objective space by including preferences. This way of incorporating preferences is very simple and can be used in two ways: by redefining the optimization problem and/or in the decision-making phase. The approach can be used with any multi-objective optimization algorithm. An advantage of including preferences in the optimization process is that the solutions obtained are focused on the region of interest to the designer and the number of solutions is reduced, which facilitates the interpretation and analysis of the results. The article shows an example of the use of the preference basis and its associated dominance basis in the reformulation of the optimization problem, as well as in the decision-making phase., This work has been supported by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00.

Multi-criteria decision-making methods (MCDM) represent a very powerful tool for making decisions in different areas. Making a rational and reliable decision, while respecting different factors, is a challenging and difficult task, MCDM models have a great impact on achieving this goal. In this paper, a new MCDM technique is presented—ranking alternatives by defining relations between the ideal and anti-ideal alternative (RADERIA), which was tested for the evaluation of human resources (HR) in a transportation company. The RADERIA model has three key advantages that recommend it for future use: (1) the RADERIA model has a new approach for data normalization that enables defining the normalization interval according to the judgments of a decision-maker, (2) an adaptive model for data normalization of the RADERIA model allows tough conversion into various forms of decreasing functions (linear, quadratic equation, etc.), and (3) the resistance of the RADERIA model to the rank reversal problem. Furthermore, in many simulations, the RADERIA method has shown stability when processing a larger number of datasets. This was also confirmed by a case study with 36 alternatives, as considered in this paper. The results and verification of the proposed new method were acquired through a comprehensive verification of the complexity of the results. The complexity of the results was executed through (1) comparison with four other multi-criteria methods, (2) checking the resistance of the RADERIA model to the rank reversal problem, and (3) the analysis of the impact of changes in the measurement scale on the ranking results.

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Leveraging from the online search index of Chinese listed companies from 2012 to 2018, we empirically test the relationship between investors’ attention and corporate innovation performance for the first time. The main results are as follows: (1) investors’ attention significantly improves listed companies’ innovation performance, which is reflected in the increase of patent applications. This indicates that investors’ active information collection behaviour affects China’s economic development by promoting enterprise innovation. (2) This paper’s conclusion remains intact after a battery of robustness checks, such as alternative measures of key variables and empirical specifications and a series of endogenous treatment. (3) The mechanisms tests show that: “information asymmetry”, “financing constraint”, and “agency cost” are supported. In other words, with the increase of investors’ attention, not only the information asymmetry is reduced, which greatly improved the information environment of the capital market, but also the external financing constraints of enterprises are alleviated. The opportunistic management behaviour is effectively suppressed, thus motivating the corporate innovation incentives and improving the corporate innovation of input, output and quality. (4) Further research shows that investor attention to listed companies also improves the efficiency of capital allocation. This paper’s conclusion shows that investors’ initiative information acquisition behaviour can improve enterprises innovation performance, thus providing a driving force for China’s economic development.

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

The existing spatial panel structural vector auto-regressive model can effectively capture the time and spatial dynamic dependence of endogenous variables. However, the hypothesis that the common factors have the same effect for all spatial units is unreasonable. Therefore, incorporating time effects, spatial effects, and time-individual effects, this paper develops a more general spatial panel structural vector autoregressive model with interactive effects (ISpSVAR) that can reflect the different effects of common factors on different spatial units. Additionally, based on whether or not the common factors can be observed, this paper proposes procedures to estimate ISpSVAR separately and studies the finite sample properties of estimators by Monte Carlo simulation. The simulation results show the effectiveness of the proposed ISpSVAR model and its estimation procedures.

Let Z(s)=(Z1(s),…,Zp(s))t be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between the p random components of Z with the correlation coefficients and measure the spatial dependence with variograms. If two of the Z components are correlated, the spatial information provided by one of them can improve the information of the other. To capture this association, both within components of Z(s) and across s, we use a cross-variogram. Only two robust cross-variogram estimators have been proposed in the literature, both by Lark, and their sample distributions were not obtained. In this paper, we propose new robust cross-variogram estimators, following the location estimation method instead of the scale estimation one considered by Lark, thus extending the results obtained by García-Pérez to the multivariate case. We also obtain accurate approximations for their sample distributions using saddlepoint techniques and assuming a multivariate-scale contaminated normal model. The question of the independence of the transformed variables to avoid the usual dependence of spatial observations is also considered in the paper, linking it with the acceptance of linear variograms and cross-variograms.

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function (FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar.

In this paper, we define (p,q)-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using (p,q)-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results.

In this paper daily confirmed cases of COVID -19 in different countries are modelled using different mathematical regression models. The mathematical curve fitting is used as a prediction tool to model both pervious and next upcoming Coronavirus waves. The used models cover virus spreading from 1/3/2020 to 10/4/2021. According to virus spreading, countries under study in this paper are categorized into three main categories. First category in which Coronavirus first wave takes about two year seasons (about 180 days) to make a complete virus cycle. Second category is countries with higher transmission rates with one year season (about 90 days) to make the first complete virus cycle. These countries take offline periods with low spreading rates. The third category is countries with the highest transmission rates and make complete virus cycles without offline periods. All categories are modelled with different mathematical fitting models. Finally, predictions of different upcoming scenarios for these countries are made. Funding Statement: The research is partially supported by P.R.I.N. 2019 and the RUDN University Program 5-100". Declaration of Interests: The authors have no competing interests.

In this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider applying generalized Hurst laws to obtain a new set of reduced parameters in data associated with communication systems. We analyze three hypotheses. The first one contains one power-law exponent. The second one incorporates two power-law exponents, which are in many cases complex-conjugated. The third hypothesis has three power-law exponents, two of which are complex-conjugated as well. These hypotheses describe with acceptable accuracy (relative error does not exceed 2%) a wide set of trendless sequences (TLS) associated with radiometric measurements. Generalized Hurst laws operate with R/S curves not only in the asymptotic region, but in the entire domain. The fitting parameters can be used as the reduced parameters for the description of the given data. The paper demonstrates that this general approach can also be applied to other TLS.

Given a digital image (or digital object) (X,k),X⊂Zn, this paper initially establishes a group structure of the set of self-k-isomorphisms of (X,k) with the function composition, denoted by Isok(X) or Autk(X). In particular, let Ckn,l be a simple closed k-curve with l elements in Zn. Then, the group Isok(Ckn,l) is proved to be isomorphic to the standard dihedral group Dl with order l. The calculation of this quantity Isok(Ckn,l) is a key step for obtaining many new results. Indeed, it is essential for exploring many features of Isok(X). Furthermore, this quantity is proved to be a digital topological invariant. After proceeding with an Isok(X)-action on (X,k), we investigate some properties of fixed point sets by this action. Finally, we explore various features of fixed point sets by this action from the viewpoint of digital k-curve theory. This paper only deals with k-connected digital images (X,k) whose cardinality is equal to or greater than 2. Besides, we discuss some errors that have appeared in the lilterature.

The mean-variance (MV) portfolio is typically formulated as a quadratic programming (QP) problem that linearly combines the conflicting objectives of minimizing the risk and maximizing the expected return through a risk aversion profile parameter. In this formulation, the two objectives are expressed in different units, an issue that could definitely hamper obtaining a more competitive set of portfolio weights. For example, a modification in the scale in which returns are expressed (by one or percent) in the MV portfolio, implies a modification in the solution of the problem. Motivated by this issue, a novel mean squared variance (MSV) portfolio is proposed in this paper. The associated optimization problem of the proposed strategy is very similar to the Markowitz optimization, with the exception of the portfolio mean, which is presented in squared form in our formulation. The resulting portfolio model is a non-convex QP problem, which has been reformulated as a mixed-integer linear programming (MILP) problem. The reformulation of the initial non-convex QP problem into an MILP allows for future researchers and practitioners to obtain the global solution of the problem via the use of current state-of-the-art MILP solvers. Additionally, a novel purely data-driven method for determining the optimal value of the hyper-parameter that is associated with the MV and MSV approaches is also proposed in this paper. The MSV portfolio has been empirically tested on eight portfolio time series problems with three different estimation windows (composing a total of 24 datasets), showing very competitive performance in most of the problems.

The fractional calculus is useful in describing the natural phenomena with memory effect. This paper addresses the fractional form of Ambartsumian equation with a delay parameter. It may be a challenge to obtain accurate approximate solution of such kinds of fractional delay equations. In the literature, several attempts have been conducted to analyze the fractional Ambartsumian equation. However, the previous approaches in the literature led to approximate power series solutions which converge in subdomains. Such difficulties are solved in this paper via the Homotopy Perturbation Method (HPM). The present approximations are expressed in terms of the Mittag-Leffler functions which converge in the whole domain of the studied model. The convergence issue is also addressed. Several comparisons with the previous published results are discussed. In particular, while the computed solution in the literature is physical in short domains, with our approach it is physical in the whole domain. The results reveal that the HPM is an effective tool to analyzing the fractional Ambartsumian equation.

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function F:X&rarr, cc(Y), where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X. Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where X=R2 and Y=Rn, n&isin, N, and G is the unitary group U(1).

In this paper we investigate the unified theory for solutions of differential equations without impulses and with impulses, even at variable times, allowing the presence of beating phenomena, in the space of regulated functions. One of the aims of the paper is to give sufficient conditions to ensure that a regulated solution of an impulsive problem is globally defined.

The paper shows that, in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility analysis of PDEs with a single constraint (or the nonclassical method of symmetry reductions based on an invariant surface condition). This fact is illustrated by examples of nonlinear reaction-diffusion and convection-diffusion equations with variable coefficients, and nonlinear Klein&ndash, Gordon-type equations. Hydrodynamic boundary layer equations, nonlinear Schr&ouml, dinger type equations, and a few third-order PDEs are also investigated. Several new exact functional separable solutions are given. A possibility of increasing the efficiency of the Clarkson&ndash, Kruskal direct method is discussed. A generalization of the direct method of the functional separation of variables is also described. Note that all nonlinear PDEs considered in the paper include one or several arbitrary functions.

In the fields of continuous casting and the roll stepped cooling, the heat transfer coefficient is piecewise linear. However, few papers discuss the solution of the backward heat conduction problem in this situation. Therefore, the aim of this paper is to solve the backward heat conduction problem, which has the piecewise linear heat transfer coefficient. Firstly, the ill-posed of this problem is discussed and the truncated regularized optimization scheme is introduced to solve this problem. Secondly, because the regularization parameter is the key factor for the regularization method, this paper presents an improved method for choosing the regularization parameter to reduce the iterative number and proves the fourth-order convergence of this method. Furthermore, the numerical simulation experiments show that, compared with other methods, the improved method of fourth-order convergence effectively reduces the iterative number. Finally, the truncated regularized optimization scheme is used to estimate the initial temperature, and the results of numerical simulation experiments illustrate that the inverse values match the exact values very well.

The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security is an ordered fuzzy number of the orientation identical to the oriented present value that determines it. All classical methods of portfolio analysis are based on the definition of the return rate. In the case of securities with a fuzzy present value, a discount factor is a better tool for portfolio analysis than the return rate, which implies the chosen methods of management of securities should be revised and transformed to equivalent methods based on a discount factor. This would enable the use of those methods in the case of a financial instrument of the oriented fuzzy present value. This paper presents example results of the realization of such a postulate. The main aim of the paper is to generalize Sharpe&rsquo, s ratio to a case of investment recommendations management formulated for a security characterized by an oriented discount factor. A five-degree rating scale was used. The whole deliberation is illustrated by broad numerical examples.

In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n &minus, 1 , and 2, which are the lower and upper extremal cases. Furthermore, in the first part of the paper, a method is presented to locate fault-tolerant resolving sets by using classical resolving sets in graphs. The second part of the paper applies the proposed method to three infinite families of regular graphs and locates certain fault-tolerant resolving sets. By accumulating the obtained results with some known results in the literature, we present certain lower and upper bounds on the fault-tolerant metric dimension of these families of graphs. As a byproduct, it is shown that these families of graphs preserve a constant fault-tolerant resolvability structure.

This paper is concerned with a class of the discrete Mackey–Glass model that describes the process of the production of blood cells. Prior to proceeding to the main results, we prove the boundedness and extinction of its solutions. By means of the contraction mapping principle and under appropriate assumptions, we prove the existence of almost periodic positive solutions. Furthermore and by the implementation of the discrete Lyapunov functional, sufficient conditions are established for the exponential convergence of the almost periodic positive solution. Examples, as well as numerical simulations are illustrated to demonstrate the effectiveness of the theoretical findings of the paper. Our results are new and generalize some previously-reported results in the literature.

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results of the proposed algorithm and improves the relevant results of researchers in this field. In the end, this paper gives numerical examples to support the main results.

This paper introduces a new numerical approach to solving a system of fractional differential equations (FDEs) using the Legendre wavelet operational matrix method (LWOMM). We first formulated the operational matrix of fractional derivatives in some special conditions using some notable characteristics of Legendre wavelets and shifted Legendre polynomials. Then, the system of fractional differential equations was transformed into a system of algebraic equations by using these operational matrices. At the end of this paper, several examples are presented to illustrate the effectivity and correctness of the proposed approach. Comparing the methodology with several recognized methods demonstrates that the advantages of the Legendre wavelet operational matrix method are its accuracy and the understandability of the calculations.

By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich–Rus–Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121–124, Boll. Unione Mat. Ital. 1972, 4, 26–42 and Boll. Unione Mat. Ital. 1971, 4, 1–11.) is not applicable.

The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics.

The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse Stackelberg solutions and under additional concavity conditions establish the existence theorem., 12 pages

This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm&ndash, Liouville problems. Next, a concrete implementation to the inverse Sturm&ndash, Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm&ndash, Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm&ndash, Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.