Axioms, Volume 12, Issue 1 (January 2023) – 95 articles

This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics. Full article

Based on a quantum logistic map and a Caputo-like delta difference operator, a fractional-order improved quantum logistic map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, dynamical mapping, and 0-1 testing. It is shown that the proposed fractional-order map is influenced by both the parameters and the fractional order. Then, the complexity of the map is explored through spectral entropy and approximate entropy. The results show that the fractional-order improved quantum logistic map has stronger robustness within chaos and higher complexity, so it is more suitable for engineering applications. In addition, the fractional-order chaotic map can be controlled for different periodic orbits by the improved nonlinear mapping on the wavelet function. Full article

Stress is the body’s response to something that requires action or attention. In general, anything that poses a real challenge or threat to a person’s well-being can cause stress. Stress can slow down a person’s well-being activities. Often, you might not know whether you are stressed, if you are under too much stress, or when it is time to seek help. This paper presents a mathematical model with time delay subject to a person’s stress for early stress detection to assess whether a person is stress-free, has stress but is undetected, or has stress in any specific state such as minor, moderate, or severe stress. Being more alert to the effects of stress and reducing the uncertainty of undetected stress, or better, preventing it, may help people, especially teens, manage it more effectively and cope better, even a person happens to be stressed. The model can be extended to study the effects of multiple stress factors in light of the prolonged COVID-19 pandemic on people’s mental stress. Full article

Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions g, such that $|arg\left\{g^{\prime }\left(z\right)\right\}| <{\displaystyle \frac{\alpha \pi }{2}}$ in the open unit disk $\Delta$ where $0<\alpha <2$. Our results include the results of Mocanu, Nunokawa and others on the Libera transform. Full article

We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics, and thus, bypasses the constraints imposed by the Kochen–Specker theorem and its subsequent reformulations. We notice that these renowned theorems crucially rely on the implicitly assumed existence of an absolute frame of reference with respect to which physically indistinguishable tests related by spurious gauge transformations can supposedly be assigned well-defined distinct identities. We observe that the existence of such an absolute frame of reference is not required by fundamental physical principles, and hence, assuming it is an unnecessarily restrictive demand. Full article

Measures generating classical orthogonal polynomials are determined by Pearson’s equation, whose parameters usually provide the positivity of the measures. The case of general complex parameters (nonstandard) is also of interest; the non-Hermitian orthogonality with respect to (now complex-valued) measures is considered on curves in $\mathbb{C}$. Some applications lead to multiple orthogonality with respect to a number of such measures. For a system of r orthogonality measures, the perfectness is an important property: in particular, it implies the uniqueness for the whole family of corresponding multiple orthogonal polynomials and the $(r+2)$-term recurrence relations. In this paper, we introduce a unified approach which allows to prove the perfectness of the systems of complex measures satisfying Pearson’s equation with nonstandard parameters. We also study the polynomials satisfying multiple orthogonality relations with respect to a system of discrete measures. The well-studied families of multiple Charlier, Krawtchouk, Meixner and Hahn polynomials correspond to the systems of measures defined by the difference Pearson’s equation with standard real parameters. Using the same approach, we verify the perfectness of such systems for general parameters. For some values of the parameters, discrete measures should be replaced with the continuous measures with non-real supports. Full article

We analyze the asymptotic behavior of infinite products of non-linear operators which take a non-empty, closed subset of a complete metric space into the space, taking into account summable computational errors. Our results can be applied in methods for solving convex feasibility and optimization problems. Full article

In this paper, we introduce a notion of free cofibrations of permutative categories. We show that each cofibration of permutative categories is a retract of a free cofibration. The main goal of this paper is to show that the natural model category of permutative categories is a left proper model category. Full article

Let A be a non-commutative prime ring with involution $\ast ,$ of characteristic $\ne 2\left(\mathrm{and}3\right),$ with Z as the center of A and $\Pi$ a mapping $\Pi :A\to A$ such that $[\Pi (x),x]\in Z$ for all (skew) symmetric elements $x\in A.$ If $\Pi$ is a non-zero CE-Jordan derivation of $A,$ then A satisfies $s_4,$ the standard polynomial of degree $4.$ If $\Pi$ is a non-zero CE-Jordan ∗-derivation of $A,$ then A satisfies $s_4$ or $\Pi \left(y\right)=\lambda (y-y^{*})$ for all $y\in A,$ and some $\lambda \in C,$ the extended centroid of $A.$ Furthermore, we give an example to demonstrate the importance of the restrictions put on the assumptions of our results. Full article

Second-order Ordinary Differential Equations (ODEs) with discontinuous forcing have numerous applications in engineering and computational sciences. The analysis of the solution spaces of non-homogeneous ODEs is difficult due to the complexities in multidimensional systems, with multiple discontinuous variables present in forcing functions. Numerical solutions are often prone to failures in the presence of discontinuities. Algebraic decompositions are employed for analysis in such cases, assuming that regularities exist, operators are present in Banach (solution) spaces, and there is finite measurability. This paper proposes a generalized, finite-dimensional algebraic analysis of the solution spaces of second-order ODEs equipped with periodic Dirac delta forcing. The proposed algebraic analysis establishes the conditions for the convergence of responses within the solution spaces without requiring relative smoothness of the forcing functions. The Lipschitz regularizations and Lebesgue measurability are not considered as preconditions maintaining generality. The analysis shows that smooth and locally finite responses can be admitted in an exponentially stable solution space. The numerical analysis of the solution spaces is computed based on combinatorial changes in coefficients. It exhibits a set of locally uniform responses in the solution spaces. In contrast, the global response profiles show localized as well as oriented instabilities at specific neighborhoods in the solution spaces. Furthermore, the bands of the expansions–contractions of the stable response profiles are observable within the solution spaces depending upon the values of the coefficients and time intervals. The application aspects and distinguishing properties of the proposed approaches are outlined in brief. Full article

Due to the importance of cutting-edge nanomaterials applications in energy generation and storage devices, electrochemical impedance spectroscopy (EIS) has been adopted to fully understand the electronic and chemical reactions occurring inside these emerging technologies. Electronic behavior can be correlated with electrochemical properties such as electron transfer resistance, rate of mass diffusion, and the number of electrons in the electrochemical reaction. Although there is a lot of information about the electronic diagrams and methods for parameter estimation, some readers have difficulty analyzing and interpreting EIS curves. Thus, this work proposed using a heuristic approach and genetic algorithms to successfully estimate the resistance and capacitance value of a previously defined circuit model. To assess the potential of the genetic algorithm in electrochemical parameters estimation, we carried out practical measurements with known elements, and then the experimental and theoretical values were compared. Furthermore, the versatility and effectiveness of the algorithm were validated by determining the parameters in an Li-ion battery. The results revealed that the heuristic genetic algorithm (HGA) is a powerful tool for EIS parameters estimation because it can handle large below and upper limits with more pragmatic results in a shorter computational time. Full article

The use of enormous amounts of material is required for production. Due to the current emphasis on the environment and sustainability of materials, waste products and by-products, including silica fume and fly ash (FA), are incorporated into concrete as a substitute partially for cement. Additionally, concrete fine aggregate has indeed been largely replaced by waste materials like crumb rubber (CR), thus it reduces the mechanical properties but improved some other properties of the concrete. To decrease the detrimental effects of the CR, concrete is therefore enhanced with nanomaterials such nano silica (NS). The concrete mechanical properties are essential for the designing and constRuction of concrete structures. Concrete with several variables can have its mechanical characteristics predicted by an artificial neural network (ANN) technique. Using ANN approaches, this paper predict the mechanical characteristics of concrete constructed with FA as a partial substitute for cement, CR as a partial replacement for fine aggregate, and NS as an addition. Using an artificial neural network (ANN) technique, the mechanical characteristics investigated comprise splitting tensile strength (Fs), compressive strength (Fc), modulus of elasticity (Ec) and flexural strength (Ff). The ANN model was used to train and test the dataset obtained from the experimental program. Fc, Fs, F_f and Ec were predicted from added admixtures such as CR, NS, FA and curing age (P). The modelling result indicated that ANN predicted the strength with high accuracy. The proportional deviation mean (MoD) values calculated for F_c, F_s, F_f and E_c values were −0.28%, 0.14%, 0.87% and 1.17%, respectively, which are closed to zero line. The resulting ANN model’s mean square error (MSE) values and coefficient of determination (R²) are 6.45 × 10⁻² and 0.99496, respectively. Full article

This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo’s fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann–Liouville fractional variable-order problem to equivalent standard Riemann–Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results. Full article

In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor’s series expansion and Von Neumann’s stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so. Full article

In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft compactness, soft Lindelofness, soft connectedness, soft regularity, soft normality, soft almost regularity, soft mild normality, soft almost compactness, soft almost Lindelofness, soft near compactness, soft near Lindelofness, soft paracompactness, soft near paracompactness, soft almost paracompactness, and soft metacompactness are obtained. In addition to these, the study deals with the correlation between our new concepts in soft topology and their corresponding concepts in general topology; as a result, we show that soft complete continuity (resp. soft strong continuity) in soft topology is an extension of complete continuity (resp. strong continuity) in soft topology. Full article

Using a multi-criteria decision support method (WASPAS) to analyze and rank alternatives, this article proposes a method to assist in the selection of helicopter models that are the most suitable for police air activity in the State of Rio de Janeiro. A robust technical basis for defining the essential requirements of an aircraft is established, and solutions that can ensure the effective and safe execution of missions are indicated. Helicopter models were evaluated by considering predefined criteria, and the weights of these criteria were attributed using a questionnaire that was administered to pilots and aerostatic operators of Public Air Units (UAP) in several states of the federation. As a result of the evaluation of the 15 helicopter models used by police services in the State of Rio de Janeiro, the modeling with the WASPAS method ranked the Sikorsky UH-60 (Black Hawk) model in first place, the Leonardo AW 139 model in second place, and the Bell 412 model in third place. Based on the available data, we suggest that a comparative study integrating the Entropy and CRITIC methods be conducted to measure the weights of the criteria associated with the application of other multi-criteria techniques, such as COMET, MACAB, SPOTIS, VIKOR, SAPEVO, and PROMETHEE. Full article

In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled dynamical system from a given reference signal. We assume that the two decision-makers do not cooperate. Under these conditions, we state the considered tracking problem as a problem of finding a Nash equilibrium strategy for a stochastic differential game. Explicit formulae of a Nash equilibrium strategy are provided. To this end, we use the solutions of two given terminal value problems (TVPs). The first TVP is associated with a hybrid system formed by two backward nonlinear differential equations coupled by two algebraic nonlinear equations. The second TVP is associated with a hybrid system formed by two backward linear differential equations coupled by two algebraic linear equations. Full article

The spread of COVID-19 started in late December 2019 and is still ongoing. Many countries around the world have faced an outbreak of COVID-19, including Thailand, which must keep an eye on the spread and find a way to deal with this extreme outbreak. Of course, we are unable to determine the number of people who will contract this disease in the future. Therefore, if there is a tool that helps to predict the outbreak and the number of people infected, it will be able to find preventive measures in time. This paper aims to develop a mathematical model suitable for the lifestyle of the Thai population facing the COVID-19 situation. It has been established that after close contact with an infected person, a group of individuals will be quarantined and non-quarantined. If they contract COVID-19, they will enter the incubation period of the infection. The incubation period is divided into the quarantine class and the exposed class. Afterwards, both classes will move to the hospitalized infected class and the infected class, wherein the infected class is able to spread the disease to the surrounding environment. This study describes both classes in the SQEIRP model based on the population segmentation that was previously discussed. After that, the positive and bounded solutions of the model are examined, and we consider the equilibrium point, as well as the global stability of the disease-free point according to the Castillo-Chavez method. The SQEIRP model is then numerically analyzed using MATLAB software version R2022a. The cumulative percentage of hospitalized and non-hospitalized infections after 7 days after the commencement of the infection was determined to be 11 and 34 percent of the entire population, respectively. The Next-Generation Matrix approach was used to calculate the Basic Reproduction Numbers ($R_0$). The SQEIRP model’s $R_0$ was 3.78, indicating that one infected individual can result in approximately three additional infections. The results of this SQEIRP model provide a preliminary guide to identifying trends in population dynamics in each class. Full article

Using biometric modalities for person recognition is crucial to guard against impostor attacks. Commonly used biometric modalities, such as fingerprint scanners and facial recognition, are effective but can easily be tampered with and deceived. These drawbacks have recently motivated the use of electroencephalography (EEG) as a biometric modality for developing a recognition system with a high level of security. The majority of existing EEG-based recognition methods leverage EEG signals measured either from many channels or over a long temporal window. Both set limits on their usability as part of real-life security systems. Moreover, nearly all available methods use hand-engineered techniques and do not generalize well to unknown data. The few EEG-based recognition methods based on deep learning suffer from an overfitting problem, and a large number of model parameters must be learned from only a small amount of available EEG data. Leveraging recent developments in deep learning, this study addresses these issues and introduces a lightweight convolutional neural network (CNN) model consisting of a small number of learnable parameters that enable the training and evaluation of the CNN model on a small amount of available EEG data. We present a robust and efficient EEG-based recognition system using this CNN model. The system was validated on a public domain benchmark dataset and achieved a rank-1 identification result of 99% and an equal error rate of authentication performance of 0.187%. The system requires only two EEG channels and a signal measured over a short temporal window of 5 s. Consequently, this method can be used in real-life settings to identify or authenticate biometric security systems. Full article

In the predator–prey system, predators can affect the prey population by direct killing and predation fear. In the present study, we consider a delayed predator–prey model with fear and Beddington–DeAngelis functional response. The model incorporates not only the fear of predator on prey with an intraspecific competition relationship, but also fear delay and pregnancy delay. Apart from the local stability analysis of the equilibrium points of the model, we find that time delay can change the stability of the system and cause Hopf bifurcation. Taking time delay as the bifurcation parameter, the critical values of delays in several cases are derived. In addition, we extend it to the random environment and study the stochastic ultimate boundedness of the stochastic process. Finally, our theoretical results are validated by numerical simulation. Full article

Functional epistemology is about ways to access functional objects by using varieties of methods and procedures. Not all such means are equally capable of reproducing these functions in the desired consistency and resolution. Dyson’s argument against the perturbative expansion of quantum field theoretic terms, in a radical form (never pursued by Dyson), is an example of epistemology taken as ontology. Full article

This study points out a new explanation of the non-trading effect of financial derivatives from the perspective of hedging demand. We examine the influence of hedging demand on the non-trading effect of TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) Futures. By dividing the sample period into trading period and non-trading period and testing the difference between the risk premiums in these two intervals, we find that there is a non-trading effect in TAIEX Futures, which means that the holding returns of TAIEX Futures in the non-trading period are higher than those in the trading period. By estimating a dummy-regression model, the evidence shows that when the VIX (Taiwan Index Option Volatility Index) indicator is relatively high, the non-trading effect will be more significant, indicating that the non-trading effect may come from investors’ hedging needs. In addition, it is found that when the futures index is higher than the spot index, the non-trading effect becomes less obvious. The possible reason is that when there is a positive spread in index futures, investors will expect a bull market, thus reducing the hedging demand of index futures. In the end, we find that the liquidity in the after-hours trading session is poor, resulting in high hedging costs, and forcing investors to hedge during the regular trading period. Therefore, the after-hours trading of TAIEX Futures fails to reduce the non-trading effect. Full article

This paper provides a meta-heuristic hybridized version called multi-objective golden flower pollination algorithm (MOGFPA) as the best method for choosing the optimal reconfiguration for distribution networks (DNs) in order to reduce power losses (PLs). Aside from PLs, another parameter is considered: the load balance index (LBI). The expression for the LBI is stated using real and reactive indices. It makes the optimal distributed generation (DG) placement and DN routing of the multi-objective (MO) problem have PLs and the LBI as the main parameters that need to be optimized. For that purpose, the MOGFPA is proposed in this paper. The MOGFPA consists of a golden search (GS) and tangent flight with Pareto distribution that only needs a few tuning parameters. Therefore, it is simple to alter these parameters to reach the best values compared to other existing methodologies. Its performance is predicted using different case studies on multiple test bus systems, namely the IEEE systems such as 33, 69, 119, and Indian 52 bus. Through simulation outcomes, the MOGFPA computes the optimum distribution of DG units and reconfigures the DNs with the aim of minimal PLs and LBI. Furthermore, another state-of-the-art technology and comparing convergence charts provide optimal outputs in less time, with minimum iterations. Full article

In this work, we consider weakly generalized operators, which extend the Geraghty mappings that are studied with regard to the existence and uniqueness of their fixed points, in the setting offered by strong b-metric spaces. Classic results are obtained as corollaries. An example is provided to support these outcomes. Full article

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calculate certain infinite sums and study the properties of zeroes of a few analytical functions. On many occasions, this enables to facilitate the obtaining of known results thus having important methodological meaning. Additionally, some new results, to the best of our knowledge, are also obtained in this way. For example, we established new properties of the sum of inverse zeroes of a digamma function, new formulae for the sums ${\displaystyle \sum _{}^{}\frac{k_i}{{\rho }_i^2}}$ for zeroes ρ_i of incomplete gamma and Riemann zeta functions having the order k_i (These results can be straightforwardly generalized for the sums ${\displaystyle \sum _{}^{}\frac{k_i}{{\rho }_i^n}}$ with integer n > 2, and so on.) Full article

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model. Full article

One of the most severe problems in power plants, petroleum and petrochemical industries is the accurate determination of phase fractions in two-phase flows. In this paper, we carried out experimental investigations to validate the simulations for water–air, two-phase flow in an annular pattern. To this end, we performed finite element simulations with COMSOL Multiphysics, conducted experimental investigations in concave electrode shape and, finally, compared both results. Our experimental set-up was constructed for water–air, two-phase flow in a vertical tube. Afterwards, the simulated models in the water–air condition were validated against the measurements. Our results show a relatively low relative error between the simulation and experiment indicating the validation of our simulations. Finally, we designed an Artificial Neural Network (ANN) model in order to predict the void fractions in any two-phase flow consisting of petroleum products as the liquid phase in pipelines. In this regard, we simulated a range of various liquid–gas, two-phase flows including crude oil, oil, diesel fuel, gasoline and water using the validated simulation. We developed our ANN model by a multi-layer perceptron (MLP) neural network in MATLAB 9.12.0.188 software. The input parameters of the MLP model were set to the capacitance of the sensor and the liquid phase material, whereas the output parameter was set to the void fraction. The void fraction was predicted with an error of less than 2% for different liquids via our proposed methodology. Using the presented novel metering system, the void fraction of any annular two-phase flow with different liquids can be precisely measured. Full article