Mathematics

This manuscript considers the design of a slotted adaptive hydrostatic thrust bearing with a regulator of the lubricant output flow. A theoretical study of its static and dynamic characteristics was carried out. The aim of the study was to test the reliability of the hypothesis concerning the possibility of obtaining a stable-to-oscillation adaptive thrust bearing of negative compliance, avoiding the need for a complex system of external combined throttling by replacing it with a simple slotted throttle. Mathematical modeling of the thrust bearing movement was carried out. The possibility of reducing the compliance to negative values is shown, providing the bearing with an adaptive function, consisting of using the structure as a bearing and as an active deformation compensator of the elastic system of a metal-cutting machine in order to improve the quality of the metalwork. Analysis of load static characteristics showed that negative compliance is provided over a wide range of loads, which can be up to 75% or more of the range of permissible bearing loads. Based on the study of dynamic characteristics, it was concluded that with a targeted selection of parameters that have a major effect on the dynamics of the structure, the considered adaptive hydrostatic thrust bearing can attain a very high quality of dynamics. It is shown that the viscous damping of the lubricating film enclosed in the gaps and the damping of the material of the elastic ring of the regulator are important resources for ensuring the optimal dynamics of the thrust bearing. Full article

In this paper, we study the effect of the introduction of a time delay on the dynamics of toxoplasmosis. This time delay is the elapsed time from when oocysts become present in the environment and when they become infectious. We construct a mathematical model that includes cats and oocysts in the environment. We include the effect of oocysts, since they are crucial for the dynamics of toxoplasmosis. The likelihood of the acquisition of Toxoplasma Gondii infection depends on the environmental load of the parasite. Furthermore, the model considers the possibility of vaccination of the feline host. In the mathematical model, we consider directly the infection of cats through the oocysts shed by other cats. We prove that the basic reproduction number ${\mathcal{R}}_0$ is a secondary parameter that determines the global dynamics of toxoplasmosis in cat populations. We study the effect of the time delay on the stability of the steady states. We find that the time delay cannot change the stability of the endemic state, which is an important result from the biological point of view. Numerical simulations are performed to support the theoretical results and obtain further insight into understanding toxoplasmosis dynamics in cat populations. Full article

Bivariate continuous negatively correlated proportional data defined in the unit square ${(0,1)}^2$ often appear in many different disciplines, such as medical studies, clinical trials and so on. To model this type of data, the paper proposes two new bivariate continuous distributions (i.e., negatively correlated proportional inverse Gaussian (NPIG) and negatively correlated proportional gamma (NPGA) distributions) for the first time and provides corresponding distributional properties. Two mean regression models are further developed for data with covariates. The normalized expectation–maximization (N-EM) algorithm and the gradient descent algorithm are combined to obtain the maximum likelihood estimates of parameters of interest. Simulations studies are conducted, and a data set of cortical thickness for schizophrenia is used to illustrate the proposed methods. According to our analysis between patients and controls of cortical thickness in typical mutual inhibitory brain regions, we verified the compensatory of cortical thickness in patients with schizophrenia and found its negative correlation with age. Full article

Prognostics and health management (PHM) applications can prevent engines from potential serious accidents by predicting the remaining useful life (RUL). Recently, data-driven methods have been widely used to solve RUL problems. The network architecture has a crucial impact on the experiential performance. However, most of the network architectures are designed manually based on human experience with a large cost of time. To address these challenges, we propose a neural architecture search (NAS) method based on gradient descent. In this study, we construct the search space with a directed acyclic graph (DAG), where a subgraph represents a network architecture. By using softmax relaxation, the search space becomes continuous and differentiable, then the gradient descent can be used for optimization. Moreover, a partial channel connection method is introduced to accelerate the searching efficiency. The experiment is conducted on C-MAPSS dataset. In the data processing step, a fault detection method is proposed based on the k-means algorithm, which drops large valueless data and promotes the estimation performance. The experimental result shows that our method achieves superior performance with the highest estimation accuracy compared with other popular studies. Full article

This paper proposes a novel variant of the Grey Wolf Optimization (GWO) algorithm, named Velocity-Aided Grey Wolf Optimizer (VAGWO). The original GWO lacks a velocity term in its position-updating procedure, and this is the main factor weakening the exploration capability of this algorithm. In VAGWO, this term is carefully set and incorporated into the updating formula of the GWO. Furthermore, both the exploration and exploitation capabilities of the GWO are enhanced in VAGWO via stressing the enlargement of steps that each leading wolf takes towards the others in the early iterations while stressing the reduction in these steps when approaching the later iterations. The VAGWO is compared with a set of popular and newly proposed meta-heuristic optimization algorithms through its implementation on a set of 13 high-dimensional shifted standard benchmark functions as well as 10 complex composition functions derived from the CEC2017 test suite and three engineering problems. The complexity of the proposed algorithm is also evaluated against the original GWO. The results indicate that the VAGWO is a computationally efficient algorithm, generating highly accurate results when employed to optimize high-dimensional and complex problems. Full article

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution based on a characterization of the cumulative distribution function (CDF). The new tests are of weighted L²-type depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a broad class of alternative distributions. These results guarantee that the parametric bootstrap procedure, which we employ to implement the test, is asymptotically valid and that the whole test procedure is consistent. A comparative simulation study for finite sample sizes shows that the new procedure is competitive to classical and recent tests, outperforming these other methods almost uniformly over a large set of alternative distributions. The use of the newly proposed test is illustrated with two observed data sets. Full article

Music is considered a powerful brain stimulus, as listening to it can activate several brain networks. Music of different kinds and genres may have a different effect on the human brain. The goal of this study is to investigate the change in the brain’s functional connectivity (FC) when music is used as a stimulus. Secondly, the effect of listening to the subject’s favorite music is compared with listening to specifically formulated relaxing music with alpha binaural beats. Finally, the effect of the duration of music listening is studied. Subjects’ electroencephalographic (EEG) signals were captured as they listened to favorite and relaxing music. After preprocessing and artifact removal, the EEG recordings were decomposed into the delta, theta, alpha, and beta frequency bands, and the grand-averaged connectivity matrices were generated using Inter-Site Phase Clustering (ISPC) for each frequency band and each type of music. Furthermore, each lobe of the brain was analyzed separately to understand the effect of music on specific regions of the brain. EEG-FC among different channels was accessed by using graph theory and Network-based Statistics (NBS). To determine the significance of the changes in brain networks after listening to music, statistical analysis was conducted using Analysis of Variance (ANOVA) and t-test. The study of listening to music for a short duration verifies that either favorite or preferred music can affect the FC of the subject and induce a relaxation state. The short duration study also verifies a significant (ANOVA and t-test: p < 0.05) effectiveness of relaxing music over favorite music to induce relaxation and alertness in the subject. In the study of long duration, it is concluded that listening to relaxing music can increase functional connectivity and connections strength in the frontal lobe of the subject. A significant increase (ANOVA and t-test: p < 0.05) in FC in alpha and theta band and a significant decrease (ANOVA and t-test: p < 0.05) in FC in beta band in the frontal and parietal lobe of the brain verifies the hypothesis that the relaxing music can help the subject to achieve relaxation, activeness, and alertness. Full article

The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Then, the system of ODEs is solved numerically using the MATLAB software. The impacts of different parameters, such as copper nanoparticles volume fraction, radiation, rotation, unsteadiness, and stretching parameters are graphically displayed. It is found that two solutions exist for the flow induced by the stretching sheet. Furthermore, the increasing nanoparticle volume fraction enhances the skin friction coefficient. It is noticed that the skin friction coefficient, as well as the heat transfer rate at the surface, decrease as the rotating parameter increases. Additionally, the thermal radiation as well as the unsteadiness parameter stimulate the temperature. Full article

The production management system in Industry 4.0 is emphasizes the improvement of productivity within limited constraints by sustainable production planning models. To accomplish this, several approaches are used which include lean manufacturing, kaizen, smart manufacturing, flexible manufacturing systems, cyber–physical systems, artificial intelligence, and the industrial Internet of Things in the present scenario. These approaches are used for operations management in industries, and specifically productivity maximization with cleaner shop floor environmental management, and issues such as worker safety and product quality. The present research aimed to develop a methodology for cleaner production management using lean and smart manufacturing in industry 4.0. The developed methodology would able to enhance productivity within restricted resources in the production system. The developed methodology was validated by production enhancement achieved in two case study investigations within the automobile manufacturing industry and a mining machinery assembly unit. The results reveal that the developed methodology could provide a sustainable production system and problem-solving that are key to controlling production shop floor management in the context of industry 4.0. It is also capable of enhancing the productivity level within limited constraints. The novelty of the present research lies in the fact that this type of methodology, which has been developed for the first time, helps the industry individual to enhance production in Industry 4.0 within confined assets by the elimination of several problems encountered in shop floor management. Therefore, the authors of the present study strongly believe that the developed methodology would be beneficial for industry individuals to enhance shop floor management within constraints in industry 4.0. Full article

In this study, an optimization algorithm called chaotic turbulent flow of water-based optimization (CTFWO) algorithm is proposed to find the optimal solution for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a complicated, mixed-integer nonlinear optimization problem, comprising control variables which are discrete and continuous. The CTFWO algorithm is used to minimize voltage deviation (VD) and real power loss (P_loss) for IEEE 30-bus and IEEE 57-bus power systems. These goals can be achieved by obtaining the optimized voltage values of the generator, the transformer tap changing positions, and the reactive compensation. In order to evaluate the ability of the proposed algorithm to obtain ORPD problem solutions, the results of the proposed CTFWO algorithm are compared with different algorithms, including artificial ecosystem-based optimization (AEO), the equilibrium optimizer (EO), the gradient-based optimizer (GBO), and the original turbulent flow of water-based optimization (TFWO) algorithm. These are also compared with the results of the evaluated performance of various methods that are used in many recent papers. The experimental results show that the proposed CTFWO algorithm has superior performance, and is competitive with many state-of-the-art algorithms outlined in some of the recent studies in terms of solution accuracy, convergence rate, and stability. Full article

The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach (MWFA). In order to use the MWFA, an integral over a full rotation period needs to be computed. Nevertheless, this typically requires the performance of numerical integration, and thus it is affected by integration error, requires relatively high computational effort and, at the same time, it does not easily allow for performance of the analysis of the inductance harmonics. In this work, an exact analytical solution to the MWFA equation is provided in a form that allows to highlight the harmonic content of the inductances. After a thorough mathematical derivation of the solution, a numerical investigation is proposed for verification purposes. Full article

We consider the Steffensen–Hayashi inequality and remainder identity for $\mathcal{V}$-fractional differentiable functions involving the six parameters truncated Mittag–Leffler function and the Gamma function. In view of these, we obtain some integral inequalities of Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, and Grüss type to the $\mathcal{V}$-fractional calculus. Full article

This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number $R_0$. We calculated the analytic solutions by HPM (homotopy perturbation method) and used Mathematica 12 software for numerical analysis up to 8th order approximation. It checked the error values of the approximation while the system has residual error, absolute error and h curve initial derivation of square error at up to 8th order approximation. The basic reproduction number ranges between $0.8454$ and $2.0317$ to form numerical simulation, it helps to identify the whole system fluctuations. Finally, our proposed model validated (from real life data) the highly affected five states of COVID-19 and the Omicron variant. The algorithm guidelines are used for international arrivals, with Omicron variant cases updated by the Union Health Ministry in January 2022. Right now, the third wave is underway in India, and we conclude that it may peak by the end of May 2022. Full article

Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index $\left(n\right)$. Elevation in the Nusselt number for the shear thinning case $\left(\mathrm{i}.\mathrm{e}., n=0.5\right)$ adheres as compared to Newtonian $\left(\mathrm{i}.\mathrm{e}., n=1\right)$ and shear thickening cases $\left(\mathrm{i}.\mathrm{e}., n=1.5\right)$. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain. Full article

The teaching of mathematics has always concerned all the professionals involved in engineering degrees. Curently students have less interest in these studies, what has caused an increase of this concern. The lack of awareness of students about the significance of mathematics in their careers, provoke the decrease of undergraduate students’ motivation, which derives in a low interest in engineering degrees. The aim of this work is that engineering students achieve a greater motivation and involvement in first academic courses, through the implementation of real and technological applications related to their degrees in the learning of mathematical concepts. To this end, the 2019/2020 and 2020/2021 academics years, the seminar “Applications of Multivariable Calculus in Engineering” has been held in Universitat Politècnica de Catalunya-BarcelonaTech (UPC), based on the teaching of Multivariable Calculus by the execution of real problems where calculus concepts are necessary to solve them. With the aim of analyzing students’ motivation and assessment of the seminar, anonymous surveys and personal interviews have been conducted. The number of attending students to the sessions in each academic year has been 16 and all of them have been participants in the surveys and interviews. The results show that students’ responses were generally positive and they agree that their motivation to the subject Multivariable Calculus has increased with the use of real applications of mathematics. The execution of practical problems with engineering applications improves the acquirement of mathematical concepts, what could imply an increase of students’ performance and a decrease of the dropout in the first academic courses of engineering degrees. Full article

The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions $\{B_t^H,t\ge 0\}$ and sub-fractional Brownian motions $\{{\xi }_t^H,t\ge 0\}$ with Hurst parameter $H\in (\frac{1}{2},1)$. We start by establishing the connection between a fPDE and SDE via the Feynman–Kac Theorem, which provides a stochastic representation of a general Cauchy problem. In hindsight, we extend this connection by assuming SDEs with fractional- and sub-fractional Brownian motions and prove the generalized Feynman–Kac formulas under a (sub-)fractional Brownian motion. An application of the theorem demonstrates, as a by-product, the solution of a fractional integral, which has relevance in probability theory. Full article

This paper presents a novel adaptive sliding mode controller for a class of robot manipulators with unknown disturbances and system failures, which can well achieve the asymptotic tracking, and avoid some possible singularity problems. A new virtual controller is designed such that the chosen Lyapunov function can be transformed into a non-Lipschitz function, based on which, the system states can arrive at the specified sliding surface within a finite time regardless of the existence of system failures/faults. By fusing an integral fast terminal nonsingular SMC and a robust adaptive technique, the tracking error can be steered into a preset range in a set time and some possible singularity problems are avoided elegantly. With our proposed scheme, the loss coefficient is well estimated, and the stability of the system can be guaranteed even in the presence of the total loss of actuator outputs. The experiment and simulation results are presented to illustrate the effectiveness of the proposed control scheme. Full article

In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion equation to represent the evolution of the temperature in the soil. The thermal interaction between the vegetation cover and the soil is studied and the distribution of temperatures in the soil with depth is also obtained. The vegetation cover acts in this model as a dynamic and diffusive boundary condition for the soil. The developed model takes into account the latent heat of fusion, which appears when the transformation of ice into liquid water or vice versa occurs inside the soil. The numerical approach for the solution of the mathematical model conducted in this work is based on the finite volume method with Weighted Essentially Non-Oscillatory technique for spatial reconstruction and the third-order Runge–Kutta Total Variation Diminishing numerical scheme is used for time integration, which is very efficient to obtain the numerical solution of this type of model. Some numerical examples are solved to obtain the distribution of temperature both in the vegetation cover and the soil. Full article

Non-linear activation functions are integral parts of deep neural architectures. Given the large and complex dataset of a neural network, its computational complexity and approximation capability can differ significantly based on what activation function is used. Parameterizing an activation function with the introduction of learnable parameters generally improves the performance. Herein, a novel activation function called Sinu-sigmoidal Linear Unit (or SinLU) is proposed. SinLU is formulated as $SinLU\left(x\right)=(x+asinbx)·\sigma \left(x\right)$, where $\sigma \left(x\right)$ is the sigmoid function. The proposed function incorporates the sine wave, allowing new functionalities over traditional linear unit activations. Two trainable parameters of this function control the participation of the sinusoidal nature in the function, and help to achieve an easily trainable, and fast converging function. The performance of the proposed SinLU is compared against widely used activation functions, such as ReLU, GELU and SiLU. We showed the robustness of the proposed activation function by conducting experiments in a wide array of domains, using multiple types of neural network-based models on some standard datasets. The use of sine wave with trainable parameters results in a better performance of SinLU than commonly used activation functions. Full article