Artificial neural network scheme to solve the hepatitis B virus model

This article aims to describe the simulation studies of the hepatitis B virus non-linear system using supervised neural networks procedures supported by Levenberg-Marquardt back propagation methodology. The proposed strategy has five distinct quantities: susceptible X(t), symptomatic infections Y(t), chronic infections W(t), recovered population R(t), and a population that has received vaccinations Z(t). The reference data set for all three distinct cases has been obtained utilizing the ND-Solver and Adams method in Mathematica software. The outcomes have been validated with performance plots for all cases. To check the accuracy and effectiveness of proposed methodology mean square error has are presented. State transition, and regression plots are illustrated to elaborated the testing, training, and validation methodology. Additionally, absolute errors for different components of hepatitis B virus model are demonstrated to depict the error occurring during distinct cases. Whereas the data assigned to training is 81%, and 9% for each testing and validation. The mean square error for all three cases is 10−12 this show the accuracy and correctness of proposed methodology

FEM analysis of the impact of surface undulations on the natural convective flow of viscous fluid in a permeable trapezoidal enclosure

Examination of the transport mechanism in a permeable trapezoidal enclosure with an undulation effect is commenced. A formulation describing naturally convective flow in a permeable domain is conceded by employing Boussinesq and Darcy approximations. Uniform temperature is provided at the circular cylinder and base wall of the enclosure, whereas non-parallel side extremities are kept cold. No heat flux condition is applied at a wavy surface (upper) to maintain the potential difference in temperature for generation of convection. A finite element scheme is opted to resolve the governing system for accounted physical problems. The grid sensitivity test is also executed to assure the credibility of the code and results. A wide range of physical parameters is selected to comprehend their impact on streamlines and isotherm patterns. Results are revealed comparatively for zero undulation (upper solid straight wall) and with undulations (wavy wall). Heat flux and kinetic energy are also enumerated as key quantities against concerning parameters. It is depicted that the average Nusselt number and kinetic energy are more in the absence of undulations than when it is present. Additionally, it is manifested that the placement of a heated cylinder helps transfer heat in the domain and the production of thermal convective potential

Some well known inequalities for (h1, h2)-convex stochastic process via interval set inclusion relation

This note introduces the concept of (h1, h2)-convex stochastic processes using intervalvalued functions. First we develop Hermite-Hadmard (H.H) type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for (h1, h2)-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.http://www.aimspress.com/journal/MathMathematics and Applied Mathematic

Novel decision aid model for green supplier selection based on extended EDAS approach under pythagorean fuzzy Z-numbers

The main objective of this study is to identify the green suppliers that would most effectively assist manufacturing producers in implementing green manufacturing production while including uncertainty and reliability in their decision-making. For this firstly, we justify and manifest the idea of Pythagorean Fuzzy Z-numbers (PyFZNs). It has significant implications for improving the effectiveness of decision-making processes in several theories of uncertainty. It can more flexibly explain real-world data and human cognition due to its capacity to express imprecise and reliable information. Thus it is a more accurate mathematical tool for addressing accuracy and uncertainty. Secondly, we defined the Pythagorean fuzzy Z-number arithmetic aggregation operators and geometric aggregation operators. Thirdly, based on the proposed operators and EDAS (Evaluation based on distance from average solution) approach, a fast decision model is designed to deal with the issue of multi-criteria decision-making. Finally, using PyFZN data we also provide a numerical example to demonstrate the usability of the created multicriteria decision-making (MDM) approach. Moreover, a case study also proves its efficacy

Study of optical stochastic solitons of Biswas-Arshed equation with multiplicative noise

In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero

Collapsing cylindrically symmetric filamentary stellar object

This work investigates the collapsing behavior of filamentary objects under the influence of dark matter. For this purpose, we use f(R, T) gravity as a candidate for dark matter. The collapse equation is obtained by imposing the Darmois junction condition at the collapsing boundary. At the collapsing boundary, it is observed that the radial pressure is non-zero and is proportional to the field time-dependent component. Finally, we check the relationship between gravitational waves and dark source terms. It is concluded that the dark source terms disrupt the propagation of gravitational waves

Multiple attribute decision-making based on Fermatean fuzzy number

Multiple attribute decision-making concerns with production significant in our everyday life. To resolve the problems that decision makers might feel uncertain to choose the suitable assessment values among several conceivable ideals in the procedure. Fuzzy model, and its extensions are extensively applied to MADM problems. In this study, we proposed an innovative Schweizer-Sklar t-norm and t-conorm operation of FFNs, Fermatean fuzzy Schweizer-Sklar operators. They were used as a framework for the development of an MCDM method, which was illustrated by an example to demonstrate its effectiveness and applicability. Finally, a complete limitation study, rational examination, and comparative analysis of the presented approaches has been exhibited, we originate that our technique is superior in offering DMs a better decision-making choice and reducing the restrictions on stating individual partialities

Lane Line Detection and Object Scene Segmentation Using Otsu Thresholding and the Fast Hough Transform for Intelligent Vehicles in Complex Road Conditions

An Otsu-threshold- and Canny-edge-detection-based fast Hough transform (FHT) approach to lane detection was proposed to improve the accuracy of lane detection for autonomous vehicle driving. During the last two decades, autonomous vehicles have become very popular, and it is constructive to avoid traffic accidents due to human mistakes. The new generation needs automatic vehicle intelligence. One of the essential functions of a cutting-edge automobile system is lane detection. This study recommended the idea of lane detection through improved (extended) Canny edge detection using a fast Hough transform. The Gaussian blur filter was used to smooth out the image and reduce noise, which could help to improve the edge detection accuracy. An edge detection operator known as the Sobel operator calculated the gradient of the image intensity to identify edges in an image using a convolutional kernel. These techniques were applied in the initial lane detection module to enhance the characteristics of the road lanes, making it easier to detect them in the image. The Hough transform was then used to identify the routes based on the mathematical relationship between the lanes and the vehicle. It did this by converting the image into a polar coordinate system and looking for lines within a specific range of contrasting points. This allowed the algorithm to distinguish between the lanes and other features in the image. After this, the Hough transform was used for lane detection, making it possible to distinguish between left and right lane marking detection extraction; the region of interest (ROI) must be extracted for traditional approaches to work effectively and easily. The proposed methodology was tested on several image sequences. The least-squares fitting in this region was then used to track the lane. The proposed system demonstrated high lane detection in experiments, demonstrating that the identification method performed well regarding reasoning speed and identification accuracy, which considered both accuracy and real-time processing and could satisfy the requirements of lane recognition for lightweight automatic driving systems

Importance of bioconvection flow on tangent hyperbolic nanofluid with entropy minimization

The amalgamation of microorganisms in the nanofluid is significant in beautifying the thermal conductivity of several systems, such as microfluid devices, chip-shaped microdevices, and enzyme biosensors. The current investigation studies mixed convective flow of the entropy minimization of unsteady MHD tangent hyperbolic nanoliquid because a stretching surface has motile density via convective and slip conditions. For the novelty of this work, the variable transport characteristics caused by dynamic viscosity, thermal conductivity, nanoparticle mass permeability, and microbial organism diffusivity are considered. It is considered that the vertical sheet studying the flow. By using the appropriate alteration, the governing equations for the most recent flow analysis were altered into a non-dimension relation. Through MATLAB Software bvp4c, the PDE model equations have been made for these transformed equations. Engineering-relevant quantities against various physical variables include force friction, Nusselt number, Sherwood number, and microorganism profiles. The results showed good consistency compared to the current literature. Moreover, these outcomes revealed that augmentation in the magnitude of the magnetic field and velocity slip parameter declines the velocity profile. The reverse impact is studied in We. In addition, heat transfer is typically improved by the influence of thermal radiation parameters, Brownian movement, and thermophoretic force. The physical interpretation has existed through graphical and tabular explanations

Impact of irregular heat sink/source on the wall jet flow and heat transfer in a porous medium induced by a nanofluid with slip and buoyancy effects

In many industries, extremely high-performance cooling is a crucial requirement. However, the fundamental challenge to developing energy-efficient heat transfer fluids required for cooling is insufficient thermal conductivity. In this case, the utilization of nanofluid is effective to overcome these challenges. The current study aims to examine the two-dimensional (2D) stretching wall jet heat transfer fluid flow induced by a water-based alumina nanofluid embedded in a porous medium with buoyancy force. In addition, irregular heat sink/source and slip effects are assessed. The leading partial differential equations are changed into ordinary differential equations by incorporating similarity variables, then these equations are computationally or numerically worked out via the boundary-value problem of fourth-order (bvp4c) technique. The pertinent factors influencing the symmetry of the hydrothermal performance including friction factor, velocity, and temperature profiles, are illustrated using tables and graphs. The symmetrical outcomes reveal that the velocity declines in the presence of nanoparticles, whereas the temperature uplifts both assisting and opposing flows. Moreover, the friction factor augments due to porosity while the heat transfer rate declines