Showing papers in "Symmetry in 2022"

A Comparative Analysis of Fractional-Order Kaup-Kupershmidt Equation within Different Operators

Abstract: In this paper, we find the solution of the fractional-order Kaup–Kupershmidt (KK) equation by implementing the natural decomposition method with the aid of two different fractional derivatives, namely the Atangana–Baleanu derivative in Caputo manner (ABC) and Caputo–Fabrizio (CF). When investigating capillary gravity waves and nonlinear dispersive waves, the KK equation is extremely important. To demonstrate the accuracy and efficiency of the proposed technique, we study the nonlinear fractional KK equation in three distinct cases. The results are given in the form of a series, which converges quickly. The numerical simulations are presented through tables to illustrate the validity of the suggested technique. Numerical simulations in terms of absolute error are performed to ensure that the proposed methodologies are trustworthy and accurate. The resulting solutions are graphically shown to ensure the applicability and validity of the algorithms under consideration. The results that we obtain confirm that the proposed method is the best tool for handling any nonlinear problems arising in science and technology.

Analytical Investigation of Fractional-Order Korteweg-De-Vries-Type Equations under Atangana-Baleanu-Caputo Operator: Modeling Nonlinear Waves in a Plasma and Fluid

Abstract: This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three examples. It is also shown that the fractional and integer-order solutions have closed contact with the exact result. The suggested technique is found to be reliable, efficient, and straightforward to use for many related models of engineering and several branches of science, such as modeling nonlinear waves in different plasma models.

Lie Symmetries, Closed-Form Solutions, and Various Dynamical Profiles of Solitons for the Variable Coefficient (2+1)-Dimensional KP Equations

Abstract: This investigation focuses on two novel Kadomtsev–Petviashvili (KP) equations with time-dependent variable coefficients that describe the nonlinear wave propagation of small-amplitude surface waves in narrow channels or large straits with slowly varying width and depth and non-vanishing vorticity. These two variable coefficients, Kadomtsev–Petviashvili (VCKP) equations in (2+1)-dimensions, are the main extensions of the KP equation. Applying the Lie symmetry technique, we carry out infinitesimal generators, potential vector fields, and various similarity reductions of the considered VCKP equations. These VCKP equations are converted into nonlinear ODEs via two similarity reductions. The closed-form analytic solutions are achieved, including in the shape of distinct complex wave structures of solitons, dark and bright soliton shapes, double W-shaped soliton shapes, multi-peakon shapes, curved-shaped multi-wave solitons, and novel solitary wave solitons. All the obtained solutions are verified and validated by using back substitution to the original equation through Wolfram Mathematica. We analyze the dynamical behaviors of these obtained solutions with some three-dimensional graphics via numerical simulation. The obtained variable coefficient solutions are more relevant and useful for understanding the dynamical structures of nonlinear KP equations and shallow water wave models.

Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview

Abstract: In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter aM, which we calculate for the cases of f(R,ϕ) gravity, Chern–Simons-corrected f(R,ϕ) gravity, Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity. The exact form of aM is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for aM expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum.

Introducing Urdu Digits Dataset with Demonstration of an Efficient and Robust Noisy Decoder-Based Pseudo Example Generator

Abstract: In the present work, we propose a novel method utilizing only a decoder for generation of pseudo-examples, which has shown great success in image classification tasks. The proposed method is particularly constructive when the data are in a limited quantity used for semi-supervised learning (SSL) or few-shot learning (FSL). While most of the previous works have used an autoencoder to improve the classification performance for SSL, using a single autoencoder may generate confusing pseudo-examples that could degrade the classifier’s performance. On the other hand, various models that utilize encoder–decoder architecture for sample generation can significantly increase computational overhead. To address the issues mentioned above, we propose an efficient means of generating pseudo-examples by using only the generator (decoder) network separately for each class that has shown to be effective for both SSL and FSL. In our approach, the decoder is trained for each class sample using random noise, and multiple samples are generated using the trained decoder. Our generator-based approach outperforms previous state-of-the-art SSL and FSL approaches. In addition, we released the Urdu digits dataset consisting of 10,000 images, including 8000 training and 2000 test images collected through three different methods for purposes of diversity. Furthermore, we explored the effectiveness of our proposed method on the Urdu digits dataset by using both SSL and FSL, which demonstrated improvement of 3.04% and 1.50% in terms of average accuracy, respectively, illustrating the superiority of the proposed method compared to the current state-of-the-art models.

Novel Aczel-Alsina Operators for Pythagorean Fuzzy Sets with Application in Multi-Attribute Decision Making

Abstract: Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets.

Electromagnetic Flow of SWCNT/MWCNT Suspensions in Two Immiscible Water- and Engine-Oil-Based Newtonian Fluids through Porous Media

Abstract: This article deals with steady-state laminar, electrically conducting immiscible fluids. The Newtonian fluid considered passes between two parallel vertical plates in a porous medium. The channel consists of two regions, one of them filled with engine-oil-based carbon nanotubes (CNTs) and the second region filled with water through a porous medium. The assumptions for the channel walls are electrically non-conducting and are at two different temperatures. Mathematical formulation is formed using rules for the conservation of mass, momentum and energy in both regions. Continuous conditions are used for velocity, temperature and also for shear pressure at the crossing area. The governing equations are first transformed in a non-dimensional form by using appropriate transformations, and then the subsequent differential equations are solved using a topological approach by means of the homotopy analysis method. It is found that the impact of the actual boundaries utilized in the issue is directed, and the outcomes are introduced graphically and discussed. It is noted that the engine-oil SWCNTs experience a significant increase in temperature profiles as compared to the engine-oil MWCNTs, while the movement of fluid slowdown in the nanofluid region due to the concentration of nanoparticles and the thickness of the thermal boundary layer increases by increasing the volume fraction of the carbon nanotubes.

A New Meta-Heuristics Data Clustering Algorithm Based on Tabu Search and Adaptive Search Memory

Abstract: Clustering is a popular data analysis and data mining problem. Symmetry can be considered as a pre-attentive feature, which can improve shapes and objects, as well as reconstruction and recognition. The symmetry-based clustering methods search for clusters that are symmetric with respect to their centers. Furthermore, the K-means (K-M) algorithm can be considered as one of the most common clustering methods. It can be operated more quickly in most conditions, as it is easily implemented. However, it is sensitively initialized and it can be easily trapped in local targets. The Tabu Search (TS) algorithm is a stochastic global optimization technique, while Adaptive Search Memory (ASM) is an important component of TS. ASM is a combination of different memory structures that save statistics about search space and gives TS needed heuristic data to explore search space economically. Thus, a new meta-heuristics algorithm called (MHTSASM) is proposed in this paper for data clustering, which is based on TS and K-M. It uses TS to make economic exploration for data with the help of ASM. It starts with a random initial solution. It obtains neighbors of the current solution called trial solutions and updates memory elements for each iteration. The intensification and diversification strategies are used to enhance the search process. The proposed MHTSASM algorithm performance is compared with multiple clustering techniques based on both optimization and meta-heuristics. The experimental results indicate the superiority of the MHTSASM algorithm compared with other multiple clustering algorithms.

RGB Image Encryption through Cellular Automata, S-Box and the Lorenz System

Abstract: The exponential growth in transmission of multimedia over the Internet and unsecured channels of communications is putting pressure on scientists and engineers to develop effective and efficient security schemes. In this paper, an image encryption scheme is proposed to help solve such a problem. The proposed scheme is implemented over three stages. The first stage makes use of Rule 30 cellular automata to generate the first encryption key. The second stage utilizes a well-tested S-box, whose design involves a transformation, modular inverses, and permutation. Finally, the third stage employs a solution of the Lorenz system to generate the second encryption key. The aggregate effect of this 3-stage process insures the application of Shannon’s confusion and diffusion properties of a cryptographic system and enhances the security and robustness of the resulting encrypted images. Specifically, the use of the PRNG bitstreams from both of the cellular automata and the Lorenz system, as keys, combined with the S-box, results in the needed non-linearity and complexity inherent in well-encrypted images, which is sufficient to frustrate attackers. Performance evaluation is carried out with statistical and sensitivity analyses, to check for and demonstrate the security and robustness of the proposed scheme. On testing the resulting encrypted Lena image, the proposed scheme results in an MSE value of 8923.03, a PSNR value of 8.625 dB, an information entropy of 7.999, NPCR value of 99.627, and UACI value of 33.46. The proposed scheme is shown to encrypt images at an average rate of 0.61 Mbps. A comparative study with counterpart image encryption schemes from the literature is also presented to showcase the superior performance of the proposed scheme.

Sustainable and Robust Home Healthcare Logistics: A Response to the COVID-19 Pandemic

Abstract: Today, research on healthcare logistics is an important challenge in developing and developed countries, especially when a pandemic such as COVID-19 occurs. The responses required during such a pandemic would benefit from an efficiently designed model for robust and sustainable healthcare logistics. In this study, we focus on home healthcare logistics and services for planning the routing and scheduling of caregivers to visit patients’ homes. Due to the need for social distancing during the COVID-19 pandemic, these services are highly applicable for reducing the growth of the epidemic. In addition to this challenge, home healthcare logistics and services must be redesigned to meet the standards of a triple bottom line approach based on sustainable development goals. A triple bottom line approach finds a balance between economic, environmental, and social criteria for making a sustainable decision. Although, recently, the concept of green home healthcare has been studied based on the total cost and green emissions of home healthcare logistics and services, as far as we know, no research has been conducted on the formulation of a triple bottom line approach for home healthcare logistics and services. To achieve social justice for caregivers, the goal of balancing working time is to find a balance between unemployment time and overtime. Another contribution of this research is to develop a scenario-based robust optimization approach to address the uncertainty of home healthcare logistics and services and to assist with making robust decisions for home healthcare planning. Since our multi-objective optimization model for sustainable and robust home healthcare logistics and services is more complex than other studies, the last novel contribution of this research is to establish an efficient heuristic algorithm based on the Lagrangian relaxation theory. An initial solution is found by defining three heuristic algorithms. Our heuristic algorithms use a symmetric pattern for allocating patients to pharmacies and planning the routing of caregivers. Then, a combination of the epsilon constraint method and the Lagrangian relaxation theory is proposed to generate high-quality Pareto-based solutions in a reasonable time period. Finally, an extensive analysis is done to show that our multi-objective optimization model and proposed heuristic algorithm are efficient and practical, as well as some sensitivities are studied to provide some managerial insights for achieving sustainable and robust home healthcare services in practice.

Hybrid Reptile Search Algorithm and Remora Optimization Algorithm for Optimization Tasks and Data Clustering

Abstract: Data clustering is a complex data mining problem that clusters a massive amount of data objects into a predefined number of clusters; in other words, it finds symmetric and asymmetric objects. Various optimization methods have been used to solve different machine learning problems. They usually suffer from local optimal problems and unbalance between the search mechanisms. This paper proposes a novel hybrid optimization method for solving various optimization problems. The proposed method is called HRSA, which combines the original Reptile Search Algorithm (RSA) and Remora Optimization Algorithm (ROA) and handles these mechanisms’ search processes by a novel transition method. The proposed HRSA method aims to avoid the main weaknesses raised by the original methods and find better solutions. The proposed HRSA is tested on solving various complicated optimization problems—twenty-three benchmark test functions and eight data clustering problems. The obtained results illustrate that the proposed HRSA method performs significantly better than the original and comparative state-of-the-art methods. The proposed method overwhelmed all the comparative methods according to the mathematical problems. It obtained promising results in solving the clustering problems. Thus, HRSA has a remarkable efficacy when employed for various clustering problems.

Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge

Abstract: Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick’s second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ, thermal radiation Rd, thermophoresis parameter Nt and endothermic/exothermic reaction Ω, and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.

Significance of Chemical Reaction and Lorentz Force on Third-Grade Fluid Flow and Heat Transfer with Darcy-Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium

Abstract: The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. Thisis due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increasein the magnitude of chemical reaction parameter , the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient and the permeability parameter , the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination . The current results are compared with the available results in the existing literature for thisspecial case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions.

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Abstract: The current study investigates the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix equations. Accordingly, the necessary and sufficient conditions for the consistency of these systems are determined, and the general solutions of the systems are thereby deduced. An algorithm and a numerical example are constructed over the quaternions to validate the results of this paper.

Man-in-the-Middle Attacks in Mobile Ad Hoc Networks (MANETs): Analysis and Evaluation

Abstract: Mobile ad hoc networks (MANETs) are being used more and more in a variety of fields, including the environment, energy efficiency, smart transportation, intelligent agriculture, and in Internet of Things (IoT) ecosystems. They are also anticipated to play an increasingly significant role in the future of the Internet due to the strong evolution of wireless technology in recent years. Nevertheless, this inter-node communication is vulnerable to various security attacks such as Man-In-The-Middle (MITM) attacks, which are considered to be the main challenge in MANETs. This happens when a harmful node intercepts data shared by legal nodes. Therefore, the main goal of this work is to investigate the impact of attackers’ strategies to execute MITM assaults in MANETs, such as message-delayed and message-dropped assaults. The output of this work shows that these assaults have a severe impact on legal entities in MANETs as the network experiences a high number of compromised messages as well as high E2ED and PLD. Finally, by using symmetry or asymmetry cryptographies, our proposal will avoid MITM attacks that intercept the communication between legal nodes.

The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space

Abstract: In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other.

Extended Approach to the Asymptotic Behavior and Symmetric Solutions of Advanced Differential Equations

Abstract: We studied the asymptotic behavior of fourth-order advanced differential equations of the form aυw′′′υβ′+qυgwδυ=0. New results are presented for the oscillatory behavior of these equations in the form of Philos-type and Hille–Nehari oscillation criteria. Some illustrative examples are presented.

The Regulation of an Electric Oven and an Inverted Pendulum

Abstract: In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error decays to zero after a convergence time; it has the problem of chattering in the output. A second-order sliding-mode regulator is a smooth method to counteract the chattering effect where the integral of the sign-mapping is used. A second-order sliding-mode regulator is presented as a new class of algorithm where the trajectory is asymptotic and stable; it is shown to greatly improve the convergence time in comparison with other regulators considered. Simulation and experimental results are described in which an electric oven is considered as a stable linear mathematical model, and an inverted pendulum is considered as an asymmetrical unstable non-linear mathematical model.

An Exact Solution to a Quaternion Matrix Equation with an Application

Abstract: In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations to be consistent, and present an expression of the general solution of the system when it is solvable. We present an algorithm and an example to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.

Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

Abstract: In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

New "Conticrete" Hermite-Hadamard-Jensen-Mercer Fractional Inequalities

Abstract: The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.

AI-Based Automatic Detection and Classification of Diabetic Retinopathy Using U-Net and Deep Learning

Abstract: Artificial intelligence is widely applied to automate Diabetic retinopathy diagnosis. Diabetes-related retinal vascular disease is one of the world’s most common leading causes of blindness and vision impairment. Therefore, automated DR detection systems would greatly benefit the early screening and treatment of DR and prevent vision loss caused by it. Researchers have proposed several systems to detect abnormalities in retinal images in the past few years. However, Diabetic Retinopathy automatic detection methods have traditionally been based on hand-crafted feature extraction from the retinal images and using a classifier to obtain the final classification. DNN (Deep neural networks) have made several changes in the previous few years to assist overcome the problem mentioned above. We suggested a two-stage novel approach for automated DR classification in this research. Due to the low fraction of positive instances in the asymmetric Optic Disk (OD) and blood vessels (BV) detection system, preprocessing and data augmentation techniques are used to enhance the image quality and quantity. The first step uses two independent U-Net models for OD (optic disc) and BV (blood vessel) segmentation. In the second stage, the symmetric hybrid CNN-SVD model was created after preprocessing to extract and choose the most discriminant features following OD and BV extraction using Inception-V3 based on transfer learning, and detects DR by recognizing retinal biomarkers such as MA (microaneurysms), HM (hemorrhages), and exudates (EX). On EyePACS-1, Messidor-2, and DIARETDB0, the proposed methodology demonstrated state-of-the-art performance, with an average accuracy of 97.92%, 94.59%, and 93.52%, respectively. Extensive testing and comparisons with baseline approaches indicate the efficacy of the suggested methodology.

Novel Oscillation Theorems and Symmetric Properties of Nonlinear Delay Differential Equations of Fourth-Order with a Middle Term

Abstract: The goal of this paper was to study the oscillations of a class of fourth-order nonlinear delay differential equations with a middle term. Novel oscillation theorems built on a proper Riccati-type transformation, the comparison approach, and integral-averaging conditions were developed, and several symmetric properties of the solutions are presented. For the validation of these theorems, several examples are given to highlight the core results.

Short-Term Energy Forecasting Using Machine-Learning-Based Ensemble Voting Regression

Abstract: Meeting the required amount of energy between supply and demand is indispensable for energy manufacturers. Accordingly, electric industries have paid attention to short-term energy forecasting to assist their management system. This paper firstly compares multiple machine learning (ML) regressors during the training process. Five best ML algorithms, such as extra trees regressor (ETR), random forest regressor (RFR), light gradient boosting machine (LGBM), gradient boosting regressor (GBR), and K neighbors regressor (KNN) are trained to build our proposed voting regressor (VR) model. Final predictions are performed using the proposed ensemble VR and compared with five selected ML benchmark models. Statistical autoregressive moving average (ARIMA) is also compared with the proposed model to reveal results. For the experiments, usage energy and weather data are gathered from four regions of Jeju Island. Error measurements, including mean absolute percentage error (MAPE), mean absolute error (MAE), and mean squared error (MSE) are computed to evaluate the forecasting performance. Our proposed model outperforms six baseline models in terms of the result comparison, giving a minimum MAPE of 0.845% on the whole test set. This improved performance shows that our approach is promising for symmetrical forecasting using time series energy data in the power system sector.

Timelike Circular Surfaces and Singularities in Minkowski 3-Space

Abstract: The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.

One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes

Abstract: E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived.

Generating Soft Topologies via Soft Set Operators

Abstract: As daily problems involve a great deal of data and ambiguity, it has become vital to build new mathematical ways to cope with them, and soft set theory is the greatest tool for doing so. As a result, we study methods of generating soft topologies through several soft set operators. A soft topology is known to be determined by the system of special soft sets, which are called soft open (dually soft closed) sets. The relationship between specific types of soft topologies and their classical topologies (known as parametric topologies) is linked to the idea of symmetry. Under this symmetry, we can study the behaviors and properties of classical topological concepts via soft settings and vice versa. In this paper, we show that soft topological spaces can be characterized by soft closure, soft interior, soft boundary, soft exterior, soft derived set, or co-derived set operators. All of the soft topologies that result from such operators are equivalent, as well as being identical to their classical counterparts under enriched (extended) conditions. Moreover, some of the soft topologies are the systems of all fixed points of specific soft operators. Multiple examples are presented to show the implementation of these operators. Some of the examples show that, by removing any axiom, we will miss the uniqueness of the resulting soft topology.

The Characterizations of Parallel q-Equidistant Ruled Surfaces

Abstract: In this paper, parallel q-equidistant ruled surfaces are defined such that the binormal vectors of given two differentiable curves are parallel along the striction curves of their corresponding binormal ruled surfaces, and the distance between the asymptotic planes is constant at proper points, which is related to symmetry. The characterizations and some other useful relations are drawn for these surfaces as well. If the surfaces are considered to be closed, then the integral invariants such as the pitch, the angle of the pitch, and the drall of them are given. Finally, some examples are presented to indicate that the distance between the proper points on the corresponding asymptotic planes is always constant.

A Multi-Attention UNet for Semantic Segmentation in Remote Sensing Images

Abstract: In recent years, with the development of deep learning, semantic segmentation for remote sensing images has gradually become a hot issue in computer vision. However, segmentation for multicategory targets is still a difficult problem. To address the issues regarding poor precision and multiple scales in different categories, we propose a UNet, based on multi-attention (MA-UNet). Specifically, we propose a residual encoder, based on a simple attention module, to improve the extraction capability of the backbone for fine-grained features. By using multi-head self-attention for the lowest level feature, the semantic representation of the given feature map is reconstructed, further implementing fine-grained segmentation for different categories of pixels. Then, to address the problem of multiple scales in different categories, we increase the number of down-sampling to subdivide the feature sizes of the target at different scales, and use channel attention and spatial attention in different feature fusion stages, to better fuse the feature information of the target at different scales. We conducted experiments on the WHDLD datasets and DLRSD datasets. The results show that, with multiple visual attention feature enhancements, our method achieves 63.94% mean intersection over union (IOU) on the WHDLD datasets; this result is 4.27% higher than that of UNet, and on the DLRSD datasets, the mean IOU of our methods improves UNet’s 56.17% to 61.90%, while exceeding those of other advanced methods. The implementation code is available on the following Github Link.

Improved Path Planning for Indoor Patrol Robot Based on Deep Reinforcement Learning

Abstract: To solve the problems of poor exploration ability and convergence speed of traditional deep reinforcement learning in the navigation task of the patrol robot under indoor specified routes, an improved deep reinforcement learning algorithm based on Pan/Tilt/Zoom(PTZ) image information was proposed in this paper. The obtained symmetric image information and target position information are taken as the input of the network, the speed of the robot is taken as the output of the next action, and the circular route with boundary is taken as the test. The improved reward and punishment function is designed to improve the convergence speed of the algorithm and optimize the path so that the robot can plan a safer path while avoiding obstacles first. Compared with Deep Q Network(DQN) algorithm, the convergence speed after improvement is shortened by about 40%, and the loss function is more stable.