Symmetry, Volume 16, Issue 5 (May 2024) – 50 articles

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism. Full article

Quantitative precipitation estimation (QPE) by radar observation data is a crucial aspect of meteorological forecasting operations. Accurate QPE plays a significant role in mitigating the impact of severe convective weather. Traditional QPE methods mainly employ an exponential Z–R relationship to map the radar reflectivity to precipitation intensity on a point-to-point basis. However, this isolated point-to-point transformation lacks an effective representation of convective systems. Deep learning-based methods can learn the evolution patterns of convective systems from rich historical data. However, current models often rely on 2 km-height CAPPI images, which struggle to capture the complex vertical motions within convective systems. To address this, we propose a novel QPE model: combining the classic extrapolation model ConvLSTM with Unet for an encoder-decoder module assembly. Meanwhile, we utilize three-dimensional radar echo images as inputs and introduce the convolutional block attention module (CBAM) to guide the model to focus on individual cells most likely to trigger intense precipitation, which is symmetrically built on both channel and spatial attention modules. We also employ asymmetry in training using weighted mean squared error to make the model concentrate more on heavy precipitation events which are prone to severe disasters. We conduct experiments using radar data from North China and Eastern China. For precipitation above 1 mm, the proposed model achieves 0.6769 and 0.7910 for CSI and HSS, respectively. The results indicate that compared to other methods, our model significantly enhances precipitation prediction accuracy, with a more pronounced improvement in forecasting accuracy for heavy precipitation events. Full article

Wearable devices are paramount in health monitoring applications since they provide contextual information to identify and recognize human activities. Although sensor-based human activity recognition (HAR) has been thoroughly examined, prior studies have yet to definitively differentiate between symmetric and asymmetric motions. Determining these movement patterns might provide a more profound understanding of assessing physical activity. The main objective of this research is to investigate the use of wearable motion sensors and deep convolutional neural networks in the analysis of symmetric and asymmetric activities. This study provides a new approach for classifying symmetric and asymmetric motions using a deep residual network incorporating channel and spatial convolutional block attention modules (CBAMs). Two publicly accessible benchmark HAR datasets, which consist of inertial measurements obtained from wrist-worn sensors, are used to assess the model’s efficacy. The model we have presented is subjected to thorough examination and demonstrates exceptional accuracy on both datasets. The ablation experiment examination also demonstrates noteworthy contributions from the residual mappings and CBAMs. The significance of recognizing basic movement symmetries in increasing sensor-based activity identification utilizing wearable devices is shown by the enhanced accuracy and F1-score, especially in asymmetric activities. The technique under consideration can provide activity monitoring with enhanced accuracy and detail, offering prospective advantages in diverse domains like customized healthcare, fitness tracking, and rehabilitation progress evaluation. Full article

Recently, nonlinear fractional models have become increasingly important for describing phenomena occurring in science and engineering fields, especially those including symmetric kernels. In the current article, we examine two reliable methods for solving fractional coupled nonlinear Schrödinger models. These methods are known as the Sardar-subequation technique (SSET) and the improved generalized tanh-function technique (IGTHFT). Numerous novel soliton solutions are computed using different formats, such as periodic, bell-shaped, dark, and combination single bright along with kink, periodic, and single soliton solutions. Additionally, single solitary wave, multi-wave, and periodic kink combined solutions are evaluated. The behavioral traits of the retrieved solutions are illustrated by certain distinctive two-dimensional, three-dimensional, and contour graphs. The results are encouraging, since they show that the suggested methods are trustworthy, consistent, and efficient in finding accurate solutions to the various challenging nonlinear problems that have recently surfaced in applied sciences, engineering, and nonlinear optics. Full article

In mechanical equipment, rolling bearing components are constantly exposed to intricate and diverse environmental conditions, rendering them vulnerable to wear, performance degradation, and potential malfunctions. To precisely extract and discern rolling bearing vibration signals amidst intricate noise interference, this paper introduces a fault feature extraction and diagnosis methodology that seamlessly integrates an improved Fourier decomposition method (FDM), singular value decomposition (SVD), and maximum second-order cyclostationary blind convolution (CYCBD). Initially, the FDM is employed to meticulously decompose the bearing fault signals into numerous signal components. Subsequently, a comprehensive weighted screening criterion is formulated, aiming to strike a balance between multiple indicators, thereby enabling the selective screening and reconstruction of pertinent signal components. Furthermore, SVD and CYCBD techniques are introduced to carry out intricate processing and envelope demodulation analysis of the reconstructed signals. Through rigorous simulation experiments and practical rolling bearing fault diagnosis tests, the method’s noteworthy effectiveness in suppressing noise interference, enhancing fault feature information, and efficiently extracting fault features is unequivocally demonstrated. Furthermore, compared to traditional time–frequency analysis methods such as EMD, EEMD, ITD, and VMD, as well as traditional deconvolution methods like MED, OMEDA, and MCKD, this method exhibits significant advantages, providing an effective solution for diagnosing rolling bearing faults in environments with strong background noise. Full article

A new generalized definition of Mersenne numbers is proposed of the form $\left(a^n-{\left(a-1\right)}^n\right)$, called global generalized Mersenne numbers and noted $G{M}_{a,n}$ with base a and exponent n positive integers. The properties are investigated for prime n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. It is found that for any a, $\left(G{M}_{a,n}-1\right)$ is even and divisible by n, a and $\left(a-1\right)$ for any prime $n>2$, and by $\left(a\left(a-1\right)+1\right)$ for any prime $n>5$. The remaining factor is a function of triangular numbers of $\left(a-1\right)$, specific for each prime n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, showing first that $G{M}_{a,n}\equiv \left(1\mathrm{or}7\right)\left(\mathrm{mod}12\right)$ depending on the congruence of $a\left(\mathrm{mod}4\right)$; second, that $\left(G{M}_{a,n}-1\right)$ are divisible by 10 if $n\equiv 1\left(\mathrm{mod}4\right)$ and, if $n\equiv 3\left(\mathrm{mod}4\right)$, $G{M}_{a,n}\equiv \left(1\mathrm{or}7\mathrm{or}9\right)\left(\mathrm{mod}10\right)$, depending on the congruence of $a\left(\mathrm{mod}5\right)$; third, that all factors $c_i$ of $G{M}_{a,n}$ are of the form $\left(2n{f}_i+1\right)$ such that $c_i$ is either prime or the product of primes of the form $\left(2nj+1\right)$, with $f_i,j$ natural integers; fourth, that for prime $n>2$, all $G{M}_{a,n}$ are periodically congruent to $\left(\pm 1\mathrm{or}\pm 3\right)\left(\mathrm{mod}8\right)$ depending on the congruence of $a\left(\mathrm{mod}8\right)$; and fifth, that the factors of a composite $G{M}_{a,n}$ are of the form $\left(2n{f}_i+1\right)$ with $f_i\equiv u\left(\mathrm{mod}4\right)$ with $u=0$, 1, 2 or 3 depending on the congruences of $n\left(\mathrm{mod}4\right)$ and of $a\left(\mathrm{mod}8\right)$. The potential use of generalized Mersenne primes in cryptography is shortly addressed. Full article

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the formation mechanism of a tetraquark state within the next-to-leading order perturbative QCD. This framework builds on the basis of a spin physics-inspired model, taken as a proxy for the lowest-scale input of the constituent heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation functions are consistently obtained via the above-threshold DGLAP evolution in a variable-flavor number scheme. We provide predictions for a series of differential distributions calculated by the hands of the method, well-adapted to $\mathrm{NLL}/{\mathrm{NLO}}^{+}$ hybrid-factorization studies, where the resummation of next-to-leading energy logarithms and beyond is included in the collinear picture. We provide corroborating evidence that high-energy observables sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair stability under radiative corrections, as well as MHOU studies. Our analysis constitutes a prime contact point between QCD resummations and the exotic matter. Full article

This study aims to address the issue of redundancy and interference in data-collection systems by proposing a novel feature-selection method based on maximum information coefficient (MIC) and graph symmetry structure in complex-network theory. The method involves establishing a weighted feature network, identifying key features using dominance set and node strength, and employing the binary particle-swarm algorithm and LS-SVM algorithm for solving and validation. The model is implemented on the UNSW-NB15 and UCI datasets, demonstrating noteworthy results. In comparison to the prediction methods within the datasets, the model’s running speed is significantly reduced, decreasing from 29.8 s to 6.3 s. Furthermore, when benchmarked against state-of-the-art feature-selection algorithms, the model achieves an impressive average accuracy of 90.3%, with an average time consumption of 6.3 s. These outcomes highlight the model’s superiority in terms of both efficiency and accuracy. Full article

The use of instrumental methods of analysis in the assessment of indices that record changes in symmetry in the structure of grains to evaluate the quality of durum and soft wheat grain is currently considered a search tool that will allow us to obtain previously unavailable data by finding correlations associated with differences in the shape and ratio of starch granules in conditionally symmetrical and asymmetrical wheat fruits (kernels) formed in different field conditions and with different genotypes. Indicators that had previously shown their effectiveness were used to analyze the obviously complex unique material obtained as a result of growing under critically unique sowing conditions in 2022, which affected the stability of grain development and filling. For the evaluation, a typical agronomic comparative experiment was chosen, which was used to evaluate the soil tillage practices (fallow, non-moldboard loosening, and plowing) and sowing dates (early and after excessive rainfalls), which made it possible to analyze a wider range of factors influencing the studied indices. The soil tillage methods were found to affect the uniformity of kernel fullness and their symmetry, and the sowing dates did not lead to significant differences. This study presents detailed changes in the shape of the middle cut of a wheat kernel, associated with assessing the efficiency of kernel filling and the symmetrical distribution of storage substances under the influence of external and internal physical factors that affect the formation of the wheat kernel. The data obtained may be of interest to breeders and developers of predictive phenotyping programs for cereal grain and seeds of other crops, as well as plant physiologists. Full article

Large-scale symmetric and asymmetric matrices have emerged in predicting the relationship between genes and diseases. The emergence of large-scale matrices increases the computational complexity of the problem. Therefore, using low-rank matrices instead of original symmetric and asymmetric matrices can greatly reduce computational complexity. In this paper, we propose an approximation conjugate gradient method for solving the low-rank matrix recovery problem, i.e., the low-rank matrix is obtained to replace the original symmetric and asymmetric matrices such that the approximation error is the smallest. The conjugate gradient search direction is given through matrix addition and matrix multiplication. The new conjugate gradient update parameter is given by the F-norm of matrix and the trace inner product of matrices. The conjugate gradient generated by the algorithm avoids SVD decomposition. The backtracking linear search is used so that the approximation conjugate gradient direction is computed only once, which ensures that the objective function decreases monotonically. The global convergence and local superlinear convergence of the algorithm are given. The numerical results are reported and show the effectiveness of the algorithm. Full article

The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair of finite families of $\beta$-enriched, strictly pseudocontractive mappings in the setup of a real Hilbert space. In view of this, we constructed an iterative scheme that properly included these two mappings into the formula. Under this iterative scheme, an appropriate condition for the existence of solutions and strong and weak convergent results are presented. No sum condition is imposed on the countably finite family of the iteration parameters in obtaining our results unlike for several other results in this direction. In addition, we prove that a slight modification of our iterative scheme could be applied in studying hierarchical variational inequality problems in a real Hilbert space. Our results improve, extend and generalize several results currently existing in the literature. Full article

Shape memory alloys (SMAs) represent an exceptional class of smart materials as they are able to recover their shape after mechanical deformation, making them suitable for use in actuators, sensors and smart devices. These unique properties are due to the thermoelastic martensitic transformation that can occur during both thermal and mechanical deformation. Cu-based SMAs, especially those incorporating Al and Ag, are attracting much attention due to their facile production and cost-effectiveness. Among them, Cu-Al-Ag SMAs stand out due to their notably high temperature range for martensitic transformation. In this study, a Cu-based SMA with a new ternary composition of Cu-10Al-7Ag wt.% was prepared by arc melting and the samples cut from this casting alloy were quenched in water. Subsequently, the phase composition and the development of the microstructure were investigated. In addition, the morphology of the martensite was studied using advanced techniques such as electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The analyzes confirmed the presence of martensitic structures in both samples; mainly 18R (b_1′) martensite was present but a small volume fraction of (γ_1′) martensite also was noticed in the as-quenched sample. The observation of fine, twinned martensite plates in the SMA alloy with symmetrically occurring basal plane traces between the twin variants underlines the inherent correlation between microstructural symmetry and the properties of the material and provides valuable insights into its behavior. The hardness of the quenched sample was found to be lower than the as-cast counterpart, which can be linked to the solutioning of Ag particles during the heat treatment. Full article

It is already known that a simple nonlocal de Sitter gravity model, which we denote as $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution that mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of $\sqrt{dS}$ gravity motivated us to investigate how it works at a lower-than-cosmic scale—galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild–de Sitter metric of the $\sqrt{dS}$ gravity model. To obtain an exact solution, it is necessary to solve the corresponding nonlinear differential equation, which is a very complicated and difficult problem. What we obtained is a solution to a linearized equation, which is related to space metrics far from the massive body, where the gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of nonlocal de Sitter gravity $\sqrt{dS}$ in describing the effects in galactic dynamics that are usually attributed to dark matter. This solution was tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements. Full article

Although the probability of a rollover accident is lower than that of other forms of collision, rollover is a serious accident that can break the symmetry of the vehicle and cause serious loss of life and property. There are many factors affecting rollovers, such as the environment, the vehicle, and the driving control. A coach comprises a complex dynamic system; as such, the accuracy and rationality of the used mathematical model are decisive in the study of coach rollover warning and control. By analogy with the modeling method of an automobile collision accident, the general process of a coach rollover accident is analyzed in this study in combination with the contact form and freedom of motion characteristic of the coach body and external environment. According to the principle of conservation of energy, the mathematical models of critical rollover impact force in a collision between vehicles and obstacles and in a collision between two vehicles are established, allowing for analysis of the relationships between the critical tripped rollover impact forces required for a 90° rollover and the continuous action time and collision point height. During the collision between the vehicle and the obstacle, the occurrence of a vehicle rollover is related not only to the impact force in the collision process but also to the collision duration time. Even if the impact force is relatively small, the collision lasts long enough that a second collision may occur until the vehicle rolls over. In the process of a two-vehicle collision, the critical rollover impact force is not only related to the vehicle mass but also to the vehicle wheelbase and the height of the collision point. Based on the law of conservation of momentum, the mathematic models of 90-degree rollover and 180-degree rollover are established, and the critical rollover velocities are calculated. The purpose of this study is to provide reference and guidance for the research methods of vehicle rollover stability and anti-rollover control in the intelligent vehicle era. Full article

This article proposes a novel method for calculating radar cross-sections (RCSs) that combines the spectral element method and the integral method, allowing for RCS calculations at any position in a free space or a half-space. This approach replaces the field source with an incident field using the scattered field equation of the spectral element method, enabling the arbitrary placement of the field source without being limited by the computational domain. By applying the superposition theorem and the volume equivalence principle, the scattered field of the objects at any position is obtained through integral equations, eliminating limitations on the computation points imposed by the computational domain. Based on Green’s function’s important role throughout the calculation process and its symmetry properties, the RCS calculation of symmetric models will be more advantageous. Finally, several examples, including symmetry models, are provided to validate both the feasibility and accuracy of this proposed method. Full article

Cavitation bubbles near narrow gaps widely exist within microfluidic control devices. In the present paper, a laser-induced cavitation bubble is arranged in a narrow gap composed of two parallel plates. The inception position of the bubble is set to be at the same distance from the two plates so that the dynamic behaviors of the bubble are symmetrical. The collapse and rebound dynamics of the bubble near the boundary of a narrow gap are investigated through high-speed photography. The bubble behaviors (e.g., shape deformation, translational movement, and jet characteristics) are analyzed while considering the influence of the dimensionless distance between the bubble and the boundary and the dimensionless gap width. The principal findings include the following: (1) When the dimensionless distance is small, a violent jet towards the gap is generated during the bubble collapse stage, along with a weak counter-jet towards the boundary appearing during the rebound stage. (2) As the dimensionless distance increases, the translational distance of the bubble during the collapse stage initially decreases, then increases, and finally decreases to zero. (3) Within the parameter range considered in this paper, the dimensionless width mainly affects the expansion degree and movement direction of the bubble cloud during its rebound and subsequent stages. The above research findings can provide experimental support for bubble-driven flow control, pumping, and liquid mixing in microfluidic channels. Full article

In this research, a logarithmic-type estimator was formulated for estimating the finite population variance in stratified random sampling. By ensuring that the sampling process is symmetrically conducted across the population, biases can be minimized, and the sample is more likely to be representative of the population as a whole. We conducted a comprehensive numerical study and simulation study to evaluate the performance of the proposed estimator. The mean squared error values were computed for both our proposed estimator and several existing ones, including the standard unbiased variance estimator, difference-type estimator, and other considered estimators. The results of the numerical study and simulation study demonstrated that the proposed log-type estimator outperforms the other considered estimators in terms of MSE and percentage relative efficiency. Graphical representations of the results are also provided to illustrate the efficiency of the proposed estimator. Based on the findings of this study, we conclude that the proposed log-type estimator is a valuable addition to the existing literature on variance estimation in stratified random sampling. It provides a more efficient and accurate estimate of the population variance, which can be beneficial for various statistical applications. Full article

This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the PINN utilizing the continuous symmetry data inherent in PDEs, which is called the symmetry-enhanced Physics-Informed Neural Network. This innovative approach combines artificial neural networks (ANNs) integrating physical equations, which provide enhanced efficiency and accuracy when modeling various complex processes related to physics with a symmetric and asymmetric nature. The presented mathematical model, based on the system of Euler equations, has been carefully implemented using Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In this research, a comparative and comprehensive analysis was carried out comparing the outcomes obtained using the symmetry-enhanced PINN method and those from conventional computational fluid dynamics (CFD) approaches. The analysis highlighted the advantages of the symmetry-enhanced PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing the computation time, demonstrating its capacity as a revolutionary modeling tool. The estimated results derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulations has the potential to improve the integrity of our energy infrastructure and utilization of gas resources, contributing to advancing our understanding of symmetry principles in nature. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations. The numerical data covered the physics of the process related to the modeling of high-pressure gas flows in pipelines with regard to density, velocity and pressure, where the PINN model was able to outperform the classical CFD method for velocity by 170% and for pressure by 360%, based on $L_{\infty }$ values. Full article

Accurate and fast traffic prediction is the data-based foundation for achieving traffic control and management, and the accuracy of prediction results will directly affect the effectiveness of traffic control and management. This paper proposes a new spatiotemporal periodic polynomial model for road traffic, which integrates the temporal, spatial, and periodic features of speed time series and can effectively handle the nonlinear mapping relationship from input to output. In terms of the model, we establish a road traffic speed prediction model based on polynomial regression. In terms of spatial feature extraction methods, we introduce a maximum mutual information coefficient spatial feature extraction method. In terms of periodic feature extraction methods, we introduce a periodic trend modeling method into the prediction of speed time series, and effective fusion is carried out. Four strategies are evaluated based on the Guangzhou road speed dataset: a univariate polynomial model, a spatiotemporal polynomial model, a periodic polynomial model, and a spatiotemporal periodic polynomial model. The test results show that the three methods proposed in this article can effectively improve prediction accuracy. Comparing the spatiotemporal periodic polynomial model with multiple machine learning models and deep learning models, the prediction accuracy is improved by 5.94% compared to the best feedforward neural network. The research in this article can effectively deal with the temporal, spatial, periodic, and nonlinear characteristics of speed prediction, and to a certain extent, improve the accuracy of speed prediction. Full article

The jet dynamics during cavitation bubble collapsing between unequal-sized dual particles are investigated utilizing a numerical model that combines the finite volume approach alongside the volume of fluid approach. The model incorporates the compressibility of the two-phase fluid and accounts for mass and heat transfer between two phases. The computational model utilizes an axisymmetric model, where the axis of symmetry is defined as the line that connects the centers of the particles and the bubble. A comprehensive analysis is presented on the influence of the particle radius and bubble–particle distance on the jet behavior. Furthermore, the variations of surface pressure on the particles induced by jet impingement are quantitatively analyzed. Four distinct jet behaviors are categorized, depending on the formation mechanism, as well as the number and the direction of the jets. For case 1, the bubble produces a single jet directed toward a small particle; for case 2, the bubble fragments produces double jets receding from each other; for case 3, the bubble produces double jets approaching each other; and for case 4, the bubble produces a single jet directed toward a large particle. The pressure perturbations induced by jet impingement upon the particles exceed those caused by shock wave impacts. The larger the bubble volume at the moment of jet formation, the longer the duration of the pressure variation caused by the jet impinging on the particles. Full article

This paper investigates the performance of coplanar waveguide (CPW) structures loaded with symmetric circular and polygonal split-ring resonators (SRRs) for microwave and RF applications, leveraging their unique electromagnetic properties. These properties make them suitable for metamaterials, sensors, filters, resonators, antennas, and communication systems. The objectives of this study are to analyze the impact of different SRR shapes on the transmission characteristics of CPWs and to explore their potential for realizing compact and efficient microwave components. The CPW-SRR structures are fabricated on a dielectric substrate, and their transmission properties and spectrogram are experimentally characterized in the frequency range of 4 GHz to 10 GHz with the rotation angles of the SRR gap. The simulation results demonstrate that the resonant frequencies and magnitude of the transmission coefficient of the CPW-SRR structures are influenced by the geometry of the SRR shapes and the rotation angles of the SRR gap, with certain shapes exhibiting enhanced performance characteristics compared to others. Moreover, the symmetric circular and polygonal SRRs offer design flexibility and enable the realization of miniaturized microwave components with improved performance metrics. Overall, this study provides valuable insights into the design and optimization of CPW-based microwave circuits utilizing symmetric SRR shapes, paving the way for advancements in the miniaturization and integration of RF systems. Full article

This paper presents an improved swarming algorithm that enhances low-illumination images. The algorithm combines a hybrid Harris Eagle algorithm with double gamma (IHHO-BIGA) and incomplete beta (IHHO-NBeta) functions. This paper integrates the concept of symmetry into the improvement steps of the image adaptive enhancement algorithm. The enhanced algorithm integrates chaotic mapping for population initialization, a nonlinear formula for prey energy calculation, spiral motion from the black widow algorithm for global search enhancement, a nonlinear inertia weight factor inspired by particle swarm optimization, and a modified Levy flight strategy to prevent premature convergence to local optima. This paper compares the algorithm’s performance with other swarm intelligence algorithms using commonly used test functions. The algorithm’s performance is compared against several emerging swarm intelligence algorithms using commonly used test functions, with results demonstrating its superior performance. The improved Harris Eagle algorithm is then applied for image adaptive enhancement, and its effectiveness is evaluated on five low-illumination images from the LOL dataset. The proposed method is compared to three common image enhancement techniques and the IHHO-BIGA and IHHO-NBeta methods. The experimental results reveal that the proposed approach achieves optimal visual perception and enhanced image evaluation metrics, outperforming the existing techniques. Notably, the standard deviation data of the first image show that the IHHO-NBeta method enhances the image by 8.26%, 120.91%, 126.85%, and 164.02% compared with IHHO-BIGA, the single-scale Retinex enhancement method, the homomorphic filtering method, and the limited contrast adaptive histogram equalization method, respectively. The processing time of the improved method is also better than the previous heuristic algorithm. Full article

Conventional quality control methodologies are inadequate for fully elucidating the aberrant patterns of product quality. A multitude of factors influence product quality, yet the limited number of controlled quality characteristics is insufficient for accurately diagnosing quality abnormalities. Additionally, there are asymmetries in data collection, data pre-processing, and model interpretation. In this context, a quality anomaly recognition and diagnosis model for the complex product manufacturing process is constructed based on a deep residual network, support vector machine (SVM), and Shapley additive explanation (SHAP). Given the numerous complex product quality characteristic indexes and unpredictable accidental factors in the production process, it is necessary to mine the deep relationship between quality characteristic data and quality state. This mining is achieved by utilizing the strong feature extraction ability of the deep residual shrinkage network (DRSN) through self-learning. The symmetry of the data within the model has also been taken into account to ensure a more balanced and comprehensive analysis. The excellent binary classification ability of the support vector machine is combined with the DRSN to identify the quality anomaly state. The SHAP interpretable model is employed to diagnose the quality anomaly problem of a single product and to identify and diagnose quality anomalies in the manufacturing process of complex products. The effectiveness of the model is validated through case analysis. The accuracy of the DRSN-SVM quality anomaly recognition model reaches 99%, as demonstrated by example analysis, and the model exhibits faster convergence and significantly higher accuracy compared with the naive Bayesian model classification and support vector machine classification models. Full article

This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation. Full article

Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions belonging to the category of analytical and bi-univalent functions. This investigation incorporates the utilization of Euler polynomials. Full article

The increasing availability of longitudinal data (repeated numerical observations of the same units at different times) requires the development of flexible techniques to automatically detect errors in such data. Besides standard types of errors, which can be treated with generic error correction techniques, large longitudinal datasets may present specific problems not easily traceable by the generic techniques. In particular, after applying those generic techniques, time series in the data may contain trends, natural fluctuations and possible surviving errors. To study the data evolution, one main issue is distinguishing those elusive errors from the rest, which should be kept as they are and not flattened or altered. This work responds to this need by identifying some types of elusive errors and by proposing a statistical-mathematical approach to capture their complexity that can be applied after the above generic techniques. The proposed approach is based on a system of indicators and works at the formal level by studying the differences between consecutive values of data series and the symmetries and asymmetries of these differences. It operates regardless of the specific meaning of the data and is thus applicable in a variety of contexts. We implement this approach in a relevant database of European Higher Education institutions (ETER) by analyzing two key variables: “Total academic staff” and “Total number of enrolled students”, which are two of the most important variables, often used in empirical analysis as a proxy for size, and are considered by policymakers at the European level. The results are very promising. Full article

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the double covering of the general affine group $\overline{GA}(4,\mathbb{R})$. Then, by means of an appropriate decomposition of the metalinear double-covering group $\overline{SL}(5,\mathbb{R})$ with respect to the general linear double-covering group $\overline{GL}(4,\mathbb{R})$, one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations, allowing us to build the observables of the theory by means of the BRST algebra constructed using a $\overline{sa}(5,\mathbb{R})$ algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion. Full article

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine’s notions of generalized closed sets and Maki’s $\mathsf{\Lambda }$ sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine’s generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine’s method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of $\mathsf{\Lambda }$-sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. Full article