Symmetry

Images are frequently disrupted by noise of all kinds, making image restoration very challenging. There have been many different image denoising models proposed over the last few decades. Some models preserve the image’s smooth region, while others preserve the texture margin. One of these methods is by using quantum calculus. Quantum calculus is a branch of mathematics that deals with the manipulation of functions and operators in a quantum mechanical setting. It has been used in image processing to improve the speed and accuracy of image-processing algorithms. In quantum computing, entropy can be defined as a measure of the disorder or randomness of a quantum state. The concept of local fractional entropy has been used to study a wide range of quantum systems. In this study, an image denoising model is proposed based on the quantum calculus of local fractional entropy (QC-LFE) to remove a Gaussian noise. The local fractional entropy is used to estimate the image pixel probability, while the quantum calculus is used to estimate the convolution window mask for image denoising. A processing fractional mask with n x n elements was used in the suggested denoising algorithm. The proposed image denoising algorithm uses mask convolution to process each corrupted pixel one at a time. The proposed denoising algorithm’s effectiveness is assessed using peak signal-to-noise ratio and visual perception (PSNR). The experimental findings show that, compared to other similar fractional operators, the proposed method can better preserve texture details when denoising. Full article

The World Wide Web has revolutionized the way we live, causing the number of web pages to increase exponentially. The web provides access to a tremendous amount of information, so it is difficult for internet users to locate accurate and useful information on the web. In order to categorize pages accurately based on the queries of users, methods of categorizing web pages need to be developed. The text content of web pages plays a significant role in the categorization of web pages. If a word’s position is altered within a sentence, causing a change in the interpretation of that sentence, this phenomenon is called polysemy. In web page categorization, the polysemy property causes ambiguity and is referred to as the polysemy problem. This paper proposes a fine-tuned model to solve the polysemy problem, using contextual embeddings created by the symmetry multi-head encoder layer of the Bidirectional Encoder Representations from Transformers (BERT). The effectiveness of the proposed model was evaluated by using the benchmark datasets for web page categorization, i.e., WebKB and DMOZ. Furthermore, the experiment series also fine-tuned the proposed model’s hyperparameters to achieve 96.00% and 84.00% F1-Scores, respectively, demonstrating the proposed model’s importance compared to baseline approaches based on machine learning and deep learning. Full article

The manuscript solves a modified Kawahara equation (mKE) within two cases with and without a damping term by applying the Laplace homotopy perturbation method (LHPM). Since the damped mKE is non-integrable (i.e., it does not have analytic integrals) and does not have exact initial conditions, this challenge makes many numerical methods fail to solve non-integrable equations. In this article, we suggested a new modification at LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for mKE as the initial condition for non-damped mKE. The results proved that this mathematical approach is an effective method for solving damped mKE. Thus, we believe that the presented method will be helpful for solving many non-integrable equations that describe phenomena in sciences, such as nonlinear symmetrical wave propagation in plasma. Full article

Privacy security and property rights protection have gradually attracted the attention of people. Users not only hope that the images edited by themselves will not be forensically investigated, but also hope that the images they share will not be tampered with. Aiming at the problem that inpainted images can be located by forensics, this paper proposes a general anti-forensics framework for image inpainting with copyright protection. Specifically, we employ a hierarchical attention model to symmetrically reconstruct the inpainting results based on existing deep inpainting methods. The hierarchical attention model consists of a structural attention stream and a texture attention stream in parallel, which can fuse hierarchical features to generate high-quality reconstruction results. In addition, the user’s identity information can be symmetrically embedded and extracted to protect copyright. The experimental results not only had high-quality structural texture information, but also had homologous features with the original region, which could mislead the detection of forensics analysis. At the same time, the protection of users’ privacy and property rights is also achieved. Full article

Pairs of lepton and antilepton (dilepton) in a continuous mass range are one of the most experimentally challenging and golden probes of the quark-gluon plasma (QGP) produced in heavy ion collisions because they do not strongly interact with the hot and dense medium, and reflect the properties of the medium at the time the dilepton is generated. The measurements of dileptons require lepton identification with high purity and high efficiency at large detector acceptance. STAR is one of two large experiments at the relativistic heavy ion collider with a primary goal of searching for the QGP and studying its properties. The STAR experiment launched a comprehensive dielectron ($e^{+}{e}^{-}$) program enabled by the time-of-flight (TOF) detector that had been fully installed in 2010. In this article, we review the decade-long $R\&D$, the construction and performance of the STAR TOF detector, and dielectron measurements, including thermal dielectron production and dielectron production from the Breit–Wheeler process. Future perspectives are also discussed. Full article

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions $\left({\Delta _a^{\mathrm{LC}}}^{\mu }f\right)(a+J_0+1-\mu )\ge (1-\mu )f(a+J_0)$ and $\left({\Delta _a^{\mathrm{LC}}}^{\mu }f\right)(a+J_0+1-\mu )\le (1-\mu )f(a+J_0)$ to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results. Full article

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether’s theorem) on the (pre)multisymplectic phase spaces. Full article

In this paper, a new analytical technique is proposed for solving fractional partial differential equations. This method is referred to as the general conformal multiple Laplace transform decomposition method. It is a combination of the multiple Laplace transform method and the Adomian decomposition method. The main theoretical results of using this method are presented. In addition, illustrative examples are provided to demonstrate the validity and symmetry of the presented method. Full article

A review of computational–theoretical and experimental works devoted to the study of the flow of bodies by two-phase (dispersed) flows is carried out. The features of particle motion in the vicinity of bodies of various shapes, as well as the effect of the dispersed phase on resistance and heat transfer, are considered. Some consequences of the interaction of particles and droplets with the surface of streamlined bodies (erosive destruction, gas-dynamic spraying, icing, glowing) are analyzed. Full article

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use $k$-means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers’ evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai “6.18” Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper. Full article

We review the status of dark matter (DM) candidates in supersymmetric Twin Higgs models in light of the first results of the LUX-ZEPLIN (LZ) experiment. We found that, for twin bino-dominated DM, the new results strengthened the lower bound on the higgsino mass. However, a large part of the parameter space consistent with natural electroweak symmetry breaking is still allowed. In the case of twin-stau DM, the new results imply that, if the thermal abundance of the twin-stau LSP fits the observed density of DM, the twin stau cannot have a large left-handed component anymore. Full article

The current analysis discusses Jeffery nanofluid’s thermally radiative flow with convection over a stretching wedge. It takes into account the Brownian movement and thermophoresis of the Buongiorno nanofluid model. The guiding partial differential equations (PDEs) are modified by introducing the symmetry variables, leading to non-dimensional ordinary differential equations (ODEs). To solve the generated ODEs, the MATLAB function bvp4c is implemented. Examined are the impacts of different flow variables on the rate of transmission of heat transfer (HT), temperature, mass, velocity, and nanoparticle concentration (NC). It has been noted that the velocity and mass transfer were increased by the pressure gradient factor. Additionally, the thermal boundary layer (TBL) and nanoparticle concentration are reduced by the mixed convection (MC) factor. In order to validate the present research, the derived numerical results were compared to previous findings from the literature while taking into account the specific circumstances. It was found that there was good agreement in both sets of data. Full article

This work investigates the containment control for linear multiagent systems. We assume that the systems are subject to periodic energy-limited denial-of-service (DoS) attacks, which prevent agent-to-agent data transmission. It is assumed that the DoS attacks occur periodically based on the time sequence method. It is also assumed that some devices can be used to predict the duration of DoS attacks and uniform lower bound of communication areas. To achieve containment control, state and disturbance estimators are proposed for each following agent to estimate the relative state information. Under suitable conditions, the containment control problem can be solved with the designed controllers and observers. Finally, we provide a simulation result to confirm the theoretical analysis. Full article

Wormholes require negative energy, and therefore an exotic matter source. Since Casimir’s energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently a full solution for $3+1$ dimensions has been found by Garattini, thus the Casimir energy can be a source of traversable wormholes. We have recently shown that this can be generalized to higher dimensional spacetimes. Lately, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, his approach breaks down the usual relation between the energy density and the radial pressure of the Casimir field. In this work, we study the effects of the same three Yukawa-type corrective factors on the shape function of the Casimir wormhole keeping the usual way to obtain the radial pressure from the energy density. We show that, in addition to being able to construct traversable wormholes that satisfy all the necessary conditions, it is possible to obtain adequate constraints on the constants to recover the standard case with no double limit used by Garatinni. We show that, for some values of the Yukawa parameter, it is possible to generate a repulsive gravitational wormhole. Finally, we analyze the stability of the solutions and find the upper bounds for the Yukawa factor. Full article

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy. Full article

The aim of this manuscript was to study the influence of alloying elements on the phase transformation behavior in advanced high-strength multiphase steels. Continuous cooling transformation (CCT) and time–temperature–transformation (TTT) diagrams were calculated to analyze the stability of phases at variable time–temperature processing parameters. The analyzed materials were lean-alloyed transformation induced plasticity (TRIP) medium manganese steels. The simulations of the phase diagrams, the stability of the phases during simulated heat treatments, and the chemical composition evolution diagrams were made using Thermo-Calc and JMatPro material simulation softwares. The influence of alloying elements, i.e., Mn and C, were studied in detail. The computational and modelling results allowed the influence of alloying elements on equilibrium and non-equilibrium phase diagrams and microstructural and chemical composition evolutions to be studied. Good symmetry and correlation between computational softwares were achieved. The study allows for future optimization of the heat-treatment temperature and time conditions of modern medium-Mn automotive sheet steels. Full article

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs. Full article

The digestive tract, often known as the gastrointestinal (GI) tract or the gastrointestinal system, is affected by digestive ailments. The stomach, large and small intestines, liver, pancreas and gallbladder are all components of the digestive tract. A digestive disease is any illness that affects the digestive system. Serious to moderate conditions can exist. Heartburn, cancer, irritable bowel syndrome (IBS) and lactose intolerance are only a few of the frequent issues. The digestive system may be treated with many different surgical treatments. Laparoscopy, open surgery and endoscopy are a few examples of these techniques. This paper proposes transfer-learning models with different pre-trained models to identify and classify digestive diseases. The proposed systems showed an increase in metrics, such as the accuracy, precision and recall, when compared with other state-of-the-art methods, and EfficientNetB0 achieved the best performance results of 98.01% accuracy, 98% precision and 98% recall. Full article

Since the end of the 19th century, radioelectronic devices (REDs) have actively penetrated into all modern community spheres. Achievements in the fields of radio engineering and electronics, as well as computing, information, telecommunications, and other technologies, have greatly contributed to this. The main elements of REDs are antennas and microwave devices. For example, linear (wire) antennas are the basis of long-distance communication agency networks of various law enforcement agencies and departments. The manufacturing of REDs requires the regular and rapid appearance of more and more advanced types with minimal costs. At the same time, the design complexity of REDs and the tightening of EMC requirements caused by the growth of upper frequencies of useful and interfering signals, the mounting density, as well as the capabilities of generators of intentional electromagnetic impacts, together with the need to take into account inter-element, inter-unit, and inter-system interference, require more and more accurate designs of REDs. However, this becomes impossible without computer modeling, which saves the time and financial resources required for their development, as well as to evaluate the correctness of the proposed technical solutions. During the design process, as a rule, a multivariate analysis or optimization of the product is performed. In this case, methods of computational electrodynamics (one of which is the method of moments) are used. They are based on the replacement of continuous functions with their discrete analogues (construction of a grid), which reduces the problem to the solution of a system of linear algebraic equations (SLAE). The problem’s complexity depends on the complexity of the SLAE solution, which is determined by its order (which in turn is determined by the complexity of the simulated object and its surrounding area) and by the number of the required SLAE solutions for each problem (determined by the upper frequency of the signal, the number, and range of the optimized parameters). This dramatically increases the computational cost, which becomes the main constraint for the optimal design. Therefore, reducing the computational cost for the analysis and optimization of RED elements (in particular, linear antennas) is an important scientific problem. Meanwhile, finding new antenna structures that meet all the desired features (low price, required characteristics, manufacturable design with small dimensions and windage, etc.) is no less important today. One of the promise solutions for these problems is using a wire grid and sparse antennas for modeling and constructing antennas. Since the last century, a lot of research has been performed on them. The aim of this paper is to review their history and the main related aspects such as computational, acceleration, and optimization used methods, the fields of their application, and their evolution to this moment. In addition, this paper provides a possible future implementation of wire-grid and sparse antennas from the authors’ point of view by presenting a new method that is under research to obtain effective wire sparse antennas. Full article