Symmetry

In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper. Full article

The q-rung orthopair fuzzy (q-ROF) set is an efficient tool for dealing with uncertain and inaccurate data in real-world multi-attribute decision-making (MADM). In MADM, aggregation operators play a significant role. The majority of well-known aggregation operators are formed using algebraic, Einstein, Hamacher, Frank, and Yager t-conorms and t-norms. These existing t-conorms and t-norms are some special cases of Archimedean t-conorms (ATCNs) and Archimedean t-norms (ATNs). Therefore, this article aims to extend the ATCN and ATN operations under the q-ROF environment. In this paper, firstly, we present some new operations for q-ROF sets based on ATCN and ATN. After that, we explore a few desirable characteristics of the suggested operational laws. Then, using these operational laws, we develop q-ROF Archimedean weighted averaging (geometric) operators, q-ROF Archimedean order weighted averaging (geometric) operators, and q-ROF Archimedean hybrid averaging (geometric) operators. Next, we develop a model based on the proposed aggregation operators to handle MADM issues. Finally, we elaborate on a numerical problem about site selection for software operating units to highlight the adaptability and dependability of the developed model. Full article

Data mining is an analytical approach that contributes to achieving a solution to many problems by extracting previously unknown, fascinating, nontrivial, and potentially valuable information from massive datasets. Clustering in data mining is used for splitting or segmenting data items/points into meaningful groups and clusters by grouping the items that are near to each other based on certain statistics. This paper covers various elements of clustering, such as algorithmic methodologies, applications, clustering assessment measurement, and researcher-proposed enhancements with their impact on data mining thorough grasp of clustering algorithms, its applications, and the advances achieved in the existing literature. This study includes a literature search for papers published between 1995 and 2023, including conference and journal publications. The study begins by outlining fundamental clustering techniques along with algorithm improvements and emphasizing their advantages and limitations in comparison to other clustering algorithms. It investigates the evolution measures for clustering algorithms with an emphasis on metrics used to gauge clustering quality, such as the F-measure and the Rand Index. This study includes a variety of clustering-related topics, such as algorithmic approaches, practical applications, metrics for clustering evaluation, and researcher-proposed improvements. It addresses numerous methodologies offered to increase the convergence speed, resilience, and accuracy of clustering, such as initialization procedures, distance measures, and optimization strategies. The work concludes by emphasizing clustering as an active research area driven by the need to identify significant patterns and structures in data, enhance knowledge acquisition, and improve decision making across different domains. This study aims to contribute to the broader knowledge base of data mining practitioners and researchers, facilitating informed decision making and fostering advancements in the field through a thorough analysis of algorithmic enhancements, clustering assessment metrics, and optimization strategies. Full article

Graphene is a new type of carbon material with excellent properties that has been developed in recent years. Graphene composites have potential application value in solving the problem of water pollution. In this study, we investigated the properties and performance of graphene composites prepared through polymer modification and inorganic particle doping modification. Our research focused on the composites’ ability to adsorb heavy metal ions and degrade organic compounds through photocatalysis. In this study, we prepared graphene oxide (GO) first and then grafted p-phenylenediamine onto its surface. The process was successful and yielded promising results. The aniline grafted onto the graphene oxide surface was used as anchor point for the in situ redox polymerization of aniline, and a polyaniline macromolecular chain was grafted onto the edge of graphene oxide. The structure of the composite was determined using Fourier transform infrared spectroscopy, thermogravimetry, X-ray diffraction, and Raman spectroscopy and transmission electron microscopy. The adsorption performance of Pb⁺ on GO-PANI composite was studied. The maximum adsorption capacity of the GO-PANI composite for Pb⁺ is 1416 mg/g, 2.3 times that of PANI. Graphene/polyaniline composites can be used as an excellent adsorbent for Pb²⁺ heavy metal ions and have great application prospects in heavy metal wastewater treatment. Full article

In this paper, we introduce a comprehensive and expanded framework for generalized calculus and generalized polynomials in discrete calculus. Our focus is on $(q;h)$-time scales. Our proposed approach encompasses both difference and quantum problems, making it highly adoptable. Our framework employs forward and backward jump operators to create a unique approach. We use a weighted jump operator $\alpha$ that combines both jump operators in a convex manner. This allows us to generate a time scale $\alpha$, which provides a new approach to discrete calculus. This beneficial approach enables us to define a general symmetric derivative on time scale $\alpha$, which produces various types of discrete derivatives and forms a basis for new discrete calculus. Moreover, we create some polynomials on $\alpha$-time scales using the $\alpha$-operator. These polynomials have similar properties to regular polynomials and expand upon the existing research on discrete polynomials. Additionally, we establish the $\alpha$-version of the Taylor formula. Finally, we discuss related binomial coefficients and their properties in discrete cases. We demonstrate how the symmetrical nature of the derivative definition allows for the incorporation of various concepts and the introduction of fresh ideas to discrete calculus. Full article

A total perfect Roman dominating function (TPRDF) on a graph $G=(V,E)$ is a function f from V to $\{0,1,2\}$ satisfying (i) every vertex v with $f\left(v\right)=0$ is a neighbor of exactly one vertex u with $f\left(u\right)=2$; in addition, (ii) the subgraph of G that is induced by the vertices with nonzero weight has no isolated vertex. The weight of a TPRDF f is ${\sum }_{v\in V}f\left(v\right)$. The total perfect Roman domination number of G, denoted by ${\gamma }_{tR}^p\left(G\right)$, is the minimum weight of a TPRDF on G. In this paper, we initiated the study of total perfect Roman domination. We characterized graphs with the largest-possible ${\gamma }_{tR}^p\left(G\right)$. We proved that total perfect Roman domination is NP-complete for chordal graphs, bipartite graphs, and for planar bipartite graphs. Finally, we related ${\gamma }_{tR}^p\left(G\right)$ to perfect domination ${\gamma }^p\left(G\right)$ by proving ${\gamma }_{tR}^p\left(G\right)\le 3{\gamma }^p\left(G\right)$ for every graph G, and we characterized trees T of order $n\ge 3$ for which ${\gamma }_{tR}^p\left(T\right)=3{\gamma }^p\left(T\right)$. This notion can be utilized to develop a defensive strategy with some properties. Full article

In this paper, we introduce a new dynamic model for time series based on the Chen distribution, which is useful for modeling asymmetric, positive, continuous, and time-dependent data. The proposed Chen autoregressive moving average (CHARMA) model combines the flexibility of the Chen distribution with the use of covariates and lagged terms to model the conditional median response. We introduce the CHARMA structure and discuss conditional maximum likelihood estimation, hypothesis testing inference along with the estimator asymptotic properties of the estimator, diagnostic analysis, and forecasting. In particular, we provide closed-form expressions for the conditional score vector and the conditional information matrix. We conduct a Monte Carlo experiment to evaluate the introduced theory in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications in a wind-speed and maximum-temperature time-series dataset. Full article

In view of the subclass $S{L}^{*}\left(\beta \right),$ which for $\beta =0$ reduces to the class $S{L}^{*},$ two more subclasses $\mathcal{C}L\left(\beta \right)$ and $\mathcal{G}L\left(\beta \right)$ are introduced. For all these three subclasses, we investigate upper bounds of second Hankel and second inverse Hankel determinates. In most of the cases, the results are sharp. Full article

The sixth-generation (6G) wireless cellular network integrates several wireless bands and modes with the objectives of improving quality of service (QoS) and increasing network connectivity. The 6G environment includes asymmetrical heterogeneous networks (HetNets) with the intention of making effective use of the available frequencies. However, selecting a suitable gNB and a communication channel that works for users in the network is an enormous challenge in 6G HetNets. This paper investigates a joint user association (UA) and channel allocation (CA) problem in two-tier HetNets by considering the downlink scenario to improve QoS. Our study presents an innovative scheme for user association and channel allocation, wherein the user can be connected to either the macro base station (MBS) or a possible small base station (SBS) in a direct or relay-assisted link. Furthermore, the proposed scheme identifies the optimal channel to be allocated to each user so that the overall network QoS can be maximized. A symmetric matching game-based user association is proposed to find the optimal association for users. Moreover, a modified auction game is applied to allocate the optimal channel by considering the quota of each gNB. Regarding connection probability, throughput, energy efficiency (EE), and spectrum efficiency (SE), the simulation results show that the proposed approach performs well over the state-of-the-art techniques. Full article

We present a quaternion representation of quantum mechanics that allows its ontological interpretation. The correspondence between classical and quaternion quantum equations permits one to consider the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. Tension induced by the compression and twisting of the elastic medium would increase energy density, and as a result, generate gravity forcing and affect the wave speed. Consequently, gravity could be described by an index of refraction. Full article

Generalized progressive hybrid censoring approaches have been developed to reduce test time and cost. This paper investigates the difficulties associated with estimating the unobserved model parameters and the reliability time functions of the Kavya Manoharan Kumaraswamy (KMKu) distribution based on generalized type-II progressive hybrid censoring using classical and Bayesian estimation techniques. The frequentist estimators’ normal approximations are also used to construct the appropriate estimated confidence intervals for the unknown parameter model. Under symmetrical squared error loss, independent gamma conjugate priors are used to produce the Bayesian estimators. The Bayesian estimators and associated highest posterior density intervals cannot be derived analytically since the joint likelihood function is provided in a complicated form. However, they may be evaluated using Monte Carlo Markov chain (MCMC) techniques. Out of all the censoring choices, the best one is selected using four optimality criteria. Full article

This paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary of the support of an unknown density, the proposed method incorporates the information contained in the boundary conditions into the kernel density estimators. The proposed method provides an exact kernel function that satisfies the boundary conditions, even for small samples. Existing methods primarily deal with a one-sided boundary in a one-dimensional problem. We consider density in a two-sided interval and extend it to a multi-dimensional problem. Full article

False data injection attack (FDIA) is a deliberate modification of measurement data collected by the power grid using vulnerabilities in power grid state estimation, resulting in erroneous judgments made by the power grid control center. As a symmetrical defense scheme, FDIA detection usually uses machine learning methods to detect attack samples. However, existing detection models for FDIA typically require large-scale training samples, which are difficult to obtain in practical scenarios, making it difficult for detection models to achieve effective detection performance. In light of this, this paper proposes a novel FDIA sample generation method to construct large-scale attack samples by introducing a hybrid Laplacian model capable of accurately fitting the distribution of data changes. First, we analyze the large-scale power system sensing measurement data and establish the data distribution model of symmetric Laplace distribution. Furthermore, a hybrid Laplace-domain symmetric distribution model with multi-dimensional component parameters is constructed, which can induce a deliberate deviation in the state estimation from its safe value by injecting into the power system measurement. Due to the influence of the multivariate parameters of the hybrid Laplace-domain distribution model, the sample deviation generated by this model can not only obtain an efficient attack effect, but also effectively avoid the recognition of the FDIA detection model. Extensive experiments are carried out over IEEE 14-bus and IEEE 118-bus test systems. The corresponding results unequivocally demonstrate that our proposed attack method can quickly construct large-scale FDIA attack samples and exhibit significantly higher resistance to detection by state-of-the-art detection models, while also offering superior concealment capabilities compared to traditional FDIA approaches. Full article

Symmetries in the context of hypergroups and their generalizations are closely related to the algebraic structures and transformations that preserve certain properties of hypergroup operations. Symmetric LA-hypergroups are indeed commutative hypergroups. This paper considers a category of cyclic hyperstructures called the cyclic LA-semihypergroup that is a conception of LA-semihypergroups and cyclic hypergroups. We inaugurate the idea of cyclic LA-hypergroups. The interconnected notions of single-power cyclic LA-hypergroups, non-single power cyclic LA-hypergroups and some of their properties are explored. Full article

A rigorous analysis is undertaken based on the analysis of both Galilean and Lorentz (Poincaré) invariance in field theories in general in order to (i) identify a unique analytical scheme for canonical pairs of Lagrangians, one of them having Galilean, the other one Poincaré invariance; and (ii) to obtain transition conditions for the state function purely from Hamilton’s principle and extended Noether’s theorem applied to the aforementioned symmetries. The general analysis is applied on Schrödinger and Klein–Gordon theory, identifying them as a canonical pair in the sense of (i) and exemplified for the scattering problem for both theories for a particle beam against a potential step in order to show that the transition conditions that result according to (ii) in a ‘natural’ way reproduce the well-known ‘methodical’ continuity conditions commonly found in the literature, at least in relevant cases, closing a relevant argumentation gap in quantum mechanical scattering problems. Full article

In this paper, we propose two efficient methods for solving the fractional-order Schrödinger–KdV system. The first method is the Laplace residual power series method (LRPSM), which involves expressing the solution as a power series and using residual correction to improve the accuracy of the solution. The second method is a new iterative method (NIM) that simplifies the problem and obtains a recursive formula for the solution. Both methods are applied to the Schrödinger–KdV system with fractional derivatives, which arises in many physical applications. Numerical experiments are performed to compare the accuracy and efficiency of the two methods. The results show that both methods can produce highly accurate solutions for the fractional Schrödinger–KdV system. However, the new iterative method is more efficient in terms of computational time and memory usage. Overall, our study demonstrates the effectiveness of the residual power series method and the new iterative method in solving fractional-order Schrödinger–KdV systems and provides a valuable tool for researchers and practitioners in applied mathematics and physics. Full article

One of the frequently studied approaches in metric fixed-point theory is the generalization of the used metric space. Under this approach, in this study, we introduce a new extension of M-metric spaces, called controlled M-metric spaces, achieved by modifying the triangle inequality and keeping the symmetric condition of the space. The investigation focuses on exploring fundamental properties of this newly defined space, incorporating topological aspects. Several fixed-point theorems and fixed-circle results are established within these spaces complemented by illustrative examples to demonstrate the implications of our findings. Moreover, we present an application involving high-degree polynomial equations. Full article

The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability results with respect to the 2-norms. In four examples, we show how to deduce them from the already known outcomes obtained for classical normed spaces. We also provide some simple consequences of our results. Thus, we demonstrate that there is a significant symmetry between such results in classical normed spaces and in 2-normed spaces. Full article

In recent years, growing interest has been paid to the exploration of the concepts of entropy, heat and information, which are closely related to the symmetry properties of the physical systems in quantum theory. In this paper, we follow this line of research on the the validity of the concepts in quantum field theory by studying Landauer’s principle for a Dirac field interacting perturbatively with an Unruh–DeWitt detector in a $1+1$-dimensional MIT bag cavity. When the field is initially prepared in the vacuum state, we find that the field always absorbs heat, while the Unruh–DeWitt detector can either gain or lose entropy, depending on its motion status, as a result of the Unruh effect. When the field is initially prepared in the thermal state and the detector remains still, the heat transfer and entropy change can be obtained under two additional but reasonable approximations: (i) one is where the duration of the interaction is turned on for a sufficiently long period, and (ii) the other is where the Unruh–DeWitt detector is in resonance with one of the field modes. Landauer’s principle is verified for both considered cases. Compared to the results of a real scalar field, we find that the formulas of the vacuum initial state differ solely in the internal degree of freedom of the Dirac field, and the distinguishability of the fermion and anti-fermion comes into play when the initial state of the Dirac field is thermal. We also point out that the results for a massless fermionic field can be obtained by taking the particle mass $m\to 0$ straightforwardly. Full article