Symmetry

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. Full article

Coronal loops are bright, filamentary structures formed by thermal plasmas constrained by the sun’s magnetic field. Studying coronal loops provides insights into magnetic fields and their role in coronal heating processes. We propose a new automatic coronal loop detection method to optimize the problem of existing algorithms in detecting low-intensity coronal loops. Our method employs a line-Gaussian filter to enhance the contrast between coronal loops and background pixels, facilitating the detection of low-intensity ones. Following the detection of coronal loops, each loop is extracted using a method based on approximate local direction. Compared with the classical automatic detection method, Oriented Coronal Curved Loop Tracing (OCCULT), and its improved version, OCCULT-2, the proposed method demonstrates superior accuracy and completeness in loop detection. Furthermore, testing with images from the Transition Region and Coronal Explorer (TRACE) at 173 Å, the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) at 193 Å, and the High-Resolution Coronal Imager (Hi-C) at 193 Å and 172 Å confirms the robust generalization capabilities of our method. Statistical analysis of the cross-section width of coronal loops shows that most of the loop widths are resolved in Hi-C images. Full article

Immersion tests with 5 wt.% Na₂SO₄ solution were carried out to investigate the deterioration of calcium silicate hydrate (C-S-H) gel in a sulfate environment. C-S-H gels with different Ca/(Si + Al) molar ratios were used for comparison. Particular attention was paid to the changes in element composition and Si-O-Si chain structure of the C-S-H gel. The results show that the C-S-H gels with a low Ca/(Si + Al) ratio (0.8–1.0) and appropriate Si-O-Si chain length (14.8) presented better stability in a severe sulfate environment. The C-S-H gels with a higher Ca/(Si + Al) ratio (>2.0) were more sensitive to the attack of sulfate ions. Calcium ions dissolved rapidly during the immersion process, causing the loss of cohesive strength of the C-S-H gel, and then decomposed into fine particles. The C-S-H gel with a lower Ca/(Si + Al) ratio (about 1.1) rarely leached out calcium ions and maintained good micromorphology. The ²⁹Si MAS-NMR results indicate that the Si-O-Si chains with too short or too long chain lengths will break and recombine under the attack of sulfate ions. The Si-O-Si chains with an appropriate chain length (14.8) maintained the stability of the structure of the C-S-H gel in a sulfate environment. These changes are closely related to the asymmetric layered structure of amorphous C-S-H gel. Partial calcium ions between the layers of the main chain structure of Si-O-Si are easily taken away by sulfate ions, leading to the structural instability of the C-S-H gel. Full article

After rapid approval and installation, the SND@LHC Collaboration was able to gather data successfully in 2022 and 2023. Neutrino interactions from ν_μs originating at the LHC IP1 were observed. Since muons constitute the major background for neutrino interactions, the muon flux entering the acceptance was also measured. To improve the rejection power of the detector and to increase the fiducial volume, a third Veto plane was recently installed. The energy resolution of the calorimeter system was measured in a test beam. This will help with the identification of ν_e interactions that can be used to probe charm production in the pseudo-rapidity range of SND@LHC (7.2 < η < 8.4). Events with three outgoing muons have been observed and are being studied. With no vertex in the target, these events are very likely from muon trident production in the rock before the detector. Events with a vertex in the detector could be from trident production, photon conversion, or positron annihilation. To enhance SND@LHC’s physics case, an upgrade is planned for HL-LHC that will increase the statistics and reduce the systematics. The installation of a magnet will allow the separation of ν_μ from ${\overline{\nu }}_{\mu }$ Full article

Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer’s supply, and distributor’s demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. Full article

This paper considers a nonlinear fractional-order boundary value problem ${}^H{\mathbb{D}}_{a,g}^{{\alpha }_1,\beta ,\mu }x\left(t\right)+f(t,x\left(t\right){,}^H{\mathbb{D}}_{a,g}^{{\alpha }_2,\beta ,\mu }x\left(t\right))=0,$ for $t\in [a,b]$, ${\alpha }_1\in (1,2]$, ${\alpha }_2\in (0,1]$, $\beta \in [0,1]$ with appropriate integral boundary conditions on the Hölder spaces. Here, f is a real-valued function that satisfies the Hölder condition, and ${}^H{\mathbb{D}}_{a,g}^{\alpha ,\beta ,\mu }$ represents the tempered-Hilfer fractional derivative of order $\alpha >0$ with parameter $\mu \in {\mathbb{R}}^{+}$ and type $\beta \in [0,1]$. The corresponding integral problem is introduced in the study of this issue. This paper addresses a fundamental issue in the field, namely the circumstances under which differential and integral problems are equivalent. This approach enables the study of differential problems using integral operators. In order to achieve this, tempered fractional calculus and the equivalence problem of the studied problems are introduced and studied. The selection of an appropriate function space is of fundamental importance. This paper investigates the applicability of these operators on Hölder spaces and provides a comprehensive rationale for this choice. Full article

With the continuous emergence of intelligent network applications and complex tasks for mobile terminals, the traditional single computing model often fails to meet the greater requirements of computing and network technology, thus promoting the formation of a new computing power network architecture, of ‘cloud, edge and end’ three-level heterogeneous computing. For complex divisible computing tasks in the network, task decomposition and offloading help to realize a distributed execution of tasks, thus reducing the overall running time and improving the utilization of fragmented resources in the network. However, in the process of task decomposition and offloading, there are problems, such as there only being a single method of task decomposition; that too large or too small decomposition granularity will lead to an increase in transmission delay; and the pursuit of low-delay and low-energy offloading requirements. Based on this, a complex divisible computing task decomposition and offloading scheme is proposed. Firstly, the computational task is decomposed into multiple task elements based on code partitioning, and then a density-peak-clustering algorithm with an improved adaptive truncation distance and clustering center (ATDCC-DPC) is proposed to cluster the task elements into subtasks based on the task elements themselves and the dependencies between the task elements. Secondly, taking the subtasks as the offloading objects, the improved Double Deep Q-Network subtask offloading algorithm (ISO-DDQN) is proposed to find the optimal offloading scheme that minimizes the delay and energy consumption. Finally, the proposed algorithms are verified by simulation experiments, and the scheme in this paper can effectively reduce the task delay and energy consumption and improve the service experience. Full article

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators. Full article

Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision. Full article

Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular plate is assumed to deform axisymmetrically and expose to a radial magnetic field. The Lorentz magnetic body force is deduced via Maxwell’s relations. The effective physical properties of the upper and lower layers of the sandwich plate are obtained by employing the Halpin–Tsai model. Our technique depends on a new four-unknown shear deformation theory to depict the displacements. In addition, the motion equations are established via Hamilton’s principle. The motion equations are solved by employing the DQP. In order to study the convergence of the DQ method, the minimum number of grid points needed for a converged solution is ascertained. In addition, the current theory’s outcomes are compared with those of previous higher-order theories. The effects of the porosity distribution type, porosity factor, GPLs distribution pattern, GPLs weight fraction, inner-to-outer radius ratio, outer radius-to-thickness ratio, magnetic field parameters, core thickness, and elastic substrate parameters on the nondimensional vibration frequencies are discussed. Full article

The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiC_f/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material’s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m² to 20 J/m², the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ₂-τ₂₃ combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiC_f/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization. Full article

Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan’s mathematical expression of this situation. Recent studies using special number sequences have also revealed a new approach to the use of spinors in mathematics and have provided a different perspective for spinor research that can be used as a source for future physics studies. The purpose of this work is to expand the generalized Fibonacci quaternion polynomials to the generalized Fibonacci polynomial spinors by associating spinors with quaternions, and to introduce and investigate a new polynomial sequence that can be used to benefit from the potential advantages of spinors in physical applications, and thus, to provide mathematical arguments, such as new polynomials, for studies using spinors and quaternions in quantum mechanics. Starting from this point of view, in this paper we introduce and investigate a new family of sequences called generalized Fibospinomials (or generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we use $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. We present Binet’s formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some special identities of these new sequences and matrices related to these polynomials. The importance of this study is that generalized Fibospinomials are currently the most generalized sequence in the literature when moving from Fibonacci quaternions to spinor structure, and that a wide variety of new spinor sequences can be obtained from this particular polynomial sequence. Full article

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy $\beta$-neighborhoods (IHF $\beta$-neighborhoods) and intuitionistic hesitant fuzzy complementary $\beta$-neighborhoods (IHFC $\beta$-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF $\beta$-neighborhoods and IHFC $\beta$-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. Full article

This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the solid volume fraction of graphene ($\mathsf{\phi }$), the Hartmann number (Ha), and the fins’ length (W). The results show complex flow patterns and thermal behavior within the cavity, indicating the interactive effects of nanofluid properties, the tree-shaped obstacle, and magnetic field effects. The MHD effects reduce the convection, while the addition of graphene improves the thermal conductivity of the fluid, which enhances the heat transfer observed with increasing Rayleigh numbers. The increase in the fins’ length on the heat transfer efficiency is found to be slightly negative, which is attributed to the complex interplay between the enhanced heat transfer surface area and fluid flow disruption. This study presents an original combination of non-destructive methods (magnetic field) and a destructive method (tree-shaped obstacle) for the control of the fluid flow and heat transfer characteristics in a 3D cavity filled with graphene–water nanofluids. In addition, it provides valuable information for optimizing heat transfer control strategies, with applications in electronic cooling, renewable energy systems, and advanced thermal management solutions. The application of a magnetic field was found to reduce the maximum velocity and total entropy generation by about 82% and 76%, respectively. The addition of graphene nanoparticles was found to reduce the maximum velocity by about 5.5% without the magnetic field and to increase it by 1.12% for Ha = 100. Varying the obstacles’ length from W = 0.2 to W = 0.8 led to a reduction in velocity by about 23.6%. Full article

This article addresses certain fixed-point results in a metric space equipped with a locally transitive binary relation under a functional contraction containing three auxiliary functions. The findings proved herein enrich and improve a number of existing results. In order to prove the credibility of our findings, an illustrative example is provided. Making use of our findings, we study the genuineness of the unique solution to a Fredholm integral equation. Full article

This paper proposes a flexible travel recommender model (FTRM) that emphasizes the symmetry between user preferences and travel constraints, addressing key challenges in the field such as the integration of diverse constraint types and the customization of travel itineraries. The key contribution of the proposed model lies in its integration with the item constraints data model (ICDM), which effectively manages a plethora of constraint types. Additionally, this study develops a novel algorithm inspired by ant colony optimization (ACO) principles, demonstrating performance metrics that are comparable to state-of-the-art algorithms in this field. A comprehensive set of systematic experimental analyses is conducted, employing various models across diverse situational contexts, with the primary goal of illustrating the capabilities of the proposed symmetrical FTRM using real-world data from the Durham dataset. The obtained results highlight the model’s ability to accommodate diverse constraint types, facilitating the customization of travel itineraries to suit individual user preferences and achieve a balanced and symmetrical travel experience. Specifically, our model outperforms existing models in terms of flexibility and customization, showing significant improvements in user satisfaction and itinerary efficiency. Full article

Some numerical simulations were used to study the effects of blowing ratio (0.25–0.5), hole diameters(0.65~1 mm), and hole inclination angle (30~60°) of the film cooling structure on the cooling and aerodynamic characteristics of the axisymmetric plug nozzle under the condition of transonic. The results showed that the bow shocks appear near the film holes on the plug wall in the supersonic region, which cause the wall cooling effectiveness of the plug to decrease. Compared with the baseline plug, the blowing ratio ranged from 0.25 to 0.5, the wall average temperature of the rear plug decreased by 34.4~48.1%, the thrust coefficient and total pressure recovery coefficient decreased by 0.31~0.61% and 0.52~0.93%, respectively. When the perforated percentage is constant, the wall cooling effectiveness increases with the decrease of the hole diameters. The increase in the inclination angle of the film holes lead to the decrease in cooling effectiveness and aerodynamic performance. This is because the penetration ability of the cooling air to the mainstream is enhanced, and the obstruction to the mainstream boundary layer is increased, resulting in the increase of bow shock intensity near the film holes in the supersonic region. Full article

In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system. Full article

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation. Full article