Symmetry, Volume 15, Issue 11 (November 2023) – 130 articles

This manuscript delineates an innovative artificial intelligence-based methodology for forecasting the displacement of retaining walls due to extensive deep excavation processes. In our selection of 17 training cases, we strategically chose a wall configuration that was not influenced by the corner effects. This careful selection was conducted with the intention of ensuring that each deep excavation instance included in our study was supported symmetrically, thereby streamlining the analysis in the ensuing phases. Our proposed multilayer functional-link network demonstrates superior performance over the traditional backpropagation neural network (BPNN), excelling in the precise prediction of displacements at predetermined observation points, peak wall displacements, and their respective locations. Notably, the predictive accuracy of our advanced model surpassed that of the conventional BPNN and RIDO assessment tools by a substantial 5%. The network process model formulated through this research offers a valuable reference for future implementations in diverse geographical settings. Furthermore, by utilizing local datasets for the training, testing, and validation phases, our system ensures the effective and accurate execution of displacement predictions. Full article

This article proposes several solutions for the use of novel AC voltage regulators as electrical energy quality conditioners and for the use of a half-bridge voltage inverter circuit as an active filter. This study was carried out with a real object, and more attention was paid to it. Structural models of electrical energy quality assurance systems, the calculation of control system elements and experimental results are presented. In particular, the use of a half-bridge voltage inverter circuit was considered as a replacement for the passive filter of the battery charger and rectifier device. AC voltage regulators are also used as compensators for higher-current harmonics, namely active filters and reactive power, voltage drop, voltage unbalance and flicker effect compensators. Block diagrams of power quality conditioners are presented, control algorithms are developed and the results of the current high-frequency harmonics compensation, reactive power and signal balancing are presented. The results of an active filter experiment based on the NRT 160.220 charge-rectifier device circuit showed a reduction in ripple of up to 1% with smaller dimensions compared to a passive filter. The control characteristics and external characteristics of the regulators are removed. The dependences of the current THD factor and the power factor are presented depending on the modulation depth for AC voltage regulator circuits used as power quality conditioners. Full article

With the continuous improvement in human awareness of environmental protection, energy savings, and emission reduction, as well as the vigorous development of precision machinery and process technology, energy-saving and efficient diaphragm pumps have become a hot research topic at home and abroad. The diaphragm pump is a membrane-isolated reciprocating transport pump that isolates the transport medium from the piston through the diaphragm and can be used to transport high-viscosity, volatile, and corrosive media, and the symmetrical structure can make it easier for the diaphragm pump to achieve stable operation, reduce vibration and noise, and extend the life of the pump. This paper summarizes the development and research status of diaphragm pumps in recent years, including diaphragm pump structure, working principle, category, cavitation research, wear research, fault diagnosis research, vibration and noise research, fluid–solid-interaction research, and optimum research on one-way valves and diaphragms. It also puts forward some reasonable and novel viewpoints, such as applying the theory of entropy production to explore the motion mechanism of diaphragm pumps, optimizing the performance of diaphragm pumps, using new technologies to study new materials for diaphragm pumps, and designing diaphragm protection devices. This review provides valuable references and suggestions for the future development and research of diaphragm pumps. Full article

In the last few years, numerous subfamilies of univalent functions, whether directly or indirectly associated with exponential functions, have been introduced and thoroughly investigated. Among these, the families ${\mathcal{S}}_e^{*}$, ${\mathcal{C}}_e$ and ${\mathcal{R}}_e$ defined by subordination to $e^z$ have been intensively investigated. While the coefficient problem on the class ${\mathcal{S}}_e^{*}$ and ${\mathcal{C}}_e$ has been solved in many cases, in this paper, we mainly intend to compute the sharp estimates of some initial coefficients, the Feketo–Szegö inequality, and the sharp bounds of second- and third-order Hankel determinants for functions belonging to the class ${\mathcal{R}}_e$. This work has the potential to significantly enrich and enhance the exploration of univalent functions in conjunction with exponential functions, making the field more comprehensive and robust. Full article

In this paper, we initiate the study of shape vector fields on the hypersurfaces of a Riemannian manifold. We use a shape vector field on a compact hypersurface of a Euclidean space to obtain a characterization of round spheres. We also find a condition, under which a shape vector field that is on a compact hypersurface of a Euclidean space is a Killing vector field. Full article

Currently, there is interest in investigating how interlimb asymmetries (IA) of body composition impact sport-specific performance outcomes. This study aimed to examine the relationship between body composition inter-limb asymmetry and specific performance outcomes in taekwondo athletes. Seventeen national and international athletes (males, n = 8, mean age = 23.3 ± 3.1 years, mean stature = 177.2 ± 8.5 cm, mean body mass = 80.0 ± 7.3 kg; females, n = 9, mean age = 25.0 ± 4.0 years, mean stature = 161.1 ± 4.4 cm, mean body mass = 59.8 ± 5.7 kg) participated in the study. During a non-consecutive 2-day period, body composition (BC) and IA were assessed using dual X-ray absorptiometry, and the magnitude (%) of IA was calculated. Specific-performance included taekwondo specific agility test (TSAT) and Frequency Speed of Kick Test Multiple (FSKT_MULT). The relationship between BC asymmetry and performance outcomes was analyzed using a partial correlation approach (controlling for gender, age, and training time). The influence of the significant results was examined using forward stepwise linear regression models. The main results showed no significant differences between the lower limbs (p < 0.05). The IA ranged from 1.37% to 2.96%. Moderate to large negative correlations (r = −0.56 to −0.76, p < 0.05) were documented between IA of body mass, free fat mass (FFM), and lean soft tissue mass (LSTM) with most FSKT_MULT outcomes. Bone mineral density (BMD) was correlated with set 5 (rho = −0.49, p = 0.04). The FFM and LSTM asymmetries influenced the KDI reduction by 21%. Meanwhile, IA BMD negatively influenced set 5 performance by 48%. The findings of our study indicate that asymmetries independent of the magnitude of muscle and bone mass-related outcomes may have detrimental effects on high-intensity performance in taekwondo athletes. This underscores the importance of implementing comprehensive training programs and paying attention to achieving body composition inter-limb symmetry to improve overall performance levels in this sport. Full article

The Randić index of a graph G is the sum of ${\left(d_G\left(u\right)d_G\left(v\right)\right)}^{-\frac{1}{2}}$ over all edges $uv$ of G, where $d_G\left(u\right)$ denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease the Randić index of a graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs and characterize the corresponding extremal graphs. Full article

In this paper, we propose an efficient viscosity type subgradient extragradient algorithm for solving pseudomonotone variational inequality on Hadamard manifolds which is of symmetrical characteristic. Under suitable conditions, we obtain the convergence of the iteration sequence generated by the proposed algorithm to a solution of a pseudomonotone variational inequality on Hadamard manifolds. We also employ our main result to solve a constrained convex minimization problem and present a numerical experiment to illustrate the asymptotic behavior of the algorithm. Our results develop and improve some recent results. Full article

The study of electromagnetic interactions among test particles with electric charges and magnetic dipole moments is of great significance when examining the dynamics of particles within strong gravitational fields surrounding black holes. In this work, we focus on investigating the dynamics of particles possessing both electric charges and magnetic dipole moments in the spacetime of a Schwarzschild black hole within the framework of modified gravity (MOG), denoted as a Schwarzschild-MOG black hole. Our approach begins by offering a solution to Maxwell’s equations for the angular component of the electromagnetic four potentials within Schwarzschild-MOG spacetime. Subsequently, we derive the equations of motion and establish the effective potential for particles engaged in circular motion. This is achieved using a hybrid formulation of the Hamilton–Jacobi equation, encompassing interactions between electric charges and magnetic dipole moments, the external magnetic field (assumed to be asymptotically uniform), and interactions between the particles and the MOG field. Furthermore, we investigate the impacts of these three types of interactions on critical parameters, including the radius of innermost stable circular orbits (ISCOs), as well as the energy and angular momentum of particles when situated at their respective ISCOs. Finally, a detailed analysis concerning the effects of these interactions on the center-of-mass energy is presented in collisions involving neutral, electrically charged, and magnetized particles. Full article

At this stage, the application of Private Set Intersection (PSI) protocols is essential for smart homes. Oblivious Key-Value Stores (OKVS) can be used to design efficient PSI protocols. Constructing OKVS with a cuckoo hashing graph is a common approach. It increases the number of hash functions while reducing the possibility of collisions into rings. However, the existing OKVS construction scheme requires a high time overhead, and such an OKVS applied to PSI protocols would also have a high communication overhead. In this paper, we propose a method called 3-Hash Garbled Cuckoo Graph (3H-GCG) for constructing cuckoo hash graphs. Specifically, this method handles hash collisions between different keys more efficiently than existing methods, and it can also be used to construct an OKVS structure with less storage space. Based on the 3H-GCG, we design a PSI protocol using the Vector Oblivious Linear Evaluation (VOLE) and OKVS paradigm, which achieves semi-honest security and malicious security. Extensive experiments demonstrate the effectiveness of our method. When the set size is $2^{18}$–$2^{20}$, our PSI protocol is less computationally intensive than other existing protocols. The experiments also show an increase in the ratio of raw to constructed data of about 7.5%. With the semi-honest security setting, our protocol achieves the fastest runtime with the set size of $2^{18}$. With malicious security settings, our protocol has about 10% improvement in communication compared with other existing protocols. Full article

Using the coefficients of a system semilinear cubic in the first derivative second order differential equations one defines a connection in the space of the independent and dependent variables, which is specified modulo two free parameters. In this way, to any such equation one associates an affine space which is not necessarily Riemannian, that is, a metric is not required. If such a metric exists, then under the Cartan parametrization the geodesic equations of the metric coincide with the system of the considered semilinear equations. In the present work, we consider semilinear cubic in the first derivative second order differential equations whose Lie symmetry algebra is the $sl(3,\mathbb{R})$. The covariant condition for these equations is the vanishing of the curvature tensor. We demonstrate the method in the solution of the Painlevé-Ince equation and in a system of two equations. Because the approach is geometric, the number of equations in the system is not important besides the complication in the calculations. It is shown that it is possible to linearize an equation in this form using a different covariant condition, for example, assuming the space to be of constant non-vanishing curvature. Finally, it is shown that one computes the associated metric to a semilinear cubic in the first derivatives differential equation using the inverse transformation derived from the transformation of the connection. Full article

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology. Full article

Object detection methods based on deep learning typically require devices with ample computing capabilities, which limits their deployment in restricted environments such as those with embedded devices. To address this challenge, we propose Mini-YOLOv4, a lightweight real-time object detection network that achieves an excellent trade-off between speed and accuracy. Based on CSPDarknet-Tiny as the backbone network, we enhance the detection performance of the network in three ways. We use a multibranch structure embedded in an attention module for simultaneous spatial and channel attention calibration. We design a group self-attention block with a symmetric structure consisting of a pair of complementary self-attention modules to mine contextual information, thereby ensuring that the detection accuracy is improved without increasing the computational cost. Finally, we introduce a hierarchical feature pyramid network to fully exploit multiscale feature maps and promote the extraction of fine-grained features. The experimental results demonstrate that Mini-YOLOv4 requires only 4.7 M parameters and has a billion floating point operations (BFLOPs) value of 3.1. Compared with YOLOv4-Tiny, our approach achieves a 3.2% improvement in mean accuracy precision (mAP) for the PASCAL VOC dataset and obtains a significant improvement of 3.5% in overall detection accuracy for the MS COCO dataset. In testing with an embedded platform, Mini-YOLOv4 achieves a real-time detection speed of 25.6 FPS on the NVIDIA Jetson Nano, thus meeting the demand for real-time detection in computationally limited devices. Full article

We consider a newly introduced integral operator that depends on an analytic normalized function and generalizes many other previously studied operators. We find the necessary conditions that this operator has to meet in order to preserve convex meromorphic functions. We know that convexity has great impact in the industry, linear and non-linear programming problems, and optimization. Some lemmas and remarks helping us to obtain complex functions with positive real parts are also given. Full article

A $(2,6)$-fullerene F is a 2-connected cubic planar graph whose faces are only $2$-length and $6$-length. Furthermore, it consists of exactly three $2$-length faces by Euler’s formula. The $(2,6)$-fullerene comes from Došlić’s $(k,6)$-fullerene, a 2-connected 3-regular plane graph with only $k$-length faces and hexagons. Došlić showed that the $(k,6)$-fullerenes only exist for $k=2$, 3, 4, or 5, and some of the structural properties of $(k,6)$-fullerene for $k=3$, 4, or 5 were studied. The structural properties, such as connectivity, extendability, resonance, and anti−Kekulé number, are very useful for studying the number of perfect matchings in a graph, and thus for the study of the stability of the molecular graphs. In this paper, we study the properties of $(2,6)$-fullerene. We discover that the edge-connectivity of $(2,6)$-fullerenes is 2. Every $(2,6)$-fullerene is 1-extendable, but not 2-extendable (F is called $n\text{-}$$extendable$ ($\left|V\right(F\left)\right|\ge 2n+2$) if any matching of n edges is contained in a perfect matching of F). F is said to be k-resonant ($k\ge 1$) if the deleting of any i ($0\le i\le k$) disjoint even faces of F results in a graph with at least one perfect matching. We have that every $(2,6)$-fullerene is 1-resonant. An edge set, S, of F is called an anti−Kekulé set if $F-S$ is connected and has no perfect matchings, where $F-S$ denotes the subgraph obtained by deleting all edges in S from F. The anti−Kekulé number of F, denoted by $ak\left(F\right)$, is the cardinality of a smallest anti−Kekulé set of F. We have that every $(2,6)$-fullerene F with $\left|V\right(F\left)\right|>6$ has anti−Kekulé number 4. Further we mainly prove that there exists a $(2,6)$-fullerene F having $f_F$ hexagonal faces, where $f_F$ is related to the two parameters n and m. Full article

The Diversity-Maintained Adaptive Rafflesia Optimization Algorithm represents an enhanced version of the original Rafflesia Optimization Algorithm. The latter draws inspiration from the unique characteristics displayed by the Rafflesia during its growth, simulating the entire lifecycle from blooming to seed dispersion. The incorporation of the Adaptive Weight Adjustment Strategy and the Diversity Maintenance Strategy assists the algorithm in averting premature convergence to local optima, subsequently bolstering its global search capabilities. When tested on the CEC2013 benchmark functions under a dimension of 30, the new algorithm was compared with ten optimization algorithms, including commonly used classical algorithms, such as PSO, DE, CSO, SCA, and the newly introduced ROA. Evaluation metrics included mean and variance, and the new algorithm outperformed on a majority of the test functions. Concurrently, the new algorithm was applied to six real-world engineering problems: tensile/compressive spring design, pressure vessel design, three-bar truss design, welded beam design, reducer design, and gear system design. In these comparative optimizations against other mainstream algorithms, the objective function’s mean value optimized by the new algorithm consistently surpassed that of other algorithms across all six engineering challenges. Such experimental outcomes validate the efficiency and reliability of the Diversity-Maintained Adaptive Rafflesia Optimization Algorithm in tackling optimization challenges. The Diversity- Maintained Adaptive Rafflesia Optimization Algorithm is capable of tuning the parameter values for the optimization of symmetry and asymmetry functions. As part of our future research endeavors, we aim to deploy this algorithm on an even broader array of diverse and distinct optimization problems, such as the arrangement of wireless sensor nodes, further solidifying its widespread applicability and efficacy. Full article

To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniformly spaced meshes or the roots of shifted Legendre and Chebyshev polynomials. Müntz-Legendre polynomials have the interesting property that their fractional derivative is also a Müntz-Legendre polynomial. This property ensures that these bases do not face the problems associated with using the classical orthogonal polynomials when solving fractional equations using the collocation method. The numerical simulations illustrate the method’s effectiveness and accuracy. Full article

In this article, the stochastic Riemann wave equation (SRWE) forced by white noise in the Itô sense is considered. The extended tanh function and mapping methods are applied to obtain new elliptic, rational, hyperbolic, and trigonometric stochastic solutions. Furthermore, we generalize some previous studies. The obtained solutions are important in explaining some exciting physical phenomena, since the SRWE is required for describing wave propagation. We plot numerous 3D and 2D graphical representations to explain how the multiplicative white noise influences the exact solutions of the SRWE. We can infer that the introduction of multiplicative white noise disrupts the symmetry of the solutions and serves to stabilize the solutions of the SRWE. Full article

The nature and strength of the molecular interactions were established by solvatochromic studies of 22 binary and 42 ternary diluted solutions of pyridinium–carbethoxy–anilidomethylid (PCAnM). The visible absorption band of PCAnM, due to an intramolecular charge transfer (ICT) from the carbanion towards the heterocycle, shows a great sensitivity to the solvent nature. The spectral data are analysed by linear energy relationship (LERS) and the contribution of each type of interaction to the total spectral shift is estimated. The results from the solvatochromic study and those obtained by quantum mechanical computations were correlated in order to estimate the excited state dipole moment of the studied methylid. The decrease of the dipole moment by excitation emphasized in this study corresponds to the ICT nature of the visible absorption band of the solute. The ternary solutions of PCAnM achieved in mixtures of water with primary alcohols (ethanol and methanol) show the dependence of the visible band on the molar fraction of water and give the difference between the interaction energies in molecular pairs of the type water–methylid and alcohol–methylid, computed based on the statistical cell model of ternary solutions. The decrease in strength of the hydrogen bond between PCAnM and the protic solvent molecules was estimated in the following order: water $>$ methanol $>$ ethanol. The results from this study can be utilized in Organic Chemistry to generate knowledge of the interactions with solvents when cycloimmonium methylids are used as precursors to obtain new heterocycles and also in Quantum Chemistry to obtain a better description of their excited electronic states. Full article

This article mainly deals with the blow-up properties of nonnegative solutions for a reaction–diffusion system coupled with norm-type sources under positive boundary value conditions. The local existence of a nonnegative solution and the comparison principle are given. The criteria for the global existence or finite time blow-up of the solutions are obtained by constructing new functions and utilizing the super- and -sub-solution method. The results reveal a correlation between the blow-up profiles of the solutions and the size of the domain, as well as the positive boundary value. Full article

The distribution of real noise in images can disrupt the inherent symmetry present in many natural visuals, thus making its effective removal a paramount challenge. However, traditional denoising methods often require tedious manual parameter tuning, and a significant portion of deep learning-driven techniques have proven inadequate for real noise. Moreover, the efficiency of end-to-end algorithms in restoring symmetrical patterns in noisy images remains questionable. To harness the principles of symmetry for improved denoising, we introduce a dual deep learning model with a focus on preserving and leveraging symmetrical patterns in real images. Our methodology operates in two stages. In the first, we estimate the noise level using a four-layer neural network, thereby aiming to capture the underlying symmetrical structures of the original image. To enhance the extraction of symmetrical features and overall network performance, a dual attention mechanism is employed before the final convolutional layer. This innovative module adaptively assigns weights to features across different channels, thus emphasizing symmetry-preserving elements. The subsequent phase is devoted to non-blind denoising. It integrates the estimated noise level and the original image, thus targeting the challenge of denoising while preserving symmetrical patterns. Here, a multi-scale architecture is used, thereby amalgamating image features into two branches. The first branch taps into dilation convolution, thus amplifying the receptive field without introducing new parameters and making it particularly adept at capturing broad symmetrical structures. In contrast, the second branch employs a standard convolutional layer to focus on finer symmetrical details. By harnessing varied receptive fields, our method can recognize and restore image symmetries across different scales. Crucial skip connections are embedded within this multi-scale setup, thus ensuring that symmetrical image data is retained as the network deepens. Experimental evaluations, conducted on four benchmark training sets and 12 test datasets, juxtaposed with over 20 contemporary models based on the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) metrics, underscore our model’s prowess in not only denoising but also in preserving and accentuating symmetrical elements, thereby setting a new gold standard in the field. Full article

Aiming at the problem that the bus voltage in a low-inertia DC microgrid is prone to be affected by internal power fluctuations, an adaptive virtual inertia control strategy for a grid-connected converter of a DC microgrid based on an improved model prediction is proposed. Firstly, the adaptive analog virtual synchronous generator (AVSG) is introduced into the voltage outer loop by combining the inertial parameters with the voltage change rate, and the flexible adjustment of the inertial parameters is realized. Secondly, the improved model predictive control is introduced into the current inner loop to realize the fast-tracking of the given current value and improve the dynamic characteristics of the control system. Finally, a system model is established based on Matlab/Simulink for simulation. The results show that compared with the traditional virtual inertia control strategy, the proposed control strategy has smaller bus voltage fluctuation amplitude and better dynamic performance; when a 10 kW load mutation occurs, the magnitude of bus voltage drop is reduced by 60%, and the voltage recovery time is shortened by 30%. The proposed control strategy can effectively improve the stability of DC bus voltage and the operation ability of the system under asymmetric conditions. Full article

Mobile robotics has been used in recent years to provide various types of services in fields such as agriculture, surveillance, rehabilitation, space exploration, and logistics, among others. In many cases, mobile robots need to overcome complex obstacles where traditional wheels are not the best solution, and many researchers have proposed legged wheel hybrid designs. This paper presents a comprehensive study on the effect of the geometry of legged wheels on the performance of mobile robots in climbing stairs. The method used to develop this research is dynamic simulation, in which the parameters that affect the kinematics and dynamics of the robot are included. Subsequently, the results of how the robot manages to perform the test, the torque of the motors, and the contact force of the wheels are analyzed. The main hypothesis of this research is that the opening of the legs of the wheels is a geometric parameter that determines whether the structure will be able to climb the stairs. After 63 simulations, the proportional relationship between the diagonal of the stands and the opening of the wheel legs ranges between 1.11 and 1.53. This parameter showed a strong correlation with the torque of the motors and significant differences in terms of the simulations that succeeded in climbing the stairs and those that did not. These results were used to state a design method for flat, robotic structures using legged wheels. This method was validated by an additional simulation that was performed for a four-legged wheel. It can be concluded that the contribution of this work is a series of steps with which to design these mechanical structures to climb the stairs based on the proposed indicator. Full article

In this paper, the coupling effect of multiphysical fields of droplet migration is deeply studied by constructing a physical model of droplet migration with multiphysical fields. Digital holographic interferometry and particle image velocimetry are used to simultaneously measure the temperature and velocity fields of the mother liquor in the process of droplet migration for the first time. Due to the advancements of measuring, the zero-velocity region is also in the region where the thermal wake appears, four vortexes appear in the droplet migration and the off-axis behavior of double-droplet migration is found. The aim of this work is to analyze the coupling relationship of multiphysical fields, so as to reveal the physical laws of thermocapillary migration of single droplet and multiple droplets with the same phase and heterophase and to study the driving mechanism of the thermocapillary force and the flow of the mother liquor. Full article

Reducing the time spent on computational simulations is an active area in solid mechanics, and efforts are being made to implement novel techniques and apply them to time-sensitive areas in the industry and research. One of these techniques is called global–local non-intrusive analysis, a methodology that enriches a local patch model using 3D elements with non-linear behavior (such as crack propagation), coupled with a linear, global 1D frame model that solves iteratively, thereby reducing overall times compared to a monolithic solution. However, engineers do not know the length of the local model (also known as the patch model) to be considered, which affects the convergence, computational time, and overall quality of the solution. Therefore, this study considered the use of categorical analyses for performing linear and quadratic discriminant solvers for a given set of simple cases with symmetric crack propagation within the local model and defining the convergence boundary with a certain probability of a successful convergence. In addition, a practical case was analyzed for different lengths of the local model, giving strong correlations to the results of the discriminant analysis. The solution of all the cases was also analyzed, considering the number of degrees of freedom, computational times, and the number of iterations for convergence. This aimed to establish a functional relation for engineering practice, enabling the determination of a suitable patch length for performing global–local non-intrusive analysis with crack propagation in doubly symmetric steel sections. Full article

The partitions in which the parts of size n can come in n different colors are known as n-color partitions. For $r\in \{0,1\}$, let $Q{L}_r\left(n\right)$ be the number of n-color partitions of n into distinct parts which have a number of parts congruent to r modulo 2. In this paper, we consider specializations of complete and elementary symmetric functions in order to establish two kinds of formulas for $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$ as sums over partitions of n in terms of binomial coefficients. The first kind of formulas only involve partitions in which the parts of size n appear at most n times, while the second kind of formulas involve unrestricted partitions. Similar results are obtained for the first differences of $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$ and the partial sums of $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$. Full article

It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution. Full article

In wireless sensor networks, terminal devices with restricted cost and size have limited battery life. Meanwhile, these energy-constrained devices are not easy to access, especially when the terminal devices are located in severe environments. To recharge the energy-constrained devices and extend their network service time, unmanned aerial vehicles (UAVs) equipped with wireless power chargers are leased by the third-party control center. To incent the participation of UAVs with different charging capabilities and ensure the strategy-proofness of the incentive mechanism, a hidden information based contract theory model, specifically adverse selection, is introduced. By leveraging individual rationality and incentive compatibility, a contract theory based optimization problem is then formulated. After reducing redundant constraints, the optimal contract items are derived by Lagrangian multiplier. Finally, numerical simulation results are implemented to compare the prepared algorithm with three other baselines, which validates the effectiveness of our proposed incentive mechanism. Full article

In this paper, we study the entanglement structure of a system of N quantum oscillators with distinctive coupling strengths, all linearly coupled to a common massless scalar quantum field. This study is helpful in characterizing the notion of an entanglement domain and its symmetry features, which is useful for understanding the interplay between different levels of structure in many-body quantum systems. The effect of the quantum field on the system is derived via the influence functional and the correlation functions are obtained from the solutions of the evolutionary operator of the reduced density matrix. They are then used to construct the covariance matrix, which forms the basis for our analysis of the structure of quantum entanglement in this open system. To make the physical features explicit, we consider a system of three quantum coupled oscillators placed at the vertices of an equilateral triangle with disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As a physical illustration, we apply the results for these two different configurations to address some basic issues in macroscopic quantum phenomena from the quantum entanglement perspective. Full article