Symmetry

In order to solve connectivity problems in metropolitan areas, the development of underground metro lines constitutes an unquestionable requirement. However, the construction work thereof encounters unfavourable circumstances when surface excavations must be carried out that cross historical areas of the city, due to the need to control surface movements. The design of the metro in the city of Seville (Spain) from 2004 to 2006 provides a representative example of this situation and triggered major upheavals that exerted repercussions on historical buildings. For these reasons, the excavation stages of Line 1 of this metro have been simulated by numerical methods using FLAC3D software and validated with the results provided by the real conditions. Consequently, various surface settlements have been evaluated by taking not only variates of the main parameters that characterise the soil of Seville, but also of the various load situations and excavation conditions. Notable results have been achieved through calibration of 54 variants of the same model corresponding to Line 1, and their comparison with the real results obtained in nine critical areas of the itinerary. The results obtained have made it possible to determine the effects of excavation on the subsoil of the city of Seville with great accuracy, since the percentage error of calculated vertical surface movements varies from 0.1% to 5.3%. Full article

Essential oils have a vast number of applications in different areas of our daily life. Detailed chiral analysis and structural characterization of their constituents remains an important subject in analytical chemistry. Here, we report on a broadband rotational spectroscopy study of peppermint oil in the frequency range 2–8 GHz. We focus on an unambiguous determination of the excess enantiomers of the oil constituents menthone and isomenthone in the oil by applying chirality-sensitive rotational spectroscopy, the so-called microwave three-wave mixing (M3WM) technique. Additionally, a new menthol conformer, not previously characterized, was experimentally observed, and the gas-phase structures of the two conformers of menthol and menthone were determined experimentally based on the assignment of their ${}^{13}\mathrm{C}$-isotopologues in natural abundance. Full article

The internal structure of steel cylinder concrete pipe in large buildings is complex. Traditionally, the safety monitoring method is unable to accurately monitor the situation of every stress point in the structure. Therefore, the wireless sensor network with practical value in the field of building safety monitoring was introduced. A monitoring algorithm for stress points in pipeline structure was put forward. The distribution law of circumferential prestress produced by prestress steel wire on the pipe core concrete was analyzed. According to the influencing factors, the mechanical performance of tube concrete pipe structure was discussed, and the method of calculating prestress of pipe structure was constructed. Combined with sensor network nodes, a series of basic hypothesis information was set. Moreover, the force between node and stress point was analyzed by virtual potential field. Based on the force analysis for the centroid of the sensing area, the monitoring of the stress point in pipeline structures was completed. After that, a rectangular area to be monitored was selected and the force points were established randomly. According to the relationship between network coverage rate and monitoring efficiency, we found that the proposed algorithm had good network immunity. According to the different number of nodes, sensing radii and perception angles, the influence of index on the monitoring accuracy was discussed. Experimental results show that the accuracy of the proposed algorithm is sensitive to the change of node parameter. When the number of nodes, sensing radius and sensing angle change, the maximum fluctuation range of monitoring accuracy is 0.08–0.99. From the application effect of the algorithm, we can see that the detection effect of the algorithm has obvious advantage. Full article

Sharp bounds for $\frac{cosh\left(x\right)}{x},\frac{sinh\left(x\right)}{x}$, and $\frac{sin\left(x\right)}{x}$ were obtained, as well as one new bound for $\frac{e^x+arctan\left(x\right)}{\sqrt{x}}$. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral. Full article

Midline crossing problems have been associated with children with atypical development. When compared to typical development (TD) children, they are less likely to cross the midline into contralateral space with their preferred hand. A motor skills training program is the most beneficial intervention for children with developmental coordination disorder (DCD). However, there is not enough information on how this intervention will affect crossing the midline. The goal of this study was to find out midline crossing behavior after an intervention program for children with DCD. The Movement Assessment Battery for Children (MABC-2) was used to assess motor coordination, and Bishop’s card-reaching task measured the ability of children to cross the midline. The study included 48 right-handed children, 28 with TD and 20 with DCD (5.17 ± 0.70 years) from four preschools in the Khorezm region (Uzbekistan). Participants identified as having DCD were placed in an experimental group (EG: n = 15), receiving ten weeks of a motor skills training program, and a control group (CG: n = 5). Concerning midline crossing behavior before intervention, DCD children showed more contralateral and less midline right-hand use compared to TD children. After intervention, a significant group × position interaction was found between the EG and CG at positions 1 and 4, and between the EG and TD group at position 4. Concerning the midline reaching, fewer right-hand reaches were made by the EG group compared to the other two groups. The same could be seen at position 1 when compared to the CG group. It can be concluded that, after intervention, DCD children in the EG showed fewer right-hand reaches in the contralateral space, but they improved their right-hand reaches in the midline, showing a similar behavior to TD children. Full article

Let k and n be two positive integers. Firefighting is a discrete dynamical process of preventing the spread of fire. Let G be a connected graph G with n vertices. Assuming a fire starts at one of the vertices of G, the firefighters choose k unburned vertices at each step, and then the fire spreads to all unprotected neighbors of the burning vertices. The process continues until the fire stops spreading. The goal is to protect as many vertices as possible. When a fire breaks out randomly at a vertex of G, its k-surviving rate, ${\rho }_k\left(G\right)$, is the expected number of saved vertices. A graph is IC-planar if it has a drawing in which each edge cross once and their endpoints are disjoint. In this paper, we prove that ${\rho }_4\left(G\right)>\frac{1}{124}$ for every IC-planar graph G. This is proven by the discharging method and the locally symmetric of the graph. Full article

Dental aesthetics is an essential factor affecting people’s psychosocial wellbeing. One of the most critical components of an aesthetic smile is symmetry within the dentition. Dentists and orthodontists, unlike laypersons, are critical in assessing dental aesthetics. This study aimed to evaluate the accuracy of patients’ assessment of the symmetry of their maxillary incisors and some factors that influence it. The study was conducted on 83 participants aged from 11 to 39 years. First, the participants filled out a questionnaire to obtain patients’ opinions of the symmetry of their upper incisors. This stage was followed by an intraoral examination, during which we used a digital caliper to measure the width of four maxillary incisors. The data were entered into STATISTICA v. 13.3. The following conclusions were drawn from the study. First, the respondents were generally able to determine the asymmetry of the incisors. Second, among the maxillary incisors, the participants defined the symmetry of maxillary central incisors more accurately than the maxillary lateral incisors. The cut-off value for incisor asymmetry noticeable to a layperson is 0.2 mm for maxillary medial incisors and 0.55 for maxillary lateral incisors. Third, we found no dependence of the accuracy of the assessment of incisor asymmetry on the age of the subjects; however, in our study group, the age range (spread) was not significant, so further studies are recommended. Finally, results concerning the relationship with gender showed that males assess the level of symmetry of their maxillary incisors more accurately than females. Full article

With the development of artificial intelligence, LiDAR finds significant applications in robotics and autonomous driving. Aiming at increasing the compactness and the integration of 2-D LiDAR, this paper presents a highly digitally integrated 2-D LiDAR system implemented in a low-cost FPGA. The system is made of off-the-shelf components to limit the cost to USD 100. A laser transceiver with a symmetrical transmitting and receiving lens emits and collects laser pulses to range distance using the time-of-flight (ToF) method. As a key component in ToF, the FPGA-based time-to-digital converter (TDC) is adopted for counting the round-trip time of pulses, which is implemented in a low-cost FPGA of ZYNQ7010 with limited resources. The symmetrical structure of the delay line is used to design a more efficient TDC. The FPGA-TDC enables flexibility of design and integration with more functional logics and is microcontroller-free. All the digital logics including data processing and controlling are integrated into an FPGA with the TDC logics to realize fully digital integration and compact dimensions. The utilization of the whole architecture in the FPGA is about 15%. The experimental results demonstrated that the ranging accuracy of the LiDAR is about 2 cm, which is suitable for consumer electronics. Full article

The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces with variable exponent. The existence and uniqueness of the solutions are treated by using the penalty method and the reduction method in the weak sense. The authors also discuss the nonexistence and long-time behavior of solutions. Full article

The distributed denial of service (DDoS) vulnerabilities have rapidly extended and have been given different possibilities for even more advanced assaults on specific targets in recent times, thanks to the growth of innovative technology such as the Internet of Things (IoT) and Software-Defined Networking (SDN). The attack patterns route comprises unprotected and susceptible IoT systems that are internet-connected, as well as denial of service weaknesses in the SDN controllers, such as southbound connection exhaustion. (1) Background: The review does not go into detail about the symmetry blockchain approaches used to mitigate DDoS attacks, nor does it classify them in IoT; (2) To overcome the privacy issues, a novel deep learning-based privacy preservation method was proposed named ShChain_3D-ResNet. This novel method combines Sharding, blockchain and Residual Network for securing the SDN. Under this network, the proposed efficient attention module jointly learns attention to enforce the symmetry on weights for various channels in spatial dimension as well as attention weights of multiple frames in temporal dimension assistance of pre-training, updating, and dense convolution process; (3) Results: the proposed ShChain_3D-ResNet achieves 95.6% of accuracy, 97.3% of precision, 95.2% of recall, 94.4% of F1-score, 32.5 ms of encryption time and 35.2 ms of decryption time for dataset-1. Further, it achieves 97.3% accuracy, 95.3% precision, 96.1% recall, 98.2% F1-score, 32.1 ms of encryption time, and 36.2 ms of decryption time for dataset-2; (4) Conclusions: The Sharding strategy can increase ShChain performance while simultaneously utilizing Multi User (MU) resources for SDN. Full article

Acoustic emission (AE) as a non-destructive monitoring method is used to identify small damage in various materials effectively. However, AE signals acquired during the monitoring of oil and gas steel pipelines are always contaminated with noise. A noisy signal can be a threat to the reliability and accuracy of the findings. To address these shortcomings, this study offers a technique based on discrete wavelet transform to eliminate noise in these signals. The denoising performance is affected by several factors, including wavelet basis function, decomposition level, thresholding method, and the threshold selection criteria. Traditional threshold selection rules rely on statistical and empirical variables, which influence their performance in noise reduction under various conditions. To obtain the global best solution, a threshold selection approach is proposed by integrating particle swarm optimization and the late acceptance hill-climbing heuristic algorithms. By comparing five common approaches, the superiority of the suggested technique was validated by simulation results. The enhanced thresholding solution based on particle swarm optimization algorithm outperformed others in terms of signal-to-noise ratio and root-mean-square error of denoised AE signals, implying that it is more effective for the detection of AE sources in oil and gas steel pipelines. Full article

A subgraph H of an edge-colored graph G is called rainbow if all of its edges have different colors. Let $ar(G,H)$ denote the maximum positive integer t, such that there is a t-edge-colored graph G without any rainbow subgraph H. We denote by $k{K}_2$ a matching of size k and ${\mathcal{O}}_n$ the class of all maximal outer-planar graphs on n vertices, respectively. The outer-planar anti-Ramsey number of graph H, denoted by $ar({\mathcal{O}}_n,H)$, is defined as $max\left\{ar(O_n,H)\right|O_n\in {\mathcal{O}}_n\}$. It seems nontrivial to determine the exact values for $ar({\mathcal{O}}_n,H)$ because most maximal outer-planar graphs are asymmetry. In this paper, we obtain that $ar({\mathcal{O}}_n,k{K}_2)\le n+3k-8$ for all $n\ge 2k$ and $k\ge 6$, which improves the existing upper bound for $ar({\mathcal{O}}_n,k{K}_2)$, and prove that $ar({\mathcal{O}}_n,k{K}_2)=n+2k-5$ for $n=2k$ and $k\ge 5$. We also obtain that $ar({\mathcal{O}}_n,6K_2)=n+6$ for all $n\ge 29$. Full article

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and four-order symplectic Runge–Kutta–Nyström method (SRKN4), symplectic Euler method and RK4 method, and symplectic Euler method and SRKN4 method in preserving structure are compared from theoretical and numerical simulations, the symmetry and structure preserving and numerical stability of symplectic scheme are demonstrated. Moreover, the analytic solution of the primary and subharmonic simultaneous resonance of this system is obtained by using the multi-scale method. Finally, based on the resonance relation of the system, the chaotic dynamics behaviors with different parameters are studied. Full article

In this paper, through complex analysis, the convergence rate is given on a quadrature of a Fourier integral with symmetrical Jacobi weight. The interpolation nodes of this quadrature formula are expressed by the frequency, and the coefficients can be expressed by the Bessel function. When the frequency is close to 0, the nodes are close to those in the Gauss quadrature. When the frequency tends to infinity, the nodes tend symmetrically to the two ends of the integrand. The higher the frequency is, the higher the accuracy of this quadrature will be. Numerical examples are provided to illustrate the theoretical results. Full article

For solving the large sparse generalized absolute value equations, recently a Newton-based accelerated over-relaxation (NAOR) method was investigated. In this paper, we widen the convergence regions for the parameters and establish a new convergence theorem of the NAOR method when the system matrix is an $H_{+}$-matrix. Numerical examples demonstrate that the NAOR method has a better convergence performance when the parameters are taken according to the proposed convergence theorem. Full article

By reformulating the circuit system of Lü as a set of two second order differential equations, we investigate the nonlinear dynamics of Lü’s circuit system from the Jacobi stability point of view, using Kosambi–Cartan–Chern geometric theory. We will determine the five KCC invariants, which express the intrinsic geometric properties of the system, including the deviation curvature tensor. Finally, we will obtain necessary and sufficient conditions on the parameters of the system to have the Jacobi stability near the equilibrium points. Full article

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA), were applied to suppress the undesired oscillations of the harmonically-excited car. 2D and 3D graphical plots are included based upon the equations resulting from the harmonic balance method. Moreover, a numerical simulation was established using the fourth order Rung–Kutta technique in order to confirm the overall controlled behavior of the studied model. Full article

In this paper, we derive some new quantum estimates of generalized Hermite–Hadamard–Jensen–Mercer type of inequalities, essentially using q-differentiable convex functions. With the help of numerical examples, we check the validity of the results. We also discuss some special cases which show that our results are quite unifying. To show the efficiency of our main results, we offer some interesting applications to special means. Full article

The user equipment and directory server stay in the state of asymmetric information in anonymous networks, so that it is hard to coordinate information leakage prevention and information sharing when we explore the routing addressing technology. The severe security risk faced by existing anonymous networks, such as Tor and I2P, is the leakage of privacy information of routing nodes. This paper tries to resolve this problem and proposes a novel secure querying scheme of the routing table (SQRT) based on oblivious transfer, which can effectively ensure that both user equipment and directory server faithfully follow the routing querying protocol and protect the privacy information of both parties to the greatest extent. The SQRT scheme can realize that the directory server cannot only send the required routing nodes to the user equipment, but can also ensure that the directory server cannot know the exact routing nodes received by the user equipment and protect the information of other routing nodes in the directory server from disclosure. Security analysis shows that in the scenario where the directory server and user equipment are semi-honest, respectively, the SQRT scheme can ensure the privacy of both directory server and user equipment. The experimental simulation results show that compared with existing schemes, the SQRT scheme has obvious performance advantages in terms of the degree of anonymity, protocol running time, and communication traffic. Full article