Symmetry

In this paper, we substantiate the analytical approximate method for Cauchy problem of the Van der Pol equation in the complex domain. These approximate solutions allow analytical continuation for both real and complex cases. We follow the influence of variation in the initial data of the problem in order to control the computational process and improve the accuracy of the final results. Several simple applications of the method are given. A numerical study confirms the consistency of the developed method. Full article

This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and n scalar fields coupled to n Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank n. The set of n moduli functions $H_s\left(z\right)$ comply with n non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in z (so-called “fluxbrane” polynomials) depending upon certain parameters $p_s>0$, $s=1,\cdots ,n$. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks $n=1,2,3,4,5$ and exceptional algebra $E_6$. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored. Full article

The simple leaves of deciduous forest trees in temperate zones have more irregular and asymmetric shapes than comparable non-deciduous leaves of trees in the tropics and subtropics. These shapes manifest as the irregular lobes and sinuses of temperate species of Quercus and Acer, as well as the greater bilateral asymmetry of Ulmaceae and Betulaceae, the serrated margins of many species, and the greater frequency of compound leaves generally (Fraxinus and Carya). These modifications may contribute to an early transition from laminar to turbulent flow, thus reducing the lateral movement of leaves when they drop during the onset of either winter or the dry season, or when they are simply shed for replacement. Such leaves are more likely to drop over the critical root zone than large, thin, broadly elliptic, and symmetric leaves. Here, we evaluate evidence for and against self-mulching as an explanation for differences in leaf shape between temperate and tropical forests. We suggest that the main evolutionary trade-offs are between competition for (1) light among tropical trees and temperate subcanopy trees, and (2) competition for water and soil nutrients among temperate canopy trees. Full article

A review of several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage of symmetries. This enables us to describe very involved systems in a greatly simplified manner. Some problems are also discussed, when ignoring basic principles of nature, such as the Pauli exclusion principle. We also show that occasionally one can rescue these omissions. In a couple of representative models, applications of symmetries are explicitly applied in order to illustrate how extremely complicated systems can be treated. This contribution is meant as a review of the use of algebraic models in nuclear physics, leading to a better understanding of the articles in the same special volume. Full article

Differential fault analysis (DFA) was introduced by Biham and Shamir. It is a powerful analysis technique to retrieve the secret key by injecting fault into an internal state and utilizing the differences between the correct ciphertexts and the faulty ciphertexts. Based on the idea of meet-in-the-middle, some differential characters can help to recover the key of some symmetric ciphers. At CHES 2011, this technique was utilized to give analyses on AES. In this article, we propose several DFA schemes on ITUbee, a software-oriented block symmetric cipher for resource-constrained devices based on the meet-in-the-middle idea. Our attacks are efficient enough and more powerful than previous works. Furthermore, the attacks in this article break the protection countermeasure, meaning we have to review the protection method on devices for ITUbee. Full article

Chaotic intermittency is characterized by a signal that alternates aleatory between long regular (pseudo-laminar) phases and irregular bursts (pseudo-turbulent or chaotic phases). This phenomenon has been found in physics, chemistry, engineering, medicine, neuroscience, economy, etc. As a control parameter increases, the number of chaotic phases also increases. Therefore, intermittency presents a continuous route from regular behavior to chaotic motion. In this paper, a review of different types of intermittency is carried out. In addition, the description of two recent formulations to evaluate the reinjection processes is developed. The new theoretical formulations have allowed us to explain several tests previously called pathological. The theoretical background also includes the noise effects in the reinjection mechanism. Full article

Multiple-Object Tracking (MOT) has become more popular because of its commercial and academic potential. Though various techniques were devised for managing this issue, it becomes a challenge because of factors such as severe object occlusions and abrupt appearance changes. Tracking presents the optimal outcomes whenever the object moves uniformly without occlusion and in the same direction. However, this is generally not a real scenario, particularly in complicated scenes such as dance events or sporting where a greater number of players are tracked, moving quickly, varying their speed and direction, along with distance and position from the camera and activity they are executing. In dynamic scenes, MOT remains the main difficulty due to the symmetrical shape, structure, and size of the objects. Therefore, this study develops a new reptile search optimization algorithm with deep learning-based multiple object detection and tracking (RSOADL–MODT) techniques. The presented RSOADL–MODT model intends to recognize and track the objects that exist with position estimation, tracking, and action recognition. It follows a series of processes, namely object detection, object classification, and object tracking. At the initial stage, the presented RSOADL–MODT technique applies a path-augmented RetinaNet-based (PA–RetinaNet) object detection module, which improves the feature extraction process. To improvise the network potentiality of the PA–RetinaNet method, the RSOA is utilized as a hyperparameter optimizer. Finally, the quasi-recurrent neural network (QRNN) classifier is exploited for classification procedures. A wide-ranging experimental validation process takes place on DanceTrack and MOT17 datasets for examining the effectual object detection outcomes of the RSOADL–MODT algorithm. The simulation values confirmed the enhancements of the RSOADL–MODT method over other DL approaches. Full article

This manuscript focuses on the statistical inference of the Kavya–Manoharan generalized exponential distribution under the generalized type-I progressive hybrid censoring sample (GTI-PHCS). Different classical approaches of estimation, such as maximum likelihood, the maximum product of spacing, least squares (LS), weighted LS, and percentiles under GTI-PHCS, are investigated. Based on the squared error and linear exponential loss functions, the Bayes estimates for the unknown parameters utilizing separate gamma priors under GTI-PHCS have been derived. Point and interval estimates of unknown parameters are developed. We carry out a simulation using the Monte Carlo algorithm to show the performance of the inferential procedures. Finally, real-world data collection is examined for illustration purposes. Full article

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator $D_q\left(0<q<1\right)$ and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc $\mathsf{\Lambda }=\left\{\wp :\wp \in \mathbb{C}\mathrm{and}\left|\wp \right|<1\right\}.$ For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete–Szegö inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper. Full article

A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. Full article

Despite over a century of research, the physics of galaxy rotation is not yet fully understood, and there is a clear discrepancy between the observed mass of galaxies and their rotational velocity. Here, we report on another observation of tension between the physical properties of galaxies and their rotational velocity. We compare the apparent magnitude of galaxies and find a statistically significant asymmetry between galaxies that rotate in the same direction relative to the Milky Way and galaxies that rotate in the opposite direction relative to the Milky Way. While asymmetry in the brightness is expected due to the Doppler shift effect, such asymmetry is expected to be subtle. The observations shown here suggest that the magnitude difference is sufficiently large to be detected by Earth-based telescopes. The asymmetry is consistent in both the northern and southern galactic poles. The difference is also consistent across several different instruments such as DECam, SDSS, Pan-STARRS, and HST as well as different annotation methods, which include automatic, manual, or crowdsourcing annotations through “Galaxy Zoo”. The observation can also explain other anomalies such as the $H_o$ tension. Analysis of Ia supernovae where the host galaxies rotate in the same direction relative to the Milky Way shows a much smaller tension with the $H_o$ value as estimated by the CMB. Full article

In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions. Full article

In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the probabilistic dominance relationship between alternatives, which can lead to inconsistent and inaccurate rankings. In this paper, we propose a new ranking method for IFNs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method is able to handle incomplete and uncertain information and can generate consistent and accurate rankings. Full article

Vulnerability refers to the ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. In this paper, the rupture degree of graphs is employed to measure the vulnerability of uniform linear hypergraphs. First, we discuss the bounds of the rupture degrees of k-uniform linear hypergraphs. Then, we give a recursive algorithm for computing the rupture degree of k-uniform hypertrees. Full article

The increasing penetration of distributed generation sources in low-voltage distribution grids, electric vehicles, and new appliances from the consumer side can generate short repetitive overloads on the low-voltage cable network. This work investigates the change in the dielectric properties of low-voltage cable insulation caused by short-term overloads, examining how the cable structure affects the dielectric characteristics of the cable specimens in the case of cyclic short-term thermal aging. PVC-insulated low-voltage cable samples were exposed to an accelerated aging test in a temperature-controlled oven after changing their structures by removing different layers. Three aging cycles, each of six hours, were applied to the samples. After each cycle, the tan $\delta$ and capacitance were measured by an Omicron DIRANA Dielectric Response Analyzer in the laboratory at room temperature 24 $\pm 0.5$ °C. Furthermore, the polarization and depolarization currents were also studied. The results show that changing the cable structure impacts the dielectric parameters; in particular, the effect of the belting layer is significant. From the point of view of aging, the PVC belting layer protects the diffusion of the plasticizers of the inner structure. The findings of the study show that an asymmetric aging phenomenon can be observed in different polymeric components of the cables, even though the cables were aged in an air-circulated oven ensuring a homogeneous temperature distribution in the samples. Full article

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of q-starlike and q-convex functions in the open unit disc $\mathcal{U}$. For this novel family, bounds of the first two Taylor-Maclaurin coefficients, the Fekete-Szegö-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of q-starlike and q-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions. Full article

In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner–Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities, including probability density plots, scaled trajectories, and arrival times, was analyzed. Full article

Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of $\delta =P(Y<X)$ were proposed when the strength variable was subjected to the step–stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of $\delta$. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out. Full article

Link prediction accuracy in temporal networks is easily affected by the time granularity of network snapshots. This is due to the insufficient information conveyed by snapshots and the lack of temporal continuity between snapshots. We propose a temporal network link prediction method based on the optimized exponential smoothing model and node interaction entropy (OESMNIE). This method utilizes fine-grained interaction information between nodes within snapshot periods and incorporates the information entropy theory to improve the construction of node similarity in the gravity model as well as the prediction process of node similarity. Experiment results on several real-world datasets demonstrate the superiority and reliability of this proposed method in adapting to link prediction requirements over other methods across different time granularities of snapshots, which is essential for studying the evolution of temporal networks. Full article