Symmetry

Along with the adoption of three-dimensional electron diffraction (3D ED/MicroED) as a mainstream tool for structure determination from sub-micron single crystals, questions about best practices regarding each step along the workflow, from data collection to structure solutions, arise. In this paper, we discuss three particular aspects of a 3D ED/MicroED experiment which, after hundreds of structures solved in Rigaku’s laboratories, we have found to be important to consider carefully. First, for a representative model system of a hydrated compound (trehalose dihydrate), we show that cryo-transfer of the sample into the diffractometer is an effective means to prevent dehydration, while cooling of the sample without cryo-transfer yields a marginal improvement only. Next, we demonstrate for a small (tyrosine) and a large (clarithromycin) organic compound, how a simplified and fast workflow for dynamical diffraction calculations can determine absolute crystal structures with high confidence. Finally, we discuss considerations and trade-offs for choosing an optimal effective crystal-to-detector distance; while a long distance is mandatory for a protein (thaumatin) example, even a small molecule with difficult diffraction behavior (cystine) yields superior results at longer distances than the one used by default. Full article

We analyze the transverse momentum ($p_T$) spectra of ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, p, $\overline{p}$, $\Lambda$, $\overline{\Lambda }$, $\Xi$, $\overline{\Xi }$, ${\Omega }^{-}$, ${\overline{\Omega }}^{+}$ or ${\Omega }^{-}+{\overline{\Omega }}^{+}$ in different centrality intervals in gold–gold (Au–Au) and lead–lead (Pb–Pb) symmetric collisions at 200 GeV and 2.76 TeV, respectively, by Tsallis–Pareto-type function. Proton–proton collisions at the same centre of mass energies are also analyzed for these particles to compare the results obtained from these systems. The present work extracts the effective temperature T, non-extensivity parameter $\left(q\right)$, the mean transverse momentum spectra ($⟨p_T⟩$), the multiplicity parameter ($N_0$), kinetic freeze-out temperature ($T_0$) and transverse flow velocity (${\beta }_T$). We reported a plateau structure of $p_T$, T, $T_0$, ${\beta }_T$, $p_T$ and q in central collisions. Beyond the plateau region, the excitation function of all the above parameters decreases towards the periphery, except q, which has a reverse trend. The multiplicity parameter is also extracted, which is found to be decreasing towards the periphery from the central collisions. In addition, we observed that the excitation function of pp collisions is nearly the same to that of the most peripheral symmetric nucleus–nucleus collisions at the same colliding energy. Throughout the analyses, the same multiplicity parameters for particles and their antiparticles have been reported, which show the symmetric production of particles and their antiparticles. Full article

The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, ${\left(LPS\right)}_n$) to its tangent bundle $TM$ associated with a Riemannian connection $D^C$ and a quarter-symmetric metric connection (QSMC) ${\overline{D}}^C$. Full article

Symmetry and asymmetry play vital roles in prediction. Symmetrical data, which follows a predictable pattern, is easier to predict compared to asymmetrical data, which lacks a predictable pattern. Symmetry helps identify patterns within data that can be utilized in predictive models, while asymmetry aids in identifying outliers or anomalies that should be considered in the predictive model. Among the various factors associated with storms and their impact on surface temperatures, wind speed stands out as a significant factor. This paper focuses on predicting wind speed by utilizing unified hybrid censoring data from the three-parameter Burr-XII distribution. Bayesian prediction bounds for future observations are obtained using both one-sample and two-sample prediction techniques. As explicit expressions for Bayesian predictions of one and two samples are unavailable, we propose the use of the Gibbs sampling process in the Markov chain Monte Carlo framework to obtain estimated predictive distributions. Furthermore, we present a climatic data application to demonstrate the developed uncertainty procedures. Additionally, a simulation research is carried out to examine and contrast the effectiveness of the suggested methods. The results reveal that the Bayes estimates for the parameters outperformed the Maximum likelihood estimators. Full article

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties. Full article

This review considers the chiral phosphorus-containing drugs used to treat patients in the clinic, as well as the promising and experimental drugs that are in the process of being researched. Natural and synthetic representatives of phosphorus-containing drugs, such as tenofovir (hepatitis B and HIV treatment), fosfomycin (antibiotic), valinofos (antibiotic), phosphazinomycin A (antibiotic), (R)-phospholeucine, various antibacterial and antifungal agents, renin inhibitors, etc., have found practical applications as medicines and bioregulators and other medicines. The influence of the chirality of both carbon atoms and phosphorus atoms on the pharmacodynamics, pharmacokinetics, and toxicological properties of phosphorus drugs has been demonstrated. Therefore, the choice of enantiomers is critical since the wrong choice of a chiral drug can lead to undesirable consequences, carcinogenicity, and teratogenicity. New chiral technologies affecting drug development are discussed, such as the “chiral switch” of racemates already on the market, as well as phosphorus-containing prodrugs with a higher biological selectivity and low adverse effects. Full article

The solar sail spacecraft utilizing a hybrid approach of solar sail and solar electric propulsion in the heliocentric displaced orbit is affected by external disturbances, internal unmodeled dynamics, initial injection errors, and input saturation. To solve the station-keeping control problem under such complex conditions, an adaptive control strategy is proposed. First, the dynamical equations of the spacecraft utilizing hybrid low-thrust propulsion in the cylindrical coordinate system are derived. Second, the combined disturbance acceleration introduced by external disturbances and internal unmodeled dynamics is constructed, and a radial basis function neural network estimator is designed to estimate it online in real time. Third, an adaptive high-performance station-keeping controller based on an improved integral sliding surface and multivariate super-twisting sliding mode approaching law is designed. Then, stability analysis is conducted using Lyapunov theory, adaptive laws are designed, and the introduced virtual control accelerations are converted into actual control variables. Finally, simulations are conducted under different simulation conditions based on the disturbance sources. The results show that although the use of hybrid low-thrust propulsion breaks the symmetry of the solar sail in configuration, the proposed control strategy can effectively achieve the station-keeping and disturbance estimation of the spacecraft with only a small amount of propellant consumed and position tracking errors up to decimeters. Full article

We obtain some properties of a hyperbolic Ricci soliton with certain types of potential vector fields, and we point out some conditions when it reduces to a trivial Ricci soliton. We also study those soliton submanifolds whose vector fields are the tangential components of a concurrent vector field on the ambient manifold, and in particular, we show that a totally umbilical hyperbolic Ricci soliton is an Einstein manifold. We prove that if the hyperbolic Ricci soliton hypersurface of a Riemannian manifold of constant curvature and endowed with a concurrent vector field has a parallel shape operator, then it is a metallic-shaped hypersurface, and we determine some conditions for it to be minimal. Moreover, we show that it is also a pseudosymmetric hypersurface. Full article

Numerous combustion applications are concerned with the stabilization of diffusion flames formed by injecting gaseous fuels into a co-flowing stream containing an oxidizer. The smooth operation of these devices depends on the attachment and lift-off characteristics of the edge flame at the base of the diffusion flame. In this paper, we address fundamental issues pertinent to the structure and dynamics of edge flames, which have attributes of both premixed and diffusion flames. The adopted configuration is the mixing layer established in the wake of a splitter plate where two streams, one containing fuel and the other oxidizer, merge. The analysis employs a diffusive-thermal model which, although it excludes effects of gas expansion, systematically includes the influences of the overall flow rate, unequal strain rates in the incoming streams, stoichiometry, differential and preferential diffusion, heat loss and gas–solid thermal interaction, and their effect on the edge structure, speed, and temperature. Conditions when the edge flame is anchored to the plate, lifted-off and stabilized in the flow, or blown-off, are identified. Two stable modes of stabilization are observed for lifted flames; the edge flame either remains stationary at a specified location or undergoes spontaneous oscillations along a direction that coincides with the trailing diffusion flame. Full article

In this paper, we have constructed new families of derivative-free three- and four-parametric methods with and without memory for finding the roots of nonlinear equations. Error analysis verifies that the without-memory methods are optimal as per Kung–Traub’s conjecture, with orders of convergence of 4 and 8, respectively. To further enhance their convergence capabilities, the with-memory methods incorporate accelerating parameters, elevating their convergence orders to 7.5311 and 15.5156, respectively, without introducing extra function evaluations. As such, they exhibit exceptional efficiency indices of 1.9601 and 1.9847, respectively, nearing the maximum efficiency index of 2. The convergence domains are also analysed using the basins of attraction, which exhibit symmetrical patterns and shed light on the fascinating interplay between symmetry, dynamic behaviour, the number of diverging points, and efficient root-finding methods for nonlinear equations. Numerical experiments and comparison with existing methods are carried out on some nonlinear functions, including real-world chemical engineering problems, to demonstrate the effectiveness of the new proposed methods and confirm the theoretical results. Notably, our numerical experiments reveal that the proposed methods outperform their existing counterparts, offering superior precision in computation. Full article

This study presents an extended vector polar histogram (EVPH) method for efficient robot navigation using omni-directional LiDAR data. Although the conventional vector polar histogram (VPH) method is a powerful technique suitable for LiDAR sensors, it is limited in its sensing range by the single LiDAR sensor to a semicircle. To address this limitation, the EVPH method incorporates multiple LiDAR sensor’s data for omni-directional sensing. First off, in the EVPH method, the LiDAR sensor coordinate systems are directly transformed into the robot coordinate system to obtain an omni-directional polar histogram. Several techniques are also employed in this process, such as minimum value selection and linear interpolation, to generate a uniform omni-directional polar histogram. The resulting histogram is modified to represent the robot as a single point. Subsequently, consecutive points in the histogram are grouped to construct a symbol function for excluding concave blocks and a threshold function for safety. These functions are combined to determine the maximum cost value that generates the robot’s next heading angle. Robot backward motion is made feasible based on the determined heading angle, enabling the calculation of the velocity vector for time-efficient and collision-free navigation. To assess the efficacy of the proposed EVPH method, experiments were carried out in two environments where humans and obstacles coexist. The results showed that, compared to the conventional method, the robot traveled safely and efficiently in terms of the accumulated amount of rotations, total traveling distance, and time using the EVPH method. In the future, our plan includes enhancing the robustness of the proposed method in congested environments by integrating parameter adaptation and dynamic object estimation methods. Full article

In 2012, new classes of analytic functions on $U\times \overline{U}$ with coefficient holomorphic functions in $\overline{U}$ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator $D_z^{-\gamma }{H}_m^l\left[{\alpha }_1,{\beta }_1\right]$ that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on $U\times \overline{U}.$ Several strong differential subordinations and superordinations concerning the operator $D_z^{-\gamma }{H}_m^l\left[{\alpha }_1,{\beta }_1\right]$ are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties. Full article

We discuss the double-copy formulation of Moyal–Weyl-type noncommutative gauge theories from the homotopy algebraic perspective of factorisations of $L_{\infty }$-algebras. We define new noncommutative scalar field theories with rigid colour symmetries taking the role of the zeroth copy, where the deformed colour algebra plays the role of a kinematic algebra; some of these theories have a trivial classical limit but exhibit colour–kinematics duality, from which we construct the double copy theory explicitly. We show that noncommutative gauge theories exhibit a twisted form of colour–kinematics duality, which we use to show that their double copies match with the commutative case. We illustrate this explicitly for Chern–Simons theory, and for Yang–Mills theory where we obtain a modified Kawai–Lewellen–Tye relationship whose momentum kernel is linked to a binoncommutative biadjoint scalar theory. We reinterpret rank-one noncommutative gauge theories as double copy theories and discuss how our findings tie in with recent discussions of Moyal–Weyl deformations of self–dual Yang–Mills theory and gravity. Full article

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic. Full article

The integrity of real-time data streams has not been solved for a long time and has gradually become a difficult problem in the field of data security. Most of the current data integrity verification schemes are constructed using cryptographic algorithms with complex computation, which cannot be directly applied to real-time stream computing systems. Aiming at the above issue, this paper adopts the Carter–Wegman MAC method, pseudo-random function and symmetric cryptography mechanism to construct the Real-Time Data Integrity Verification scheme based on symmetric key in stream computing systems (RT-DIV), which converts a one-time MAC to a multiple-time MAC and retains the advantage of security performance. Then, a security analysis is given under the standard model. Finally, experiments and data analysis are conducted in a simulated environment, and the experimental results show that the RT-DIV scheme can effectively guarantee the integrity of real-time data streams. Furthermore, the RT-DIV scheme lays the foundation for the secure application of the stream computing system. Full article

This research work introduces a novel method called the Sumudu–generalized Laplace transform decomposition method (SGLDM) for solving linear and nonlinear non-homogeneous dispersive Korteweg–de Vries (KdV)-type equations. The SGLDM combines the Sumudu–generalized Laplace transform with the Adomian decomposition method, providing a powerful approach to tackle complex equations. To validate the efficacy of the method, several model problems of dispersive KdV-type equations are solved, and the resulting approximate solutions are expressed in series form. The findings demonstrate that the SGLDM is a reliable and robust method for addressing significant physical problems in various applications. Finally, we conclude that this transform is a symmetry to other symmetric transforms. Full article

For any experiment with two entangled photons, some joint measurement outcomes can have zero probability for a precise choice of basis. These perfect anti-correlations would seem to be a purely quantum phenomenon. It is, therefore, surprising that these very anti-correlations are also evident when the input to the same experiment is analyzed via classical electromagnetic theory. Demonstrating this quantum–classical connection for arbitrary two-photon states and analyzing why it is successful motivates alternative perspectives concerning entanglement, the path integral, and other topics in quantum foundations. Full article

Representations of braid group $B_n$ on $n\ge 2$ strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group $V{B}_n$ on $n\ge 2$ strands is an extension of the classical braid group $B_n$ by the symmetric group $S_n$. In this paper, we consider flat virtual braid groups $FV{B}_n$ on $n\ge 2$ strands and construct a family of representations of $FV{B}_n$ by automorphisms of free groups of rank $2n$. It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case $n=2$ and proved that the kernel contains a free group of rank two for $n\ge 3$. Full article

Sensitively altered news, commonly referred to as rumors, can lead an individual, organization, or nation astray, potentially resulting in harm, even to the extent of causing violence among large groups of people. In this digital age, news can be easily twisted and rapidly spread through the internet and social media. It becomes challenging for consumers to discern whether the information they encounter online has been manipulated. Unfortunately, the rise of internet forgeries has facilitated the dissemination of false or distorted information by unscrupulous individuals, particularly on sensitive matters, to serve their own interests. Once a rumor is generated and made public on the internet, it quickly spreads through sharing and discussions by anonymous individuals, sometimes intentionally, without thorough fact-checking. In this manuscript, we investigate the dynamical model of rumor propagation in a social network using the classical Caputo piecewise derivative. We examine the existence and uniqueness of a solution for the aforementioned problem and analyze the equilibrium, stability, boundedness, and positivity of the model. To obtain the numerical simulation of the piecewise derivative, we employ various fractional orders, and the approximate solution of the considered model is found using the fractional piecewise numerical iterative approach of the Newton polynomial. This approach allows us to gain valuable insights into the dynamics of rumor propagation and its effects within a social network. Full article