Symmetry

Developing earth-abundant electrocatalysts useful for hydrogen evolution reactions (HER) is critical for electrocatalytic water splitting driven by renewable energy. Molybdenum carbide (Mo₂C) with the crystal structure of hexagonal symmetry has been identified to be an excellent HER catalyst due to its platinum-like electronic structure while the synthesis of Mo₂C is generally time consuming and energy intensive. Herein, we demonstrated the ultrafast synthesis of a Mo₂C-based electrocatalyst with Joule heating at 1473 K for only 6 s. Benefitting from several advantages including efficient catalytic kinetics, enhanced charge transport kinetics and high intrinsic activity, the as-prepared catalyst exhibited drastically enhanced HER performance compared with commercial Mo₂C. It showed an overpotential of 288 mV for achieving a current density of −50 mA cm⁻² and good stability, which highlighted the feasibility of the Joule heating method towards preparing efficient electrocatalysts. Full article

This paper proposes a novel wheel−leg hybrid robot that can be applied on both flat and rugged terrains, it utilizes two passive transformable symmetrical wheels that combine the stability of the circular wheel and the obstacle climbing ability of the legged wheel. To minimize the number of actuators, the transformation process of the wheel is designed to be triggered passively when in contact with the obstacles. A new triggering mechanism is employed to eliminate the adverse effect of the robot’s weight on the transformation torque. The parameters of the wheel are optimized to maximize the climbing ability in low-friction conditions. The robot’s body length and angular velocity are also tuned based on the dynamic model during the obstacle climbing process. The simulation experiment results show that the robot can switch modes stably on terrain with a friction coefficient as low as 0.2, and can climb over an obstacle 3.9 times as tall as its wheel radius. Full article

The masses of hadrons in the vacuum, where the chiral symmetry is restored, and in the medium are generally different even when the changes in the order parameters of chiral symmetry are the same. Here, we first discuss the relation between the hadron masses and the chiral symmetry breaking in approaches based on operator product expansion (OPE). We then discuss what additional changes occur to the hadron masses when going from the chiral symmetry restored vacuum to nuclear medium and/or finite temperature. The work will highlight how we can identify the effects of chiral symmetry restoration from experimental observations. Full article

We propose a new, data-driven model for the prediction of the outcomes of NBA and possibly other basketball league games by using machine learning methods. The paper starts with a strict mathematical formulation of the basketball statistical quantities and the performance indicators derived from them. The backbone of our model is the extended team efficiency index, which consists of two asymmetric parts: (i) the team efficiency index, generally based on some individual efficiency index—in our case, the NBA player efficiency index, and (ii) the comparing part, in which the observed team is rewarded for every selected feature in which it outperforms its rival. Based on the average of the past extended indices, the predicted extended indices are calculated symmetrically for both teams competing in the observed future game. The relative value of those indices defines the win function, which predicts the game outcome. The prediction model includes the concept of the optimal time window (OTW) for the training data. The training datasets were extracted from maximally four and the testing datasets from maximally two of the five consecutive observed NBA seasons (2013/2014–2017/2018). The model uses basic, derived, advanced, and league-wise basketball game elements as its features, whose preparation and extraction were briefly discussed. The proposed model was tested for several choices of the training and testing sets’ seasons, without and with OTWs. The average obtained prediction accuracy is around 66%, and the maximal obtained accuracy is around 78%. This is satisfactory and in the range of better results in the works of other authors. Full article

The factorization method was introduced by Schrödinger in 1940. Its use in bound-state problems is widely known, including in supersymmetric quantum mechanics; one can create a factorization chain, which simultaneously solves a sequence of auxiliary Hamiltonians that share common eigenvalues with their adjacent Hamiltonians in the chain, except for the lowest eigenvalue. In this work, we generalize the factorization method to continuum energy eigenstates. Here, one does not generically have a factorization chain—instead all energies are solved using a “single-shot factorization”, enabled by writing the superpotential in a form that includes the logarithmic derivative of a confluent hypergeometric function. The single-shot factorization approach is an alternative to the conventional method of “deriving a differential equation and looking up its solution”, but it does require some working knowledge of confluent hypergeometric functions. This can also be viewed as a method for solving the Ricatti equation needed to construct the superpotential. Full article

Shannon developed the idea of entropy in 1948, which relates to the measure of uncertainty associated with a random variable X. The contribution of the extropy function as a dual complement of entropy is one of the key modern results based on Shannon’s work. In order to develop the inferential aspects of the extropy function, this paper proposes a non-parametric kernel type estimator as a new method of measuring uncertainty. Here, the observations are exhibiting $\alpha$-mixing dependence. Asymptotic properties of the estimator are proved under appropriate regularity conditions. For comparison’s sake, a simple non-parametric estimator is proposed, and in this respect, the performance of the estimator is investigated using a Monte Carlo simulation study based on mean-squared error and using two real-life data. Full article

A quasi-affine transformation evolutionary algorithm improved by the Taguchi strategy, levy flight and the restart mechanism (TLR-QUATRE) is proposed in this paper. This algorithm chooses the specific optimization route according to a certain probability, and the Taguchi strategy helps the algorithm achieve more detailed local exploitation. The latter two strategies help particles move at random steps of different sizes, enhancing the global exploration ability. To explore the new algorithm’s performance, we make a detailed analysis in seven aspects through comparative experiments on CEC2017 suite. The experimental results show that the new algorithm has strong optimization ability, outstanding high-dimensional exploration ability and excellent convergence. In addition, this paper pays attention to the demonstration of the process, which makes the experimental results credible, reliable and explainable. The new algorithm is applied to fault detection in wireless sensor networks, in which TLR-QUATRE is combined with back-propagation neural network (BPNN). This study uses the symmetry of generation and feedback for network training. We compare it with other optimization structures through eight public datasets and one actual landing dataset. Five classical machine learning indicators and ROC curves are used for visualization. Finally, the robust adaptability of TLR-QUATRE on this issue is confirmed. Full article

The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Positively right-skewed data applicable to the log-normal distribution are frequently observed in the fields of environmental studies, biology, and medicine. The number of zero observations follows a binomial distribution. However, problems can arise in the analysis of data containing zero observations along with log-normally distributed data, for which the delta-lognormal distribution is often referred to for using the analysis of the data. In statistics, the percentile provides the relative standing of a numerical data point when compared to all of the others in a distribution with reference to the observations at or below it. In this study, estimates for the confidence interval for the ratio of the percentiles of two delta-lognormal distributions are constructed using fiducial generalized confidence interval approaches based on the fiducial quantity and the optimal generalized fiducial quantity, the Bayesian approach, and the parametric bootstrap method. As assessed by Monte Carlo simulations using the RStudio programming in terms of the coverage probability and the average length, the Bayesian approach performed quite well by providing adequate coverage probabilities along with the shortest average lengths in all of the scenarios tested. Daily rainfall data contain both zero and positive values. The daily rainfall data can usually be fitted to the delta-lognormal distribution. Their application to rainfall data is also provided to illustrate their efficacies with real data. The efficacy of the approach is used to compare two rainfall dispersion populations. Full article

In cases when it is desirable to transport medication through blood vessels, especially when dealing with brain cancer being confronted with the narrow arteries in the brain, the blood–brain barrier makes medical treatment difficult. There is a need of expanding the diameters of the arteries in order to facilitate the transport of medications. Recent research has pointed to various ways to improve this situation; in particular, the use an ultrasound acting on microbubbles in the blood stream has turned out to be a promising option. Here, a different possibility of enlarging the diameters of arteries is discussed, namely to exploit the electrostrictive pressure produced by internal strong, ultrashort and repetitive laser pulses. Each pulse will at first give rise to inward-directed optical forces, and once the pulse terminates, there will be a hydrodynamical bouncing flow in the outward radial direction, giving an outward impulse to the vessel wall. In the absence of friction, a symmetric oscillation picture emerges. Clearly, a supply of repetitive pulses will be needed (at a parametric resonance) to make the effect appreciable. The effect has, to our knowledge, not been discussed before. We give an approximate optical and hydrodynamical theory of it. The calculations indicate promising results for the wall pressure, although experimental work is desirable to demonstrate whether the idea can be useful in practice. Our calculation is made from a general physical perspective that is not necessarily linked to medical applications. Full article

Reference data on the asymmetry of facial thirds of children is still scarce, although it can offer meaningful comparative information for clinical studies. This study aims to provide reference data on the facial asymmetry of Italian children using a 3D analysis of facial thirds divided according to the trigeminal nerve distribution (upper, middle, and lower). A 3D surface-based approach was conducted on the digital models of the faces of 135 children (74 M, 61 F), acquired by stereophotogrammetry. In addition to sex, two different age classes were analyzed (4–8 years and 9–12 years). For each facial third, the asymmetry was expressed as root-mean-square distance (RMS) by calculating the point-to-point distances between the original and the reflected 3D models. A 3-way ANOVA test verified significant differences between the two sexes, the two age classes, and the three facial thirds (p-value < 0.05), and also their interaction. Significant differences were found between the sexes (females were more symmetric, p = 0.005) and the two age groups (younger were more symmetric p < 0.001). According to Tukey’s HSD post-hoc test, among the thirds, the middle one proved to be significantly more symmetrical (p < 0.001). No significant interaction impacting the asymmetry was found when the main factors were considered in any combination. Reference data on the “normal” facial asymmetry of Italian children was provided for further clinical purposes. Normal children have low average RMS values (0.30–0.51 mm) and younger, in particular females, proved more symmetrical than older children, while among the facial surfaces, the middle proved most symmetrical in both sexes, although with little clinical relevance. Since there is no consensus on the amount of symmetry deemed clinically acceptable, further studies on larger randomized samples are auspicial. Full article

Mathematical concepts are aesthetic tools that are useful to create methods or solutions to real-world problems in theory and practice, and that sometimes contain symmetrical and asymmetrical structures due to the nature of the problems. In this study, we investigate whether the sequence spaces ${\mathcal{X}}_p^q,$ $0\le p<\infty ,$ and ${\mathcal{X}}_{\infty }$, which are constructed by q-Cesáro matrix, satisfy some of the further properties described with respect to the bounded linear operators on them. More specifically, we answer to the question: “Which of these spaces have the Approximation, Dunford-Pettis, Radon–Riesz and Hahn–Banach extension properties?”. Furthermore, we try to investigate some geometric properties such as rotundity and smootness of these spaces. Full article

We studied a superbounce scenario in a set up of the Brans–Dicke (BD) theory. The BD parameter was considered to be time-dependent and was assumed to evolve with the Brans–Dicke scalar field. In the superbounce scenario, the model bounced at an epoch corresponding to a Big Crunch provided the ekpyrotic phase continued until that time. Within the given superbounce scenario, we investigated the evolution of the BD parameter for different equations of state. We chose an axially symmetric metric that has an axial symmetry along the x-axis. The metric was assumed to incorporate an anisotropic expansion effect. The effect of asymmetric expansion and the anisotropic parameter on the evolving and non-evolving parts of the BD parameter was investigated. Full article

In this article, Euler’s technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter ($\rho$) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator’s suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances. Full article

A particular form of the time-dependent deceleration parameter is used to examine the accelerated expansion of the universe and the phase transition in this expansion in the context of $f(R,T)$ gravity theory for the flat FRW model. The modified field equations are solved under the choice of $f(R,T)=R+2f\left(T\right)$. The best fit values of the model parameters that would be consistent with the recent observational datasets that are estimated. For this estimation, 57 points from Cosmic Chronometers (CC) datasets and 1048 points from Pantheon supernovae datasets are used. Bayesian analysis and likelihood function are applied together with Markov Chain Monte Carlo (MCMC) method at $1\sigma$ and $2\sigma$ confidence levels. Then, the physical behavior of parameters such as density, pressure and cosmographic parameters corresponding to these constrained values of the model parameters are analyzed. Looking at the deceleration parameter, it is seen that the universe has passed from a decelerating expansion phase to an accelerating phase. As a result, it has been shown that the cosmological model $f(R,T)$ that we discussed can explain the accelerating expansion of the late universe well without resorting to any dark energy component in the energy-momentum tensor. Full article

Background: Studies have shown that symmetry plays an aesthetic role and has a positive effect on the perception of human faces. Our work hypothesizes that facial symmetry positively correlates with physical attractiveness and, thus, with higher visual evaluations of future doctors. Materials and methods: Observational study of 46 students (26 women and 20 men), comparing subjective indicators, symmetry of their facial features, and students’ academic performance. Results: We found no correlation between these subjective results and an objective factor of symmetry facial recognition. User evaluators’ subjective assessments of students’ physical appearance showed significant gender differences for almost all the domains assessed. Moreover, these variables were correlated to each other: women were perceived more positively than men. There were also correlations in the variables related to academic performance but no gender differences. We did not observe any relationship between subjective variables related to physical appearance and objective ones related to academic performance. Conclusion: Facial symmetry was not correlated with positive physical appearance and, therefore, with a better evaluation of future doctors by patients. Users perceive women physicians more positively, despite there being no difference at an academic level. Full article

The distributed assembly scheduling problem with a hybrid-flow shop for fabrication is seldom studied, and some real-life constraints such as factory eligibility are seldom handled. In this study, a distributed assembly hybrid-flow shop-scheduling problem (DAHFSP) with factory eligibility is investigated, which has some symmetries on machines. A shuffled frog-leaping algorithm with cooperations (CSFLA) is applied to minimize makespan. A problem-related feature is used. Memeplexes are evaluated, and group 1, with the two best memeplexes, and group 2, with the two worst memeplexes, are formed. A new cooperation between memeplexes and an adaptive search strategy are implemented in groups 1 and 2, respectively. An adaptive cooperation between groups 1 and 2 is also given. Population shuffling is executed every T generations. A number of computational experiments are conducted. Computational results demonstrate that new strategies are effective and CSFLA is a very competitive algorithm for DAHFSP with factory eligibility. Full article

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of bi-univalent functions via the principle of subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on the estimation of the coefficients $|a_{\ell }|(\ell =2,3)$ and the Fekete–Szegö inequality for functions belonging to these subfamilies of bi-univalent functions. Several corollaries and implications of the findings are discussed. Overall, this study presents a new approach for constructing bi-univalent functions and provides valuable insights for further research in this area. Full article

With the purpose of achieving current control by using intense laser field manipulation, we investigate the effect of carrier-envelope phase (CEP) on residual current in SiO₂ crystals. By solving semiconductor Bloch equations, we found that the CEP can strongly influence the carrier population of the conduction band, which means that it can act as a simple, but useful, tool to control residual current. That is, the resultant asymmetric distribution in the first Brillouin zone gave rise to non-zero residual current. Additionally, we further consider the two-color laser scheme to achieve better control of residual current, showing that asymmetric two-color laser fields can induce the maximum residual current. Full article

We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and $\Lambda$ term. We study so-called cosmological-type solutions defined on the product manifold $M=\mathbb{R}\times {\mathbb{R}}^3\times K$, where K is $6d$ a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: $H>0$ and h obeying $H+2h\ne 0$. We also present static analogs of these cosmological solutions (for $H\ne 0$, $h\ne H$, and $H+2h\ne 0$). The islands of stability for both classes of solutions are outlined. Full article