Symmetry

The article addresses the issue of mobile robotic platform positioning in GNSS-denied environments in real-time. The proposed system relies on fusing data from an Inertial Measurement Unit (IMU), magnetometer, and encoders. To get symmetrical error gauss distribution for the measurement model and achieve better performance, the Error-state Extended Kalman Filter (ES EKF) is chosen. There are two stages of vector state determination: vector state propagation based on accelerometer and gyroscope data and correction by measurements from additional sensors. The error state vector is composed of the velocities along the x and y axes generated by combining encoder data and the orientation of the magnetometer around the axis z. The orientation angle is obtained from the magnetometer directly. The key feature of the algorithm is the IMU measurements’ isolation from additional sensor data, with its further summation in the correction step. Validation is performed by a simulation in the ROS (Robot Operating System) and the Gazebo environment on the grounds of the developed mathematical model. Trajectories for the ES EKF, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms are obtained. Absolute position errors for all trajectories are calculated with an EVO package. It is shown that using the simplified version of IMU’s error equations allows for the achievement of comparable position errors for the proposed algorithm, EKF and UKF. Full article

Navier–Stokes equations (NS-equations) are applied extensively for the study of various waves phenomena where the symmetries are involved. In this paper, we discuss the NS-equations with the time-fractional derivative of order $\beta \in (0,1)$. In fractional media, these equations can be utilized to recreate anomalous diffusion equations which can be used to construct symmetries. We examine the initial value problem involving the symmetric Stokes operator and gravitational force utilizing the Caputo fractional derivative. Additionally, we demonstrate the global and local mild solutions in $H^{\alpha ,p}$. We also demonstrate the regularity of classical solutions in such circumstances. An example is presented to demonstrate the reliability of our findings. Full article

Inter- and intra-molecular proton-transfers between functional groups in nucleobases play a principal role in their interactions (pairing) in nucleic acids. Although prototropic rearrangements (intramolecular proton-transfers) for neutral pyrimidine bases are well documented, they have not always been considered for their protonated and deprotonated forms. The complete isomeric mixtures in acid-base equilibria and in acidity–basicity parameters have not yet been examined. Taking into account the lack of literature and data, research into the question of prototropy for the ionic (protonated and deprotonated) forms has been undertaken in this work. For the purposes of this investigation, two isomeric pyrimidine bases (C—cytosine and iC—isocytosine) were chosen. They exhibit analogous (symmetrical) general acid-base equilibria (intermolecular proton-transfers). Being similar polyfunctional tautomeric systems, C and iC possess two labile protons and five conjugated tautomeric sites. However, positions of exo groups are different. Consequently, structural conversions such as prototropy, rotational, and geometrical isomerism of exo groups (=O/−OH and =NH/−NH₂) and their intramolecular interactions with endo groups (=N−/>NH) possible in neutral C and iC and in their ionic forms lead to some differences in compositions of isomeric mixtures. By application of quantum–chemical methods to the isolated (in vacuo) species, stability of all possible neutral and ionic isomers has been examined and the candidate isomers selected. The complete isomeric mixtures have been considered for the first time for di-deprotonated, mono-deprotonated, mono-protonated, and di-protonated forms. Protonation–deprotonation reactions have been analyzed in the gas phase that models non-polar environment. The gas-phase microscopic (kinetic) and macroscopic (thermodynamic) acidity–basicity parameters have been estimated for each step of acid-base equilibria. When proceeding from di-anion to di-cation in four steps of protonation–deprotonation reaction, the macroscopic proton affinities for C and iC differ by less than 10 kcal mol⁻¹. Their DFT-calculated values are as follows: 451 and 457, 340 and 339, 228 and 224, and 100 and 104 kcal mol⁻¹, respectively. Differences between the microscopic proton affinities for analogous isomers of C and iC seem to be larger for the exo than endo groups. Owing to variations of relative stabilities for neutral and ionic isomers, in some cases they are even larger than 10 kcal mol⁻¹. Full article

In recent years, due to the slowdown of the global economy and the instability of the stock market and real estate market, the art market has gradually become the third-largest investment market after the former two. As more and more funds flow into the art market, the two seemingly unrelated industries, art, and finance have increasingly close cooperation due to the growing prosperity of the art market. As a very important part of the process of art financialization, the development of art banks has also received extensive attention from all walks of life. In addition, blockchain, as a technology to jointly maintain reliable databases through trustlessness and decentralization, has grown rapidly in recent years, and is gradually applied in various fields. The advantages of blockchain technology are decentralization, anonymity, immutability, and traceability of stored information. The proposed scheme applies the characteristics of blockchain technology to Art Bank’s art rental system, and will have the following advantages: the use of Hyperledger technology, various art banks being merged into an alliance, and information among alliance members being shared, which is convenient for tenants to comprehensively query a single item. Using blockchain technology, in an environment where there is no central authority, under the premise of preventing the tampering of artwork-related information, ensures that the detailed information of the artwork is shared. Traditional leasing agreements can be compiled into smart contract leasing contracts to automatically run and manipulate data. The proposed protocol satisfies the following security requirements: identities’ mutual authentication, non-repudiation between every two parties, and other major security requirements based on blockchain. When a dispute arises, our proposed scheme also has an arbitration mechanism to clarify responsibilities. Full article

This work reports supercritical water oxidation (SCWO) of organic pollutants in industrial wastewater in the absence and presence of catalysts. To increase the efficiency of the oxidation process, the SCWO of organic compounds in industrial wastewater was performed in the presence of various iron- and manganese-containing heterogeneous catalysts (Fe-Ac, Fe-OH, and Mn-Al). The catalytic and non-catalytic SCWO of organic compounds in wastewater from PJSC “Nizhnekamskneftekhim”, generated from the epoxidation of propylene with ethylbenzene hydroperoxide in the process of producing propylene oxide and styrene (PO/SM), was performed. The effect of operational parameters (temperature, pressure, residence time, type of catalysts, oxygen excess ratio, etc.) on the efficiency of the process of oxidation of organic compounds in the wastewater was studied. SCWO was studied in a flow reactor with induction heating under different temperatures (between 673.15 and 873.15 K) and at a pressure of 22.5 MPa. The reaction time ranged from 1.8 to 4.83 minutes. Compressed air was used as an oxidizing agent (oxidant) with an oxidant ratio of two to four. A pseudo-first-order model expressed the kinetics of the SCWO processes, and the rate constants were evaluated. In the present work, in order to optimize the operation parameters of the SCWO process, we used the thermodynamic properties of near- and supercritical water by taking into account the asymmetric behavior of the liquid–vapor coexistence curve. Full article

The eco-evolutionary theory of developmental instability predicts that small, non-directional deviations from perfect symmetry in morphological traits (termed fluctuating asymmetry, FA) emerge when an individual is unable to buffer environmental or genetic stress during its development. Consequently, FA is widely used as an index of stress. The goal of the present study was to experimentally test a seemingly trivial prediction derived from the theory of developmental instability—and from previous observational studies—that significant growth retardation (which indicates stress) in plants is accompanied by an increase in FA of their leaves. We induced stress, evidenced by a significant decrease in biomass relative to control, in cucumber (Cucumis sativus), sweet pepper (Capsicum annuum), and common bean (Phaseolus vulgaris) by applying water solutions of copper and nickel to the soil in which plants were grown. Repeated blind measurements of plant leaves revealed that leaf FA did not differ between stressed and control plants. This finding, once again, demonstrated that FA cannot be seen as a universal indicator of environmental stress. We recommend that the use of FA as a stress index is discontinued until the scope of the developmental instability theory is clarified and its applicability limits are identified. Full article

Scientific support depot location and reasonable spare parts transportation are the keys to improving the support level of complex systems. The current equipment support system has the problems of chaotic warehouse layout and low efficiency of spare parts. The reliability and completeness of spare parts’ historical data are hard to believe. In order to deal with the cognitive uncertainty caused by the asymmetry of data, this paper adopts the uncertainty theory to optimize the depot location and transportation volume. Under the constraints of shortage rate, supply availability, average logistic delay time, and inventory limit, the uncertain chance-constrained model of equipment supporting depot is established. The optimization model is transformed into a deterministic model by using the inverse uncertainty distribution. The genetic algorithm is used to optimize the solution of this model. Finally, the practicability and operability of the model method are verified through the example analysis. Full article

Cyber threat intelligence (CTI) sharing has gradually become an important means of dealing with security threats. Considering the growth of cyber threat intelligence, the quick analysis of threats has become a hot topic at present. Researchers have proposed some machine learning and deep learning models to automatically analyze these immense amounts of cyber threat intelligence. However, due to a large amount of network security terminology in CTI, these models based on open-domain corpus perform poorly in the CTI automatic analysis task. To address this problem, we propose an automatic CTI analysis method named K-CTIAA, which can extract threat actions from unstructured CTI by pre-trained models and knowledge graphs. First, the related knowledge in knowledge graphs will be supplemented to the corresponding position in CTI through knowledge query and knowledge insertion, which help the pre-trained model understand the semantics of network security terms and extract threat actions. Second, K-CTIAA reduces the adverse effects of knowledge insertion, usually called the knowledge noise problem, by introducing a visibility matrix and modifying the calculation formula of the self-attention. Third, K-CTIAA maps corresponding countermeasures by using digital artifacts, which can provide some feasible suggestions to prevent attacks. In the test data set, the F1 score of K-CTIAA reaches 0.941. The experimental results show that K-CTIAA can improve the performance of automatic threat intelligence analysis and it has certain significance for dealing with security threats. Full article

Laser scanners with rotational Risley prisms produce scan patterns that can be classified as a type of rhodonea curve, because of their symmetry. The present study builds upon the novel, graphical method that we have developed to simulate and analyze such patterns using a commercially available mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France). This graphical method has both the advantage of simplicity (regarding analytical methods) and of generating exact scan patterns (in contrast to approximate methods). The aim of this work is to utilize this method to study symmetry properties of scan patterns produced by a pair of rotational Risley prisms. A multi-parameter analysis is performed, considering the characteristic parameters of the approached scanner: refractive indexes and angles of the prisms, as well as their rotational velocities. Furthermore, Marshall’s parameters are considered: ratios of the rotational velocities and of the prism angles. Because the symmetries are identical for scan patterns generated by all the four possible configurations of a pair of prisms (and only their dimensions are different), the shape of these patterns is studied only for one of these configurations. Therefore, without losing generality, the symmetries of the patterns produced by such scanners are determined, as well as some of their characteristic dimensions. Rules-of-thumb were obtained to be able to generate patterns that are appropriate for a specific application. Moreover, we demonstrated that the existing symmetries simplify the process of obtaining the scan patterns by identifying repetitive parts (defined as structures of symmetry) of a pattern. Full article

A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let $\mathcal{R}$ be a commutative ring with identity, and $Z^{*}\left(\mathcal{R}\right)$ is the set of all non-zero zero divisors of $\mathcal{R}$. Then, $\Gamma \left(\mathcal{R}\right)$ is said to be a zero-divisor graph if and only if $a·b=0$, where $a,b\in V\left(\Gamma \left(\mathcal{R}\right)\right)=Z^{*}\left(\mathcal{R}\right)$ and $(a,b)\in E\left(\Gamma \right(\mathcal{R}\left)\right)$. We define $a\sim b$ if $a·b=0$ or $a=b$. Then, ∼ is always reflexive and symmetric, but ∼ is usually not transitive. Then, $\Gamma \left(\mathcal{R}\right)$ is a symmetric structure measured by the ∼ in commutative rings. Here, we will draw the zero-divisor graph from commutative rings and discuss topological indices for a zero-divisor graph by vertex eccentricity. In this paper, we will compute the total eccentricity index, eccentric connectivity index, connective eccentric index, eccentricity based on the first and second Zagreb indices, Ediz eccentric connectivity index, and augmented eccentric connectivity index for the zero-divisor graph associated with commutative rings. These will help us understand the characteristics of various symmetric physical structures of finite commutative rings. Full article

Geometric function theory combines geometric tools and their applications for information and communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech and sound recognition. Various new subclasses of analytic functions have been defined using quantum calculus to investigate many interesting properties of these subclasses. This article defines a new class of q-starlike functions in the open symmetric unit disc ∇ using symmetric quantum calculus. Extreme points for this class as well as coefficient estimates and closure theorems have been investigated. By fixing several coefficients finitely, all results were generalized into families of analytic functions. Full article

We discuss the hadron–quark crossover accompanied by the formation of Cooper triples (three-body counterpart of Cooper pairs) by analogy with the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer crossover in two-component fermionic systems. Such a crossover is different from a phase transition, which often involves symmetry breaking. We calculate the in-medium three-body energy from the three-body T-matrix with a phenomenological three-body force characterizing a bound hadronic state in vacuum. With increasing density, the hadronic bound-state pole smoothly undergoes a crossover toward the Cooper triple phase where the in-medium three-body clusters coexist with the quark Fermi sea. The relation to the quarkyonic matter model can also be found in a natural manner. Full article

We address classification of permutation matrices, in terms of permutation similarity relations, which play an important role in investigating the reducible solutions of some symmetric matrix equations. We solve the three problems. First, what is the canonical form of a permutation similarity class? Second, how to obtain the standard form of arbitrary permutation matrix? Third, for any permutation matrix A, how to find the permutation matrix T, such that $T^{-1}AT$ is in canonical form? Besides, the decomposition theorem of permutation matrices and the factorization theorem of both permutation matrices and monomial matrices are demonstrated. Full article

We study cold and dense nuclear matter by using the gauge/gravity duality. To this end, we use the Witten–Sakai–Sugimoto model and the V-QCD models with an approach where the nuclear matter is taken to be spatially homogeneous. We focus on the “popcorn” transitions, which are phase transitions in the nuclear matter phases induced by changes in the layer structure of the configuration on the gravity side. We demonstrate that the equation of state for the homogeneous nuclear matter becomes approximately conformal at high densities, and compare our results to other approaches. Full article

In this paper, we suggest an iterative method for solving nonlinear equations that can be used in the physical sciences. This response is broken down into three parts. Our methodology is inspired by both the standard Taylor’s method and an earlier Halley’s method. Three evaluations of the given function and two evaluations of its first derivative are all that are needed for each iteration with this method. Because of this, the unique methodology can complete its goal far more quickly than many of the other methods currently in use. We looked at several additional practical research models, including population growth, blood rheology, and neurophysiology. Polynomiographs can be used to show the convergence zones of certain polynomials with complex values. Polynomiographs are produced as a byproduct, and these end up having an appealing look and being artistically engaging. The twisting of polynomiographs is symmetric when the parameters are all real and asymmetric when some of the parameters are imaginary. Full article

We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potential of the geodesic motion. The Lyapunov stability analysis leads to the same results. Hence, we can conclude that, in the particular case of the geodesic motion on circular orbits in the Gibbons–Maeda–Garfinkle–Horowitz–Strominger, the Lyapunov and the Jacobi stability analysis gives equivalent results. Full article

The aluminum–matrix composites possess are very important for future applications because they have unique mechanical properties. Here, molecular dynamics is used to analyze the bonding of dissimilar metals on the interface of Al/Mg, Al/Ti, and Al/Cu interfaces during deformation treatment – compression combined with shear at room temperature. The terminal-mechanical treatment used in this simulation is a variant of the experimental technique applied to fabricate Al/Metal composites. It is found that there is a critical value of compressive and shear strain required to obtain the strong mixed Al/Metal interface. The diffusion depth of atoms of both components is dependent on the applied strain: (i) linear relationship for Al/Mg; (ii) logarithmic relationship for Al/Ti and Al/Cu. The mechanical behavior under tension and fracture analysis of the obtained interfaces are discussed in terms of atomic-level structural features which allow an understanding of the interconnection between the mechanical behavior and structure mixture near the interface. One of the important criteria for atomic mixing is the symmetry of the interface. After atomic mixing, Al/Ti composite has the highest ultimate tensile strength, Al/Cu—the average, and Al/Mg—the lowest between the considered interfaces, while the fracture strain of Al/Mg and Al/Ti composites are very close and higher than for Al/Cu. The obtained results are significant for the development of fabrication of Al/Metal interface by high-pressure torsion in practice. Full article

The spectral properties of several azulene-oxazolone derivatives containing a phenyloxazolone moiety linked to a substituted azulene ring via a C=C double bond were studied in different solvents of varying polarity. The solvatochromism and the ability of azulene-oxazolone derivatives to recognize heavy metal ions were investigated. In order to estimate the contribution of the non-specific and specific solute–solvent interactions, multiple linear regression analysis using Kamlet–Taft, Catalan and Laurence parameters was applied. These azulene derivatives demonstrate positive solvatochromism. The methyl and isopropyl substituents at the seven-membered azulene ring determine the highest red shifts of the absorption maxima of these azulenyl-vinyl-oxazolones. According to Catalan and Laurence models, the solvent polarizability is a more significant parameter in describing the solvatochromic properties of the azulene-oxazolone derivatives. The azulene-oxazolone compounds under study showed a good response to heavy metal cations (Cd²⁺, Hg²⁺, Cu²⁺ and Pb²⁺). Full article

In this study, we present a new approach with semi-analytical and numerical findings for
solving equations of motion of small orbiter m, which is moving under the combined gravitational
attraction of three primaries, M₁, M₂, and M₃ , in case of the bi-elliptic restricted problem
of four bodies (BiER4BP), where three such primaries, M₁, M₂, and M₃, are moving on elliptic
orbits with hierarchical configuration M₃ << M₂ << M₁ within one plane as follows: third
primary body M₃ is moving on elliptical orbit around second M₂, and second primary M₂ is moving on elliptical orbit around first M₁. Our aim for constructing the aforementioned quasi-
planar motion of planetoid m is obtaining its coordinates supporting its orbit in a regime of close
motion to the plane of orbiting the main bodies M₁, M₂, and M₃. Meanwhile, the system of
equations of motion was successfully numerically explored with respect to the existence and stable
positioning of approximate solution for a Dyson sphere. As a result, the concept of the Dyson sphere
for possible orbiting variety of solar energy absorbers was transformed to the elongated Dyson
space net with respect to their trajectories for the successful process of absorbing the energy from
the Sun; this can be recognized as symmetry reduction. We obtain the following: (1) the solution for
coordinates {x, y} is described by the simplified system of two nonlinear ordinary differential
equations of second order, depending on true anomaly f; (2) the expression for coordinate z is given
by an equation of Riccati-type where small orbiter that quasi-oscillates close to the fixed plane
{x, y, 0}. Full article