Symmetry

After the appearance of relation-theoretic contraction principle due to Alam and Imdad, the domain of fixed point theory applied to relational metric spaces has attracted much attention. Existence and uniqueness of fixed/coincidence points satisfying the different types of contractivity conditions in the framework of relational metric space have been studied in recent times. Such results have the great advantage to solve certain types of matrix equations and boundary value problems for ordinary differential equations, integral equations and fractional differential equations. This article is devoted to proving the coincidence and common fixed point theorems for a pair of mappings $(\mathcal{T},\mathcal{S})$ employing relation-theoretic $(\varphi ,\psi )$-contractions in a metric space equipped with a locally finitely $\mathcal{T}$-transitive relation. Our results improve, modify, enrich and unify several existing coincidence points as well as fixed point results. Several examples are provided to substantiate the utility of our results. Full article

A Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). This research seeks to examine the topological properties of FFSs and to establish the notion of “Fermatean fuzzy topology” (FFT). An FFT is the generalisation of existing fuzzy topologies. Several aspects of FFT are examined and various novel concepts are proposed, which include Fermatean fuzzy $\alpha$-continuity between FFTSs and Fermatean fuzzy connectedness. To deal multiple challenges in sustainable supply chain management, a Fermatean fuzzy “combinative distance-based assessment” (CODAS) method was developed. The proposed FF CODAS technique involves various key features for MCDM. Firstly, a known reputation vector or equal expert weights is determined based on the reputation, experience and qualifications of the experts. Secondly, the Fermatean fuzzy direct rating approach is used to establish the relative relevance of criteria based on the expert group’s evaluation preferences. Thirdly, the Fermatean fuzzy CODAS approach is used to construct alternative orderings based on their assessment scores. Finally, an application is developed to show the benefit of the suggested supplier selection approach. Additionally, the symmetry of an optimal decision in application is carried out by a comparison analysis of the suggested models with some existing models. Full article

In flat spacetime, the Dirac equation is the “square root” of the Klein–Gordon equation in the sense that, by applying the square of the Dirac operator to the Dirac spinor, one recovers the equation duplicated for each component of the spinor. In the presence of gravity, applying the square of the curved-spacetime Dirac operator to the Dirac spinor does not yield the curved-spacetime Klein–Gordon equation, but instead yields the Schrödinger–Dirac covariant equation. First, we show that the latter equation gives rise to a generalization to spinors of the covariant Gross–Pitaevskii equation. Then, we show that, while the Schrödinger–Dirac equation is not conformally invariant, there exists a generalization of the equation that is conformally invariant but which requires a different conformal transformation of the spinor than that required by the Dirac equation. The new conformal factor acquired by the spinor is found to be a matrix-valued factor obeying a differential equation that involves the Fock–Ivanenko line element. The Schrödinger–Dirac equation coupled to the Maxwell field is then revisited and generalized to particles with higher electric and magnetic moments while respecting gauge symmetry. Finally, Lichnerowicz’s vanishing theorem in the conformal frame is also discussed. Full article

Depending on their motivation, offenders have different goals, and disclosure of information is not always such a goal. It often happens that the purpose of the offender is to disrupt the normal operation of the system. This can be achieved both by acting directly on the information and by acting on the elements of the system. Actions of this kind lead to a violation of integrity and availability, but not confidentiality. It follows that the process of forming a threat model for the integrity and availability of information differs from a similar process for confidentiality threats. The purpose of this study is to develop an information integrity threat model that focuses on threats disrupting the normal operation of the system. The research methodology is based on the methods of system analysis, graph theory, discrete mathematics, and automata theory. As a result of the research, we proposed a model of threats to the integrity and availability of information. The proposed threat model differs from analogues by a high level of abstraction without reference to the subject area and identification of threats to the availability of information as a subset of threats to the integrity of the information transmission channel. Full article

The importance of partial differential equations in physics, mathematics and engineering cannot be emphasized enough. Partial differential equations are used to represent physical processes, which are then solved analytically or numerically to examine the dynamical behaviour of the system. The new iterative approach and the Homotopy perturbation method are used in this article to solve the fractional order Fokker–Planck equation numerically. The Caputo sense is used to characterize the fractional derivatives. The suggested approach’s accuracy and applicability are demonstrated using illustrations. The proposed method’s accuracy is expressed in terms of absolute error. The proposed methods are found to be in good agreement with the exact solution of the problems using graphs and tables. The results acquired using the given approaches are also obtained at various fractional orders of the derivative. It is observed from the graphs and tables that fractional order solutions converge to an integer solution when the fractional orders approach the integer-order of the problems. The tabular and graphical view for the given problems is obtained through Maple. The presented approaches can be applied to existing non-linear fractional partial differential equations due to their accurate, simple and straightforward implementation. Full article

This numerical analysis aims to observe and analyze the combined convection characteristics of the micropolar tri-hybrid nano-liquid that moves around a cylindrical object, and, in addition, to compare its thermal behavior to that of hybrid and mono nano-fluids. For this purpose, the problem is modeled by developing the Tiwari and Das models, then the governing model is converted into dimensionless expressions, and finally, the problem is solved using the Keller box approximation. The current findings are compared with previously published results to show that the present method is sufficiently accurate for physical and engineering applications. By examining and analyzing the extent to which skin friction, the Nusselt number, velocity, angular velocity, and temperature are affected by some critical factors, the following points are revealed: A greater value of the micropolar and magnetic factors can result in curtailing the heat transmission rate, velocity, and angular velocity. Higher values of the mixed convection factor can contribute to a better rate of energy transfer and can grant the micropolar tri-hybrid nano-liquid a higher velocity. Regardless of the influencing factors, the maximum value of all considered physical groups is achieved by using ternary hybrid nano-liquids. Full article

We present the dipole cosmological principle, i.e., the notion that the Universe is a Copernican cosmology that agrees with the cosmic flow. It suits the most symmetric paradigm that generalizes the Friedmann–Lemaître–Robertson–Walker ansatz in the context of numerous suggestions that have appeared in the literature for non-kinematic components in the cosmic microwave background dipole. Field equations in our “dipole cosmology” are still ODEs, but we now have four instead of two Friedmann equations. The two extra functions can be regarded as additional scale factors that break the isotropy group from SO(3) to U(1) and a “tilt” that denotes the cosmic flow. The result is an axially isotropic Universe. We examined the dynamics of the expansion rate, anisotropic shear, and tilt in some cases. One important observation is that the cosmic flow (tilt) can grow while the anisotropy (shear) dies down. Full article

With the help of molecular dynamics simulations and an artificial sodium channel model, we corroborated that the application of terahertz stimulation at a characteristic frequency can largely increase the permeability of the sodium channel by a factor of 33.6. The mechanism is that the carboxylate groups in the filter region transfer the absorbed terahertz photon energy to the sodium ions, which increase the ions’ kinetic energy; this results in breaking the hydrated hydrogen bonding network between the hydrosphere layer of the ions and the carboxylate groups, thereby increasing their diffusion and reducing the energy barrier for them to cross the channel. This study on terahertz-driven particle transmembrane transport offers new ideas for targeted therapy of channel diseases and for developing novel integrated engineering systems in energy conversion and storage. Full article

Vacuum polarization of a scalar field on the short throat wormhole background is investigated. The scalar field is assumed to be massless, having an arbitrary coupling to the scalar curvature of spacetime. In addition, it is supposed that the field is in a thermal state with an arbitrary temperature. Full article

The precise and effective prognosis of safety risks is vital to ensure structural safety. This study proposed an intelligent method for the health monitoring of cable network structures, based on the fusion of twin simulation and sensory data. Firstly, the authors have established a framework that integrate simulation data with sensory data. The authors have established a high-fidelity twin model using genetic algorithm. The mechanical parameters of the structures were obtained based on the twin model. The key components of the structure are captured by using Bayesian probability formula and multiple mechanical parameters. The fusion mechanism of twin simulation and random forest (RF) was established to capture the key influencing factors. The coupling relationship between structural safety state and key factors was obtained, and the safety maintenance mechanism was finally formed. In view of the risk prognosis of the structure, the establishment method for the database of influencing factors and maintenance measures was formed. The authors used the Speed Skating Gymnasium of 2022 Winter Olympic Games (symmetric structure) as the case study for validating the feasibility and effectiveness of the proposed method. The theoretical method formed in this study has been applied to the symmetric structure, which provides ideas for the safety maintenance of large symmetric structures. Meanwhile, this research method also provides a reference for the health monitoring of asymmetric structures. Full article

This study focuses on selected members of the general salen-analogues family possessing two O-H⋯N hydrogen bonds, namely three isomers of N,N’-bis(salicylidene)-X-phenylenediamine, denoted as ortho, meta and para. Two of the isomers are not planar in the published crystal structures. The current study tackles the problem of symmetry and interactions within the molecules, as well as in the crystal lattice. The aromaticity of the phenyl rings is evaluated using the Harmonic Oscillator Model of Aromaticity (HOMA) index. Intra- and inter-molecular non-covalent interactions are studied via Hirshfeld surface analysis, Independent Gradient Model (IGM), Quantum Theory of Atoms in Molecules (QTAIM), Non-Covalent Interaction (NCI) index, Electron Localisation Function (ELF), Core-Valence Bifurcation (CVB) index and Symmetry-Adapted Perturbation Theory (SAPT). Density Functional Theory (DFT) simulations were carried out in vacuo and with solvent reaction field based on Polarisable Continuum Model (IEF-PCM formulation) at the $\omega$B97XD/6-311+G(2d,2p) level. Crystal structure analyses were performed for the data reported previously in the literature. The obtained results demonstrate that the three isomers differ greatly in their structural properties (molecular symmetry is broken for the ortho and meta isomers in the solid state) and ability to form intermolecular interactions, while retaining overall similar physico-chemical characteristics, e.g., aromaticity of the phenyl rings. It was found that the presence of the polar solvent does not significantly affect the structure of the studied compounds. An application of the Hirshfeld surface analysis revealed the nature of the non-covalent interactions present in the investigated crystals. The SAPT results showed that the stability of the dimers extracted from the crystals of the Schiff base derivatives arises from electrostatics and dispersion. Full article

Recently, decentralized file systems are widely used to overcome centralized file systems’ load asymmetry between nodes and the scalability problem. Due to the lack of a metadata server, decentralized systems require more RPC requests to control metadata processing between clients and servers, which adversely impacts the I/O performance and traffic imbalance by increasing RPC latency. In this paper, we propose an efficient I/O scheme to reduce the RPC overhead in decentralized file systems. Instead of sending a single RPC request at a time, we enqueued the RPCs in the global queue and merged them into larger RPC requests, thus avoiding excessive RPC latency overheads. The experimental results showed that our scheme improves write and read performance by up to 13% and 16%, respectively, compared with those of the original. Full article

The polarization dependence of the cross sections of two-photon transitions including X-ray scattering was analyzed. We developed the regular approach to the derivation of the polarization parameters of photoprocesses. Our approach is based on the tensor representation of the photon density matrix, which is written in terms of the unit vectors directed along the major axis of the polarization ellipse ($\widehat{\mathbf{ϵ}}$) and the photon propagation ($\widehat{\mathbf{k}}$). Explicit expressions for the product of two photon density matrices were derived. As an example, the parametrization of the polarization dependence of the X-ray scattering by closed-shell atoms is given both in terms of (i) scalar products of photon vectors ${\widehat{\mathbf{ϵ}}}_{1,2}$, ${\widehat{\mathbf{k}}}_{1,2}$ and (ii) X-ray Stokes parameters. We discuss the applicability of the atomic scattering for the measurement of the polarization of X-rays. Full article

Based on the density functional theory and crystal structure prediction approaches, we found a novel high-pressure structure of Fe${}_2$CO${}_4$-$P\overline{1}$. It is characterized by the presence of ethane-like O${}_3$C–CO${}_3$ groups or so-called orthooxalate groups. The formation of such O${}_3$C–CO${}_3$ groups has been proposed earlier in melts and aqueous carbonate solutions, but no such examples were known in inorganic crystalline materials. We found that this structure is dynamically and thermally stable at pressures of 50 GPa. Similar structures were also predicted to be dynamically stable for Mn${}_2$CO${}_4$, Ni${}_2$CO${}_4$, and Co${}_2$CO${}_4$. In addition, FeCO${}_3$ was found to transform into a similar structure with O${}_3$C–CO${}_3$ orthooxalate groups at a pressure above 275 GPa. Additionally, for the first time, we describe the self-diffusion of metal atoms in carbonates at high pressure and at high temperatures. The prediction of novel carbonate structures extends the crystal chemistry of inorganic carbonates beyond the established ones with [CO${}_3$] triangles, [C${}_2$O${}_5$] pyro-groups, and [CO${}_4$] tetrahedra. Full article

The present study aimed to measure and compare anatomic parameters in contralateral maxillary second molars. A total of 18 intact maxillary second molar pairs (n = 36) extracted from 18 patients were scanned with micro-computed tomography (micro-CT) and then reconstructed. Axial, sagittal, and cross-sectional slices were used to analyze the parameters (lengths, widths, and thicknesses) and evaluate the symmetry of the right and left sides. The number of root canals and their internal patterns were classified following Vertucci’s classification. The number of lateral canals and their locations were also noted. Contralateral second molar pairs demonstrated a high degree of similarity in terms of the linear measurements (lengths, widths, and thicknesses). The root canal anatomy configuration symmetry of mesiobuccal, distobuccal, and palatal roots according to Vertucci’s classification were 41.1%, 88.2%, and 94.4%, respectively. In total, 41.6% of mesiobuccal roots, 2.7% of distobuccal roots, and 30.6% of palatal roots had at least one lateral canal. The apical third (38.7%) was the most frequent location of lateral canals, followed by the middle third (32.3%) of the root. This study provides insight into the anatomy of the root canals of contralateral maxillary second molars, which is valuable for both practitioners and researchers. Full article

The article provides an $\alpha$-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using $\alpha$-cut of fuzzy numbers wherein the $\alpha$- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of $r\in (0,1]$ are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique. Full article

In order to meet the requirements of high performance, miniaturization, low cost, low power consumption and multi-function, three-dimensional (3D) integrated technology has gradually become a core technology. With the development of 3D integrated technology, it has been used in imaging sensors, optical integrated microsystems, inertial sensor microsystems, radio-frequency microsystems, biological microsystems and logic microsystems, etc. Through silicon via (TSV) is the core technology of a 3D integrated system, which can achieve vertical interconnection between stacked chips. In this paper, the development and progress of multi-physics simulation design for TSV-based 3D integrated systems are reviewed. Firstly, the electrical simulation design of TSV in a 3D integrated system is presented, including the lumped parameters model-based design and numerical computation model-based design. Secondly, the thermal simulation design of TSV in a 3D integrated system is presented based on the analytical model or numerical computation model. Thirdly, the multi-physics co-simulation design of TSV in a 3D integrated system is presented, including the thermal stress and electron thermal coupling simulation design. Finally, this paper is concluded, and the future perspectives of 3D integrated systems are presented, including the advanced integrated microsystems, the crossed and reconfigurable architecture design technology and the standardized and intelligent design technology. Full article

Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and it has logarithmic corrections and polynomials of logarithms of the black hole area. Full article

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: $\wp (s,r)\le \wp (s,z)+\eta (z,r)\wp (z,r),$ and keeping the symmetry condition that is $\wp (s,r)=\wp (r,s)\mathrm{for}\mathrm{all}r,s$. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations. Full article