Symmetry Of Problem Research Articles

Integral formulas for a class of curvature PDE’s and applications to isoperimetric inequalities and to symmetry problems

Integral formulas for a class of curvature PDE’s and applications to isoperimetric inequalities and to symmetry problems

Multiple-cell cavity design for high mass axion searches: An extended study

The invisible axion is a well-motivated hypothetical particle which could address two fundamental questions in modern physics—the CP symmetry problem in the strong interactions and the dark matter mystery of our universe. The plausible mass (frequency) range of the QCD axion as a dark matter candidate spans from μeV to meV (O(GHz) to O(THz)). The axion haloscope using a resonant cavity has provided the most sensitive search method in the microwave region. However, experimental searches have been limited to relatively low mass regions mainly due to the reduced cavity volume at high masses. As an effective approach for high-mass axion searches, a unique cavity design, featured by multiple identical cells divided by equidistant thin metal partitions in a single cylindrical cavity, was proposed and successfully demonstrated. We perform an extended study to characterize the multiple-cell cavity design and discuss the various advantages it offers for high-mass axion searches.

Making and Breaking—Insight into the Symmetry of Salen Analogues

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 ωB97XD/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.

A Tent Lévy Flying Sparrow Search Algorithm for Wrapper-Based Feature Selection: A COVID-19 Case Study

The “Curse of Dimensionality” induced by the rapid development of information science might have a negative impact when dealing with big datasets, and it also makes the problems of symmetry and asymmetry increasingly prominent. Feature selection (FS) can eliminate irrelevant information in big data and improve accuracy. As a recently proposed algorithm, the Sparrow Search Algorithm (SSA) shows its advantages in the FS tasks because of its superior performance. However, SSA is more subject to the population’s poor diversity and falls into a local optimum. Regarding this issue, we propose a variant of the SSA called the Tent Lévy Flying Sparrow Search Algorithm (TFSSA) to select the best subset of features in the wrapper-based method for classification purposes. After the performance results are evaluated on the CEC2020 test suite, TFSSA is used to select the best feature combination to maximize classification accuracy and simultaneously minimize the number of selected features. To evaluate the proposed TFSSA, we have conducted experiments on twenty-one datasets from the UCI repository to compare with nine algorithms in the literature. Nine metrics are used to evaluate and compare these algorithms’ performance properly. Furthermore, the method is also used on the coronavirus disease (COVID-19) dataset, and its classification accuracy and the average number of feature selections are 93.47% and 2.1, respectively, reaching the best. The experimental results and comparison in all datasets demonstrate the effectiveness of our new algorithm, TFSSA, compared with other wrapper-based algorithms.

New Data on the Isomorphism in Eudialyte-Group Minerals. XII: Refined Structure of the Hydrated Mineral from the Inagli Massif

A hydrated eudialyte-group mineral from the Inagli alkaline massif (Kola Peninsula) has been investigated by electron-probe and X-ray diffraction analyses. The parameters of the trigonal unit cell are as follows: a = 14.1558(3) Å, c = 30.998(1) Å, V = 5378.6(3) Å3, sp. gr. R3; the calculated density is 2.661 g/cm3. The crystal structure is refined to the final reliability factor of R = 3.8% within the anisotropic approximation of atomic displacements using 1230 reflections with F 3σ(F). The simplified formula of the mineral (Z = 3) is (H3O)7Na7.5(K,Sr,Ba,Ce)1.5Zr3Ca6[Si24O68(OH)3(O,OH)]Si1.5Cl1(OH)2H2O1.5. The problems of symmetry of calcium-rich hydrated eudialyte-group minerals are discussed.

The Homily in The Eyes of The Youth: The Problem of Symmetry. A Sociological and Textual Analysis

The article discusses the category of symmetry. As a linguistic category, it is mainly studied in the context of ‘linguistic politeness.’ In textual studies, symmetry defines the shape of an utterance. In the process of communication, symmetry helps prevent differences between the subjects regarding their professional status, different social position or knowledge levels. The sociological studies (survey data from ca. 1 400 participants) show the urgent need to apply symmetry in homiletics as a response to various shortcomings of the process of exchanging thoughts during liturgy. Symmetry in sermons should be achieved in a twofold manner: 1. by maintaining the dialogical structure of the sermon; 2. by precisely defining the questio of the homily.

The Temporal Bias Approach to the Symmetry Problem and Historical Closeness

In addressing the Lucretian symmetry problem, the temporal bias approach claims that death is bad because it deprives us of something about which it is rational to care (e.g., future pleasures), whereas prenatal nonexistence is not bad because it only deprives us of something about which it is rational to remain indifferent (e.g., past pleasures). In a recent contribution to the debate on this approach, Miguel and Santos argue that a late beginning can deprive us of a future pleasure. Their argument is based on the claim that for birth or death to deprive a person of any value in life, the historically closest counterfactual situation that contains the value is such that the person begins to exist earlier or dies later. This is what they call the Historical Condition. However, the Historical Condition is untenable for several reasons. First, this condition substantially weakens the explanatory capacity of the deprivation account because it implies that most ordinary sorts of pleasures are not deprived by death. In addition, the Historical Condition is vulnerable to counterexamples. In particular, what they offer as a standard case of the deprivation of future pleasure due to a late beginning (what they call Seeing The Beatles), or some of its variants, can be used to falsify this condition. Finally, the Historical Condition is theoretically indefensible because it is based on a faulty analysis of deprivation.

Testing axial symmetry by means of integrated rank scores

The article addresses the recently emerging inferential problem of testing axial symmetry up to a shift, which is useful even for testing certain hypotheses of exchangeability, independence, goodness-of-fit or equality of scale. In particular, it introduces a new test of axial symmetry based on integrated rank scores for directional quantile regression. The test outperforms existing competitors in terms of size, power, robustness, moment conditions or computational feasibility. All that is illustrated with a series of simulated examples.

Whole-grain Petri Nets and Processes

We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an algebraic semantics in the style of Meseguer and Montanari, in terms of free coloured props, and allows the following unification: for P a Petri net, the Segal space of P -processes is shown to be the free coloured prop-in-groupoids on P . There is also an unfolding semantics à la Winskel, which bypasses the classical symmetry problems: with the new formalism, every Petri net admits a universal unfolding, which in turn has associated an event structure and a Scott domain. Since everything is encoded with explicit sets, Petri nets and their processes have elements. In particular, individual-token semantics is native. (Collective-token semantics emerges from rather drastic quotient constructions à la Best–Devillers, involving taking π 0 of the groupoids of states.)

Development of a method for determining the rational installation location of technical means of symmetry in an electrical complex with the presence of an electric motor load

The work is devoted to the development of a methodological approach to correcting the level of supply voltage in the electrical network by developing an algorithmized method for determining the rational installation location of technical means of symmetry in an electrical complex with the presence of an electric motor load. The developed method makes it possible to implement processes aimed at ensuring the effective functioning of the electrical complex with the presence of an electric motor load in conditions of low-quality supply voltage. The proposed method, based on software, provides design procedures for calculating various options for symmetry and choosing the most economically feasible. Attention is focused on the main criteria for evaluating decisions made when designing the location of technical means of symmetry in the electrical complex. The architecture, the main functional features of the application program as a tool for implementing the calculation method are considered. The program ensures the implementation of electrical calculations in the design, modernization and operation of electrical networks. It provides for the construction of schematic diagrams of sections of electrical complexes with installed means of symmetry. The results of experimental studies demonstrating the effectiveness of the developed method in solving problems of voltage symmetry in the supply electrical network are presented. It is obvious that the developed approach, based on the automatic selection of the locations of the means of symmetry depending on the operating conditions of the electric motor load, makes it possible to automate the design procedures for voltage normalization in the electrical network. Provides minimization of voltage asymmetry in the supply electrical network, contributes to improving the operational reliability of low-voltage asynchronous electric motors. The obtained research results and prospects for the application of the developed approach are discussed, both for solving complex design problems and for the economic justification of local design solutions. A detailed analysis and formalization of the results of the study with relevant conclusions were carried out.

Intuition and Symmetries in Electromagnetism: Eigenstates of Four Antennas

Symmetries play an essential role in the field of physics. In this paper, we examine the relationship between the eigen-amplitudes of four (2 × 2) symmetrical antennas and the symmetry of the amplitudes of their sources (excitations) using mirroring effects. In our case, we find that changing mirrors using symmetry is identical to the point group theory. By exploiting the symmetry problem, we can show the advantage of reducing the size of the analysis domain, at least by a factor of two or more (2, 4, and 8…etc.) (depending on the problem). Several simulation examples have been developed by the MoM-GEC and HFSS to validate this approach.

Approximate Nonlocal Symmetries for a Perturbed Schrödinger Equation with a Weak Infinite Power-Law Memory

A nonlocally perturbed linear Schrödinger equation with a small parameter was derived under the assumption of low-level fractionality by using one of the known general nonlocal wave equations with an infinite power-law memory. The problem of finding approximate symmetries for the equation is studied here. It has been shown that the perturbed Schrödinger equation inherits all symmetries of the classical linear equation. It has also been proven that approximate symmetries corresponding to Galilean transformations and projective transformations of the unperturbed equation are nonlocal. In addition, a special class of nonlinear, nonlocally perturbed Schrödinger equations that admits an approximate nonlocal extension of the Galilei group is derived. An example of constructing an approximately invariant solution for the linear equation using approximate scaling symmetry is presented.

A Comprehensive Study on Pythagorean Fuzzy Normal Subgroups and Pythagorean Fuzzy Isomorphisms

The Pythagorean fuzzy set is an extension of the intuitionistic fuzzy set used to handle uncertain circumstances in various decisions making problems. Group theory is a mathematical technique for dealing with problems of symmetry. This study deals with Pythagorean fuzzy group theory. In this article, we characterize the notion of a Pythagorean fuzzy subgroup and examine various algebraic properties of this concept. An extensive study on Pythagorean fuzzy cosets of a Pythagorean fuzzy subgroup, Pythagorean fuzzy normal subgroups of a group and Pythagorean fuzzy normal subgroup of a Pythagorean fuzzy subgroup is performed. We define the notions of Pythagorean fuzzy homomorphism and isomorphism and generalize the notion of factor group of a classical group W relative to its normal subgroup S by defining a PFSG of WS. At the end, the Pythagorean fuzzy version of fundamental theorems of isomorphisms is proved.

Source and defect localization in thin elastic plates of arbitrary geometry using eigenmodes

In this paper, we experimentally demonstrate how discrete resonances can be used to image acoustic sources and mechanical changes in thin plates with different boundary shapes. The proposed method uses coupled numerical and experimental data processing, and it only requires the knowledge of the sample geometry (and not its elastic properties). If a limited number of measurement points is available in experiments, the free modes of the plates are not orthogonal from the receivers’ point of view, and this induces an artificial coupling in the post-processing of the experimental signals. However, we show that this effect can be corrected using numerical simulations and a mathematical transformation of the antenna geometry. After this correction, imaging of active sources is performed using coherent summation of the elastic field over the natural frequencies of the plates, leading to an unique localization of the sources. Imaging mechanical changes in the two plates, instead, is addressed using incoherent summation over the modes, leading to symmetry problems for the plates. This work experimentally illustrates the spatial resolution, perspectives and limitations in the use of eigenmodes to produce images in complex elastic systems of arbitrary shape and materials.

Railway Fault Text Clustering Method Using an Improved Dirichlet Multinomial Mixture Model

Railway signal equipment fault data (RSEFD) are one of the issues with in-depth traffic big data analysis throughout the life cycle of intelligent transportation. In the course of daily operation and maintenance, the railway electrical maintenance department records equipment malfunction information in a natural language. The data have the characteristics of strong professionalism, short text, unbalanced category, and low efficiency of manual analysis and processing. How to effectively mine the information contained in these fault texts to provide help for on-site operation and maintenance plays an important role. Therefore, we propose a railway fault text clustering method using an improved Dirichlet multinomial mixture model called ICH-GSDMM. In this method, first, the railway signal terminology thesaurus is established to overcome the inaccurate problem of RSEFD segmentation. Second, the traditional Chi square statistics is improved to overcome the learning difficulties caused by the imbalance of RSEFD. Finally, the Gibbs sampling algorithm for Dirichlet multinomial mixture model (GSDMM) is modified using an improved chi-square statistical method (ICH) to overcome the symmetry problem of the word Dirichlet prior parameters in the traditional GSDMM. Compared to the traditional GSDMM model and the GSDMM model based on chi-square statistics (CH-GSDMM), the quantitative experimental results show that the GSDMM model based on improved chi-square statistics (ICH-GSDMM internal)’s evaluation index of clustering performance has greatly improved, and its external evaluation indices are also the best, with the exception of external index NMI of data set DS2. Simultaneously, the diagnostic accuracy of a select few categories in RSEFD has considerably improved, demonstrating its efficacy.

On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems

The problem of finding Lie point symmetries for a certain class of multi-dimensional nonlinear partial fractional differential equations and their systems is studied. It is assumed that considered equations involve fractional derivatives with respect to only one independent variable, and each equation contains a single fractional derivative. The most significant examples of such equations are time-fractional models of processes with memory of power-law type. Two different types of fractional derivatives, namely Riemann–Liouville and Caputo, are used in this study. It is proved that any Lie point symmetry group admitted by equations or systems belonging to considered class consists of only linearly-autonomous point symmetries. Representations for the coordinates of corresponding infinitesimal group generators, as well as simplified determining equations are given in explicit form. The obtained results significantly facilitate finding Lie point symmetries for multi-dimensional time-fractional differential equations and their systems. Three physical examples illustrate this point.

A high-order compact LOD difference method for solving the two-dimensional diffusion reaction equation with nonlinear source term

In this paper, a high-order compact local one-dimensional (LOD) method for the two-dimensional diffusion reaction equation with nonlinear source term is proposed. Firstly, the original equation is split into two one-dimensional equations. Then, the fourth-order compact difference formulas and the Crank–Nicolson method are used to approximate the space and time derivatives, respectively. The nonlinear source term is linearized based on the Taylor expansions. So we only need to solve two one-dimensional tri-diagonal systems at each time level, which makes the computation efficient. Through theoretical analysis, we find that the current LOD method produces a splitting error. Therefore, although this method has advantages for source term symmetry problems, it loses accuracy for source term asymmetry problems. The convergence and stability of the proposed scheme are proved by energy analysis method. Finally, several numerical examples are given to verify the accuracy and effectiveness of the proposed method. Furthermore, it is also applied in simulation of the quenching and blow-up phenomena.

Fractional Moore-Gibson-Thompson heat transfer model with nonlocal and nonsingular kernels of a rotating viscoelastic annular cylinder with changeable thermal properties

Long hollow cylinders are commonly utilized in various technological applications, including liquid and gas transmission. As a result, its value is growing, becoming increasingly important to many research efforts. Compared with thermal isotropic homogeneous cylinders, thermo-viscoelastic orthotropic cylinders have less relevant data. In this paper, a thermoelastic fractional heat conduction model was developed based on the Moore-Gibson-Thompson equation to examine the axial symmetry problem of a viscoelastic orthotropic hollow cylinder. Atangana and Baleanu derivative operators with nonsingular and nonlocal kernels were used in constructing the fractional model. The thermal properties of the cylinder materials are assumed to be temperature-dependent. The Laplace transform is applied to solve the system of governing equations. The numerical calculations for temperature, displacement, and stress components are performed by the effect of fractional order, rotation, and changing thermal properties of the cylinder. The results showed that due to the presence of fractional derivatives, some properties of the physical fields of the medium change according to the value of the fractional order.

Axisymmetrical analytical solution to the transient heat transfer problem in geological media

Laplace transforms were used in this paper to obtain analytical solutions for the axisymmetric problem under a constant well temperature using the convective heat transfer boundary condition, which included the conduction and convection in the aquifer as well as heat exchange at the boundary. This solution curve intuitively illustrates the temperature distribution within the aquifer. The effects of various parameters on this analytical solution were analyzed. According to this parametric analysis there exists a quasi-steady-state of temperature distribution in the axisymmetrical situation, which is different from the planar symmetry problem. In addition, the thermal breakthrough increases with the injected rate and decreases with the increasing convective heat transfer coefficient. Our analytical solution matched the results yielded by the numerical simulation quite well.

The reverse ontological argument

Abstract Modal ontological arguments argue from the possible existence of a perfect being to the actual (necessary) existence of a perfect being. But modal ontological arguments have a problem of symmetry; they can be run in both directions. Reverse ontological arguments argue from the possible nonexistence of a perfect being to the actual (necessary) nonexistence of a perfect being. Some familiar points about the necessary a posteriori, however, show that the symmetry can be broken in favour of the ontological argument.