Symmetry

53 pages, 698 KiB

Open AccessFeature PaperReview

Critical Properties of Three-Dimensional Many-Flavor QEDs

by Simon Metayer and Sofian Teber

Symmetry 2023, 15(9), 1806; https://doi.org/10.3390/sym15091806 - 21 Sep 2023

Viewed by 821

We review several variants of three-dimensional quantum electrodynamics (QED

_{3}

) with

N_{f}

fermion (or boson) flavors, including fermionic (or spinorial) QED

_{3}

, bosonic (or scalar) QED

_{3}

,

N = 1

supersymmetric QED and also models of reduced QED (supersymmetric [...] Read more.

We review several variants of three-dimensional quantum electrodynamics (QED

_{3}

) with

N_{f}

fermion (or boson) flavors, including fermionic (or spinorial) QED

_{3}

, bosonic (or scalar) QED

_{3}

,

N = 1

supersymmetric QED and also models of reduced QED (supersymmetric or not). We begin with an introduction to these models and their flow to a stable infra-red fixed point in the large-

N_{f}

limit. We then present detailed state-of-the-art computations of the critical exponents of these models within the dimensional regularization (and reduction) scheme(s), at the next-to-leading order in the

1 / N_{f}

expansion and in an arbitrary covariant gauge. We finally discuss dynamical (matter) mass generation and the current status of our understanding of the phase structure of these models. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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14 pages, 297 KiB

Open AccessArticle

Generalized Split Quaternions and Their Applications on Non-Parabolic Conical Rotations

by Mehmet Duru and Harun Barış Çolakoğlu

Symmetry 2023, 15(9), 1805; https://doi.org/10.3390/sym15091805 - 21 Sep 2023

Viewed by 622

Abstract

In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which is a generalized [...] Read more.

In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which is a generalized Lorentzian sphere, non-parabolic conical rotations with nonnull axes are expressed using the generalized split quaternions with supporting numerical examples. Full article

29 pages, 756 KiB

Open AccessArticle

Near-Miss Bi-Homogenous Symmetric Polyhedral Cages

by Bernard Piette and Árpad Lukács

Symmetry 2023, 15(9), 1804; https://doi.org/10.3390/sym15091804 - 21 Sep 2023

Viewed by 961

Abstract

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of [...] Read more.

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are equivalent. We parametrise the possible connectivity configurations for such cages, analytically derive p-cages that are regular, and numerically compute near-symmetric p-cages made of polygons with 6 to 18 edges and with deformation not exceeding 10%. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Nature-Inspired, Bio-Based Materials)

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16 pages, 5480 KiB

Open AccessReview

Triptycene Based 3D Covalent Organic Frameworks (COFs)—An Emerging Class of 3D Structures

by Monika Borkowska and Radosław Mrówczyński

Symmetry 2023, 15(9), 1803; https://doi.org/10.3390/sym15091803 - 21 Sep 2023

Cited by 3 | Viewed by 1370

Abstract

Covalent Organic Frameworks (COFs) are a newly emerged class of porous materials consisting of organic building blocks linked by strong covalent bonds. The physical and chemical properties of COFs, i.e., modularity, porosity, well-developed specific surface area, crystallinity, and chemical-thermal stability, make them a [...] Read more.

Covalent Organic Frameworks (COFs) are a newly emerged class of porous materials consisting of organic building blocks linked by strong covalent bonds. The physical and chemical properties of COFs, i.e., modularity, porosity, well-developed specific surface area, crystallinity, and chemical-thermal stability, make them a good application material, especially in the aspects of adsorption and gas separation. The organic compositions of their building blocks also render them with biocompatible properties; therefore, they also have potential in biomedical applications. Depending on the symmetry of the building blocks, COF materials form two-dimensional (2D COF) or three-dimensional (3D COF) crystal structures. 3D COF structures have a higher specific surface area, they are much lighter due to their low density, and they have a larger volume than 2D COF crystals, but, unlike the latter, 3D COF crystals are less frequently obtained and studied. Selecting and obtaining suitable building blocks to form a stable 3D COF crystal structure is challenging and therefore of interest to the chemical community. Triptycene, due to its 3D structure, is a versatile building block for the synthesis of 3D COFs. Polymeric materials containing triptycene fragments show good thermal stability parameters and have a very well-developed surface area. They often tend to be characterized by more than one type of porosity and exhibit impressive gas adsorption properties. The introduction of a triptycene backbone into the structure of 3D COFs is a relatively new procedure, the results of which only began to be published in 2020. Triptycene-based 3D COFs show interesting physicochemical properties, i.e., high physical stability and high specific surface area. In addition, they have variable porosities with different pore diameters, capable of adsorbing both gases and large biological molecules. These promising parameters, guaranteed by the addition of a triptycene backbone to the 3D structure of COFs, may create new opportunities for the application of such materials in many industrial and biomedical areas. This review aims to draw attention to the symmetry of the building blocks used for COF synthesis. In particular, we discussed triptycene as a building block for the synthesis of 3D COFs and we present the latest results in this area. Full article

(This article belongs to the Special Issue Symmetry in Organic Chemistry: Synthesis and Properties of Symmetrical Organic Compounds)

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13 pages, 5413 KiB

Open AccessArticle

Decay Law of Supercritical CO₂ Phase Transition-Induced Shock Waves in Rocky Media

by Jie Zhang, Qifu Zeng, Fangqiang Wei, Lu Liu, Fayou Wu and Haotian Li

Symmetry 2023, 15(9), 1802; https://doi.org/10.3390/sym15091802 - 21 Sep 2023

Viewed by 556

Abstract

Supercritical CO₂ phase change fracturing technology has been widely used in rock engineering, with the advantages of low disturbance and no pollution. However, the phase change shock wave inevitably affects the surrounding environment, and the influence range is still unclear. In this [...] Read more.

Supercritical CO₂ phase change fracturing technology has been widely used in rock engineering, with the advantages of low disturbance and no pollution. However, the phase change shock wave inevitably affects the surrounding environment, and the influence range is still unclear. In this paper, we present a computational model for the symmetric generation, propagation, and attenuation of supercritical CO₂ phase transition shock waves, with the center of the borehole as the origin, based on the C–J theory. The attenuation of the shock wave in the rock medium under the influence of the type of fracturing tube, the thickness of the shear sheet, and the rock performance parameters are further analyzed. The results show that the rock stress under the action of the phase change shock wave attenuates logarithmically with the propagation distance, which correlates with the magnitude of the incident rock stress at the borehole wall. The incident rock stress decreases with the increase in the initial density of CO₂ in the fracturing tube, increases linearly with the thickness of the shear sheet, and correlates with the rock wave impedance. Full article

(This article belongs to the Special Issue Symmetry, Asymmetry and Nonlinearity in Geomechanics)

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17 pages, 4890 KiB

Open AccessArticle

Analysis of the Impact of Big Data and Artificial Intelligence Technology on Supply Chain Management

by Xiao Zeng and Jing Yi

Symmetry 2023, 15(9), 1801; https://doi.org/10.3390/sym15091801 - 21 Sep 2023

Cited by 1 | Viewed by 1637

Abstract

Differentiated production and supply chain management (SCM) areas benefit from the IoT, Big Data, and the data-management capabilities of the AI paradigm. Many businesses have wondered how the arrival of AI will affect planning, organization, optimization, and logistics in the context of SCM. [...] Read more.

Differentiated production and supply chain management (SCM) areas benefit from the IoT, Big Data, and the data-management capabilities of the AI paradigm. Many businesses have wondered how the arrival of AI will affect planning, organization, optimization, and logistics in the context of SCM. Information symmetry is very important here, as maintaining consistency between output and the supply chain is aided by processing and drawing insights from big data. We consider continuous (production) and discontinuous (supply chain) data to satisfy delivery needs to solve the shortage problem. Despite a surplus of output, this article addresses the voluptuous deficiency problem in supply chain administration. This research serves as an overview of AI for SCM practitioners. The report then moves into an in-depth analysis of the most recent studies on and applications of AI in the supply chain industry. This work introduces a novel approach, Incessant Data Processing (IDP), for handling harmonized data on both ends, which should reduce the risk of incorrect results. This processing technique detects shifts in the data stream and uses them to predict future suppressions of demand. Federated learning gathers and analyzes information at several points in the supply chain and is used to spot the shifts. The learning model is educated to forecast further supply chain actions in response to spikes and dips in demand. The entire procedure is simulated using IoT calculations and collected data. An improved prediction accuracy of 9.93%, a reduced analysis time of 9.19%, a reduced data error of 9.77%, and increased alterations of 10.62% are the results of the suggested method. Full article

(This article belongs to the Special Issue Recent Advances in Fuzzy Optimization Methods and Models)

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13 pages, 3836 KiB

Open AccessArticle

Effect of Plasma Oxygen Content on the Size and Content of Silicon Nanoclusters in Amorphous SiOx Films Obtained with Plasma-Enhanced Chemical Vapor Deposition

by Vladimir A. Terekhov, Evgeniy I. Terukov, Yurii K. Undalov, Konstantin A. Barkov, Nikolay A. Kurilo, Sergey A. Ivkov, Dmitry N. Nesterov, Pavel V. Seredin, Dmitry L. Goloshchapov, Dmitriy A. Minakov, Elena V. Popova, Anatoly N. Lukin and Irina N. Trapeznikova

Symmetry 2023, 15(9), 1800; https://doi.org/10.3390/sym15091800 - 21 Sep 2023

Cited by 1 | Viewed by 686

Abstract

The influence of Ar + SiH₄ + O₂ plasma formulation on the phase composition and optical properties of amorphous SiO_x films with silicon nanoclusters obtained using PECVD with DC discharge modulation was studied. Using a unique technique of ultrasoft X-ray [...] Read more.

The influence of Ar + SiH₄ + O₂ plasma formulation on the phase composition and optical properties of amorphous SiO_x films with silicon nanoclusters obtained using PECVD with DC discharge modulation was studied. Using a unique technique of ultrasoft X-ray emission spectroscopy, it was found that at a 0.15 mol.% plasma oxygen content, amorphous silicon a-Si films are formed. At a high oxygen content (≥21.5 mol.%), nanocomposite films based on SiO_x silicon suboxide containing silicon nanoclusters ncl-Si are formed. It was found that the suboxide matrix consists of a mixture of SiO_1.3 and SiO₂ phases, and the average oxidation state x in the SiO_x suboxide matrix is ~1.5. An increase in the concentration of O₂ in the reactor atmosphere from 21.5 to 23 mol.% leads to a decrease in ncl-Si content from 40 to 15% and an increase in the average oxidation state x of SiO_x from 1.5 to 1.9. In this case, the suboxide matrix consists of two phases of silicon dioxide SiO₂ and non-stoichiometric silicon oxide SiO_1.7. Thus, according to the experimental data obtained using USXES, the phase composition of these films in pure form differs in their representation in both random coupling and random mixture models. A decrease in the ncl-Si content of SiO_x films is accompanied by a decrease in their sizes from ~3 to ~2 nm and a shift in the photoluminescence band from 1.9 eV to 2.3 eV, respectively. Full article

(This article belongs to the Special Issue Symmetry in Physics of Plasma Technologies II)

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10 pages, 336 KiB

Open AccessArticle

The Geodetic Number for the Unit Graphs Associated with Rings of Order P and P²

by Heba Adel Abdelkarim

Symmetry 2023, 15(9), 1799; https://doi.org/10.3390/sym15091799 - 21 Sep 2023

Viewed by 544

Abstract

Let

G (R)

be the unit graph associated with a ring R. Let p be a prime number and let R be a finite ring of order p or

p^{2}

and be one of the rings [...] Read more.

Let

G (R)

be the unit graph associated with a ring R. Let p be a prime number and let R be a finite ring of order p or

p^{2}

and be one of the rings

Z_{p}, Z_{p^{2}}, G F (p^{2}), Z_{p} (+) Z_{p}

or

Z_{p} \times Z_{p}

. We determine the geodetic number

g (G (R))

associated with each such ring. Full article

(This article belongs to the Special Issue Graph Theory and Its Applications)

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14 pages, 4586 KiB

Open AccessArticle

High-Field Nonresonant Response of Zundel Cations to Intense Terahertz Radiation

by Kaicheng Wang, Lianghao Guo, Qin Zhang, Hui Ning, Chang Lu, Shaomeng Wang and Yubin Gong

Symmetry 2023, 15(9), 1798; https://doi.org/10.3390/sym15091798 - 20 Sep 2023

Viewed by 690

Abstract

The fundamental unit for comprehending the physicochemical properties of water, the Zundel cation configuration H₅O₂⁺, has yet to be exhaustively evaluated in terms of its interaction with terahertz (THz) electromagnetic waves, characterized by sub-picosecond oscillation periods or pulse [...] Read more.

The fundamental unit for comprehending the physicochemical properties of water, the Zundel cation configuration H₅O₂⁺, has yet to be exhaustively evaluated in terms of its interaction with terahertz (THz) electromagnetic waves, characterized by sub-picosecond oscillation periods or pulse widths. In this study, we embark on an investigation of the broad resonance and high-field nonresonant effects of intense THz radiation (ITR) on Zundel cations, utilizing a multifaceted methodological approach that includes density functional theory (DFT) calculations, finite difference time domain (FDTD) algorithm of the Schrödinger equation, and ab initio molecular dynamics (AIMD) simulations. Our analysis reveals that the proton potential energy surface (PES) varies in response to the external electric (E) field, suggesting that the interaction frequency of the central proton with the electromagnetic wave encompasses the THz band. This resonance effect is associated with proton behavior that may oscillate or demonstrate periodic tunneling. Moreover, our work uncovers the high-field nonresonant effects of ITR on Zundel cations, manifesting in proton transfer and vibrational excitation of the system. Our findings contribute to the understanding of the interaction between Zundel species and electromagnetic waves by presenting a microscopic view of proton transfer as informed by wavefunction evolution. Full article

(This article belongs to the Section Life Sciences)

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20 pages, 375 KiB

Open AccessArticle

Some Fixed Point Theorems for α-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces

by Satish Shukla, Shweta Rai and Rahul Shukla

Symmetry 2023, 15(9), 1797; https://doi.org/10.3390/sym15091797 - 20 Sep 2023

Cited by 3 | Viewed by 1033

Abstract

This paper discusses some properties of complex-valued fuzzy metric spaces and introduces the

α

-admissible mappings in the setting of complex-valued fuzzy metric spaces. We establish fixed point theorems for mappings satisfying symmetric contractive conditions with control functions. The results of this paper [...] Read more.

This paper discusses some properties of complex-valued fuzzy metric spaces and introduces the

α

-admissible mappings in the setting of complex-valued fuzzy metric spaces. We establish fixed point theorems for mappings satisfying symmetric contractive conditions with control functions. The results of this paper generalize, extend, and improve several results from metric, fuzzy metric, and complex-valued fuzzy metric spaces. Several examples are presented that verify and illustrate the new concepts, claims, and results. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Fixed Point Theory)

14 pages, 310 KiB

Open AccessArticle

Stochastic Comparisons of Largest-Order Statistics and Ranges from Marshall–Olkin Bivariate Exponential and Independent Exponential Variables

by Narayanaswamy Balakrishnan, Ghobad Saadat Kia (Barmalzan) and Mohammad Mehrpooya

Symmetry 2023, 15(9), 1796; https://doi.org/10.3390/sym15091796 - 20 Sep 2023

Viewed by 532

Abstract

Sample range and the associated functions such as survival function and mean residual life function have found many important applications in the reliability field. In this work, we establish some results that are in two different directions. In the first part, we establish [...] Read more.

Sample range and the associated functions such as survival function and mean residual life function have found many important applications in the reliability field. In this work, we establish some results that are in two different directions. In the first part, we establish some conditions for comparing the largest-order statistics (in the sense of mean residual life order) arising from bivariate Marshall–Olkin exponential distribution. Then, in the second part, we present some sufficient conditions for comparing sample ranges (in the sense of usual stochastic order and reversed hazard rate order) arising from independent exponential random variables. Full article

(This article belongs to the Special Issue Symmetry in Probability Theory and Statistics)

18 pages, 354 KiB

Open AccessArticle

N-Hypersoft Sets: An Innovative Extension of Hypersoft Sets and Their Applications

by Sagvan Y. Musa, Ramadhan A. Mohammed and Baravan A. Asaad

Symmetry 2023, 15(9), 1795; https://doi.org/10.3390/sym15091795 - 20 Sep 2023

Cited by 3 | Viewed by 983

Abstract

This paper introduces N-hypersoft (N-HS) sets—an enriched and versatile extension of hypersoft (HS) sets—designed to handle evaluations involving both binary and non-binary data while embodying an inherent sense of structural symmetry. The paper presents several algebraic definitions, including incomplete N-HS sets, efficient N-HS [...] Read more.

This paper introduces N-hypersoft (N-HS) sets—an enriched and versatile extension of hypersoft (HS) sets—designed to handle evaluations involving both binary and non-binary data while embodying an inherent sense of structural symmetry. The paper presents several algebraic definitions, including incomplete N-HS sets, efficient N-HS sets, normalized N-HS sets, equivalence under normalization, N-HS complements, and HS sets derived from a threshold. These definitions are accompanied by illustrative examples. Additionally, the paper delves into various set-theoretic operations within the framework of N-HS sets, such as relative null/whole N-HS sets, N-HS subsets, and N-HS extended/restricted union and intersection, presented in two different ways. Finally, the paper presents and compares decision-making methodologies regarding N-HS sets. Full article

(This article belongs to the Section Mathematics)

19 pages, 3599 KiB

Open AccessArticle

Al₂O₃-Cu\Ethylene Glycol-Based Magnetohydrodynamic Non-Newtonian Maxwell Hybrid Nanofluid Flow with Suction Effects in a Porous Space: Energy Saving by Solar Radiation

by Mdi Begum Jeelani and Amir Abbas

Symmetry 2023, 15(9), 1794; https://doi.org/10.3390/sym15091794 - 20 Sep 2023

Cited by 7 | Viewed by 949

Abstract

Nanotechnology is well-known for its versatile and general thermal transport disciplines, which are used in semiconductors, spacecraft, bioengineering, functional electronics, and biosensors. As a result, process optimization has attracted the interest of scientists and technologists. The main aim of the current analysis is [...] Read more.

Nanotechnology is well-known for its versatile and general thermal transport disciplines, which are used in semiconductors, spacecraft, bioengineering, functional electronics, and biosensors. As a result, process optimization has attracted the interest of scientists and technologists. The main aim of the current analysis is to explore the enhancement of energy/heat transfer via the dispersion of cylindrical-shaped nanoparticles of alumina and copper in ethylene glycol as a base fluid using a non-Newtonian Maxwell fluid model. In the current study, the effects of solar radiation, plate suction, and magnetohydrodynamics on a Maxwell hybrid nanofluid are encountered. The flow is induced by linearly stretching a sheet angled at

ξ = π / 6

, embedded in a porous space. The proposed problem is converted into a mathematical structure in terms of partial differential equations and then reduced to ordinary differential equations by using appropriate similarity variables. In the similarity solution, all the curves for the velocity field and temperature distribution remain similar, which means that the symmetry between the graphs for the velocity and temperature remains the same. Therefore, there is a strong correlation between similarity variables and symmetry. The obtained model, in terms of ordinary differential equations, is solved using the built-in numerical solver bvp4c. It is concluded that more nanoparticles in a fluid can make it heat up faster, as they are typically better at conducting heat than the fluid itself. This means that heat is transferred more quickly, raising the temperature of the fluid. However, more nanoparticles can also slow the flow speed of the fluid to control the boundary layer thickness. The temperature field is enhanced by increasing the solar radiation parameter, the magnetic field parameter, and the porous medium parameter at an angle of

ξ = π / 6

, which serves the purpose of including radiation and the Lorentz force. The velocity field is decreased by increasing the values of the buoyancy parameter and the suction parameter effects at an angle of

ξ = π / 6

. The current study can be used in the improvement of the thermal efficiency of nanotechnological devices and in renewable energy sources to save energy in the energy sector. The present results are compared with the published ones, and it is concluded that there is excellent agreement between them, which endorses the validity and accuracy of the current study. Full article

(This article belongs to the Special Issue Symmetry Applications in Nanofluids and Nanomaterials)

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10 pages, 3246 KiB

Open AccessArticle

Evidence of Noisy Oscillations of cAMP under Nutritional Stress Condition in Budding Yeast

by Sonia Colombo, Maddalena Collini, Laura D’Alfonso, Giuseppe Chirico and Enzo Martegani

Symmetry 2023, 15(9), 1793; https://doi.org/10.3390/sym15091793 - 20 Sep 2023

Viewed by 598

Abstract

The Ras/cAMP/PKA pathway regulates responses to nutrients’ availability and stress in budding yeast. The cAMP levels are subjected to negative feedback, and we have previously simulated a dynamic model of this pathway suggesting the existence of stable oscillatory states depending on the symmetrical [...] Read more.

The Ras/cAMP/PKA pathway regulates responses to nutrients’ availability and stress in budding yeast. The cAMP levels are subjected to negative feedback, and we have previously simulated a dynamic model of this pathway suggesting the existence of stable oscillatory states depending on the symmetrical and opposed activity of the RasGEF (Cdc25) and RasGAPs (Ira proteins). Noisy oscillations related to the activity of this pathway were reported by looking at the nuclear localization of the transcription factor Msn2, and sustained oscillations of the nuclear accumulation of Msn2 under the condition of limiting glucose were observed. We were able to reproduce the periodic accumulation of Msn2-GFP protein in a yeast cell under the condition of limiting glucose, and we also detected oscillations of cAMP. We used a sensor based on a fusion protein between YFP-Epac2-CFP expressed in yeast cells. The FRET between CFP and YFP is controlled by the cAMP concentration. This sensor allows us to monitor changes in cAMP concentrations in a single yeast cell over a long time. Using this method, we were able to detect noisy oscillations of cAMP levels in single yeast cells under conditions of nutritional stress caused by limiting glucose availability. Full article

(This article belongs to the Section Life Sciences)

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21 pages, 9119 KiB

Open AccessArticle

Symmetry of Structures under Two-Dimensional Instability in a Finite-Height Horizontal Layer of Boiling Liquid

by Vladimir I. Zhukov and Aleksandr N. Pavlenko

Symmetry 2023, 15(9), 1792; https://doi.org/10.3390/sym15091792 - 20 Sep 2023

Cited by 1 | Viewed by 800

Abstract

The two-dimensional instability of a horizontal layer of boiling liquid with a finite height was experimentally studied. In this layer, “vapor columns” rose at the corners of a square rectangular grid, and the symmetry of “vapor column” location on the heating surface was [...] Read more.

The two-dimensional instability of a horizontal layer of boiling liquid with a finite height was experimentally studied. In this layer, “vapor columns” rose at the corners of a square rectangular grid, and the symmetry of “vapor column” location on the heating surface was considered. The model adopts an approach to the boiling crisis from the side of both developed nucleate boiling and transitional boiling (the Zuber problem). When dealing with developed nucleate boiling, the layer of boiling liquid is considered in calculations as an isotropic homogeneous system (foam). It is shown how the conditions on the heating surface (capillary-porous coating) affect the external hydrodynamics of the liquid layer and, ultimately, the value of the critical heat flux. The calculation ratio obtained by approaching the boiling crisis from the side of developed nucleate boiling takes into account the dependence of the critical heat flux on the void fraction of the boiling liquid layer. A new solution to the boiling crisis problem is proposed when approaching the crisis from the side of transitional boiling (the Zuber problem). This new solution eliminates some shortcomings of the classical problem (in particular, the void fraction of the layer corresponds to the experiments). Full article

(This article belongs to the Special Issue Symmetry, Sustainable Solutions and New Methodologies in Continuous Media and Plasma)

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12 pages, 4828 KiB

Open AccessArticle

Systematic Study of Vibrational Spectra of Octahedral Rhenium Clusters {Re₆S_8-xBr_x}Br_y (x = 0, 1, 2, 3, 4) with Mixed Sulfur/Bromine Inner Ligands

by Alexandra Yu. Ledneva, Mariia N. Ivanova, Pavel A. Poltarak, Spartak S. Yarovoy, Boris A. Kolesov, Vladimir E. Fedorov and Nikolay G. Naumov

Symmetry 2023, 15(9), 1791; https://doi.org/10.3390/sym15091791 - 19 Sep 2023

Cited by 1 | Viewed by 831

Abstract

A series of rhenium compounds with the octahedral cluster core {Re₆S_8-xBr_x} (x = 0–4): with molecular and polymeric structure were obtained. In these compounds the cluster core composition varies monotonically, the geometry of the cluster and the [...] Read more.

A series of rhenium compounds with the octahedral cluster core {Re₆S_8-xBr_x} (x = 0–4): with molecular and polymeric structure were obtained. In these compounds the cluster core composition varies monotonically, the geometry of the cluster and the rhenium coordination polyhedron are retained unchanged, while the symmetry of the cluster changes. The vibrational spectra (Raman and IR) were recorded and analyzed for compounds with all possible S/Br ratios in the cluster core. The group vibrations of clusters were attributed with the use of DFT calculations of vibrational spectra. It is shown that the set of main characteristic bands is retained in both ionic and polymeric compounds regardless of the composition and the symmetry of the cluster core while the observed vibration frequencies of these bands depend on the S/Br ratio in the cluster core. In particular, the group Re–S stretching vibrations (A_1g(S₈) and T_2g(S₈) modes) shifted to higher frequencies with the increase in the number of Br atoms in the cluster. The difference in the connectivity in polymeric compounds leads to an increase in the number of bands in the spectra and to the disappearance of the A_1g(Br) modes. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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11 pages, 273 KiB

Open AccessArticle

Some Fixed-Point Results in Extended S-Metric Space of Type (α,β)

by Reham Qaralleh, Abdalla Tallafha and Wasfi Shatanawi

Symmetry 2023, 15(9), 1790; https://doi.org/10.3390/sym15091790 - 19 Sep 2023

Cited by 1 | Viewed by 798

Abstract

In this paper, we introduce the notion of extended S-metric space of type

(α, β)

. This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition [...] Read more.

In this paper, we introduce the notion of extended S-metric space of type

(α, β)

. This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition of the S-metric space definition. Accordingly, we prove some fixed-point results and give some examples to illustrate the validity of our work, along with giving an application of the Fredholm integral equation. Full article

(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)

11 pages, 314 KiB

Open AccessArticle

Certain Class of Close-to-Convex Univalent Functions

by Shatha S. Alhily and Alina Alb Lupas

Symmetry 2023, 15(9), 1789; https://doi.org/10.3390/sym15091789 - 19 Sep 2023

Viewed by 677

Abstract

The purpose of this paper was to define a new class of close-to-convex function, denoted by

C V (δ, α)

, which is a subclass of all functions that are univalent in

D

and have positive coefficients normalized by the [...] Read more.

The purpose of this paper was to define a new class of close-to-convex function, denoted by

C V (δ, α)

, which is a subclass of all functions that are univalent in

D

and have positive coefficients normalized by the conditions

f (0) = 0, f^{'} (0) = 1

, if it satisfies such a condition that is dependent on positive real part. Furthermore, we proved how the power series distribution is essential for determining the sufficient and necessary condition on any function

f

in class

C V (δ, α)

. Full article

(This article belongs to the Special Issue Symmetry in Pure Mathematics and Real and Complex Analysis)

17 pages, 10737 KiB

Open AccessArticle

Distantly Supervised Relation Extraction via Contextual Information Interaction and Relation Embeddings

by Huixin Yin, Shengquan Liu and Zhaorui Jian

Symmetry 2023, 15(9), 1788; https://doi.org/10.3390/sym15091788 - 18 Sep 2023

Cited by 1 | Viewed by 989

Abstract

Distantly supervised relation extraction (DSRE) utilizes an external knowledge base to automatically label a corpus, which inevitably leads to the problem of mislabeling. Existing approaches utilize BERT to provide instances and relation embeddings to capture a wide set of relations and address the [...] Read more.

Distantly supervised relation extraction (DSRE) utilizes an external knowledge base to automatically label a corpus, which inevitably leads to the problem of mislabeling. Existing approaches utilize BERT to provide instances and relation embeddings to capture a wide set of relations and address the noise problem. However, the method suffers from a single method of textual information processing, underutilizing the feature information of entity pairs in the relation embeddings part and being interfered with by noisy labels when classifying multiple labels. For this reason, we propose the contextual information interaction and relation embeddings (CIRE) method. First, we utilize BERT and Bi-LSTM to construct a neural network model to enhance contextual information interaction by filtering and supplementing sequence information through the error repair capability of the Bi-LSTM gating mechanism. At the same time, we combine the vector difference between entity pairs and entity pairs in the relation embeddings layer to improve the relation embeddings accuracy. Finally, we choose sparse softmax as the classifier, which improves the ability to control the noise categories by controlling the number of output categories. The experimental results show that our method significantly outperforms the baseline method and improves the AUC metric by 2.6% on the NYT2010 dataset. Full article

(This article belongs to the Section Computer)

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10 pages, 329 KiB

Open AccessArticle

Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

by Reinhard Alkofer

Symmetry 2023, 15(9), 1787; https://doi.org/10.3390/sym15091787 - 18 Sep 2023

Cited by 3 | Viewed by 642

Abstract

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator [...] Read more.

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of D

χ

SB, the dynamical generation of constituent quark masses, but also makes plausible that D

χ

SB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to D

χ

SB as signalled by its scalar and tensor components but it is also a driver of D

χ

SB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, D

χ

SB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, D

χ

SB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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17 pages, 18455 KiB

Open AccessArticle

Design of Active Disturbance Rejection Controller for Trajectory-Following of Autonomous Ground Electric Vehicles

by Xianjian Jin, Huaizhen Lv, Zhihui He, Zhiwei Li, Zhaoran Wang and Nonsly Valerienne Opinat Ikiela

Symmetry 2023, 15(9), 1786; https://doi.org/10.3390/sym15091786 - 18 Sep 2023

Cited by 2 | Viewed by 859

Abstract

In this paper, the concept of symmetry is utilized in the promising trajectory-following control design of autonomous ground electric vehicles—that is, the construction and the solution of active disturbance rejection controllers are symmetrical. This paper presents an active disturbance rejection controller (ADRC) for [...] Read more.

In this paper, the concept of symmetry is utilized in the promising trajectory-following control design of autonomous ground electric vehicles—that is, the construction and the solution of active disturbance rejection controllers are symmetrical. This paper presents an active disturbance rejection controller (ADRC) for improving the trajectory-following performance of autonomous ground electric vehicles (AGEV) with an advanced active front steering system. Since AGEV trajectory dynamics are inherently affected by complex traffic conditions, various driving maneuvers, and other road environment, the main control objective is to deal with the AGEV trajectory control challenges of system uncertainties, system nonlinearities, and external disturbance. First, the vehicle dynamics trajectory-following model and its state space representation system are established. Then, the augmented control-oriented vehicle-trajectory-following system with dynamic error is developed. The resulting active disturbance rejection controller of the vehicle-trajectory-following system is finally designed using the trajectory performance index and active disturbance compensation, and the stability of the active disturbance rejection controller is also analyzed and derived via Lyapunov stability theory. The effectiveness of the proposed controller is validated through double lane change and serpentine maneuvers under the co-simulation platform of MATLAB/Simulink-Carsim^®. Simulation results show that the designed controller provides enhanced vehicle-trajectory-following performance compared to the linear quadratic regulator controller (LQR) and model predictive controller (MPC). It will provide a certain guidance for the controller engineering design of the AGEV trajectory-following system. Full article

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39 pages, 1844 KiB

Open AccessFeature PaperReview

Approximate Calculation of Functional Integrals Generated by Nonrelativistic and Relativistic Hamiltonians

by Edik Ayryan, Michal Hnatic, Juha Honkonen and Victor Malyutin

Symmetry 2023, 15(9), 1785; https://doi.org/10.3390/sym15091785 - 18 Sep 2023

Viewed by 966

Abstract

The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear physics and in other areas is presented. Methods [...] Read more.

The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear physics and in other areas is presented. Methods obtained by the authors for approximate calculation of functional integrals generated by nonrelativistic Hamiltonians are given. One of the methods is based on the expansion in eigenfunctions of the Hamiltonian. In an alternate approach, the functional integrals are tackled using the semiclassical approximation. Methods for approximate evaluation of functional integrals generated by relativistic Hamiltonians are presented. These are the methods using functional polynomial approximation (analogue of formulas of a given degree of accuracy) and methods based on the expansion in eigenfunctions of the Hamiltonian, generating a functional integral. Full article

(This article belongs to the Special Issue Cooperative Effects in Finite Systems)

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9 pages, 3207 KiB

Open AccessArticle

A Topological Approach to the Bézout’ Theorem and Its Forms

by Susmit Bagchi

Symmetry 2023, 15(9), 1784; https://doi.org/10.3390/sym15091784 - 18 Sep 2023

Cited by 1 | Viewed by 735

Abstract

The interplays between topology and algebraic geometry present a set of interesting properties. In this paper, we comprehensively revisit the Bézout theorem in terms of topology, and we present a topological proof of the theorem considering n-dimensional space. We show the role [...] Read more.

The interplays between topology and algebraic geometry present a set of interesting properties. In this paper, we comprehensively revisit the Bézout theorem in terms of topology, and we present a topological proof of the theorem considering n-dimensional space. We show the role of topology in understanding the complete and finite intersections of algebraic curves within a topological space. Moreover, we introduce the concept of symmetrically complex translations of roots in a zero-set of a real algebraic curve, which is called a fundamental polynomial, and we show that the resulting complex algebraic curve is additively decomposable into multiple components with varying degrees in a sequence. Interestingly, the symmetrically complex translations of roots in a zero-set of a fundamental polynomial result in the formation of isomorphic topological manifolds if one of the complex translations is kept fixed, and it induces repeated real roots in the fundamental polynomial as a component. A set of numerically simulated examples is included in the paper to illustrate the resulting manifold structures and the associated properties. Full article

(This article belongs to the Section Mathematics)

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15 pages, 3499 KiB

Open AccessArticle

Controlling of Unmanned Underwater Vehicles Using the Dynamic Planning of Symmetric Trajectory Based on Machine Learning for Marine Resources Exploration

by Yuriy Kozhubaev, Victor Belyaev, Yuriy Murashov and Oleg Prokofev

Symmetry 2023, 15(9), 1783; https://doi.org/10.3390/sym15091783 - 18 Sep 2023

Cited by 1 | Viewed by 794

Abstract

Unmanned underwater vehicles (UUV) are widely used tools in ocean development, which can be applied in areas such as marine scientific research, ocean resources exploration, and ocean security. However, as ocean exploration advances, UUVs face increasingly challenging operational environments with weaker communication signals. [...] Read more.

Unmanned underwater vehicles (UUV) are widely used tools in ocean development, which can be applied in areas such as marine scientific research, ocean resources exploration, and ocean security. However, as ocean exploration advances, UUVs face increasingly challenging operational environments with weaker communication signals. Consequently, autonomous obstacle avoidance planning for UUVs becomes increasingly important. With the deepening of ocean exploration, the operational environment of UUVs has become increasingly difficult to access, and the communication signals in the environment have become weaker. Therefore, autonomous obstacle avoidance planning of UUVs has become increasingly important. Traditional dynamic programming methods face challenges in terms of accuracy and real-time performance, requiring the design of auxiliary strategies to achieve ideal avoidance and requiring cumbersome perception equipment to support them. Therefore, exploring an efficient and easy-to-implement dynamic programming method has significant theoretical and practical value. In this study, an LSTM-RNN network structure suitable for UUVs was designed to learn the dynamic programming mode of UUVs in an unknown environment. The research was divided into three main aspects: collecting the required sample dataset for training deep networks, designing the LSTM-RNN network structure, and utilizing LSTM-RNN to achieve dynamic programming. Experimental results demonstrated that LSTM-RNN can learn planning patterns in unknown environments without the need for constructing an environment model or complex perception devices, thus providing significant theoretical and practical value. Consequently, this approach offers an effective solution for autonomous obstacle avoidance planning for UUVs. Full article

(This article belongs to the Special Issue Advanced Digital, Modeling and Control Applies into Various Processes II)

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18 pages, 10495 KiB

Open AccessArticle

Adaptive Reversible 3D Model Hiding Method Based on Convolutional Neural Network Prediction Error Expansion

by Guochang Hu, Kun Qian, Yinghua Li, Hong Li, Xinggui Xu and Hao Xu

Symmetry 2023, 15(9), 1782; https://doi.org/10.3390/sym15091782 - 18 Sep 2023

Viewed by 1152

Abstract

Although reversible data hiding technology is widely used, it still faces several challenges and issues. These include ensuring the security and reliability of embedded secret data, improving the embedding capacity, and maintaining the quality of media data. Additionally, irregular data types, such as [...] Read more.

Although reversible data hiding technology is widely used, it still faces several challenges and issues. These include ensuring the security and reliability of embedded secret data, improving the embedding capacity, and maintaining the quality of media data. Additionally, irregular data types, such as three-dimensional point clouds and triangle mesh-represented 3D models, lack an ordered structure in their representation. As a result, embedding these irregular data into digital media does not provide sufficient information for the complete recovery of the original data during extraction. To address this issue, this paper proposes a method based on convolutional neural network prediction error expansion to enhance the embedding capacity of carrier images while maintaining acceptable visual quality. The triangle mesh representation of the 3D model is regularized in a two-dimensional parameterization domain, and the regularized 3D model is reversibly embedded into the image. The process of embedding and extracting confidential information in carrier images is symmetrical, and the regularization and restoration of 3D models are also symmetrical. Experiments show that the proposed method increases the reversible embedding capacity, and the triangle mesh can be conveniently subjected to reversible hiding. Full article

(This article belongs to the Special Issue Symmetry in Optimization and Its Applications to Machine Learning)

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15 pages, 926 KiB

Open AccessArticle

Stochastic Dynamics Analysis of Epidemic Models Considering Negative Feedback of Information

by Wanqin Wu, Wenhui Luo, Hui Chen and Yun Zhao

Symmetry 2023, 15(9), 1781; https://doi.org/10.3390/sym15091781 - 18 Sep 2023

Viewed by 569

Abstract

In this article, we mainly consider the dynamic analysis of a stochastic infectious disease model with negative feedback, a symmetric and compatible distribution family. Based on the sir epidemic model taking into account the isolation (y) and the death (v), we consider adding [...] Read more.

In this article, we mainly consider the dynamic analysis of a stochastic infectious disease model with negative feedback, a symmetric and compatible distribution family. Based on the sir epidemic model taking into account the isolation (y) and the death (v), we consider adding a new variable (w) to control the information of non-drug interventions, which measures transformations in isolation performance that determine the epidemic, and establish a new model. We have demonstrated various properties of the model solution using Lyapunov functions for this model. To begin with, we demonstrate the existence and uniqueness of the global positive solution. After that, we obtained the conditions that need to be met for the extinction of the disease and verified the correctness of the conclusion by simulating numerical values. Afterwards, we prove the stochastic boundedness and stationary distribution of the model solution. Full article

(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)

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12 pages, 1444 KiB

Open AccessArticle

Scaled-Invariant Extended Quasi-Lindley Model: Properties, Estimation, and Application

by Mohamed Kayid, Abdulrahman Abouammoh and Ghadah Alomani

Symmetry 2023, 15(9), 1780; https://doi.org/10.3390/sym15091780 - 18 Sep 2023

Cited by 1 | Viewed by 577

Abstract

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve the [...] Read more.

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve the fit. In this study, we investigated a further extension of the quasi-Lindley model. This extension was asymmetrically distributed on the positive real number line. Maximum likelihood, least square error, Anderson–Darling, and expectation maximization algorithms were used to estimate the parameters studied. All techniques provided accurate and reliable estimates of the parameters. However, the mean square error of the expectation-maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a reliability data set, and the analysis showed that it outperformed all other alternative models. Full article

(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)

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11 pages, 543 KiB

Open AccessArticle

Investigating the Lifetime Performance Index under Ishita Distribution Based on Progressive Type II Censored Data with Applications

by Hanan Haj Ahmad, Kariema Elnagar and Dina Ramadan

Symmetry 2023, 15(9), 1779; https://doi.org/10.3390/sym15091779 - 18 Sep 2023

Cited by 4 | Viewed by 711

Abstract

In manufacturing sectors, product performance evaluation is crucial. The lifetime performance index, denoted as

C_{L}

, is widely used in product evaluation, where L signifies the lower specification limit. This study aims to refine the estimation of

C_{L}

by employing maximum-likelihood [...] Read more.

In manufacturing sectors, product performance evaluation is crucial. The lifetime performance index, denoted as

C_{L}

, is widely used in product evaluation, where L signifies the lower specification limit. This study aims to refine the estimation of

C_{L}

by employing maximum-likelihood and Bayesian methodologies, where symmetric and asymmetric loss functions are utilized. The analysis is conducted on progressive type II censored data, a requirement often imposed by budgetary constraints or the need for expedited testing. The data are assumed to follow the Ishita distribution, whose conforming rate is also evaluated. Furthermore, a hypothesis testing framework is employed to validate whether component lifetimes meet predefined standards. The theoretical findings are corroborated using real data collected from glass strength in aircraft windows. The numerical analysis emphasizes the goodness of fit of the Ishita distribution to model the data, thereby demonstrating the applicability of the proposed distribution. Full article

(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)

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20 pages, 727 KiB

Open AccessArticle

A New Bivariate Family Based on Archimedean Copulas: Simulation, Regression Model and Application

by Gabriela M. Rodrigues, Edwin M. M. Ortega, Roberto Vila and Gauss M. Cordeiro

Symmetry 2023, 15(9), 1778; https://doi.org/10.3390/sym15091778 - 18 Sep 2023

Cited by 1 | Viewed by 1179

Abstract

We use the Clayton and Frank copulas and the exponentiated odd log-logistic family to define a new flexible bivariate model to fit bimodal and asymmetry data. The copulas allow different distributions for the response variable, thus making analysis more suitable. We present some [...] Read more.

We use the Clayton and Frank copulas and the exponentiated odd log-logistic family to define a new flexible bivariate model to fit bimodal and asymmetry data. The copulas allow different distributions for the response variable, thus making analysis more suitable. We present some structural properties of the new model and describe a simulation study to show the consistency of the estimators. We construct a bivariate regression model based on the new family to fit oak lettuce plant data for different concentrations of silicon dioxide and organosilicon compounds. We check the response variables fresh weight and plant height together in order to verify the existing correlation between them. These variables exhibit a bimodal form, and the family used is able to model this behavior. Different marginal distributions are selected, which is an interesting point of the copula methodology. The variables have strong positive dependence, and the experiment is carried out comparing the control treatment with others leading to the following results: (i) the treatment 1-ethoxysilatrane (with concentrations 5 × 10

^{- 4}

mL·L

^{- 1}

and 10

^{- 3}

mL·L

^{- 1}

) is not significant for the response variables; (ii) the treatment amorphous silicon dioxide (with concentrations 50 mg·L

^{- 1}

and 100 mg·L

^{- 1}

) and the same treatment (with concentrations 5 × 10

^{- 3}

mL·L

^{- 1}

and 10

^{- 2}

mL·L

^{- 1}

) are significant and have positive effects on both responses; (iii) the treatment amorphous silicon dioxide (with concentrations 200 mg·L

^{- 1}

and 300 mg·L

^{- 1}

) are significant and have negative effects on the response variables. Overall, the proposed bivariate model is suitable for the current data and can be useful in other applications. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)

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11 pages, 8539 KiB

Open AccessArticle

Synthesis and Structure of a New Iodate Cs₅[Sc₂(IO₃)₉](IO₃)₂ with a Complex Framework Based on the Condensation of [Sc(IO₃)₆] Building Blocks

by Olga V. Reutova, Elena L. Belokoneva, Anatoly S. Volkov and Olga V. Dimitrova

Symmetry 2023, 15(9), 1777; https://doi.org/10.3390/sym15091777 - 17 Sep 2023

Viewed by 804

Abstract

Transparent single crystals of a new iodate Cs₅[Sc₂(IO₃)₉](IO₃)₂ were synthesized under mild hydrothermal conditions. X-ray diffraction of single crystal was used to determine the large crystal structure with 52 independent atoms, sp. [...] Read more.

Transparent single crystals of a new iodate Cs₅[Sc₂(IO₃)₉](IO₃)₂ were synthesized under mild hydrothermal conditions. X-ray diffraction of single crystal was used to determine the large crystal structure with 52 independent atoms, sp. gr. P2₁/c. The building blocks [Sc(IO₃)₆]³⁻ of Sc octahedra and six (IO₃) groups are condensed into a framework; the structure contains additional isolated (IO₃) groups. Large Cs cations occupy holes and form an intercrossing framework. Similar building blocks [M(IO₃)₆] are known for many iodates; however, most are isolated. Their topology and symmetry differ and determine the properties of the compounds. Full article

(This article belongs to the Collection Feature Papers in Chemistry)

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