Symmetry

19 pages, 392 KiB

Open AccessArticle

Symmetry and Asymmetry in Moment, Functional Equations, and Optimization Problems

by Octav Olteanu

Symmetry 2023, 15(7), 1471; https://doi.org/10.3390/sym15071471 - 24 Jul 2023

Cited by 3 | Viewed by 926

The purpose of this work is to provide applications of real, complex, and functional analysis to moment, interpolation, functional equations, and optimization problems. Firstly, the existence of the unique solution for a two-dimensional full Markov moment problem is characterized on the upper half-plane. [...] Read more.

The purpose of this work is to provide applications of real, complex, and functional analysis to moment, interpolation, functional equations, and optimization problems. Firstly, the existence of the unique solution for a two-dimensional full Markov moment problem is characterized on the upper half-plane. The issue of the unknown form of nonnegative polynomials on

R \times R_{+}

in terms of sums of squares is solved using polynomial approximation by special nonnegative polynomials, which are expressible in terms of sums of squares. The main new element is the proof of Theorem 1, based only on measure theory and on a previous approximation-type result. Secondly, the previous construction of a polynomial solution is completed for an interpolation problem with a finite number of moment conditions, pointing out a method of determining the coefficients of the solution in terms of the given moments. Here, one uses methods of symmetric matrix theory. Thirdly, a functional equation having nontrivial solution (defined implicitly) and a consequence are discussed. Inequalities, the implicit function theorem, and elements of holomorphic functions theory are applied. Fourthly, the constrained optimization of the modulus of some elementary functions of one complex variable is studied. The primary aim of this work is to point out the importance of symmetry in the areas mentioned above. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

30 pages, 7152 KiB

Open AccessReview

Einstein, Barcelona, Symmetry & Cosmology: The Birth of an Equation for the Universe

by Emilio Elizalde

Symmetry 2023, 15(7), 1470; https://doi.org/10.3390/sym15071470 - 24 Jul 2023

Viewed by 1783

Abstract

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern [...] Read more.

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann’s equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein’s contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo’s one, and Einstein’s special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach’s far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics. Full article

(This article belongs to the Section Physics)

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14 pages, 310 KiB

Open AccessArticle

Best Proximity Point Results for n-Cyclic and Regular-n-Noncyclic Fisher Quasi-Contractions in Metric Spaces

by Kamal Fallahi, Morteza Ayobian and Ghasem Soleimani Rad

Symmetry 2023, 15(7), 1469; https://doi.org/10.3390/sym15071469 - 24 Jul 2023

Cited by 1 | Viewed by 763

Abstract

In this work, we introduce some new concepts such as n-cyclic Fisher quasi-contraction mappings, full-n-noncyclic and regular-n-noncyclic Fisher quasi-contraction mappings in metric spaces. We then generalize the results by Safari-Hafshejani, Amini-Harandi and Fakhar. Meanwhile, we answer the question [...] Read more.

In this work, we introduce some new concepts such as n-cyclic Fisher quasi-contraction mappings, full-n-noncyclic and regular-n-noncyclic Fisher quasi-contraction mappings in metric spaces. We then generalize the results by Safari-Hafshejani, Amini-Harandi and Fakhar. Meanwhile, we answer the question “under what conditions does a full-n-noncyclic Fisher quasi-contraction mapping have

n (n - 1) / 2

unique optimal pairs of fixed points?”. Further, to support the main results, we highlight all of the new concepts via non-trivial examples. Full article

(This article belongs to the Special Issue New Trends in Fixed Point Theory with Emphasis on Symmetry)

19 pages, 1014 KiB

Open AccessArticle

The Landweber Iterative Regularization Method for Identifying the Unknown Source of Caputo-Fabrizio Time Fractional Diffusion Equation on Spherically Symmetric Domain

by Yong-Gang Chen, Fan Yang and Feng Tian

Symmetry 2023, 15(7), 1468; https://doi.org/10.3390/sym15071468 - 24 Jul 2023

Viewed by 712

Abstract

In this article, the inverse problem for identifying the space-dependent source of time fractional diffusion equation on a spherically symmetric domain with Caputo–Fabrizio fractional derivative is discussed. This problem is a typical ill-posed problem and the Landweber iterative regularization method is used to [...] Read more.

In this article, the inverse problem for identifying the space-dependent source of time fractional diffusion equation on a spherically symmetric domain with Caputo–Fabrizio fractional derivative is discussed. This problem is a typical ill-posed problem and the Landweber iterative regularization method is used to obtain the approximation solution. The convergent error estimates under a priori regularization parameter choice rule and a posteriori regularization parameter choice rule are given, respectively. The numerical examples are given to show the effectiveness of the Landweber iterative regularization method. Full article

(This article belongs to the Section Mathematics)

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22 pages, 15314 KiB

Open AccessArticle

Numerical Simulation of Conjugate Mixed Convection in 3D Channel with Heat-Generating Flat Element and Symmetrical Solid Two-Fin System

by Nikita S. Gibanov and Mikhail A. Sheremet

Symmetry 2023, 15(7), 1467; https://doi.org/10.3390/sym15071467 - 24 Jul 2023

Cited by 1 | Viewed by 849

Abstract

This paper presents the numerical simulation results of conjugate mixed convection in a three-dimensional channel with a heat-generating element and solid fins. It should be noted that the symmetrical location of fins has been studied. The system of partial differential equations, presented in [...] Read more.

This paper presents the numerical simulation results of conjugate mixed convection in a three-dimensional channel with a heat-generating element and solid fins. It should be noted that the symmetrical location of fins has been studied. The system of partial differential equations, presented in dimensionless form using velocity and vorticity vectors, has been solved by the finite difference method on a uniform grid. The central difference schemes have been used to approximate diffusive terms. In contrast, for an approximation of convective terms, the monotonic Samarskii difference schemes have been applied to improve the stable properties of central differences of the second order of accuracy. Analysis has been performed on a wide range of governing parameters, including the Reynolds number (200 ≤ Re ≤ 1000), the material of the fins (aluminum, copper, and iron), and the location of the fins on the heater surface, taking into account the identical distances between the fins and the nearest walls. Water has been considered a working cooling medium. The obtained outcomes characterize the most efficient heat removal from the surface of the energy source using the considered fin system. For example, by using copper fins, the cooling efficiency of the heating element can be increased. The average heater temperature decreases significantly with an increase in the Reynolds number. The distance between the fins also makes a significant contribution to the cooling phenomenon. It is noted that with the most successful choice of location, it is possible to decrease the temperature of the heater by more than 12%. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 907 KiB

Open AccessReview

Phase Diagram of Dense Two-Color QCD at Low Temperatures

by Victor V. Braguta

Symmetry 2023, 15(7), 1466; https://doi.org/10.3390/sym15071466 - 24 Jul 2023

Cited by 1 | Viewed by 917

Abstract

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be [...] Read more.

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be described by chiral perturbation theory (ChPT), which predicts a second-order phase transition with Bose-Einstein condensation of diquarks at

μ = m_{π} / 2

. At larger baryon chemical potentials, the interactions between baryons become important, and ChPT is not applicable anymore. At sufficiently large baryon chemical potential, the Fermi sphere composed of quarks is formed, and diquarks are condensed on the surface of this sphere. In this region, two-color baryon matter reveals properties similar to those of the Quarkyonic phase. Particular attention in this review is paid to lattice studies of dense two-color QCD phase diagram. In the low-density region, the results of lattice studies are in agreement with ChPT predictions. At sufficiently large baryon densities, lattice studies observe a Fermi sphere composed of quarks and condensation of diquarks on its surface. Thus, available lattice studies support most of the theoretical predictions. Finally, we discuss the status of the deconfinement in cold dense two-color matter, which was observed in lattice simulation with staggered fermions. Full article

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

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20 pages, 374 KiB

Open AccessArticle

Outage Performance of Asymmetrical Cognitive Simultaneous Wireless Information and Power Transfer Networks Based on Non-Orthogonal Multiple Access with an Incremental Cooperation Relay and Hardware Impairments

by Shuai Liu, Man Cui, Anxin Zhao, Chen Zhang and Yuanlong Zhang

Symmetry 2023, 15(7), 1465; https://doi.org/10.3390/sym15071465 - 24 Jul 2023

Viewed by 598

Abstract

This work aims to investigate an asymmetrical NOMA transmission network based on cognitive radio, where both the source and relay nodes of the secondary user are energy limited, and the energy could be harvested from the transmission signal of the power beacon. Considering [...] Read more.

This work aims to investigate an asymmetrical NOMA transmission network based on cognitive radio, where both the source and relay nodes of the secondary user are energy limited, and the energy could be harvested from the transmission signal of the power beacon. Considering some particular hardware impairments and asymmetry in the NOMA transmission, the closed-form expressions of outage probability for relay and destination nodes were derived using incremental relay methods. Furthermore, built on the expressions of the outage probability, the throughput performance was analyzed. Finally, the correctness of our theoretical analysis was verified using simulations. Full article

(This article belongs to the Special Issue Asymmetrical Network Control for Complex Dynamic Services)

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11 pages, 356 KiB

Open AccessArticle

A Modified Parallel Algorithm for a Common Fixed-Point Problem with Application to Signal Recovery

by Anchalee Khemphet, Raweerote Suparatulatorn, Pariwate Varnakovida and Phakdi Charoensawan

Symmetry 2023, 15(7), 1464; https://doi.org/10.3390/sym15071464 - 24 Jul 2023

Viewed by 705

Abstract

In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm [...] Read more.

In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm inspired by the inertial method and the Mann iteration process. Moreover, both weak and strong convergence theorems are provided for the algorithm. Furthermore, an application of the algorithm to a signal recovery problem with multiple blurring filters is presented. Consequently, the numerical experiment shows better results compared with the previous algorithm. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)

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17 pages, 4088 KiB

Open AccessArticle

Enhanced LDR Detail Rendering for HDR Fusion by TransU-Fusion Network

by Bo Song, Rui Gao, Yong Wang and Qi Yu

Symmetry 2023, 15(7), 1463; https://doi.org/10.3390/sym15071463 - 23 Jul 2023

Cited by 1 | Viewed by 928

Abstract

High Dynamic Range (HDR) images are widely used in automotive, aerospace, AI, and other fields but are limited by the maximum dynamic range of a single data acquisition using CMOS image sensors. High dynamic range images are usually synthesized through multiple exposure techniques [...] Read more.

High Dynamic Range (HDR) images are widely used in automotive, aerospace, AI, and other fields but are limited by the maximum dynamic range of a single data acquisition using CMOS image sensors. High dynamic range images are usually synthesized through multiple exposure techniques and image processing techniques. One of the most challenging task in multiframe Low Dynamic Range (LDR) images fusion for HDR is to eliminate ghosting artifacts caused by motion. In traditional algorithms, optical flow is generally used to align dynamic scenes before image fusion, which can achieve good results in cases of small-scale motion scenes but causes obvious ghosting artifacts when motion magnitude is large. Recently, attention mechanisms have been introduced during the alignment stage to enhance the network’s ability to remove ghosts. However, significant ghosting artifacts still occur in some scenarios with large-scale motion or oversaturated areas. We proposea novel Distilled Feature TransformerBlock (DFTB) structure to distill and re-extract information from deep image features obtained after U-Net downsampling, achieving ghost removal at the semantic level for HDR fusion. We introduce a Feature Distillation Transformer Block (FDTB), based on the Swin-Transformer and RFDB structure. FDTB uses multiple distillation connections to learn more discriminative feature representations. For the multiexposure moving scene image fusion HDR ghost removal task, in the previous method, the use of deep learning to remove the ghost effect in the composite image has been perfect, and it is almost difficult to observe the ghost residue of moving objects in the composite HDR image. The method in this paper focuses more on how to save the details of LDR image more completely after removing the ghost to synthesize high-quality HDR image. After using the proposed FDTB, the edge texture details of the synthesized HDR image are saved more perfectly, which shows that FDTB has a better effect in saving the details of image fusion. Futhermore, we propose a new depth framework based on DFTB for fusing and removing ghosts from deep image features, called TransU-Fusion. First of all, we use the encoder in U-Net to extract image features of different exposures and map them to different dimensional feature spaces. By utilizing the symmetry of the U-Net structure, we can ultimately output these feature images as original size HDR images. Then, we further fuse high-dimensional space features using Dilated Residual Dense Block (DRDB) to expand the receptive field, which is beneficial for repairing over-saturated regions. We use the transformer in DFTB to perform low-pass filtering on low-dimensional space features and interact with global information to remove ghosts. Finally, the processed features are merged and output as an HDR image without ghosting artifacts through the decoder. After testing on datasets and comparing with benchmark and state-of-the-art models, the results demonstrate our model’s excellent information fusion ability and stronger ghost removal capability. Full article

(This article belongs to the Special Issue Symmetry in Probablistic Models and Aerospace Systems)

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27 pages, 9831 KiB

Open AccessArticle

A Study on Perception of Visual–Tactile and Color–Texture Features of Footwear Leather for Symmetric Shoes

by Dan-Dan Xu, Chih-Fu Wu and Chung-Shing Wang

Symmetry 2023, 15(7), 1462; https://doi.org/10.3390/sym15071462 - 22 Jul 2023

Cited by 1 | Viewed by 1354

Abstract

The study applies Kansei engineering in analyzing the color and texture of leather footwear, utilizing neural network verification to mirror consumers’ visual and tactile imageries onto varieties of leather. This aids in the development of an advanced system for selecting leather footwear based [...] Read more.

The study applies Kansei engineering in analyzing the color and texture of leather footwear, utilizing neural network verification to mirror consumers’ visual and tactile imageries onto varieties of leather. This aids in the development of an advanced system for selecting leather footwear based on such impressions. Initially, representative word pairs denoting consumers’ visual and tactile perceptions of leather footwear were delineated. Post-evaluation of these perceptions through a sensibility assessment questionnaire was administered, using 54 samples of leather footwear provided by manufacturers, with each leather type codified in terms of visual and tactile sensibilities. Subsequently, a customized software algorithm was crafted to isolate the primary color and adhesiveness as color features from the leather sample images. Analyzing grayscale values of the images and using pixel neighborhood as a base, the associated calculation methods, such as LBP, SCOV, VAR, SAC, etc., were proposed to extract texture features from the images. The derived color and texture feature values were used as the input layer and the sensory vocabulary quantified values as the output layer. Backpropagation neural network training was conducted on 49 leather samples, with five leather samples used for testing, culminating in the verification of neural network training for three types and 17 combinations. The outcome was an optimal method for leather footwear Kansei engineering and neural network training, establishing a design process for leather footwear characteristics assisted by sensory vocabulary and a backpropagation neural network. Additionally, a computer-aided system for selecting leather footwear, based on these impressions, was designed and validated through footwear design. This study utilized symmetry in footwear design. By using the design of a single shoe to represent the imagery of a pair of symmetrical shoes, we verified whether the leather samples recommended by the leather imagery selection query system met the expected system input settings. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Computer Vision and Image Processing)

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23 pages, 929 KiB

Open AccessArticle

A Novel Algorithm for Merging Bayesian Networks

by Miroslav Vaniš, Zdeněk Lokaj and Martin Šrotýř

Symmetry 2023, 15(7), 1461; https://doi.org/10.3390/sym15071461 - 22 Jul 2023

Cited by 1 | Viewed by 1361

Abstract

The article presents a novel algorithm for merging Bayesian networks generated by different methods, such as expert knowledge and data-driven approaches, while leveraging a symmetry-based approach. The algorithm combines the strengths of each input network to create a more comprehensive and accurate network. [...] Read more.

The article presents a novel algorithm for merging Bayesian networks generated by different methods, such as expert knowledge and data-driven approaches, while leveraging a symmetry-based approach. The algorithm combines the strengths of each input network to create a more comprehensive and accurate network. Evaluations on traffic accident data from Prague in the Czech Republic and accidents on railway crossings demonstrate superior predictive performance, as measured by prediction error metric. The algorithm identifies and incorporates symmetric nodes into the final network, ensuring consistent representations across different methods. The merged network, incorporating nodes selected from both the expert and algorithm networks, provides a more comprehensive and accurate representation of the relationships among variables in the dataset. Future research could focus on extending the algorithm to deal with cycles and improving the handling of conditional probability tables. Overall, the proposed algorithm demonstrates the effectiveness of combining different sources of knowledge in Bayesian network modeling. Full article

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12 pages, 1025 KiB

Open AccessArticle

Symmetric Perfect and Symmetric Semiperfect Colorings of Groups

by Rovin B. Santos, Lilibeth D. Valdez and Ma. Lailani B. Walo

Symmetry 2023, 15(7), 1460; https://doi.org/10.3390/sym15071460 - 22 Jul 2023

Viewed by 819

Abstract

Let G be a group. A k-coloring of G is a surjection

λ : G \to {1, 2, \dots, k}

. Equivalently, a k-coloring

λ

of G is a partition [...] Read more.

Let G be a group. A k-coloring of G is a surjection

λ : G \to {1, 2, \dots, k}

. Equivalently, a k-coloring

λ

of G is a partition

P = {P_{1}, P_{2}, \dots, P_{k}}

of G into k subsets. If

g P = P

for all g in G, we say that

λ

is perfect. If

h P = P

only for all

h \in H \leq G

such that

[G : H] = 2

, then

λ

is semiperfect. If there is an element

g \in G

such that

λ (x) = λ (g x^{- 1} g)

for all

x \in G

, then

λ

is said to be symmetric. In this research, we relate the notion of symmetric colorings with perfect and semiperfect colorings. Specifically, we identify which perfect and semiperfect colorings are symmetric in relation to the subgroups of G that contain the squares of elements in G, in H, and in

G ∖ H

. We also show examples of colored planar patterns that represent symmetric perfect and symmetric semiperfect colorings of some groups. Full article

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11 pages, 4456 KiB

Open AccessArticle

Scanning Precession Electron Tomography (SPET) for Structural Analysis of Thin Films along Their Thickness

by Sara Passuti, Julien Varignon, Adrian David and Philippe Boullay

Symmetry 2023, 15(7), 1459; https://doi.org/10.3390/sym15071459 - 22 Jul 2023

Viewed by 984

Abstract

Accurate structure analysis of epitaxial perovskite thin films is a fundamental step towards the ability to tune their physical properties as desired. Precession-assisted electron diffraction tomography (PEDT) has proven to be an effective technique for performing ab initio structure solutions and refinements for [...] Read more.

Accurate structure analysis of epitaxial perovskite thin films is a fundamental step towards the ability to tune their physical properties as desired. Precession-assisted electron diffraction tomography (PEDT) has proven to be an effective technique for performing ab initio structure solutions and refinements for this class of materials. As the film thickness or the region of interest (ROI) decrease in size, the capacity to collect PEDT data with smaller electron beams is a key parameter and ROI tracking becomes a major issue. To circumvent this problem, we considered here an alternative approach to acquiring data by combining PEDT with a scan over an area, extracting the intensities collected at different positions and using them to perform accurate structure refinements. As a proof of concept, a Scanning Precession Electron Tomography (SPET) experiment is performed on a 35 nm thick perovskite

P r V O_{3}

(PVO) film deposited on a

S r T i O_{3}

(STO) substrate. This way, it was possible to detect small changes in the PVO structure along the film thickness, from the variation in unit cell parameters to atomic positions. We believe that SPET has the potential to become the standard procedure for the accurate structure analysis of ROIs as small as 10 nm. Full article

(This article belongs to the Special Issue Electron Diffraction and Structural Imaging II)

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26 pages, 838 KiB

Open AccessArticle

A Transmuted Modified Power-Generated Family of Distributions with Practice on Submodels in Insurance and Reliability

by Sidra Naz, Laila A. Al-Essa, Hassan S. Bakouch and Christophe Chesneau

Symmetry 2023, 15(7), 1458; https://doi.org/10.3390/sym15071458 - 22 Jul 2023

Cited by 4 | Viewed by 766

Abstract

In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two baseline families. For a prime study, we identify the main [...] Read more.

In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two baseline families. For a prime study, we identify the main characteristics of the new transmuted modified power family, such as the asymptotic results, quantile function, series representation, and the various kinds of moment measures. By using the exponential distribution as the baseline, a new three-parameter lifetime distribution is constructed. The associated probability functions (density and hazard rate) are flexible and have a variety of asymmetric shapes, which make them attractive for statistical purposes. In particular, for the related probability density function, reversed-J, unimodal, and right-skewed shapes are observed. Measures relating to risk theory are also computed, such as the value at risk and the expected shortfall. By using both simulation analysis and the maximum likelihood approach, the estimation of the model parameters is evaluated. The effectiveness of the proposed model is demonstrated by two real-world cases (one in insurance and the other in reliability), and we show that it yields better fits when compared to other extended models connected to the exponential model. Full article

(This article belongs to the Section Mathematics)

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14 pages, 407 KiB

Open AccessArticle

A Proposal to the ‘12 vs. 32 Puzzle’

by Qiang Li, Wei Feng and Guo-Li Wang

Symmetry 2023, 15(7), 1457; https://doi.org/10.3390/sym15071457 - 21 Jul 2023

Cited by 1 | Viewed by 711

Abstract

We reconsider the semileptonic decays of

B \to D_{1}^{(')} l {\bar{ν}}_{l}

. The previous theoretical calculations predict a significantly smaller rate for the semileptonic decay of B to [...] Read more.

We reconsider the semileptonic decays of

B \to D_{1}^{(')} l {\bar{ν}}_{l}

. The previous theoretical calculations predict a significantly smaller rate for the semileptonic decay of B to

D_{1}^{'} (J_{l} = \frac{1}{2})

compared with that to the

D_{1} (J_{l} = \frac{3}{2})

, which is not consistent with the current experimental data. This conflict is known as the so-called ‘

\frac{1}{2}

vs.

\frac{3}{2}

puzzle’. In this work, we propose a simple scheme to fix this problem, where we suppose the strong eigenstates

D_{1}^{(')}

that do not coincide with the eigenstate of the weak interaction, since no experimental results show that the weak and the strong interactions have to share the same eigenstates. Within the framework of this tentative scheme, meson B first weakly decays to the weak eigenstates

D_{α (β)}

and then the latter are detected as the

D_{1}^{(')}

by the strong decay products

D^{*} π

. We predict that there exist two new particles

D_{α (β)}

with

J^{P} = 1^{+}

, which were not previously identified. The good performance of the new scheme in describing the experimental data may hint at new symmetry in the weak decays of

B_{q}

to

1^{+}

heavy–light mesons. To test the scheme proposed here, we suggest an experiment to detect the difference in the invariant mass spectra of

D_{1}

that is reconstructed from the B weak decay and from the strong decay products. Full article

(This article belongs to the Section Physics)

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19 pages, 904 KiB

Open AccessConcept Paper

Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods

by Judel Villas Protacio

Symmetry 2023, 15(7), 1456; https://doi.org/10.3390/sym15071456 - 21 Jul 2023

Viewed by 1252

Abstract

We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any

n \times n

matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a [...] Read more.

We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any

n \times n

matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods. Full article

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24 pages, 333 KiB

Open AccessFeature PaperArticle

Deviation of Geodesics, Particle Trajectories and the Propagation of Radiation in Gravitational Waves in Shapovalov Type III Wave Spacetimes

by Konstantin Osetrin, Evgeny Osetrin and Elena Osetrina

Symmetry 2023, 15(7), 1455; https://doi.org/10.3390/sym15071455 - 21 Jul 2023

Cited by 2 | Viewed by 840

Abstract

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions [...] Read more.

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions are obtained for the equations of geodesic deviation and tidal acceleration of particles in a gravitational wave in privileged coordinate systems. An explicit analytical law of transition from a privileged coordinate system to a synchronous reference system associated with a freely falling observer with an explicit selection of time and spatial coordinates is obtained. An explicit form of the metric of a gravitational wave in a synchronous frame of reference is obtained. For a synchronous frame of reference, the trajectories of particles and radiation, the deviation of geodesics, and tidal accelerations in a gravitational wave are obtained. The presented methods and approaches are applicable both to Einstein’s general theory of relativity and to modified theories of gravity. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

18 pages, 9636 KiB

Open AccessArticle

A Feature Fusion Human Ear Recognition Method Based on Channel Features and Dynamic Convolution

by Xuebin Xu, Yibiao Liu, Chenguang Liu and Longbin Lu

Symmetry 2023, 15(7), 1454; https://doi.org/10.3390/sym15071454 - 21 Jul 2023

Cited by 1 | Viewed by 980

Abstract

Ear images are easy to capture, and ear features are relatively stable and can be used for identification. The ear images are all asymmetric, and the asymmetry of the ear images collected in the unconstrained environment will be more pronounced, increasing the recognition [...] Read more.

Ear images are easy to capture, and ear features are relatively stable and can be used for identification. The ear images are all asymmetric, and the asymmetry of the ear images collected in the unconstrained environment will be more pronounced, increasing the recognition difficulty. Most recognition methods based on hand-crafted features perform poorly in terms of recognition performance in the face of ear databases that vary significantly in terms of illumination, angle, occlusion, and background. This paper proposes a feature fusion human ear recognition method based on channel features and dynamic convolution (CFDCNet). Based on the DenseNet-121 model, the ear features are first extracted adaptively by dynamic convolution (DY_Conv), which makes the ear features of the same class of samples more aggregated and different types of samples more dispersed, enhancing the robustness of the ear feature representation. Then, by introducing an efficient channel attention mechanism (ECA), the weights of important ear features are increased and invalid features are suppressed. Finally, we use the Max pooling operation to reduce the number of parameters and computations, retain the main ear features, and improve the model’s generalization ability. We performed simulations on the AMI and AWE human ear datasets, achieving 99.70% and 72.70% of Rank-1 (R1) recognition accuracy, respectively. The recognition performance of this method is significantly better than that of the DenseNet-121 model and most existing human ear recognition methods. Full article

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17 pages, 3228 KiB

Open AccessArticle

Prediction of High-Speed Traffic Flow around City Based on BO-XGBoost Model

by Xin Lu, Cai Chen, RuiDan Gao and ZhenZhen Xing

Symmetry 2023, 15(7), 1453; https://doi.org/10.3390/sym15071453 - 20 Jul 2023

Cited by 1 | Viewed by 1047

Abstract

The prediction of high-speed traffic flow around the city is affected by multiple factors, which have certain particularity and difficulty. This study devised an asymmetric Bayesian optimization extreme gradient boosting (BO-XGBoost) model based on Bayesian optimization for the spatiotemporal and multigranularity prediction of [...] Read more.

The prediction of high-speed traffic flow around the city is affected by multiple factors, which have certain particularity and difficulty. This study devised an asymmetric Bayesian optimization extreme gradient boosting (BO-XGBoost) model based on Bayesian optimization for the spatiotemporal and multigranularity prediction of high-speed traffic flow around a city. First, a traffic flow dataset for a ring expressway was constructed, and the data features were processed based on the original data. The data were then visualized, and their spatiotemporal distribution exhibited characteristics such as randomness, continuity, periodicity, and rising fluctuations. Secondly, a feature matrix was constructed monthly for the dataset, and the BO-XGBoost model was used for traffic flow prediction. The proposed model BO-XGBoost was compared with the symmetric model bidirectional long short-term memory and integrated models (random forest, extreme gradient boosting, and categorical boosting) that directly input temporal data. The R-squared (R²) of the BO XGBoost model for predicting TF and PCU reached 0.90 and 0.87, respectively, with an average absolute percentage error of 2.88% and 3.12%, respectively. Thus, the proposed model achieved an accurate prediction of high-speed traffic flow around the province, providing a theoretical basis and data support for the development of central-city planning. Full article

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13 pages, 2201 KiB

Open AccessArticle

Security Analysis of Imperfect Gaussian Modulation Caused by Amplitude Modulator in Continuous–Variable Quantum Key Distribution

by Zhenghua Li, Xiangyu Wang, Ziyang Chen, Bingjie Xu and Song Yu

Symmetry 2023, 15(7), 1452; https://doi.org/10.3390/sym15071452 - 20 Jul 2023

Viewed by 842

Abstract

Continuous-variable quantum key distribution (CV–QKD) is a system that provides secret keys for symmetric key systems. In the application of CV–QKD, the practical security of the system is crucial. In this article, we investigate the practical security issues caused by non–ideal Gaussian modulation, [...] Read more.

Continuous-variable quantum key distribution (CV–QKD) is a system that provides secret keys for symmetric key systems. In the application of CV–QKD, the practical security of the system is crucial. In this article, we investigate the practical security issues caused by non–ideal Gaussian modulation, which is caused by fitting defects of the amplitude modulator’s (AM) modulation curve. We provide the effect of fitting error on parameter estimation. We also give the relationship between the fitting order and the secret key rate. The simulation results indicate that the system is completely unable to communicate during first–order fitting. During second–order fitting, the system’s performance decreases by more than half. During third–order fitting, the system’s performance will be consistent with the ideal. Therefore, to ensure the performance of the CV–QKD system, the fitting order must be at least three or higher. Full article

(This article belongs to the Section Physics)

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7 pages, 215 KiB

Open AccessArticle

A Study on the Centroid of a Class of Solvable Lie Algebras

by Demin Yu, Chan Jiang and Jiejing Ma

Symmetry 2023, 15(7), 1451; https://doi.org/10.3390/sym15071451 - 20 Jul 2023

Viewed by 642

Abstract

The centroid of Lie algebra is a basic concept and a necessary tool for studying the structure of Lie algebraic structure. The extended Heisenberg algebra is an important class of solvable Lie algebras. In any Lie algebra, the anti symmetry of Lie operations [...] Read more.

The centroid of Lie algebra is a basic concept and a necessary tool for studying the structure of Lie algebraic structure. The extended Heisenberg algebra is an important class of solvable Lie algebras. In any Lie algebra, the anti symmetry of Lie operations is an important property of Lie algebra. This article investigates the centroids and structures of

2 n + 2

dimensional extended Heisenberg algebras, where all invertible elements form a group and all elements form a ring. Then, its main research results are extended to infinite dimensional extended Heisenberg algebras. Full article

(This article belongs to the Special Issue Analytic/Numeric Solutions of Schrödinger-Type Equations: Applications of Lie Symmetry and Other Methods)

17 pages, 334 KiB

Open AccessArticle

Soft Groups and Characteristic Soft Subgroups

by Amlak I. Alajlan and Ahmad M. Alghamdi

Symmetry 2023, 15(7), 1450; https://doi.org/10.3390/sym15071450 - 20 Jul 2023

Cited by 1 | Viewed by 1259

Abstract

Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of [...] Read more.

Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and soft automorphisms with their basic properties. Furthermore, the concept of soft point groups is introduced and the properties of these soft groups are studied. We state the concept of characteristic soft subgroups of a given soft group. Also, some theorems related to this concept are investigated. We study the characteristic soft subgroups of a given soft point group. The characteristic soft subgroups play a significant part in the study of the soft group theory and are useful for understanding the structure of a soft group and its soft automorphisms. As an application of characteristic soft subgroups, they allow us to identify and study important soft subgroups that are preserved under soft automorphisms. Also, practical applications for our theory can be conducted in future work such as the relation with other disciplines in sciences. Full article

(This article belongs to the Section Mathematics)

26 pages, 8612 KiB

Open AccessReview

Tracking Defects of Electronic Crystals by Coherent X-ray Diffraction

by David Le Bolloc’h, Ewen Bellec, Natacha Kirova and Vincent L. R. Jacques

Symmetry 2023, 15(7), 1449; https://doi.org/10.3390/sym15071449 - 20 Jul 2023

Cited by 1 | Viewed by 1200

Abstract

In this article, we review different studies based on advanced X-ray diffraction techniques—especially coherent X-ray diffraction—that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and Spin density Wave (SDW), through their local phase. After a brief [...] Read more.

In this article, we review different studies based on advanced X-ray diffraction techniques—especially coherent X-ray diffraction—that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and Spin density Wave (SDW), through their local phase. After a brief introduction on the added value of using coherent X-rays, we show how the method can be applied to CDW and SDW systems, in both static and dynamical regimes. The approach allowed us to probe the particular sliding state of CDWs systems by observing them through their phase fluctuations, to which coherent X-rays are particularly sensitive. Several compounds stabilizing a CDW phase able to slide are presented, each with a different but clearly pronounced signature of the sliding state. Two main features emerge from this series of experiments which have been little treated until now, the influence of CDW pinning by the sample surfaces and the propagation of periodic phase defects such as charge solitons across the entire sample. Phase models describing the spatial and temporal properties of sliding CDWs are presented in the last part of this review. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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17 pages, 3560 KiB

Open AccessFeature PaperArticle

Spontaneous Symmetry Breaking in Systems Obeying the Dynamics of On–Off Intermittency and Presenting Bimodal Amplitude Distributions

by Stelios M. Potirakis, Pericles Papadopoulos, Niki-Lina Matiadou, Michael P. Hanias, Stavros G. Stavrinides, Georgios Balasis and Yiannis Contoyiannis

Symmetry 2023, 15(7), 1448; https://doi.org/10.3390/sym15071448 - 20 Jul 2023

Cited by 2 | Viewed by 818

Abstract

In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the “PNA-based symbolic time-series analysis method” (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the [...] Read more.

In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the “PNA-based symbolic time-series analysis method” (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the symbolic dynamics of two symbols produced by the 3D Ising model in its critical state. After this numerical verification of the reliability of PNA-STSM, three examples of how PNA-STSM can be applied to the category of systems that obey the dynamics of the on–off intermittency are presented. Usually, such time series, with on–off intermittency, present bimodal amplitude distributions (i.e., with two lobes). As has recently been found, the phenomenon of on–off intermittency is associated with the spontaneous symmetry breaking (SSB) of the second-order phase transition. Thus, the revelation that a system is close to SSB supports a deeper understanding of its dynamics in terms of criticality, which is quite useful in applications such as the analysis of pre-earthquake fracture-induced electromagnetic emission (also known as fracture-induced electromagnetic radiation) (FEME/FEMR) signals. Beyond the case of on–off intermittency, PNA-STSM can provide credible results for the dynamics of any two-symbol symbolic dynamics, even in cases in which there is an imbalance in the probability of the appearance of the two respective symbols since the two symbols are not considered separately but, instead, simultaneously, considering the information from both branches of the symbolic dynamics. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)

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13 pages, 1395 KiB

Open AccessArticle

Application of a Partially Invariant Exact Solution of the Thermosolutal Convection Equations for Studying the Instability of an Evaporative Flow in a Channel Heated from Above

by Victoria B. Bekezhanova and Olga N. Goncharova

Symmetry 2023, 15(7), 1447; https://doi.org/10.3390/sym15071447 - 20 Jul 2023

Cited by 1 | Viewed by 647

Abstract

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat [...] Read more.

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat and mass transfer caused by the combined action of gas pumping, buoyancy, thermocapillarity and linear heating of the channel walls in a two-layer system. The influence of heating from above on the parameters of the ground state and the stability characteristics of the basic flow is explored using an example of the ethanol–air system. We evaluate the thresholds of the linear stability and select the most dangerous modes. Heating from above results in flow stabilization. Instability appears in the form of oscillatory cellular convective patterns. Full article

(This article belongs to the Special Issue Symmetry in CFD: Convection, Diffusion and Dynamics)

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16 pages, 315 KiB

Open AccessArticle

Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions

by Mansour Alatwi, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani and Elmetwally M. Elabbasy

Symmetry 2023, 15(7), 1446; https://doi.org/10.3390/sym15071446 - 19 Jul 2023

Viewed by 598

Abstract

In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow [...] Read more.

In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow us to improve the monotonic and asymptotic properties of the positive solutions of the studied equation. Then, using an improved approach, we establish new criteria that test the oscillation of all solutions. We also rely on the principle of symmetry between positive and negative solutions to obtain the new criteria. The paper provides illustrative examples that highlight the significance of our findings. Full article

(This article belongs to the Special Issue Theories and Applications for Dynamical Systems, Symmetry Problems and Differential Equations)

20 pages, 942 KiB

Open AccessArticle

Assessing Asymmetrical Rates in Multivariate Phylogenetic Trait Evolution: An Extension of Statistical Models for Heterogeneous Rate Estimation

by Dwueng-Chwuan Jhwueng

Symmetry 2023, 15(7), 1445; https://doi.org/10.3390/sym15071445 - 19 Jul 2023

Viewed by 861

Abstract

Understanding the rate of evolution provides insight into how rapidly species have historically evolved. We investigate the often-overlooked concept of asymmetry in evolutionary rates. We observe the variation in the rates at which different traits within the same organism, or the same traits [...] Read more.

Understanding the rate of evolution provides insight into how rapidly species have historically evolved. We investigate the often-overlooked concept of asymmetry in evolutionary rates. We observe the variation in the rates at which different traits within the same organism, or the same traits across different organisms, evolve. Influenced by factors such as environmental pressures and genetic constraints, this asymmetry might lead to inconsistent rates of biological changes. To capture these diverse rates, we propose three advanced statistical models, transcending the traditionally employed Brownian motion model. These models—the phylogenetic multivariate Ornstein–Uhlenbeck model, the early burst model, and the mixed model—were applied to body length, forelimbs, and head length in salamanders. The results from our substantial dataset show these models’ effectiveness in highlighting the asymmetrical patterns of trait evolution, enhancing our understanding of the complex dynamics in species evolution. Therefore, our study underscores the importance of considering asymmetry when studying evolutionary rates. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry in Evolutionary Biology)

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9 pages, 2676 KiB

Open AccessArticle

High Circular Dichroism Optical Chiral Metasurfaces Based on Bound States in the Continuum

by Ziang Gao, Pu Wang, Shilin Yu, Zhengshan Xu and Tonggang Zhao

Symmetry 2023, 15(7), 1444; https://doi.org/10.3390/sym15071444 - 19 Jul 2023

Cited by 2 | Viewed by 1122

Abstract

In this paper, we suggest a design for a chiral metasurface at optical frequencies that shows a high level of circular dichroism (CD) of 0.94. By breaking the in-plane asymmetry and exciting the quasi-bound states in the continuum (quasi-BICs), a high Q-factor was [...] Read more.

In this paper, we suggest a design for a chiral metasurface at optical frequencies that shows a high level of circular dichroism (CD) of 0.94. By breaking the in-plane asymmetry and exciting the quasi-bound states in the continuum (quasi-BICs), a high Q-factor was obtained, which greatly enhances the interaction between light and matter. Then, the multipole decomposition was confirmed to analyze its mode of excitation. The proposed design may provide new possibilities for high-performance optical devices. Full article

(This article belongs to the Special Issue Chiral Symmetry and Spin Dynamics)

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11 pages, 1490 KiB

Open AccessCommunication

Biomechanics of Ascending and Descending Stairs in a Patient with Transfemoral Amputation and Neural Sensory Feedback: A Case Report

by Saša Bubanj, Marko Radenković, Dušan Stanković, Emilija Petković, Ana Lilić, Ivana Bojić, Nikola Aksović, Tatiana Dobrescu, Bojan Bjelica, Ivan Ćuk, Sanja Mazić, Francesco Maria Petrini, Šćepan Sinanović, Milena Tomović and Florin Valentin Leuciuc

Symmetry 2023, 15(7), 1443; https://doi.org/10.3390/sym15071443 - 19 Jul 2023

Viewed by 932

Abstract

(1) Background: Asymmetry in gait could pose a problem for patients with transfemoral amputation, due to a higher risk for secondary comorbidities. Gait analysis during ascending and descending stairs (20 stair ascends and descends) was conducted in a patient with a unilateral transfemoral [...] Read more.

(1) Background: Asymmetry in gait could pose a problem for patients with transfemoral amputation, due to a higher risk for secondary comorbidities. Gait analysis during ascending and descending stairs (20 stair ascends and descends) was conducted in a patient with a unilateral transfemoral amputation and integrated neural sensory feedback (NSFB), with the aim to compare biomechanical parameters between the healthy and the prosthetic leg in conditions with and without NSFB. (2) Methods: Transversal-type research was conducted at the beginning of the patient’s rehabilitation and without prior gait training in conditions with NSFB. Complete study included several months of different gait testing with and without the NSFB. Data analyzed in this study are just a small portion of the overall dataset (only one subject, one recording session, reduced amount of trials in one condition), used for showing the validity of the proposed methodology for gait analysis and proving proof of concept. The analyzed parameters included stance, time, and speed of ascending and descending stairs in conditions with and without NSFB, measured for both legs. The data were processed using statistical software (SPSS Statistics version 24), with descriptive statistics and paired-sample t-tests to determine differences in gait parameters between the healthy and the prosthetic leg. (3) Results: The results revealed statistically significant differences (p = 0.00) in all three examined parameters (stance, time, and speed) between conditions with and without NSFB. (4) Conclusions: Gait stance, time, and the speed of ascending and descending stairs can be controlled and tailored in real time using NSFB. Full article

(This article belongs to the Special Issue Sports Biomechanics and Symmetry)

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11 pages, 262 KiB

Open AccessArticle

Fixed Points and λ-Weak Contractions

by Laura Manolescu and Adina Juratoni

Symmetry 2023, 15(7), 1442; https://doi.org/10.3390/sym15071442 - 18 Jul 2023

Viewed by 700

Abstract

In this paper, we introduce a new type of contractions on a metric space

(X, d)

in which the distance

d (x, y)

is replaced with a function, depending on a parameter

λ

, that is not [...] Read more.

In this paper, we introduce a new type of contractions on a metric space

(X, d)

in which the distance

d (x, y)

is replaced with a function, depending on a parameter

λ

, that is not symmetric in general. This function generalizes the usual case when

λ = 1 / 2

and can take bigger values than

m_{1 / 2} .

We call these new types of contractions λ-weak contractions and we provide some of their properties. Moreover, we investigate cases when these contractions are Picard operators. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)

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Symmetry, Volume 15, Issue 7 (July 2023) – 181 articles

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