We investigate the existence of solutions for the Fredholm integral equation Φ(ϑ)=G(ϑ,Φ(ϑ))+∫01F(ϑ,ζ,Φ(ζ))dζ, for ϑ∈[0,1], in the setting of the modular function spaces Lρ. We also derive an application of this research within the framework of variable exponent Lebesgue spaces Lp(·) subject to specific conditions imposed on the exponent function p(·) and the functions F and G.
{"title":"Examining Nonlinear Fredholm Equations in Lebesgue Spaces with Variable Exponents","authors":"Mostafa Bachar, Mohamed A. Khamsi, Osvaldo Méndez","doi":"10.3390/sym15112014","DOIUrl":"https://doi.org/10.3390/sym15112014","url":null,"abstract":"We investigate the existence of solutions for the Fredholm integral equation Φ(ϑ)=G(ϑ,Φ(ϑ))+∫01F(ϑ,ζ,Φ(ζ))dζ, for ϑ∈[0,1], in the setting of the modular function spaces Lρ. We also derive an application of this research within the framework of variable exponent Lebesgue spaces Lp(·) subject to specific conditions imposed on the exponent function p(·) and the functions F and G.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"13 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Uwayezu Marie Chantal, Hong Lu, Qi Liu, Tao Jiang, Min Hu, Gashema Gaspard
Vibration in state-of-the-art machining impacts accuracy by diminishing the machine’s dynamic precision and the workpiece surface quality. The dependability of the cutters and productivity becomes a severe problem for optimizing the computer numerical control machine tools’ (CNCMT) efficiency. Therefore, investigating the twin ball screw drive system vibration properties as well as its corresponding control measures is vital. This paper thoroughly reviews the recent works on methods of analyzing and controlling vibration for dual-driven feed systems (DDFS). The research on vibration control technologies, parameter identification, and system modeling are identified and summarized; the merits and drawbacks of various methods are discussed for comparative purposes. Furthermore, the asymmetrical relation between DDFS and single-driven feed systems are thoroughly discussed based on their dynamic properties. Finally, based on existing studies, related research prospects are described systematically, and these research directions are sure to markedly contribute to developing methods for dampening vibrations on DDFS of CNCMT.
{"title":"Analysis of Dual-Driven Feed System Vibration Characteristics Based on Computer Numerical Control Machine Tools: A Systematic Review","authors":"Uwayezu Marie Chantal, Hong Lu, Qi Liu, Tao Jiang, Min Hu, Gashema Gaspard","doi":"10.3390/sym15112012","DOIUrl":"https://doi.org/10.3390/sym15112012","url":null,"abstract":"Vibration in state-of-the-art machining impacts accuracy by diminishing the machine’s dynamic precision and the workpiece surface quality. The dependability of the cutters and productivity becomes a severe problem for optimizing the computer numerical control machine tools’ (CNCMT) efficiency. Therefore, investigating the twin ball screw drive system vibration properties as well as its corresponding control measures is vital. This paper thoroughly reviews the recent works on methods of analyzing and controlling vibration for dual-driven feed systems (DDFS). The research on vibration control technologies, parameter identification, and system modeling are identified and summarized; the merits and drawbacks of various methods are discussed for comparative purposes. Furthermore, the asymmetrical relation between DDFS and single-driven feed systems are thoroughly discussed based on their dynamic properties. Finally, based on existing studies, related research prospects are described systematically, and these research directions are sure to markedly contribute to developing methods for dampening vibrations on DDFS of CNCMT.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"16 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a smart grid (SG) system with load uncertainties and the integration of variable solar and wind energies, an effective frequency control strategy is necessary for generation and load balancing. Cyberattacks are emerging threats, and SG systems are typical cyber-attack targets. This work suggests an improved gorilla troops optimizer (iGTO)-based fuzzy PD-(1+PI) (FPD-(1+PI)) structure for the frequency control of an SG system. The SG contains a diesel engine generator (DEG), renewable sources like wind turbine generators(WTGs), solar photovoltaic (PV), and storage elements such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) in conjunction with electric vehicles (EVs). Initially, the dominance of the projected iGTO over the gorilla troops optimizer (GTO) and some recently suggested optimization algorithms are demonstrated by considering benchmark test functions. In the next step, a traditional PID controller is used, and the efficacy of the GTO method is compared with that of the GTO, particle swarm optimization (PSO), and genetic algorithm (GA) methods. In the next stage, the superiority of the proposed FPD-(1+PI) structure over fuzzy PID (FPID) and PID structures is demonstrated under various symmetry operating conditions as well as under different cyberattacks, leading to a denial of service (DoS) and delay in signal transmission.
{"title":"Improved Gorilla Troops Optimizer-Based Fuzzy PD-(1+PI) Controller for Frequency Regulation of Smart Grid under Symmetry and Cyber Attacks","authors":"Rajivgandhi Pachaiyappan, Elankurisil Arasan, Kannan Chandrasekaran","doi":"10.3390/sym15112013","DOIUrl":"https://doi.org/10.3390/sym15112013","url":null,"abstract":"In a smart grid (SG) system with load uncertainties and the integration of variable solar and wind energies, an effective frequency control strategy is necessary for generation and load balancing. Cyberattacks are emerging threats, and SG systems are typical cyber-attack targets. This work suggests an improved gorilla troops optimizer (iGTO)-based fuzzy PD-(1+PI) (FPD-(1+PI)) structure for the frequency control of an SG system. The SG contains a diesel engine generator (DEG), renewable sources like wind turbine generators(WTGs), solar photovoltaic (PV), and storage elements such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) in conjunction with electric vehicles (EVs). Initially, the dominance of the projected iGTO over the gorilla troops optimizer (GTO) and some recently suggested optimization algorithms are demonstrated by considering benchmark test functions. In the next step, a traditional PID controller is used, and the efficacy of the GTO method is compared with that of the GTO, particle swarm optimization (PSO), and genetic algorithm (GA) methods. In the next stage, the superiority of the proposed FPD-(1+PI) structure over fuzzy PID (FPID) and PID structures is demonstrated under various symmetry operating conditions as well as under different cyberattacks, leading to a denial of service (DoS) and delay in signal transmission.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"59 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation.
{"title":"A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions","authors":"Daniel Condurache, Ionuț Popa","doi":"10.3390/sym15112011","DOIUrl":"https://doi.org/10.3390/sym15112011","url":null,"abstract":"The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"201 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present research, we establish an effective method for determining the time-fractional coupled Korteweg–de Vries (KdV) equation’s approximate solution employing the fractional derivatives of Caputo–Fabrizio and Atangana–Baleanu. KdV models are crucial because they can accurately represent a variety of physical problems, including thin-film flows and waves on shallow water surfaces. Some theoretical physical features of quantum mechanics are also explained by the KdV model. Many investigations have been conducted on this precisely solvable model. Numerous academics have proposed new applications for the generation of acoustic waves in plasma from ions and crystal lattices. Adomian decomposition and natural transform decomposition techniques are combined in the natural decomposition method (NDM). We first apply the natural transform to examine the fractional order and obtain a recurrence relation. Second, we use the Adomian decomposition approach to the recurrence relation, and then, using successive iterations and the initial conditions, we can establish the series solution. We note that the proposed fractional model is highly accurate and valid when using this technique. The numerical outcomes demonstrate that only a small number of terms are required to arrive at an approximation that is exact, efficient, and trustworthy. Two examples are given to illustrate how the technique performs. Tables and 3D graphs display the best current numerical and analytical results. The suggested method provides a series form solution, which makes it quite easy to understand the behavior of the fractional models.
{"title":"Novel Computations of the Time-Fractional Coupled Korteweg–de Vries Equations via Non-Singular Kernel Operators in Terms of the Natural Transform","authors":"Abdulrahman B. M. Alzahrani, Ghadah Alhawael","doi":"10.3390/sym15112010","DOIUrl":"https://doi.org/10.3390/sym15112010","url":null,"abstract":"In the present research, we establish an effective method for determining the time-fractional coupled Korteweg–de Vries (KdV) equation’s approximate solution employing the fractional derivatives of Caputo–Fabrizio and Atangana–Baleanu. KdV models are crucial because they can accurately represent a variety of physical problems, including thin-film flows and waves on shallow water surfaces. Some theoretical physical features of quantum mechanics are also explained by the KdV model. Many investigations have been conducted on this precisely solvable model. Numerous academics have proposed new applications for the generation of acoustic waves in plasma from ions and crystal lattices. Adomian decomposition and natural transform decomposition techniques are combined in the natural decomposition method (NDM). We first apply the natural transform to examine the fractional order and obtain a recurrence relation. Second, we use the Adomian decomposition approach to the recurrence relation, and then, using successive iterations and the initial conditions, we can establish the series solution. We note that the proposed fractional model is highly accurate and valid when using this technique. The numerical outcomes demonstrate that only a small number of terms are required to arrive at an approximation that is exact, efficient, and trustworthy. Two examples are given to illustrate how the technique performs. Tables and 3D graphs display the best current numerical and analytical results. The suggested method provides a series form solution, which makes it quite easy to understand the behavior of the fractional models.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Contemporary aero-engines aim for enhanced efficiency and weight reduction. They are designed to increase rotor operational speed while reducing rotor bending stiffness. This may result in bending deformation in rotor systems within the operational speed range. Such deformation can change the relative positions of rotor components, potentially causing increased mass asymmetry or unbalance. Traditional rotor dynamic models typically assume a constant rotor state. They approximate unbalance using constant mass eccentricities at certain rotor cross-sections. However, this approach has its limitations. This paper focuses on a high-speed jointed rotor system. A distributed rotational inertia load excitation model is proposed. This model explicitly considers the rotor’s variable unbalance state at different operational speeds. The study involves both simulations and experimental investigations. The results show that at high speeds, bending deformation causes the unbalance and rotational inertia load to shift from a concentrated to a distributed state. Notably, the localized rotational inertia moment from thin-disk components like turbine disks becomes significant at high speeds. This results in a rapid increase in bearing load with rotational speed. It also profoundly affects the rotor’s joints, causing interfacial slip and sudden changes in rotor vibration characteristics.
{"title":"Distributed Rotational Inertia Load Excitation Model and Its Impact on High-Speed Jointed Rotor Dynamic Response","authors":"Fayong Wu, Jie Hong, Xueqi Chen","doi":"10.3390/sym15112009","DOIUrl":"https://doi.org/10.3390/sym15112009","url":null,"abstract":"Contemporary aero-engines aim for enhanced efficiency and weight reduction. They are designed to increase rotor operational speed while reducing rotor bending stiffness. This may result in bending deformation in rotor systems within the operational speed range. Such deformation can change the relative positions of rotor components, potentially causing increased mass asymmetry or unbalance. Traditional rotor dynamic models typically assume a constant rotor state. They approximate unbalance using constant mass eccentricities at certain rotor cross-sections. However, this approach has its limitations. This paper focuses on a high-speed jointed rotor system. A distributed rotational inertia load excitation model is proposed. This model explicitly considers the rotor’s variable unbalance state at different operational speeds. The study involves both simulations and experimental investigations. The results show that at high speeds, bending deformation causes the unbalance and rotational inertia load to shift from a concentrated to a distributed state. Notably, the localized rotational inertia moment from thin-disk components like turbine disks becomes significant at high speeds. This results in a rapid increase in bearing load with rotational speed. It also profoundly affects the rotor’s joints, causing interfacial slip and sudden changes in rotor vibration characteristics.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"63 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jun Gong, Juling Zhang, Wenqiang Guo, Zhilong Ma, Xiaoyi Lv
Considering the poor effect of short text classification due to insufficient semantic information mining in the current short text matching methods, a new short text classification method is proposed based on explicit and implicit multiscale weighting semantic information interaction. First, the explicit and implicit representations of short text are obtained by a word vector model (word2vec), convolutional neural networks (CNNs), and long short-term memory (LSTM). Then, a multiscale convolutional neural network obtains the explicit and implicit multiscale weighting semantics information of short text. Finally, the multiscale weighting semantics is fused for more accurate short text classification. The experimental results show that this method is superior to the existing classical short text classification algorithms and two advanced short text classification models on the five short text classification datasets of MR, Subj, TREC, SST1 and SST2 with accuracies of 85.7%, 96.9%, 98.1%, 53.4% and 91.8%, respectively.
{"title":"Short Text Classification Based on Explicit and Implicit Multiscale Weighted Semantic Information","authors":"Jun Gong, Juling Zhang, Wenqiang Guo, Zhilong Ma, Xiaoyi Lv","doi":"10.3390/sym15112008","DOIUrl":"https://doi.org/10.3390/sym15112008","url":null,"abstract":"Considering the poor effect of short text classification due to insufficient semantic information mining in the current short text matching methods, a new short text classification method is proposed based on explicit and implicit multiscale weighting semantic information interaction. First, the explicit and implicit representations of short text are obtained by a word vector model (word2vec), convolutional neural networks (CNNs), and long short-term memory (LSTM). Then, a multiscale convolutional neural network obtains the explicit and implicit multiscale weighting semantics information of short text. Finally, the multiscale weighting semantics is fused for more accurate short text classification. The experimental results show that this method is superior to the existing classical short text classification algorithms and two advanced short text classification models on the five short text classification datasets of MR, Subj, TREC, SST1 and SST2 with accuracies of 85.7%, 96.9%, 98.1%, 53.4% and 91.8%, respectively.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"74 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135221109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sofia Ramzan, Muhammad Uzair Awan, Miguel Vivas-Cortez, Hüseyin Budak
The objective of this research is to study in detail the fractional variants of Ostrowski–Mercer-type inequalities, specifically for the first and second order differentiable s-convex mappings of the second sense. To obtain the main outcomes of the paper, we leverage the use of conformable fractional integral operators. We also check the numerical validations of the main results. Our findings are also validated through visual representations. Furthermore, we provide a detailed discussion on applications of the obtained results related to special means, q-digamma mappings, and modified Bessel mappings.
{"title":"On Fractional Ostrowski-Mercer-Type Inequalities and Applications","authors":"Sofia Ramzan, Muhammad Uzair Awan, Miguel Vivas-Cortez, Hüseyin Budak","doi":"10.3390/sym15112003","DOIUrl":"https://doi.org/10.3390/sym15112003","url":null,"abstract":"The objective of this research is to study in detail the fractional variants of Ostrowski–Mercer-type inequalities, specifically for the first and second order differentiable s-convex mappings of the second sense. To obtain the main outcomes of the paper, we leverage the use of conformable fractional integral operators. We also check the numerical validations of the main results. Our findings are also validated through visual representations. Furthermore, we provide a detailed discussion on applications of the obtained results related to special means, q-digamma mappings, and modified Bessel mappings.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"94 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135809326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Ghaffar Khan, Bilal Khan, Jianhua Gong, Fairouz Tchier, Ferdous M. O. Tawfiq
This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived.
{"title":"Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains","authors":"Muhammad Ghaffar Khan, Bilal Khan, Jianhua Gong, Fairouz Tchier, Ferdous M. O. Tawfiq","doi":"10.3390/sym15112004","DOIUrl":"https://doi.org/10.3390/sym15112004","url":null,"abstract":"This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"103 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135810214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Piet Van Isacker, Alejandro Algora, András Vitéz-Sveiczer, Gábor Gyula Kiss, Sonja Elena Agata Orrigo, Berta Rubio, Pablo Aguilera
We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state through so-called Fermi transitions and to Jπ=1+ states by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.
{"title":"Gamow–Teller Beta Decay and Pseudo-SU(4) Symmetry","authors":"Piet Van Isacker, Alejandro Algora, András Vitéz-Sveiczer, Gábor Gyula Kiss, Sonja Elena Agata Orrigo, Berta Rubio, Pablo Aguilera","doi":"10.3390/sym15112001","DOIUrl":"https://doi.org/10.3390/sym15112001","url":null,"abstract":"We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state through so-called Fermi transitions and to Jπ=1+ states by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135809666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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