This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.
{"title":"Combination Test for Mean Shift and Variance Change","authors":"Min Gao, Xiaoping Shi, Xuejun Wang, Wenzhi Yang","doi":"10.3390/sym15111975","DOIUrl":"https://doi.org/10.3390/sym15111975","url":null,"abstract":"This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"48 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168877","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}
Haroon D. S. Adam, Khalid I. A. Ahmed, Mukhtar Yagoub Youssif, Marin Marin
In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences.
{"title":"Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient","authors":"Haroon D. S. Adam, Khalid I. A. Ahmed, Mukhtar Yagoub Youssif, Marin Marin","doi":"10.3390/sym15111972","DOIUrl":"https://doi.org/10.3390/sym15111972","url":null,"abstract":"In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217335","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}
Suha B. Al-Shaikh, Mohammad Faisal Khan, Mustafa Kamal, Naeem Ahmad
This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex functions connected with generalized Janowski functions. We prove the necessary and sufficient conditions for functions that belong to newly defined classes, including the inclusion relations and estimations of the coefficients. The Fekete–Szegő problem for a more general class is also discussed. The results of this investigation expand upon those of the previous study.
{"title":"New Subclass of Close-to-Convex Functions Defined by Quantum Difference Operator and Related to Generalized Janowski Function","authors":"Suha B. Al-Shaikh, Mohammad Faisal Khan, Mustafa Kamal, Naeem Ahmad","doi":"10.3390/sym15111974","DOIUrl":"https://doi.org/10.3390/sym15111974","url":null,"abstract":"This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex functions connected with generalized Janowski functions. We prove the necessary and sufficient conditions for functions that belong to newly defined classes, including the inclusion relations and estimations of the coefficients. The Fekete–Szegő problem for a more general class is also discussed. The results of this investigation expand upon those of the previous study.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"188 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168545","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}
Fazlina Mohd Ali, Nur Arzilawati Md Yunus, Nur Nabila Mohamed, Marizuana Mat Daud, Elankovan A. Sundararajan
The Internet of Everything (IoE) represents a paradigm shift in the world of connectivity. While the Internet of Things (IoT) initiated the era of interconnected devices, the IoE takes this concept to new heights by interlinking objects, individuals, data, and processes. Symmetry in IoE innovation and technology is essential for creating a harmonious and efficient ecosystem to ensure that the benefits are accessible to a broad spectrum of society while minimizing potential drawbacks. This comprehensive review paper explores the multifaceted landscape of the IoE, delving into its core concepts, enabling technologies, real-world applications, and the intricate web of challenges it presents. A focal point of this review is the diverse array of real-world applications spanning healthcare, smart cities, industry 4.0, agriculture, and sustainability. Previous works and examples illustrate how the IoE reshapes these domains, leading to greater efficiency, sustainability, and improved decision making. However, the transformative power of the IoE is accompanied by a host of challenges, including security and privacy concerns, interoperability issues, and the ethical implications of ubiquitous connectivity. These challenges are dissected in order to comprehensively understand the obstacles and potential solutions in the IoE landscape. As we stand on the cusp of an IoE-driven future, this review paper serves as a valuable resource for researchers, policy makers, and industry professionals seeking to navigate the complexities of this emerging paradigm. By illuminating the intricacies of the IoE, this review fosters a deeper appreciation for the transformative potential and the multifaceted challenges that lie ahead in the Internet of Everything era.
{"title":"A Systematic Mapping: Exploring Internet of Everything Technologies and Innovations","authors":"Fazlina Mohd Ali, Nur Arzilawati Md Yunus, Nur Nabila Mohamed, Marizuana Mat Daud, Elankovan A. Sundararajan","doi":"10.3390/sym15111964","DOIUrl":"https://doi.org/10.3390/sym15111964","url":null,"abstract":"The Internet of Everything (IoE) represents a paradigm shift in the world of connectivity. While the Internet of Things (IoT) initiated the era of interconnected devices, the IoE takes this concept to new heights by interlinking objects, individuals, data, and processes. Symmetry in IoE innovation and technology is essential for creating a harmonious and efficient ecosystem to ensure that the benefits are accessible to a broad spectrum of society while minimizing potential drawbacks. This comprehensive review paper explores the multifaceted landscape of the IoE, delving into its core concepts, enabling technologies, real-world applications, and the intricate web of challenges it presents. A focal point of this review is the diverse array of real-world applications spanning healthcare, smart cities, industry 4.0, agriculture, and sustainability. Previous works and examples illustrate how the IoE reshapes these domains, leading to greater efficiency, sustainability, and improved decision making. However, the transformative power of the IoE is accompanied by a host of challenges, including security and privacy concerns, interoperability issues, and the ethical implications of ubiquitous connectivity. These challenges are dissected in order to comprehensively understand the obstacles and potential solutions in the IoE landscape. As we stand on the cusp of an IoE-driven future, this review paper serves as a valuable resource for researchers, policy makers, and industry professionals seeking to navigate the complexities of this emerging paradigm. By illuminating the intricacies of the IoE, this review fosters a deeper appreciation for the transformative potential and the multifaceted challenges that lie ahead in the Internet of Everything era.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135274240","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}
We propose a deep learning-based cross-layer power allocation method for asymmetric cell-free massive MIMO video communication systems. The proposed cross-layer approach considers physical layer channel state information (CSI) and the application layer rate distortion (RD) function, and it aims to enhance video quality in terms of peak signal-to-noise ratio (PSNR). Our study develops a decentralized deep neural network (DNN) model to capture intricate system patterns, enabling accurate and efficient power allocation decisions. The proposed cross-layer approach includes unsupervised and hybrid (supervised/unsupervised) learning models. The numerical results show that the hybrid method achieves convergence with just 50% of the iterations required by the unsupervised learning model and that it achieves a 1 dB gain in PSNR over the baseline physical layer scheme.
{"title":"Deep Learning-Based Cross-Layer Power Allocation for Downlink Cell-Free Massive Multiple-Input–Multiple-Output Video Communication Systems","authors":"Wen-Yen Lin, Tin-Hao Chang, Shu-Ming Tseng","doi":"10.3390/sym15111968","DOIUrl":"https://doi.org/10.3390/sym15111968","url":null,"abstract":"We propose a deep learning-based cross-layer power allocation method for asymmetric cell-free massive MIMO video communication systems. The proposed cross-layer approach considers physical layer channel state information (CSI) and the application layer rate distortion (RD) function, and it aims to enhance video quality in terms of peak signal-to-noise ratio (PSNR). Our study develops a decentralized deep neural network (DNN) model to capture intricate system patterns, enabling accurate and efficient power allocation decisions. The proposed cross-layer approach includes unsupervised and hybrid (supervised/unsupervised) learning models. The numerical results show that the hybrid method achieves convergence with just 50% of the iterations required by the unsupervised learning model and that it achieves a 1 dB gain in PSNR over the baseline physical layer scheme.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"46 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135316311","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}
We propose higher-order adaptive energy-preserving methods for a charged particle system and a guiding center system. The higher-order energy-preserving methods are symmetric and are constructed by composing the second-order energy-preserving methods based on the averaged vector field. In order to overcome the energy drift problem that occurs in the energy-preserving methods based on the average vector field, we develop two adaptive algorithms for the higher-order energy-preserving methods. The two adaptive algorithms are developed based on using variable points of Gauss–Legendre’s quadrature rule and using two different stepsizes. The numerical results show that the two adaptive algorithms behave better in phase portrait and energy conservation than the Runge–Kutta methods. Moreover, it is shown that the energy errors obtained by the two adaptive algorithms can be bounded by the machine precision over long time and do not show energy drift.
{"title":"Symmetric Adaptive Higher-Order Energy-Preserving Methods for a Charged Particle System and Guiding Center System","authors":"Beibei Zhu, Hongji Zhou","doi":"10.3390/sym15111969","DOIUrl":"https://doi.org/10.3390/sym15111969","url":null,"abstract":"We propose higher-order adaptive energy-preserving methods for a charged particle system and a guiding center system. The higher-order energy-preserving methods are symmetric and are constructed by composing the second-order energy-preserving methods based on the averaged vector field. In order to overcome the energy drift problem that occurs in the energy-preserving methods based on the average vector field, we develop two adaptive algorithms for the higher-order energy-preserving methods. The two adaptive algorithms are developed based on using variable points of Gauss–Legendre’s quadrature rule and using two different stepsizes. The numerical results show that the two adaptive algorithms behave better in phase portrait and energy conservation than the Runge–Kutta methods. Moreover, it is shown that the energy errors obtained by the two adaptive algorithms can be bounded by the machine precision over long time and do not show energy drift.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"53 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266601","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}
Fahad M. Alqahtani, Mohammed A. Noman, Saad A. Alabdulkarim, Ibrahim Alharkan, Mohammed H. Alhaag, Faisal M. Alessa
Human errors (HEs) are common problems in manual assembly processes, impacting product quality and resulting in additional costs. Based on expert judgments, this study aims to identify the most significant factors affecting HEs in manual assembly processes and explore the cause-and-effect relationships among those factors. In order to achieve this objective, a proposed model is constructed using two types of Multi-Criteria Decision-Making (MCDM) techniques. Firstly, using two rounds of the fuzzy Delphi method (FDM), twenty-seven factors with an influence score of 0.7 or higher were found to have a major impact on HEs during manual assembly processes, with at least a 75% consensus among experts. After that, the twenty-seven factors affecting HEs were given to experts in a third round to analyze the cause-and-effect relationships among those factors using the fuzzy decision-making trial and evaluation laboratory (DEMATEL) method. In MCDM techniques, symmetry refers to an important property that can be used to find relationships between variables. It is based on the principle that the relative importance or preference between two variables should remain the same regardless of their positions or roles. Therefore, symmetry is a factor that MCDM approaches take into account to ensure that the relationships between variables are accurately represented, leading to more reliable decision-making outcomes. The reliability and normality of the surveying data were examined using the SPSS 22.0 software program. The study results revealed that training level, poor workplace layout, a lack of necessary tools, and experience were the major factors affecting HEs as root causes. Moreover, a failure to address the error-causing problem, unintentional unsafe acts, fatigue, and poor error visual perception were found to be effect (dependent) factors. The findings of this study can help organizations make better-informed decisions on how to reduce worker errors and interest in the factors that contribute to assembly errors and provide a good basis for reaching the quality of final assembled parts.
{"title":"A New Model for Determining Factors Affecting Human Errors in Manual Assembly Processes Using Fuzzy Delphi and DEMATEL Methods","authors":"Fahad M. Alqahtani, Mohammed A. Noman, Saad A. Alabdulkarim, Ibrahim Alharkan, Mohammed H. Alhaag, Faisal M. Alessa","doi":"10.3390/sym15111967","DOIUrl":"https://doi.org/10.3390/sym15111967","url":null,"abstract":"Human errors (HEs) are common problems in manual assembly processes, impacting product quality and resulting in additional costs. Based on expert judgments, this study aims to identify the most significant factors affecting HEs in manual assembly processes and explore the cause-and-effect relationships among those factors. In order to achieve this objective, a proposed model is constructed using two types of Multi-Criteria Decision-Making (MCDM) techniques. Firstly, using two rounds of the fuzzy Delphi method (FDM), twenty-seven factors with an influence score of 0.7 or higher were found to have a major impact on HEs during manual assembly processes, with at least a 75% consensus among experts. After that, the twenty-seven factors affecting HEs were given to experts in a third round to analyze the cause-and-effect relationships among those factors using the fuzzy decision-making trial and evaluation laboratory (DEMATEL) method. In MCDM techniques, symmetry refers to an important property that can be used to find relationships between variables. It is based on the principle that the relative importance or preference between two variables should remain the same regardless of their positions or roles. Therefore, symmetry is a factor that MCDM approaches take into account to ensure that the relationships between variables are accurately represented, leading to more reliable decision-making outcomes. The reliability and normality of the surveying data were examined using the SPSS 22.0 software program. The study results revealed that training level, poor workplace layout, a lack of necessary tools, and experience were the major factors affecting HEs as root causes. Moreover, a failure to address the error-causing problem, unintentional unsafe acts, fatigue, and poor error visual perception were found to be effect (dependent) factors. The findings of this study can help organizations make better-informed decisions on how to reduce worker errors and interest in the factors that contribute to assembly errors and provide a good basis for reaching the quality of final assembled parts.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"49 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267076","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}
A large-scale radio astronomical telescope is a typical complex coupled system, consisting of a feed cabin, cables, and supporting structures. The system is extremely sensitive to wind loads, especially the feed cabin, which has high requirements for vibration displacement during operation, and excessive vibration may affect normal operation. To investigate the wind-induced vibration characteristics of such coupled systems, this study takes the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) as an example to conduct research. First, a refined finite element model of FAST is established, and a dynamic analysis using simulated random wind loads is conducted. The influence of the cable boundary on the time–frequency domain responses of the feed cabin is particularly considered. Then, the gust response factor (GRF) for different structural components within the coupled system is calculated. Finally, the evolution law of the GRF under various wind speeds and directions is revealed by parametric analysis. The parameter analysis only considers the wind directions ranging from 0° to 60°, because FAST is a symmetric structure. The results indicate that obvious differences are observed in both the rotational and translational displacements of the feed cabin under northward wind, especially the results along the east–west axis. When the supporting towers are considered, there is no change in the power spectral density (PSD) of the feed cabin in the low-frequency range. However, in the high-frequency range, taking the supporting towers into account leads to an increase in PSD and a resonance near the first-order natural frequency of the supporting tower. The GRF based on the dynamic response exhibits substantial deviations compared to those obtained from design codes, highlighting the need for an independent analysis when determining GRF for such coupled systems.
{"title":"Wind-Induced Vibrations and Gust Response Factors of the Cabin–Cable–Tower System","authors":"De-Xiu Mo, Hong-Nan Li, Qing-Wei Li","doi":"10.3390/sym15111965","DOIUrl":"https://doi.org/10.3390/sym15111965","url":null,"abstract":"A large-scale radio astronomical telescope is a typical complex coupled system, consisting of a feed cabin, cables, and supporting structures. The system is extremely sensitive to wind loads, especially the feed cabin, which has high requirements for vibration displacement during operation, and excessive vibration may affect normal operation. To investigate the wind-induced vibration characteristics of such coupled systems, this study takes the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) as an example to conduct research. First, a refined finite element model of FAST is established, and a dynamic analysis using simulated random wind loads is conducted. The influence of the cable boundary on the time–frequency domain responses of the feed cabin is particularly considered. Then, the gust response factor (GRF) for different structural components within the coupled system is calculated. Finally, the evolution law of the GRF under various wind speeds and directions is revealed by parametric analysis. The parameter analysis only considers the wind directions ranging from 0° to 60°, because FAST is a symmetric structure. The results indicate that obvious differences are observed in both the rotational and translational displacements of the feed cabin under northward wind, especially the results along the east–west axis. When the supporting towers are considered, there is no change in the power spectral density (PSD) of the feed cabin in the low-frequency range. However, in the high-frequency range, taking the supporting towers into account leads to an increase in PSD and a resonance near the first-order natural frequency of the supporting tower. The GRF based on the dynamic response exhibits substantial deviations compared to those obtained from design codes, highlighting the need for an independent analysis when determining GRF for such coupled systems.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"4 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273097","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}
We demonstrate that the Finite-Time-Path Field Theory is an adequate tool for calculating neutrino oscillations. We apply this theory using a mass-mixing Lagrangian which involves the correct Dirac spin and chirality structure and a Pontecorvo–Maki–Nakagawa–Sakata (PMNS)-like mixing matrix. The model is exactly solvable. The Dyson–Schwinger equations transform propagators of the input free (massless) flavor neutrinos into a linear combination of oscillating (massive) neutrinos. The results are consistent with the predictions of the PMNS matrix while allowing for extrapolation to early times.
{"title":"Neutrino Oscillations in Finite Time Path Out-of-Equilibrium Thermal Field Theory","authors":"Ivan Dadić, Dubravko Klabučar","doi":"10.3390/sym15111970","DOIUrl":"https://doi.org/10.3390/sym15111970","url":null,"abstract":"We demonstrate that the Finite-Time-Path Field Theory is an adequate tool for calculating neutrino oscillations. We apply this theory using a mass-mixing Lagrangian which involves the correct Dirac spin and chirality structure and a Pontecorvo–Maki–Nakagawa–Sakata (PMNS)-like mixing matrix. The model is exactly solvable. The Dyson–Schwinger equations transform propagators of the input free (massless) flavor neutrinos into a linear combination of oscillating (massive) neutrinos. The results are consistent with the predictions of the PMNS matrix while allowing for extrapolation to early times.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"65 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266599","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}
On the basis of a general action principle, we revisit the scale invariant field equation using the cotensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor λ, which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler’s third law is a remarkable scale-invariant property.
{"title":"Action Principle for Scale Invariance and Applications (Part I)","authors":"Andre Maeder, Vesselin G. Gueorguiev","doi":"10.3390/sym15111966","DOIUrl":"https://doi.org/10.3390/sym15111966","url":null,"abstract":"On the basis of a general action principle, we revisit the scale invariant field equation using the cotensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor λ, which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler’s third law is a remarkable scale-invariant property.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"167 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135268102","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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