Pub Date : 2023-11-30DOI: 10.3390/foundations3040042
Umar Ishtiaq, Khaleel Ahmad, Farhan Ali, Moazzama Faraz, I. Argyros
Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature.
{"title":"Common Fixed-Point Theorems for Families of Compatible Mappings in Neutrosophic Metric Spaces","authors":"Umar Ishtiaq, Khaleel Ahmad, Farhan Ali, Moazzama Faraz, I. Argyros","doi":"10.3390/foundations3040042","DOIUrl":"https://doi.org/10.3390/foundations3040042","url":null,"abstract":"Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139200111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.3390/foundations3040040
Muhammad Tariq, Sotiris K. Ntouyas, Bashir Ahmad
This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, (ζ,m)-convex functions, s-convex functions, (s,r)-convex functions, strongly convex functions, harmonically convex functions, h-convex functions, Godunova-Levin-convex functions, MT-convex functions, P-convex functions, m-convex functions, (s,m)-convex functions, exponentially s-convex functions, (β,m)-convex functions, exponential-convex functions, ζ¯,β,γ,δ-convex functions, quasi-geometrically convex functions, s−e-convex functions and n-polynomial exponentially s-convex functions. Riemann–Liouville fractional integral, Katugampola fractional integral, k-Riemann–Liouville, Riemann–Liouville fractional integrals with respect to another function, Hadamard fractional integral, fractional integrals with exponential kernel and Atagana-Baleanu fractional integrals are included. Results for Ostrowski-Mercer-type inequalities, Ostrowski-type inequalities for preinvex functions, Ostrowski-type inequalities for Quantum-Calculus and Ostrowski-type inequalities of tensorial type are also presented.
{"title":"Ostrowski-Type Fractional Integral Inequalities: A Survey","authors":"Muhammad Tariq, Sotiris K. Ntouyas, Bashir Ahmad","doi":"10.3390/foundations3040040","DOIUrl":"https://doi.org/10.3390/foundations3040040","url":null,"abstract":"This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals. We have taken into account the classical convex functions, quasi-convex functions, (ζ,m)-convex functions, s-convex functions, (s,r)-convex functions, strongly convex functions, harmonically convex functions, h-convex functions, Godunova-Levin-convex functions, MT-convex functions, P-convex functions, m-convex functions, (s,m)-convex functions, exponentially s-convex functions, (β,m)-convex functions, exponential-convex functions, ζ¯,β,γ,δ-convex functions, quasi-geometrically convex functions, s−e-convex functions and n-polynomial exponentially s-convex functions. Riemann–Liouville fractional integral, Katugampola fractional integral, k-Riemann–Liouville, Riemann–Liouville fractional integrals with respect to another function, Hadamard fractional integral, fractional integrals with exponential kernel and Atagana-Baleanu fractional integrals are included. Results for Ostrowski-Mercer-type inequalities, Ostrowski-type inequalities for preinvex functions, Ostrowski-type inequalities for Quantum-Calculus and Ostrowski-type inequalities of tensorial type are also presented.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"142 30","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136351495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.3390/foundations3040039
Ioannis K. Argyros, Manoj K. Singh, Samundra Regmi
We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these schemes. However, these derivatives are not in the schemes. These assumptions restrict the applicability of the schemes, which may converge. Numerical results along with a boundary value problem are given to examine the theoretical results. Both schemes are symmetrical not only in the theoretical results (formation and convergence order), but the numerical and dynamical results are also similar. We calculated the convergence radii of the nonlinear schemes. Moreover, we obtained the extraneous fixed points for the proposed schemes, which are repulsive and are not part of the solution space. Lastly, the theoretical and numerical results are supported by the dynamic results, where we plotted basins of attraction for a selected test function.
{"title":"Comparison between Two Competing Newton-Type High Convergence Order Schemes for Equations on Banach Spaces","authors":"Ioannis K. Argyros, Manoj K. Singh, Samundra Regmi","doi":"10.3390/foundations3040039","DOIUrl":"https://doi.org/10.3390/foundations3040039","url":null,"abstract":"We carried out a local comparison between two ninth convergence order schemes for solving nonlinear equations, relying on first-order Fréchet derivatives. Earlier investigations require the existence as well as the boundedness of derivatives of a high order to prove the convergence of these schemes. However, these derivatives are not in the schemes. These assumptions restrict the applicability of the schemes, which may converge. Numerical results along with a boundary value problem are given to examine the theoretical results. Both schemes are symmetrical not only in the theoretical results (formation and convergence order), but the numerical and dynamical results are also similar. We calculated the convergence radii of the nonlinear schemes. Moreover, we obtained the extraneous fixed points for the proposed schemes, which are repulsive and are not part of the solution space. Lastly, the theoretical and numerical results are supported by the dynamic results, where we plotted basins of attraction for a selected test function.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.3390/foundations3040038
Johan Hansson
I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples of “locally real” theories, as defined by Clauser and Horne, and are therefore already empirically refuted by the numerous tests of Bell’s theorem in real, controlled experiments in laboratories here on Earth. Observed quantum entities (i.e., events) are never superposed or entangled as they: (1) exclusively “live” (manifest) in real physical spacetime and (2) are not described by entangled wavefunctions after “measurement” effectuated by III. When separated and treated correctly in this way, a number of fundamental problems and “paradoxes” of quantum theory vs. relativity (i.e., spacetime) simply vanish, such as the black hole information paradox, the infinite zero-point energy of quantum field theory and the quantization of general relativity.
{"title":"The Magical “Born Rule” and Quantum “Measurement”: Implications for Physics","authors":"Johan Hansson","doi":"10.3390/foundations3040038","DOIUrl":"https://doi.org/10.3390/foundations3040038","url":null,"abstract":"I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples of “locally real” theories, as defined by Clauser and Horne, and are therefore already empirically refuted by the numerous tests of Bell’s theorem in real, controlled experiments in laboratories here on Earth. Observed quantum entities (i.e., events) are never superposed or entangled as they: (1) exclusively “live” (manifest) in real physical spacetime and (2) are not described by entangled wavefunctions after “measurement” effectuated by III. When separated and treated correctly in this way, a number of fundamental problems and “paradoxes” of quantum theory vs. relativity (i.e., spacetime) simply vanish, such as the black hole information paradox, the infinite zero-point energy of quantum field theory and the quantization of general relativity.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135199668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-21DOI: 10.3390/foundations3030037
Alexander Robitzsch
Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one skill and shares desirable measurement properties with the Rasch model. This article shows that the 1PLDCM is indeed a latent class Rasch model. Furthermore, the relationship of the 1PLDCM to extensions of the DCM to mixed, partial, and probabilistic memberships is treated. It is argued that the partial and probabilistic membership models are also equivalent to the Rasch model. The fit of the different models was empirically investigated using six datasets. It turned out for these datasets that the 1PLDCM always had a worse fit than the Rasch model and mixed and partial membership extensions of the DCM.
{"title":"Relating the One-Parameter Logistic Diagnostic Classification Model to the Rasch Model and One-Parameter Logistic Mixed, Partial, and Probabilistic Membership Diagnostic Classification Models","authors":"Alexander Robitzsch","doi":"10.3390/foundations3030037","DOIUrl":"https://doi.org/10.3390/foundations3030037","url":null,"abstract":"Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one skill and shares desirable measurement properties with the Rasch model. This article shows that the 1PLDCM is indeed a latent class Rasch model. Furthermore, the relationship of the 1PLDCM to extensions of the DCM to mixed, partial, and probabilistic memberships is treated. It is argued that the partial and probabilistic membership models are also equivalent to the Rasch model. The fit of the different models was empirically investigated using six datasets. It turned out for these datasets that the 1PLDCM always had a worse fit than the Rasch model and mixed and partial membership extensions of the DCM.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.3390/foundations3030036
Alexander B. Kukushkin, Andrei A. Kulichenko
The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in Shlesinger and colleagues’ about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman–Holstein approach to examine the transfer of excitation of a medium by photons, generalized in order to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson’s t3 scaling law to the combined regime of Lévy flights and Lévy walks in fluids and gases.
{"title":"Lévy Walks as a Universal Mechanism of Turbulence Nonlocality","authors":"Alexander B. Kukushkin, Andrei A. Kulichenko","doi":"10.3390/foundations3030036","DOIUrl":"https://doi.org/10.3390/foundations3030036","url":null,"abstract":"The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in Shlesinger and colleagues’ about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman–Holstein approach to examine the transfer of excitation of a medium by photons, generalized in order to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson’s t3 scaling law to the combined regime of Lévy flights and Lévy walks in fluids and gases.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136314678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-19DOI: 10.3390/foundations3030035
Santhosh George, Ioannis K. Argyros, Samundra Regmi
A method without memory as well as a method with memory are developed free of derivatives for solving equations in Banach spaces. The convergence order of these methods is established in the scalar case using Taylor expansions and hypotheses on higher-order derivatives which do not appear in these methods. But this way, their applicability is limited. That is why, in this paper, their local and semi-local convergence analyses (which have not been given previously) are provided using only the divided differences of order one, which actually appears in these methods. Moreover, we provide computable error distances and uniqueness of the solution results, which have not been given before. Since our technique is very general, it can be used to extend the applicability of other methods using linear operators with inverses along the same lines. Numerical experiments are also provided in this article to illustrate the theoretical results.
{"title":"Convergence of Derivative-Free Iterative Methods with or without Memory in Banach Space","authors":"Santhosh George, Ioannis K. Argyros, Samundra Regmi","doi":"10.3390/foundations3030035","DOIUrl":"https://doi.org/10.3390/foundations3030035","url":null,"abstract":"A method without memory as well as a method with memory are developed free of derivatives for solving equations in Banach spaces. The convergence order of these methods is established in the scalar case using Taylor expansions and hypotheses on higher-order derivatives which do not appear in these methods. But this way, their applicability is limited. That is why, in this paper, their local and semi-local convergence analyses (which have not been given previously) are provided using only the divided differences of order one, which actually appears in these methods. Moreover, we provide computable error distances and uniqueness of the solution results, which have not been given before. Since our technique is very general, it can be used to extend the applicability of other methods using linear operators with inverses along the same lines. Numerical experiments are also provided in this article to illustrate the theoretical results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135107864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-11DOI: 10.3390/foundations3030034
Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros, Samundra Regmi
Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of such methods is crucial in their development. The convergence behavior of such approaches and determining their practical applicability require conducting local as well as semi-local convergence analysis. In this study, we explore the convergence properties of a sixth-order derivative-free method. Previous local convergence studies assumed the existence of derivatives of high order even when the method itself was not utilizing any derivatives. These assumptions imposed limitations on its applicability. In this paper, we extend the local analysis by providing estimates for the error bounds of the method. Consequently, its applicability expands across a broader range of problems. Moreover, the more important and challenging semi-local convergence not investigated in earlier studies is also developed. Additionally, we survey recent advancements in this field. The outcomes presented in this paper can be proved valuable to practitioners and researchers engaged in the development and analysis of derivative-free numerical algorithms. Numerical tests illuminate and validate further the theoretical results.
{"title":"Three-Step Derivative-Free Method of Order Six","authors":"Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros, Samundra Regmi","doi":"10.3390/foundations3030034","DOIUrl":"https://doi.org/10.3390/foundations3030034","url":null,"abstract":"Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of such methods is crucial in their development. The convergence behavior of such approaches and determining their practical applicability require conducting local as well as semi-local convergence analysis. In this study, we explore the convergence properties of a sixth-order derivative-free method. Previous local convergence studies assumed the existence of derivatives of high order even when the method itself was not utilizing any derivatives. These assumptions imposed limitations on its applicability. In this paper, we extend the local analysis by providing estimates for the error bounds of the method. Consequently, its applicability expands across a broader range of problems. Moreover, the more important and challenging semi-local convergence not investigated in earlier studies is also developed. Additionally, we survey recent advancements in this field. The outcomes presented in this paper can be proved valuable to practitioners and researchers engaged in the development and analysis of derivative-free numerical algorithms. Numerical tests illuminate and validate further the theoretical results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-07DOI: 10.3390/foundations3030033
Samundra Regmi, I. Argyros, Gagan Deep
Numerous applications from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert, or Banach, to mention a few. Researchers worldwide are developing methodologies to handle the solutions of such equations. A plethora of these equations are not differentiable. These methodologies can also be applied to solve differentiable equations. A particular method is utilized as a sample via which the methodology is described. The same methodology can be used on other methods utilizing inverses of linear operators. The problem with existing approaches on the local convergence of iterative methods is the usage of Taylor expansion series. This way, the convergence is shown but by assuming the existence of high-order derivatives which do not appear on the iterative methods. Moreover, bounds on the error distances that can be computed are not available in advance. Furthermore, the isolation of a solution of the equation is not discussed either. These concerns reduce the applicability of iterative methods and constitute the motivation for developing this article. The novelty of this article is that it positively addresses all these concerns under weaker convergence conditions. Finally, the more important and harder to study semi-local analysis of convergence is presented using majorizing scalar sequences. Experiments are further performed to demonstrate the theory.
{"title":"Generalized Iterative Method of Order Four with Divided Differences","authors":"Samundra Regmi, I. Argyros, Gagan Deep","doi":"10.3390/foundations3030033","DOIUrl":"https://doi.org/10.3390/foundations3030033","url":null,"abstract":"Numerous applications from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert, or Banach, to mention a few. Researchers worldwide are developing methodologies to handle the solutions of such equations. A plethora of these equations are not differentiable. These methodologies can also be applied to solve differentiable equations. A particular method is utilized as a sample via which the methodology is described. The same methodology can be used on other methods utilizing inverses of linear operators. The problem with existing approaches on the local convergence of iterative methods is the usage of Taylor expansion series. This way, the convergence is shown but by assuming the existence of high-order derivatives which do not appear on the iterative methods. Moreover, bounds on the error distances that can be computed are not available in advance. Furthermore, the isolation of a solution of the equation is not discussed either. These concerns reduce the applicability of iterative methods and constitute the motivation for developing this article. The novelty of this article is that it positively addresses all these concerns under weaker convergence conditions. Finally, the more important and harder to study semi-local analysis of convergence is presented using majorizing scalar sequences. Experiments are further performed to demonstrate the theory.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78819034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-04DOI: 10.3390/foundations3030031
Valery Astapenko, Timur Bergaliyev
A brief review of the classical and quantum description of the interaction of electromagnetic radiation with matter based on the model of a harmonic oscillator is presented. This review includes the generalized Bohr correspondence principle, the excitation of a quantum oscillator by electromagnetic pulses including saturation effect, the harmonic limit of the Bloch equations, and a phenomenological account of the damping of the quantum oscillator. In all cases, at the mathematical level, the relationship between the classical and quantum descriptions of the electromagnetic interaction is established and the conditions for such compliance are identified.
{"title":"Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction","authors":"Valery Astapenko, Timur Bergaliyev","doi":"10.3390/foundations3030031","DOIUrl":"https://doi.org/10.3390/foundations3030031","url":null,"abstract":"A brief review of the classical and quantum description of the interaction of electromagnetic radiation with matter based on the model of a harmonic oscillator is presented. This review includes the generalized Bohr correspondence principle, the excitation of a quantum oscillator by electromagnetic pulses including saturation effect, the harmonic limit of the Bloch equations, and a phenomenological account of the damping of the quantum oscillator. In all cases, at the mathematical level, the relationship between the classical and quantum descriptions of the electromagnetic interaction is established and the conditions for such compliance are identified.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81703855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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