Foundations最新文献_第3页

Common Fixed-Point Theorems for Families of Compatible Mappings in Neutrosophic Metric Spaces 中性公设空间中相容映射族的常见定点定理

Foundations Pub Date : 2023-11-30 DOI: 10.3390/foundations3040042

Umar Ishtiaq, Khaleel Ahmad, Farhan Ali, Moazzama Faraz, I. Argyros

引用次数: 0

Ostrowski-Type Fractional Integral Inequalities: A Survey ostrowski型分数阶积分不等式综述

Foundations Pub Date : 2023-11-13 DOI: 10.3390/foundations3040040

Muhammad Tariq, Sotiris K. Ntouyas, Bashir Ahmad

{"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}

引用次数: 0

Comparison between Two Competing Newton-Type High Convergence Order Schemes for Equations on Banach Spaces Banach空间上两种竞争牛顿型高收敛阶方程格式的比较

Foundations Pub Date : 2023-10-30 DOI: 10.3390/foundations3040039

Ioannis K. Argyros, Manoj K. Singh, Samundra Regmi

引用次数: 0

The Magical “Born Rule” and Quantum “Measurement”: Implications for Physics 神奇的“天生法则”和量子“测量”:对物理学的启示

Foundations Pub Date : 2023-09-29 DOI: 10.3390/foundations3040038

Johan Hansson

{"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}

引用次数: 0

Relating the One-Parameter Logistic Diagnostic Classification Model to the Rasch Model and One-Parameter Logistic Mixed, Partial, and Probabilistic Membership Diagnostic Classification Models 将单参数Logistic诊断分类模型与Rasch模型和单参数Logistic混合、部分和概率隶属诊断分类模型联系起来

Foundations Pub Date : 2023-09-21 DOI: 10.3390/foundations3030037

Alexander Robitzsch

引用次数: 0

Lévy Walks as a Universal Mechanism of Turbulence Nonlocality 作为湍流非定域性的一种普遍机制

Foundations Pub Date : 2023-09-20 DOI: 10.3390/foundations3030036

Alexander B. Kukushkin, Andrei A. Kulichenko

{"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}

引用次数: 0

Convergence of Derivative-Free Iterative Methods with or without Memory in Banach Space Banach空间中有无记忆的无导数迭代方法的收敛性

Foundations Pub Date : 2023-09-19 DOI: 10.3390/foundations3030035

Santhosh George, Ioannis K. Argyros, Samundra Regmi

引用次数: 0

Three-Step Derivative-Free Method of Order Six 六阶的三步无导数法

Foundations Pub Date : 2023-09-11 DOI: 10.3390/foundations3030034

Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros, Samundra Regmi

{"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}

引用次数: 0

Generalized Iterative Method of Order Four with Divided Differences 具有可分差分的四阶广义迭代法

Foundations Pub Date : 2023-09-07 DOI: 10.3390/foundations3030033

Samundra Regmi, I. Argyros, Gagan Deep

{"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}

引用次数: 0

Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction 光-物质相互作用经典理论和量子理论中谐振子模型的比较

Foundations Pub Date : 2023-09-04 DOI: 10.3390/foundations3030031

Valery Astapenko, Timur Bergaliyev

引用次数: 0