scholarly journals On the Relationship between the Inhomogeneous Wave and Helmholtz Equations in a Fractional Setting

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Mateo Dulce ◽  
Alexander Getmanenko
Keyword(s):  
Wave Equation ◽  
Helmholtz Equation ◽  
Stationary Regime ◽  
Inhomogeneous Wave ◽  
Helmholtz Equations ◽  
Fractional Wave Equation ◽  
Convergence Of Solutions ◽  
Space And Time ◽  
Quarter Plane ◽  
The Relationship

We study convergence of solutions of a space and time inhomogeneous fractional wave equation on the quarter-plane to the stationary regime described by solutions of the Helmholtz equation.

scholarly journals Relation between Schrödinger’s Equation and Einstein’s Equation

2021 ◽  
Author(s):  
Aman Yadav
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Helmholtz Equation ◽  
Space Time ◽  
Wave Functions ◽  
Quantum Level ◽  
Schrödinger’S Equation ◽  
Einstein's Equation ◽  
The Relationship ◽  
Schrödinger's Equation

The relationship between Einstein's Field Equation and Schrodinger's Equation is examined in thiswork. I adjusted Schrodinger's Equation to offer the solution, and utilizing the wave equation, Icame up with two cases: In case 1, I discovered the structure and dimension of the equations in amanner similar to Einstein's Field Equation, and in case 2, the Helmholtz equation replaces themodified Schrodinger's equation. Finally, the findings suggested that wave functions may haverelevance beyond determining the position of a particle, and that they may be used to determinethe structure of space-time at the quantum level.

Hume’s System of Space and Time

2010 ◽  
Vol 13 (1) ◽  
pp. 76-89 ◽  
Author(s):  
Angela M. Coventry
Keyword(s):  
Fundamental Principle ◽  
Space And Time ◽  
The Relationship

Hume’s account of the origin and nature of our ideas of space and time is generally thought to be the least satisfactory part of his empiricist system of philosophy. The main reason is internal in that the account is judged to be inconsistent with Hume’s fundamental principle for the relationship between senses and cognition, the copy principle. This paper defends Hume against the inconsistency objection by offering a new systematic interpretation of Hume on space and time and illuminating more generally the role of the copy principle in his philosophy. Humes Theorie des Wesens und des Ursprungs unserer Vorstellungen von Raum und Zeit wird generell zu den am wenigsten befriedigenden Teilen seiner empiristischen Philosophie gezählt. Der Hauptgrund dafür ist werkimmanent: Die Raum- Zeit-Theorie einerseits und Humes „copy principle“ andererseits – d.h. dasjenige Fundamental-Prinzip, das die Relation zwischen unseren Sinnen und unserem Denken regelt – werden als miteinander inkonsistent erachtet. Dieser Beitrag bietet eine neue, systematische Interpretation der Raum-Zeit-Lehre Humes und eine umfassendere Darstellung der Rolle des „copy principles“ in seiner Philosophie an. Auf diese Weise wird Hume gegen den Vorwurf der Inkonsistenz verteidigt.

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

scholarly journals Conclusion

2021 ◽  
pp. 93-98
Author(s):  
Rosita Fibbi ◽  
Arnfinn H. Midtbøen ◽  
Patrick Simon
Keyword(s):  
Racial Discrimination ◽  
Future Research ◽  
Space And Time ◽  
The Relationship

AbstractThis chapter briefly summarizes the content of the book, emphasizing how the impressive breadth of research reveal a worrying picture of enduring discrimination in immigrant-receiving societies across space and time, suggesting the contour of troubling “three P’s” in contemporary European societies: that ethno-racial discrimination appears to be pervasive, perpetuating, and persistent. The chapter also revisits the relationship between theories of integration and discrimination, and it concludes by pointing out promising for future research on discrimination.

Adaptive complex frequency with V-cycle GMRES for preconditioning 3D Helmholtz equation

Geophysics ◽  
2021 ◽  
pp. 1-40
Author(s):  
Wenhao Xu ◽  
Yang Zhong ◽  
Bangyu Wu ◽  
Jinghuai Gao ◽  
Qing Huo Liu
Keyword(s):  
Linear System ◽  
Helmholtz Equation ◽  
3D Models ◽  
Numerical Results ◽  
Spatial Sampling ◽  
Gmres Method ◽  
Complex Frequency ◽  
Iterative Solver ◽  
Helmholtz Equations ◽  
Sampling Density

Solving the Helmholtz equation has important applications in various areas, such as acoustics and electromagnetics. Using an iterative solver together with a proper preconditioner is key for solving large 3D Helmholtz equations. The performance of existing Helmholtz preconditioners usually deteriorates when the minimum spatial sampling density is small (approximately four points per wavelength [PPW]). To improve the efficiency of the Helmholtz preconditioner at a small minimum spatial sampling density, we have adopted a new preconditioner. In our scheme, the preconditioning matrix is constructed based on an adaptive complex frequency that varies with the minimum spatial sampling density in terms of the number of PPWs. Furthermore, the multigrid V-cycle with a GMRES smoother is adopted to effectively solve the corresponding preconditioning linear system. The adaptive complex frequency together with a GMRES smoother can work stably and efficiently at different minimum spatial sampling densities. Numerical results of three typical 3D models show that our scheme is more efficient than the multilevel GMRES method and shifted Laplacian with multigrid full V-cycle and a symmetric Gauss-Seidel smoother for preconditioning the 3D Helmholtz linear system, especially when the minimum spatial sampling density is large (approximately 120 PPW) or small (approximately 4 PPW).

The Moral World

2020 ◽  
pp. 228-240
Author(s):  
Christopher J. Insole
Keyword(s):  
Highest Good ◽  
Concept Of God ◽  
The Third ◽  
Space And Time ◽  
Third Phase ◽  
Moral World ◽  
The Relationship ◽  
The Way

This chapter shows how central it is, for Kant, that the concept of God only comes downstream from, and after, the possibility of belief in the ‘moral world’. This moral world is the realm of freedom, wherein autonomy is possible. Only if (deterministic) space and time do not go ‘all the way down’, are freedom, and autonomy, possible. If space and time are ‘things-in-themselves’, Kant asserts, ‘then freedom cannot be saved’ (A536/B564). Only if there is a dimension of reality beyond mechanism, is end-setting, and so autonomy, and the highest good possible. Not even God could achieve the highest good in a universe without end-setting, and without freedom, because this universe would be a sort of ‘desert’ with no ‘inner value’. The sequence of thought we find, both in the second Critique, and in other texts is this: first of all, Kant identifies a need for happiness in proportion to virtue; then Kant identifies the obstacle to the realization of such happiness, which is the mechanistic and deterministic structure of nature; and then Kant moves to the solution, which involves leaning into the realm of freedom, which realm includes God. The significance of the third phase in the progression of thought (the realm of freedom) has not been sufficiently considered, it is argued, when considering the Kant’s ‘moral proof’, and the relationship, for Kant, between morality, the highest good, and God.

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