Derivation of Einstein's velocity addition theorem through use of the invariant double ratio

1978 ◽  
Vol 8 (1-2) ◽  
pp. 131-135
Author(s):  
Dierck-Ekkehard Liebscher
Keyword(s):  
Addition Theorem ◽  
Double Ratio ◽  
Velocity Addition

Brewster Angle and the Einstein Velocity Addition Theorem

1971 ◽  
Vol 39 (9) ◽  
pp. 1079-1084 ◽  
Author(s):  
R. G. Newburgh ◽  
T. E. Phipps
Keyword(s):  
Addition Theorem ◽  
Brewster Angle ◽  
Velocity Addition ◽  
Einstein Velocity Addition

Velocity Addition Theorem and Einstein-Dopfleh Effect

1970 ◽  
Vol 3 (11-12) ◽  
pp. 303-304 ◽  
Author(s):  
Wallace Kantor
Keyword(s):  
Addition Theorem ◽  
Velocity Addition

Special Relativity: Putting it All Together

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Special Relativity ◽  
Moving Object ◽  
Velocity Addition

We have introduced the ideas of special relativity in quick succession because none of those ideas can really be understood in isolation. This chapter works through examples in some detail so you can practice applying the ideas and solidifying your understanding.We start with an overview of how to use spacetime diagrams to solve problems in special relativity, then we walk through examples ofmeasuring the length of a moving object; the train‐in‐tunnel paradox; velocity addition; and how clock readings are arranged so that each observer measures the other’s clocks as ticking slowly.

Quadratic Double-Ratio Minimax Optimization

2021 ◽  
Author(s):  
Arezu Zare ◽  
Ali Ashrafi ◽  
Yong Xia
Keyword(s):  
Minimax Optimization ◽  
Double Ratio

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

2011 ◽  
Vol 27 (6) ◽  
pp. 1365-1383 ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Ying-Te Lee ◽  
Yi-Jhou Lin ◽  
I-Lin Chen ◽  
Jia-Wei Lee
Keyword(s):  
Addition Theorem ◽  
Point Sources ◽  
Circular Cylinders ◽  
Superposition Technique

Canonical two-range addition theorem for slater-type orbitals

2012 ◽  
Vol 113 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Daniel Gebremedhin ◽  
Charles Weatherford
Keyword(s):  
Addition Theorem ◽  
Slater Type Orbitals ◽  
Slater Type

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

scholarly journals Some properties of the growth and of the algebraic entropy of group endomorphisms

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Anna Giordano Bruno ◽  
Pablo Spiga
Keyword(s):  
Finite Groups ◽  
Addition Theorem ◽  
Finitely Generated ◽  
Growth Type ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Algebraic Entropy ◽  
Finitely Generated Groups ◽  
Identity Automorphism ◽  
Inner Automorphisms

AbstractWe study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth. We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.

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