Addition Theorem

2008 ◽  
pp. 203-226 ◽  
Author(s):  
B. He ◽  
W. C. Chew
Keyword(s):  
Addition Theorem

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.

Comment on `Addition theorem for solid harmonics and the second Born amplitudes'

1996 ◽  
Vol 29 (15) ◽  
pp. 3557-3557
Author(s):  
N C Deb ◽  
N C Sil ◽  
P Mandal
Keyword(s):  
Addition Theorem

A Proof of the Elliptic-Function Addition-Theorem

1886 ◽  
Vol 8 (3) ◽  
pp. 287
Author(s):  
J. C. Fields
Keyword(s):  
Elliptic Function ◽  
Addition Theorem

Computer Simulation Studies of Molecular Orientation in Polyethylene Networks:  Orientation Functions and the Legendre Addition Theorem†

2000 ◽  
Vol 33 (13) ◽  
pp. 4966-4971 ◽  
Author(s):  
J. I. Cail ◽  
D. J. R. Taylor ◽  
R. F. T. Stepto ◽  
M. G. Brereton ◽  
R. A. Jones ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Molecular Orientation ◽  
Addition Theorem ◽  
Simulation Studies ◽  
Computer Simulation Studies

scholarly journals Derivatives of addition theorems for Legendre functions

1995 ◽  
Vol 37 (2) ◽  
pp. 212-234 ◽  
Author(s):  
D.E. Winch ◽  
P.H. Roberts
Keyword(s):  
Spherical Harmonics ◽  
Chebyshev Polynomials ◽  
Legendre Polynomials ◽  
Addition Theorem ◽  
Legendre Functions ◽  
Addition Theorems ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Derivatives Of

AbstractDifferentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.

scholarly journals To the theory of synchronization of interacting pendulums oscillating in the parallel planes

2020 ◽  
Vol 20 (1) ◽  
pp. 15-37
Author(s):  
S.O. Gladkov ◽  
◽  
S.B. Bogdanova ◽  
Keyword(s):  
Numerical Solution ◽  
Complex Plane ◽  
Nonlinear Dynamic ◽  
Functional Equations ◽  
Electromagnetic Interaction ◽  
Theta Functions ◽  
Addition Theorem ◽  
Physical Factors ◽  
Motion Equations ◽  
Dynamic Motion

The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions.

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