The field of a spherical wave reflected from a plane absorbent surface expressed in terms of an infinite series of Legendre polynomials

1983 ◽  
Vol 89 (3) ◽  
pp. 359-363 ◽  
Author(s):  
A.D. Rawlins
Keyword(s):  
Infinite Series ◽  
Legendre Polynomials ◽  
Spherical Wave

scholarly journals Anchoring Energy for Nematic Liquid Crystals an Analysis of the Proposed Forms

1984 ◽  
Vol 39 (11) ◽  
pp. 1066-1076 ◽  
Author(s):  
G. Barbero ◽  
N. V. Madhusudana ◽  
G. Durand
Keyword(s):  
Liquid Crystal ◽  
Infinite Series ◽  
Tilt Angle ◽  
Legendre Polynomials ◽  
Fourier Expansion ◽  
Easy Axis ◽  
Practical Interest ◽  
Surface Anchoring ◽  
Functional Forms ◽  
Anchoring Energy

We analyze the proposed functional forms describing the surface anchoring energy of MBBA nematic liquid crystal. Measurements of the surface torque versus tilt angle suggest that the simple cosinus-square form is not adequate for MBBA. The generalized form in an infinite series in cosinus-square is not useful since the set of functions is not orthogonal. Analyses using the orthogonal Legendre polynomials and Fourier expansion are given. Finally we analyse the data in terms of small tilt angles compared to the easy axis, and very far from it, which are the two limits of practical interest.

scholarly journals SCALAR WAVES IN A WORMHOLE TOPOLOGY

2006 ◽  
Vol 15 (05) ◽  
pp. 669-693 ◽  
Author(s):  
NECMI BUĞDAYCI
Keyword(s):  
Wave Equation ◽  
Multiple Scattering ◽  
Infinite Series ◽  
Spherical Wave ◽  
Wave Functions ◽  
Scattering Method ◽  
Explicit Solutions ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Multiple Scattering Method

Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions (2+1) and (3+1). The solutions are in the form of infinite series involving cylindrical and spherical wave functions, and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results presented in this work constitute instances of solutions of the scalar wave equation in a space–time admitting closed time-like curves.

Elasticity Solutions for Thick-Wall Submersible Spheres

1974 ◽  
Vol 96 (4) ◽  
pp. 1136-1140
Author(s):  
F. J. Dzialo
Keyword(s):  
Hydrostatic Pressure ◽  
Infinite Series ◽  
Legendre Polynomials ◽  
Buoyancy Force ◽  
Potential Functions ◽  
Thick Wall ◽  
Arbitrary Boundary ◽  
Numerical Example ◽  
Body Forces ◽  
Elasticity Solutions

Elasticity solutions utilizing the classical Boussinesq potential functions for thick-wall submersible spheres are developed. The solutions provide field stresses and strains, which consider the effect of gravity body forces, and arbitrary boundary loadings. The boundary loadings may be due to a nonuniform hydrostatic pressure, hull equipment, ballast, and can be expressed as an infinite series of Legendre polynomials. A numerical example which considers a nonuniform hydrostatic pressure and an arbitrary counter-buoyancy force applied at the inner boundary is given. Field stresses and strains are presented for various shell thicknesses and hydrostatic pressures.

SPHERICAL WAVE CORRECTIONS IN XAFS

1986 ◽  
Vol 47 (C8) ◽  
pp. C8-31-C8-35
Author(s):  
J. J. REHR ◽  
R. C. ALBERS ◽  
C. R. NATOLI ◽  
E. A. STERN
Keyword(s):  
Spherical Wave

SPHERICAL WAVE CORRECTIONS IN ARPEFS

1986 ◽  
Vol 47 (C8) ◽  
pp. C8-213-C8-216
Author(s):  
J. J. REHR ◽  
J. MUSTRE DE LEON ◽  
C. R. NATOLI ◽  
C. S. FADLEY
Keyword(s):  
Spherical Wave

SPHERICAL WAVE APPROACH TO ELECTRON FOCUSING PROCESSES IN EXAFS

1986 ◽  
Vol 47 (C8) ◽  
pp. C8-89-C8-92 ◽  
Author(s):  
R. V. VEDRINSKII ◽  
L. A. BUGAEV
Keyword(s):  
Spherical Wave ◽  
Wave Approach ◽  
Electron Focusing

A new application of quasi monotone sequences and quasi power increasing sequences to factored infinite series

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5105-5109
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Monotone Sequences ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

In this paper, we generalize a known theorem under more weaker conditions dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. This theorem also includes some new results.

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