scholarly journals Cylindrical-wave diffraction by a rational wedge

1987 ◽  
Vol 411 (1841) ◽  
pp. 285-303 ◽  
Keyword(s):  
Half Plane ◽  
General Result ◽  
Wave Diffraction ◽  
Cylindrical Wave ◽  
Open Angle ◽  
Source Terms ◽  
Special Cases ◽  
Rational Multiple

In this paper, new expressions for the field produced by the diffraction of a cylindrical wave by a wedge, whose angle can be expressed as a rational multiple of π, are given. The solutions are expressed in terms of source terms and real integrals that represent the diffracted field. The general result obtained includes as special cases, Macdonald’s solution for diffraction by a half plane, a solution for Carslaw’s problem of diffraction by a wedge of open angle 2/3π, and a new representation for the solution of the problem of diffraction by a mixed soft-hard half plane.

scholarly journals A Green's function for diffraction by a rational wedge

1989 ◽  
Vol 105 (1) ◽  
pp. 185-192 ◽  
Author(s):  
A. D. Rawlins
Keyword(s):  
Wave Equation ◽  
Point Source ◽  
Green’S Function ◽  
Half Plane ◽  
Green's Function ◽  
General Result ◽  
Spherical Wave ◽  
Source Terms ◽  
Angular Sector ◽  
Rational Multiple

AbstractIn this paper we derive an expression for the point source Green's function for the reduced wave equation, valid in an angular sector whose angle is equal to a rational multiple of π. This Green's function can be used to find new expressions for the field produced by the diffraction of a spherical wave by a wedge whose angle can be expressed as a rational multiple of π. The expressions obtained will be in the form of source terms and real integrals representing the diffracted field. The general result obtained is used to derive a new representation for the solution of the problem of diffraction by a mixed hard–soft half plane.

scholarly journals Plane-wave diffraction by a rational wedge

1987 ◽  
Vol 411 (1841) ◽  
pp. 265-283 ◽  
Keyword(s):  
Plane Wave ◽  
Half Plane ◽  
Acoustic Field ◽  
Angular Variable ◽  
Acoustic Source ◽  
Wave Source ◽  
Easy Calculation ◽  
Special Cases ◽  
Rational Multiple ◽  
Plane Wave Diffraction

In this paper, new expressions for the acoustic field produced when a plane-wave source of sound is diffracted by a soft, hard or mixed soft-hard wedge whose angle can be expressed as a rational multiple of π are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals that represent the diffracted field. The expressions are in a form that allows easy calculation of the acoustic field. Uniformly valid expressions for the far field are also given for all values of the angular variable. The general result obtained includes, as special cases, Sommerfeld’s solution for diffraction by a half-plane, Reiche’s result for the diffraction by a right-angled wedge, and a new representation for the solution of the problem of diffraction by a mixed soft-hard half-plane.

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

Raman scattering from impurities in semiconductors. II. Special cases

1978 ◽  
Vol 56 (5) ◽  
pp. 560-564
Author(s):  
Robert Barrie ◽  
H. -C. Chow
Keyword(s):  
Raman Scattering ◽  
General Result ◽  
Phonon Scattering ◽  
Phonon Coupling ◽  
Strong Electron ◽  
Impurities In Semiconductors ◽  
Electron Phonon Coupling ◽  
Special Cases ◽  
Weak Electron

Special cases of the general result for Raman scattering from an impurity in a semiconductor are discussed. For weak electron–phonon coupling the zero-phonon and one-phonon scattering intensities are derived. For strong electron–phonon coupling a comparison is made between two different approximations that have been previously used.

Extension of normal functionals on W*-tensor products

1975 ◽  
Vol 78 (2) ◽  
pp. 301-307 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
General Result ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
Hilbert Algebras ◽  
Special Cases

A deep result in the theory of W*-tensor products, the Commutation theorem, states that if M and N are W*-algebras faithfully represented as von Neumann algebras on the Hilbert spaces H and K, respectively, then the commutant in L(H ⊗ K) of the W*-tensor product of M and N coincides with the W*-tensor product of M′ and N′. Although special cases of this theorem were established successively by Misonou (2) and Sakai (3), the validity of the general result remained conjectural until the advent of the Tomita-Takesaki theory of Modular Hilbert algebras (6). As formulated, the Commutation theorem is a spatial result; that is, the W*-algebras in its statement are taken to act on specific Hilbert spaces. Not surprisingly, therefore, known proofs rely heavily on techniques of representation theory.

scholarly journals NEW EXACT SOLUTIONS OF SPATIALLY AND TEMPORALLY VARYING REACTION-DIFFUSION EQUATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 371-381 ◽  
Author(s):  
NALINI JOSHI ◽  
TEGAN MORRISON
Keyword(s):  
Reaction Diffusion ◽  
Elliptic Functions ◽  
Point Of View ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Source Terms ◽  
Symmetry Approach ◽  
New Exact Solutions ◽  
Special Cases ◽  
New Feature

This paper considers reaction-diffusion equations from a new point of view, by including spatiotemporal dependence in the source terms. We show for the first time that solutions are given in terms of the classical Painlevé transcendents. We consider reaction-diffusion equations with cubic and quadratic source terms. A new feature of our analysis is that the coefficient functions are also solutions of differential equations, including the Painlevé equations. Special cases arise with elliptic functions as solutions. Additional solutions given in terms of equations that are not integrable are also considered. Solutions are constructed using a Lie symmetry approach.

scholarly journals Optimal Strategy for the Vardi Casino with Interest Payments

2007 ◽  
Vol 44 (01) ◽  
pp. 199-211 ◽  
Author(s):  
Ilie Grigorescu ◽  
Robert Chen ◽  
Larry Shepp
Keyword(s):  
General Result ◽  
Optimal Strategy ◽  
Critical Value ◽  
Discount Factor ◽  
Optimal Probability ◽  
Special Cases ◽  
Interest Payments

A gambler starts with fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c < 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.

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