scholarly journals Sharpening of Observational Data in Two Dimensions

1955 ◽  
Vol 8 (1) ◽  
pp. 30 ◽  
Author(s):  
EJ Burr
Keyword(s):  
Integral Equation ◽  
Observational Data ◽  
Two Dimensions ◽  
True Distribution

Distributions in two dimensions as measured are always blurred or smoothed by limitations in the observing technique. Recovery of the true distribution involves the solution of an integral equation of the form where the functions g, h are known from observation

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

The direct and inverse scattering problems for an arbitrary cylinder: Dirichlet boundary conditions

1980 ◽  
Vol 86 (1-2) ◽  
pp. 29-42 ◽  
Author(s):  
David Colton ◽  
Ralph Kleinman
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Boundary Integral Equation ◽  
Inverse Scattering ◽  
Dirichlet Boundary ◽  
Scattering Problem ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Moment Problems ◽  
Far Field

SynopsisThe exterior Dirichlet problem for the Helmholtz equation in two dimensions is reduced to a boundary integral equation which is soluble by iteration. A standard application of Green's theorem leads to boundary integral equations which are not uniquely soluble because the operator has an eigenvalue. The present approach modifies the operator in such a way that the former eigenvalue is in the resolvent spectrum for low frequencies. The results are applied to the inverse scattering problem wherein the far field is known for a limited frequency range and one seeks the curve on which a plane wave is incident and a Dirichlet boundary condition is assumed. The first iterate in the solution of the boundary integral equation is used to obtain a sequence of moment problems relating the Fourier coefficients of the far field to the coefficients of the Laurent expansion of the conformai transformation which maps the exterior of a circle onto the exterior of the unknown curve. These moment problems are soluble in terms of the mapping radius which in turn may be determined from scattered far field data for an incident plane wave from a second direction.

Dimensions of Elite Partisan Polarization: Disentangling the Effects of Incivility and Issue Polarization

2020 ◽  
pp. 1-19
Author(s):  
Rasmus Skytte
Keyword(s):  
Observational Data ◽  
Political Trust ◽  
Two Dimensions ◽  
Partisan Polarization ◽  
Attitude Polarization ◽  
Research Designs ◽  
Political Distrust ◽  
Different Types

Abstract Elite partisan polarization has been found to have several potentially problematic effects on citizens, such as creating political distrust and different types of polarization among partisans. However, it remains unclear whether these effects are caused by the parties moving apart in terms of issue positions (issue polarization) or by the rise of disrespectful rhetoric (incivility). In the literature, these two dimensions of elite polarization often appear to affect citizens in similar ways, but typical research designs have not been well suited to disentangling their effects. To determine their unique effects, four studies have been conducted using original designs and a mix of experimental and observational data. The results show that issue polarization and incivility have clearly distinct effects. A more uncivil tone lowers political trust, but increasing issue polarization does not. Conversely, only issue polarization creates attitude polarization among partisans. Both aspects of elite polarization create affective polarization.

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