On the Inverse Source Problem with Boundary Data at Many Wave Numbers

2020 ◽  
pp. 59-80
Author(s):  
Victor Isakov ◽  
Shuai Lu
Keyword(s):  
Boundary Data ◽  
Inverse Source Problem ◽  
Wave Numbers

scholarly journals On the low frequency asymptotics for the 2-D electromagnetic transmission problem

2006 ◽  
Vol 47 (3) ◽  
pp. 397-411
Author(s):  
C. N. Anestopoulos ◽  
E. E. Argyropoulos
Keyword(s):  
Boundary Data ◽  
Maxwell Equations ◽  
Low Frequency ◽  
Boundary Integral ◽  
Transmission Problem ◽  
Integral Equation Methods ◽  
Wave Numbers ◽  
Homogeneous Media ◽  
Electromagnetic Transmission ◽  
Dimensional Domain

AbstractWe examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.

scholarly journals Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Yavar Kian ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Boundary Data ◽  
Stability Estimate ◽  
Carleman Estimate ◽  
Parabolic Problems ◽  
Conditional Stability ◽  
Inverse Source Problem ◽  
Lateral Boundary ◽  
Spatial Component

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

Numerical Experimental for an Inverse Source Problem Method

2021 ◽  
pp. 125-139
Author(s):  
Abdalkaleg Atia Idris Hamad
Keyword(s):  
Boundary Data ◽  
Noise Intensity ◽  
Source Function ◽  
Elliptic Systems ◽  
Background Field ◽  
Inverse Source Problem ◽  
Performance Accuracy ◽  
Problem Method ◽  
Error Field ◽  
Well Posed

This paper examines extensions of an iterative method for inverse evaluation of the source function for two elliptic systems. The method begins with a starting value for the undetermined source. Next, a background field and equations for the error field are obtained. 2-D domains are considered. This method is suitable for Helmholtz and Poisson operators. In the presence of finite-difference grid resolution, a varying amount of boundary data, and methods of filtering the noise in the boundary data and the noise intensity of the boundary data, the performance, accuracy, and iteration count of the algorithm are investigated. Keywords: Source, Inverse Problems, Poisson, Noise, Ill-Posedness, Well-Posed

Substituent effect on wave numbers of C=O valence vibrations in ferrocene derivatives

1983 ◽  
Vol 48 (6) ◽  
pp. 1635-1646 ◽  
Author(s):  
Alexander Perjéssy ◽  
Štefan Toma
Keyword(s):  
Linear Correlation ◽  
Substituent Effect ◽  
Empirical Relation ◽  
Ferrocene Derivatives ◽  
Wave Numbers ◽  
Complex Structural ◽  
Transmission Factors

Wave numbers of C=O valence vibrations of 83 ferrocene derivatives have been measured in tetrachloromethane. For a series of 154 compounds containing ferrocene skeleton linear correlation has been found between wave numbers of C=O vibration and X+(R) constants of structural fragments in the sense of modified and extended Seth-Paul-Van Duyse equation. Validity has been verified of the recently derived empirical relation for calculation of the X+(R) constants of complex structural fragments from values of constants of substituents and transmission factors for simple structural groupings. The transmission factors γ and π' for 1,3- and 1,1'-ferrocene system have been found to be well applicable to calculation of constants of structural fragments containing ferrocene skeleton.

Infrared spectra and substituent effects in 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones

1983 ◽  
Vol 48 (2) ◽  
pp. 586-595 ◽  
Author(s):  
Alexander Perjéssy ◽  
Pavol Hrnčiar ◽  
Ján Šraga
Keyword(s):  
Substituent Effects ◽  
Phenyl Group ◽  
Wave Number ◽  
Vibrational Coupling ◽  
Wave Numbers ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
The Relationship ◽  
Derivatives Of ◽  
Effect Of Structure

The wave numbers of the fundamental C=O and C=C stretching vibrations, as well as that of the first overtone of C=O stretching vibration of 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones and 1,3-cycloheptanedione were measured in tetrachloromethane and chloroform. The spectral data were correlated with σ+ constants of substituents attached to phenyl group and with wave number shifts of the C=O stretching vibration of substituted acetophenones. The slope of the linear dependence ν vs ν+ of the C=C stretching vibration of the ethylenic group was found to be more than two times higher than that of the analogous correlation of the C=O stretching vibration. Positive values of anharmonicity for asymmetric C=O stretching vibration can be considered as an evidence of the vibrational coupling in a cyclic 1,3-dicarbonyl system similarly, as with derivatives of 1,3-indanedione. The relationship between the wave numbers of the symmetric and asymmetric C=O stretching vibrations indicates that the effect of structure upon both vibrations is symmetric. The vibrational coupling in 1,3-cycloheptanediones and the application of Seth-Paul-Van-Duyse equation is discussed in relation to analogous results obtained for other cyclic 1,3-dicarbonyl compounds.

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