Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

A uniqueness result for differential pencils with discontinuities from interior spectral data

Analysis ◽  
2019 ◽  
Vol 38 (4) ◽  
pp. 195-202
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Uniqueness Result ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Differential Pencils

Abstract In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions {q_{0}(x)} and {q_{1}(x)} applied in the diffusion operator.

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

scholarly journals Half inverse problem for the impulsive diffusion operator with discontinuous coefficient

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Yaşar Çakmak ◽  
Seval Işık
Keyword(s):  
Inverse Problem ◽  
Discontinuous Coefficient ◽  
Diffusion Operator ◽  
Impulsive Diffusion ◽  
Half Inverse Problem

The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl?s methods we show that if p(x) and q(x) are known on the interval (?/2,?), then only one spectrum suffices to determine p (x),q(x) functions and ?,h coefficients on the interval (0,?) for impulsive diffusion operator with discontinuous coefficient.

scholarly journals A Uniqueness Theorem for Bessel Operator from Interior Spectral Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Murat Sat ◽  
Etibar S. Panakhov
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Spectral Data ◽  
Bessel Operator ◽  
Uniqueness Theorems ◽  
Internal Point

Inverse problem for the Bessel operator is studied. A set of values of eigenfunctions at some internal point and parts of two spectra are taken as data. Uniqueness theorems are obtained. The approach that was used in investigation of problems with partially known potential is employed.

21,22-Disubstituted 18α,19βH-Ursane Derivatives with Oxabicyclooctane System in Ring E

1993 ◽  
Vol 58 (1) ◽  
pp. 173-190 ◽  
Author(s):  
Eva Klinotová ◽  
Jiří Klinot ◽  
Václav Křeček ◽  
Miloš Buděšínský ◽  
Bohumil Máca
Keyword(s):  
Spectral Data ◽  
Spin Systems ◽  
Coupling Constants ◽  
Complete Analysis ◽  
Nmr Spectrum ◽  
Proton Proton ◽  
H Nmr ◽  
Proton Coupling ◽  
C Nmr

Reaction of 3β-acetoxy-21,22-dioxo-18α,19βH-ursan-28,20β-olide (IIIa) and 20β,28-epoxy-21,22-dioxo-19α,19βH-ursan-3β-yl acetate (IIIb) with diazomethane afforded derivatives XII-XIV with spiroepoxide group in position 21 or 22, which were further converted into hydroxy derivatives XV and XVII. Ethylene ketals VIII-X were also prepared. In connection with the determination of position and configuration of the functional groups at C(21) and C(22), the 1H and 13C NMR spectral data of the prepared compounds are discussed. Complete analysis of two four-spin systems in the 1H NMR spectrum of bisethylenedioxy derivative Xb led to the proton-proton coupling constants from which the structure with two 1,4-dioxane rings condensed with ring E, and their conformation, was derived.

Synthesis of 4-(3-coumarinyl)-3-benzyl-4-thiazolin-2-one 4-methylbenzylidenehydrazone and determination of the isomeric structure by X-ray analysis

2003 ◽  
Vol 218 (12) ◽  
Author(s):  
Süheyla Özbey ◽  
Nilgün Karalı ◽  
Aysel Gürsoy
Keyword(s):  
Single Crystal ◽  
Diffraction Analysis ◽  
Spectral Data ◽  
X Ray Diffraction ◽  
X Ray ◽  
Isomeric Structure ◽  
Elemental Analyses

AbstractIn this study 4-(3-coumarinyl)-3-benzyl-4-thi azolin-2-one 4-methylbenzylidenehydrazone 3 was synthesised. An independent proof of the thiazolylhydrazone structure of 3 was achieved by single crystal X-ray diffraction analysis. Elemental analyses and spectral data (IR,

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

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