Uniqueness on recovery of piecewise constant conductivity and inner core with one measurement

Fang, Xiaoping; Deng, Youjun

doi:10.3934/ipi.2018031

Cited by 10 publications

(11 citation statements)

References 20 publications

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“…The proof for uniqueness of the two-layer structure is highly technical and in fact can be extended to multi-layer structure. One can also refer to [12] for similar idea in recovering the piecewise constants conductivity with one measurement.…”

Section: )mentioning

confidence: 99%

On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements

Fang

Deng

Tsui

et al. 2020

era

Self Cite

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We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

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Section: )mentioning

confidence: 99%

On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements

Fang

Deng

Tsui

et al. 2020

era

Self Cite

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“…In the inverse conductivity problem, in a single-layer structure, the uniqueness of the conductivity and unknown core can be obtained by a single measurement. In a two-layer structure, under a prior assumption, the uniqueness of the piecewise constant conductivity can also be obtained by a single measurement (see [8]).…”

Section: Introductionmentioning

confidence: 99%

Uniqueness on recovery of Lamé constants by the same boundary measurement

Tang¹,

Li²

2023

Phys. Scr.

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We consider the recovery of Lame constants and an unknown inner core in elastic system. In this paper, we use layer potential technique to represent the solution of the equation and analyze the obtained solution using transmission conditions across the boundary. Firstly, in a single-layer structure, using the same boundary measurements, we utilize the obtained solution to uniquely recover the Lame constant. Then, in a two-layer structure, we also prove a Calderon-type identity and use this identity to uniquely recover the piecewise Lame constant through the same boundary measurements. Finally, we prove that in a two-layer structure, the unique recovery of piecewise Lame constant in the quasi-static regime.

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“…Furthermore, probability is not just about flipping coins and counting cards in a disc; it is used in a wide range of real-life areas, from insurance to meteorology and politics to economics forecasting. For more applications, we refer the reader to [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions

Ahmad¹,

Khan

Cotîrlǎ

2022

Symmetry

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The main purpose of this article is to introduce the new subclass of analytic functions whose coefficients are Borel distributions in the Janowski domain. Further, we investigate some useful number of properties such as Fekete–Szeg ö inequality, necessary and sufficient condition, growth and distortion approximations, convex linear combination, arithmetic mean, radii of close-to-convexity and starlikeness and partial sums, followed by some extremal functions for this defined class. The symmetry properties and other properties of the subclass of functions introduced in this paper can be studied as future research directions.

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Uniqueness on recovery of piecewise constant conductivity and inner core with one measurement

Cited by 10 publications

References 20 publications

On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements

On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements

Uniqueness on recovery of Lamé constants by the same boundary measurement

Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions

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