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In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp pseudodifferential operator algebra and its semiclassical foliation version introduced and used by Vasy and Zachos, who showed the same type invertibility on functions. The complication of the invertibility of the tensorial X-ray transform, compared with X-ray transform on functions, is caused by the natural kernel of the transform consisting of ‘potential tensors’. We overcome this by arranging a modified solenoidal gauge condition, under which we have the invertibility of the X-ray transform.
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Invertibility Conditions for the Admittance Matrices of Balanced Power Systems
The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of invertibility. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.
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- Award ID(s):
- 2023140
- PAR ID:
- 10482177
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers
- Date Published:
- Journal Name:
- IEEE Transactions on Power Systems
- Volume:
- 38
- Issue:
- 4
- ISSN:
- 0885-8950
- Page Range / eLocation ID:
- 3841-3853
- Subject(s) / Keyword(s):
- Admittance matrix circuit analysis
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TPWRS.2022.3206285
