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203 results on '"Alexander, Angus"'

1. Spectral flow and Levinson's theorem for Schr\'o dinger operators

Author

Alexander, Angus and Rennie, Adam

Subjects
Mathematical Physics, Mathematics - Spectral Theory, 47A40, 58J30, 81U20, 81U24
Abstract

We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expressed in terms of the spectral shift function and the ``high energy corrected time delay'' following Guillop\'{e} and others.

Published
2024

2. Trace formula and Levinson's theorem as an index pairing in the presence of resonances

Author

Alexander, Angus

Subjects
Mathematics - K-Theory and Homology, Mathematical Physics, Mathematics - Spectral Theory, 19K56, 47A40, 81U20, 81U24
Abstract

We realise the number of bound states of a Schr\"{o}dinger operator on $\mathbb{R}^n$ as an index pairing in all dimensions. Expanding on ideas of Guillop\'{e} and others, we use high-energy corrections to find representatives of the $K$-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients.

Published
2024

4. Levinson's theorem as an index pairing

Author

Alexander, Angus and Rennie, Adam

Subjects
Mathematics - K-Theory and Homology, Mathematical Physics, 19K56, 47A40, 81U20, 81U24
Abstract

We build on work of Kellendonk, Richard, Tiedra de Aldecoa and others to show that the wave operators for Schr\"{o}dinger scattering theory on $\mathbb{R}^n$ generically have a particular form. As a consequence, Levinson's theorem can be interpreted as the pairing of the $K$-theory class of the unitary scattering operator and the $K$-homology class of the generator of the group of dilations., Comment: v2: 27 pages, some minor revisions, to appear in J. Funct. Anal

Published
2023
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6. An OxPLORE Initiative Evaluating Children’s Surgery Resources Worldwide: A Cross-sectional Implementation of the OReCS Document

Author

Ravi, Krupa, Killen, Annabel, Alexander, Angus, Bell-Davies, Frances, Biganiro Sebintu, James, Brazeal, Aurelia, Butoyi, Jean Marie Vianney, Diaz, Fabio Edgardo, Drabile, Romeo, Fanny, Marvin, Fernie, Lucila, Gunawardana, Shannon, Hartley, Emma, Hawu, Yolisa N., Hendron, Holly, Joseph, Stephanie Alcine, Lamahewage, Ananda, Mahagedera, Ruwantha, Manirambona, Emery, Morisho, Benjamin Kitambala, Muchunu, Patrick, Niyukuri, Alliance, Ntaganda, Edmond, Orliacq, Francisco, Orliacq, Josefina, Wobenjo, Adili, Young, Pablo, Lakhoo, Kokila, and Ford, Kathryn

Published
2022
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8. Topological Levinson's theorem via index pairings and spectral flow

Author

Alexander, Angus Stuart and Alexander, Angus Stuart

Abstract

Using techniques from noncommutative geometry, we explore how Levinson's theorem from scattering theory can be interpreted in a topological manner. We use low-energy resolvent expansions to deduce that the wave operator for short range scattering has a particular universal form. The wave operator does not have this form when certain obstructions occur in the resolvent expansions in even dimensions. Using the form of the wave operator, we apply index theoretic techniques to interpret Levinson's theorem as an index pairing between the K-theory class of the unitary scattering operator and the K-homology class of the generator of dilations on the half-line. A careful analysis of the trace class properties of the scattering operator allows us to provide new proofs of Levinson's theorem in all dimensions. We also compute the spectral ow for Euclidean Schrodinger operators, giving another new proof of Levinson's theorem in all dimensions.

Published
2024

9. Levinson’s theorem for two-dimensional scattering systems: It was a surprise, it is now topological!

Author

Alexander, Angus, Thanh Duc Nguyen, Rennie, Adam, and Richard, Serge

Subjects
SCHRODINGER operator, MOLECULAR connectivity index, RESONANCE
Abstract

We prove a general Levinson’s theorem for Schrödinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal results of Bollé, Gesztesy et al., while providing an explicit topological interpretation. We also derive explicit formulas for the wave operators, and so show that they are elements of a C -algebra introduced by Cordes. As a consequence of our approach, we provide an evaluation of the spectral shift function at zero in the presence of p-resonances. [ABSTRACT FROM AUTHOR]

Published
2024
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24. An OxPLORE Initiative Evaluating Children’s Surgery Resources Worldwide: A Cross-sectional Implementation of the OReCS Document

Author

Ravi, Krupa, primary, Killen, Annabel, additional, Alexander, Angus, additional, Bell-Davies, Frances, additional, Biganiro Sebintu, James, additional, Brazeal, Aurelia, additional, Butoyi, Jean Marie Vianney, additional, Diaz, Fabio Edgardo, additional, Drabile, Romeo, additional, Fanny, Marvin, additional, Fernie, Lucila, additional, Gunawardana, Shannon, additional, Hartley, Emma, additional, Hawu, Yolisa N., additional, Hendron, Holly, additional, Joseph, Stephanie Alcine, additional, Lamahewage, Ananda, additional, Mahagedera, Ruwantha, additional, Manirambona, Emery, additional, Morisho, Benjamin Kitambala, additional, Muchunu, Patrick, additional, Niyukuri, Alliance, additional, Ntaganda, Edmond, additional, Orliacq, Francisco, additional, Orliacq, Josefina, additional, Wobenjo, Adili, additional, Young, Pablo, additional, Lakhoo, Kokila, additional, and Ford, Kathryn, additional

Published
2021
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34. Reducing the incidence of hepatic artery thrombosis in pediatric liver transplantation: Effect of microvascular techniques and a customized anticoagulation protocol

Author

Ziaziaris, William A., primary, Darani, Alexandre, additional, Holland, Andrew J. A., additional, Alexander, Angus, additional, Karpelowsky, Jonathan, additional, Barbaro, Pasquale, additional, Stormon, Michael, additional, O'Loughlin, Edward, additional, Shun, Albert, additional, and Thomas, Gordon, additional

Published
2017
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41. Letter from Alexander Angus Airlie Kinloch to Theodore Roosevelt (1906-01-31)

Author

Kinloch, Alexander Angus Airlie, Kinloch, Alexander Angus Airlie, 1838-1919, Kinloch, Alexander Angus Airlie, and Kinloch, Alexander Angus Airlie, 1838-1919

Abstract

Alexander Angus Airlie Kinloch congratulates President Roosevelt on his book The Outdoor Pastimes of an American Hunter and thanks him for mentioning Kinloch's own publication Large Game Shooting . Kinloch details some of his hunting experience and concludes with congratulating Roosevelt for maintaining his love of nature.

Published
1906

42. Letter from Alexander Angus Airlie Kinloch to Theodore Roosevelt (1906-02-28)

Author

Kinloch, Alexander Angus Airlie, 1838-1919, Kinloch, Alexander Angus Airlie, 1838-1919, Kinloch, Alexander Angus Airlie, 1838-1919, and Kinloch, Alexander Angus Airlie, 1838-1919

Abstract

Alexander Angus Airlie Kinloch thanks President Roosevelt for his previous letter. Kinloch also includes a copy of the latest edition of his book, most likely referring to Large Game Shooting in Thibet and the North West .

Published
1906

43. Letter from Alexander Angus Airlie Kinloch to Theodore Roosevelt (1906-01-31)

Author

Kinloch, Alexander Angus Airlie, 1838-1919, Kinloch, Alexander Angus Airlie, 1838-1919, Kinloch, Alexander Angus Airlie, 1838-1919, and Kinloch, Alexander Angus Airlie, 1838-1919

Abstract

Alexander Angus Airlie Kinloch congratulates President Roosevelt on his book The Outdoor Pastimes of an American Hunter and thanks him for mentioning Kinloch's own publication Large Game Shooting . Kinloch details some of his hunting experience and concludes with congratulating Roosevelt for maintaining his love of nature.

Published
1906

45. Essay on otitis

Author

McDowall, Alexander Angus and McDowall, Alexander Angus

Abstract

No abstract available.

46. Essay on otitis

Author

McDowall, Alexander Angus and McDowall, Alexander Angus

Abstract

No abstract available.

47. Essay on otitis

Author

McDowall, Alexander Angus and McDowall, Alexander Angus

48. Essay on otitis

Author

McDowall, Alexander Angus and McDowall, Alexander Angus

Abstract

No abstract available.

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