Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

More than 9 years of continuous trastuzumab treatment in metastatic breast cancer without cardiac toxicity: a case report and literature review

Florin Badulescu,1 Adriana Badulescu,2 Doru Paul,3 Carmen Florina Popescu,4 Cristina Florescu5 1Department of Oncology, Universitatea de Medicina si Farmacie, Craiova, Romania; 2Department of Surgery, Universitatea Titu Maiorescu, Bucuresti, Romania; 3Monter Cancer Center, North Shore LIJ Cancer Institute, Lake Success, NY, USA; 4Department of Pathology, Spitalul Universitar Clinic de Urgenta, Craiova, Romania; 5Department of Cardiology, Universitatea de Medicina si Farmacie, Craiova, Romania Abstract: The main concern of long-term use of trastuzumab remains its association with potential cardiac side effects. Although these side effects are real, they are probably overemphasized. We report the case of a woman with metastatic breast cancer, who is currently in complete remission, and who received trastuzumab continuously for more than 9 years, without any significant cardiac toxicity. Keywords: metastatic breast cancer, long survival, trastuzuma

Sur une conjecture de Tadic

Let F be a non-archimedian field of characteristic zero and D a central division algebra over F of finite dimension d2. For all positive integer r, set G\u27r = GL(r,D). In 1990, M. Tadic gave a conjectural classification of the unitary dual of the G\u27r, and five statements denoted U0, ... , U4, which imply the classification. M. Tadic proved U3 and U4. Also, U0 and U1 imply U2. These statements, and the resulting classification are the natural generalization of the case D = F completely solved by M. Tadic in 1986. Here we prove U1. Thus, the classification of the unitary dual of the G\u27r is now reduced to the conjecture U0, which states that a parabolically induced representation from an irreducible unitary representation is irreducible

Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean places so that this assumption can be removed. Along the way, we collect several results about the unitary dual of general linear groups over \bbR, \bbC or \bbH of independent interest

On unitarizability in the case of classical p-adic groups

In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give additional evidence in generalized cuspidal rank (up to) three.Comment: This paper is a merged and revised version of ealier preprints arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul

Stabilizing Heteroscedastic Noise With the Generalized Anscombe Transform. Application to Accurate Prediction of the Resolution in Displacement and Strain Maps Obtained With the Grid Method.

International audienceThe objective of this paper is to show that it is possible to predict the noise level in displacement and strain maps obtained with the grid method, but that actual noise of camera sensors being heteroscedastic, it is necessary to stabilize this noise in grid images prior to employing the predicting formulas. The procedure used for this purpose relies on the Generalized Anscombe Transform. This transform is first described. It is then shown that experimental and theoretical resolutions in strain maps obtained with the grid method are in good agreement when this transform is employed

Orthogonalité des caractères pour GL n sur un corps local de caractéristique non nulle

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