Group inversion in certain finite-dimensional algebras generated by two idempotents

Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved

Drazin inversion in the von Neumann algebra generated by two orthogonal projections

Criteria for Drazin and Moore-Penrose invertibility of operators in the von Neumann algebra generated by two orthogonal projections are established and explicit representations for the corresponding inverses are given. The results are illustrated by several examples that have recently been considered in the literature. (C) 2009 Elsevier Inc. All rights reserved

A gentle guide to the basics of two projections theory

This paper is a survey of the basics of the theory of two projections. It contains in particular the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, and Krupnik\u27s theorem on two idempotents in Banach algebras. These two theorems, which deliver the desired results usually very quickly and comfortably, are missing or wrongly cited in many recent publications on the topic, The paper is intended as a gentle guide to the field. The basic theorems are precisely stated, some of them are accompanied by full proofs, others not, but precise references are given in each case, and many examples illustrate how to work with the theorems. (C) 2009 Elsevier Inc. All rights reserved

Revised Pulsar Spindown

We address the issue of electromagnetic pulsar spindown by combining our experience from the two limiting idealized cases which have been studied in great extent in the past: that of an aligned rotator where ideal MHD conditions apply, and that of a misaligned rotator in vacuum. We construct a spindown formula that takes into account the misalignment of the magnetic and rotation axes, and the magnetospheric particle acceleration gaps. We show that near the death line aligned rotators spin down much slower than orthogonal ones. In order to test this approach, we use a simple Monte Carlo method to simulate the evolution of pulsars and find a good fit to the observed pulsar distribution in the P-Pdot diagram without invoking magnetic field decay. Our model may also account for individual pulsars spinning down with braking index n < 3, by allowing the corotating part of the magnetosphere to end inside the light cylinder. We discuss the role of magnetic reconnection in determining the pulsar braking index. We show, however, that n ~ 3 remains a good approximation for the pulsar population as a whole. Moreover, we predict that pulsars near the death line have braking index values n > 3, and that the older pulsar population has preferentially smaller magnetic inclination angles. We discuss possible signatures of such alignment in the existing pulsar data.Comment: 8 pages, 7 figures; accepted to Ap

Toeplitz operators of finite interval type and the table method

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator T-G in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of T-G. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same probleminfo:eu-repo/semantics/acceptedVersio

Probabilistic Bag-Of-Hyperlinks Model for Entity Linking

Many fundamental problems in natural language processing rely on determining what entities appear in a given text. Commonly referenced as entity linking, this step is a fundamental component of many NLP tasks such as text understanding, automatic summarization, semantic search or machine translation. Name ambiguity, word polysemy, context dependencies and a heavy-tailed distribution of entities contribute to the complexity of this problem. We here propose a probabilistic approach that makes use of an effective graphical model to perform collective entity disambiguation. Input mentions (i.e.,~linkable token spans) are disambiguated jointly across an entire document by combining a document-level prior of entity co-occurrences with local information captured from mentions and their surrounding context. The model is based on simple sufficient statistics extracted from data, thus relying on few parameters to be learned. Our method does not require extensive feature engineering, nor an expensive training procedure. We use loopy belief propagation to perform approximate inference. The low complexity of our model makes this step sufficiently fast for real-time usage. We demonstrate the accuracy of our approach on a wide range of benchmark datasets, showing that it matches, and in many cases outperforms, existing state-of-the-art methods