It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...

In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homology in geometric terms. The object of this note is to go one step further and describe the Jacquet module functor on Harish-Chandra modules via geometry. Let GR be a real reductive linear algebraic group...

Effect algebras have been introduced in the 1990s in the study of the foundations of quantum mechanics, as part of a quantum-theoretic version of probability theory. This paper is part of that programme and gives a systematic account of Lebesgue integration for [0, 1]-valued functions in terms of effect algebras and effect modules. The starting point is the ‘indicator’ function for a measurable...

[2] The notation L(G) is meant to suggest the presence of the inner product on this space of functions. On a general space X with an integral, the iner product is 〈f1, f2〉 = ∫ X f1f 2. [3] The term character has different meanings in different contexts. The simplest sense is a group homomorphism to C×. However, an equally important use is for the trace of a group homomorphism ρ : G → GLn(k) fro...

In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homology in geometric terms. The object of this note is to go one step further and describe the Jacquet module functor on Harish-Chandra modules via geometry. Let GR be a real reductive linear algebraic group...

To handle the variety of scene characters, we propose a cooperative multiple-hypothesis framework which consists of an image operator set module, an Optical Character Recognition (OCR) module and an integration module. Multiple image operators activated by multiple parameters probe suspected character regions. The OCR module is then applied to each suspected region and returns multiple candidat...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...