In the present paper for two $mathfrak{A}$-module Banach algebras $A$ and $B$, we investigate relations between $varphi$-$mathfrak{A}$-module approximate amenability of $A$, $psi$-$mathfrak{A}$-module approximate amenability of $B$, and $varphioplus psi$-$mathfrak{A}$-module approximate amenability of $Aoplus B$ ($l^1$-direct sum of $A$ and $B$), where $varphiin$ Hom$_{mathfrak{A}}(A)$ and $psi...

As an abstraction of the geometric notion of translation, author in [8] has introduced two operators T+ and Tcalled the fuzzy translation operators on the fuzzy set and studied their properties and also investigated the action of these operators on the (Anti) fuzzy subgroups of a group in [8] and (Anti) fuzzy subring and ideal of a ring in [9]. The notion of anti fuzzy submodule of a module h...

We define a notion of ghost centre of a Lie superalgebra g = g0 ⊕ g1 which is a sum of invariants with respect to the usual adjoint action (centre) and invariants with respect to a twisted adjoint action (“anticentre”). We calculate the anticentre in the case when the top external degree of g1 is a trivial g0-module. We describe the Harish-Chandra projection of the ghost centre for basic classi...

Recall the setting at the end of the previous lecture: A is an abelian variety over a field F of characteristic zero, with dimension g > 0. Let L be a number field of degree 2g over Q “acting” on A; that is, we have an embedding L ↪→ End(A). The elements of L that actually act on A – i.e., O := L ⋂ End(A) – form an order in L. Since char(F ) = 0, the action of O on T0(A) (a g-dimensional F -vec...

A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a quotient space of an open subset of a vector space V by a quasitorus action and on investigation ...

We present a spoken dialogue system for navigating information (such as news articles), and which can engage in small talk. At the core is a partially observable Markov decision process (POMDP), which tracks user’s state and focus of attention. The input to the POMDP is provided by a spoken language understanding (SLU) component implemented with logistic regression (LR) and conditional random f...

Given a Hopf algebra H and an H-module algebra A it is often important to be able of extending the H-action from A to a localisation of A. In this paper we are going to discuss sufficient conditions to extend Hopf actions as well as to characterise those localisations where the action can be extended. Our particular interest lies in the maximal ring of quotients of A.

in this paper we introduce a generalization of m-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . we will use the structure of the radical of a module in  and get some suitable results about this class of modules. also the relation between injective hull in  and this kind of modules will be investigated in this article.   for a module  we show...

One of the more fruitful observations in recent years was the discovery [19] that the (normalized) character χμ of the integrable highest weight g-module L(μ) of a nontwisted Kac-Moody algebra g = X (1) r is a modular form. Thanks to the structure of the affine Weyl group, these χμ can be written as ratios of theta functions, so on them exists a natural action of SL2(Z). In fact, this action de...