Quantum Groups by Ore Extensions Associated withGroup Algebras

As a continuation of the work of Beattie on quantum groups constructed byOre extensions, in this paper, we characterize their centre and discuss the category ofquantum Yang-Baxter modules over them. In addition, we determine all finite dimen-sional irreducible representations over these quantum groups.

Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel

Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing and deeoherence. We investigate average photon number, photon statistics distributions for this mixed state.

A Novel Customer-Oriented Recommendation System for Paid Knowledge Products

With the rapid development of knowledge pal malto:wangliye@cuc.edu.cn with a large number of knowledge products when purchasing,leading to the need for an effective recommendation system.However,existing recommendation systems cannot accurately and adequately represent paid knowledge products with implicit but specialized features and sparse interactive histories,and thus are deemed not suitable for such products.In this paper,we propose a novel recommendation system for knowledge products,the core of which is the designed customer oriented representation of knowledge products.Specifically,we utilize customer activity information on the free knowledge sharing platform as the knowl-edge document for each customer of paid knowledge products,to extract customer knowledge background and preference.Then,a deep learning based model Doc2vec is adopted to transfer knowledge documents to customer knowledge background vectors.Such vectors of a particular paid knowledge product are further aggregated to a product-level vector for customer-oriented product representation,based on which two recommendation results are generated with product ratings and similarities of paid knowledge prod-ucts,respectively.Extensive comparative experiments are conducted to demonstrate the ffectiveness of the proposed system for the representation and recommendation of paid knowledge products.This paper will contribute to the literature of knowledge payment and recommendation systems,as well as provide practical implications for the information service and the operation of knowledge products on knowledge payment platforms.

On tempered and square integrable representations of classical p-adic groups

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.