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The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number and -positive maps
Positive maps which are not completely positive are used in quantum
information theory as witnesses for convex sets of states, in particular as
entanglement witnesses and more generally as witnesses for states having
Schmidt number not greater than k. It is known that such witnesses are related
to k-positive maps. In this article we propose a new proof for the
correspondence between vectors having Schmidt number k and k-positive maps
using Jamiolkowski's criterion for positivity of linear maps; to this aim, we
also investigate the precise notion of the term "Jamiolkowski isomorphism". As
consequences of our proof we get the Jamiolkowski criterion for complete
positivity, and we find a special case of a result by Choi, namely that
k-positivity implies complete positivity, if k is the dimension of the smaller
one of the Hilbert spaces on which the operators act.Comment: 9 page
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Cultural dimensions and CRM systems implementation: a preliminary framework
Customer Relationship Management Systems (CRM) in particular. Several researchers have suggested ways in which management can accommodate these dimensions or solve the problems they may pose. Ali& Alshawi (2005) have proposed a cultural dimensions framework for the management of CRM systems implementation in the multinational environment. In this paper the authors test that framework by conducting a qualitative comparative case study in a large multinational organization in two countries. The authors have investigated the implementation of CRM systems within the same organization in both Egypt and the UK. Using observation, document analysis and interviews, qualitative data has been elicited and used a Soft Systems Methodology (SSM) analysis to determine themes for each case study. The authors have used the Structurational analysis by Walsham (2002) which based on the concepts of Structuration Theory by Giddens(1979,1984 ), to propose their explanations of these themes and drag from this analysis the cultural dimensions which may have impact on CRM systems Implementation. The authors have concluded by proposing an updated framework of cultural dimensions for management of CRM systems within multinational environment organizations
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