Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Paradigm shift: a case study of transnational collaboration for a high-profile design competition in Shanghai, China

This conference is organised in conjunction with the Design and Construction Management Students Day and Competition (Organised in collaboration with BuHU, CIB TG53 and CIB W104), Design and Construction Management Industry Day (Organised in collaboration with BOSS RE&H students society)The topic of this paper centers on the paradigm shift in transnational design collaboration for high-profile design competitions which are fiercely contested in major Chinese cities. In view of the fact that most writings on design competitions prefer some successful stories rather than the equally instructive ones telling why others fail, this paper will look at the issues from a different perspective by providing an unusual case of collaboration. The intention is to offer some original insights into understanding the emerging situation which probably constitutes one of the future trends in design competitions. By reviewing the current performance of design competitions which greatly influence the development of collaboration paradigm, this paper investigates a collaboration case with an emerging form, a controversial process and mixed outcomes. Questionnaire survey and case study are used in this study. Despite a single case investigation, there are strong reasons to believe that it serves as a precursor of a major shift over the coming decades in the evolution of transnational collaboration in high-profile design competitions in China.postprintThe International Conference on Changing Roles, New Roles; New Challenge, Rotterdam, The Netherlands, 5-9 October 2009. In CRO9 International Conference on Changing Roles, New Roles; New Challenges, 2009, p. 131-14