We define the orthogonal sum of quadratic pairs and we show that there is no Witt cancellation theorem for this operation in characteristic 2. 1. Introduction. Quadratic pairs on central simple algebras were defined in [5]. They play the same role for quadratic forms as involutions for symmetric or skew-symmetric bilinear forms. In particular, they can be used to define twisted orthogonal group...

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extended abstract 1. introduction the concept of social capital is one of the most important concepts during two decades in various fields, especially in the field of organization. social capital means links and communication among members of a network, providing essential social support and energy to facilitate actions through creating norms and mutual trust. some scholars of social and behavi...

Sadamori Kojaku1, 2 and Naoki Masuda2, ∗ 1CREST, JST, Kawaguchi Center Building, 4-1-8, Honcho, Kawaguchi-shi, Saitama 332-0012, Japan 2Department of Engineering Mathematics, Merchant Venturers Building, University of Bristol, Woodland Road, Clifton, Bristol, BS8 1UB, United Kingdom Abstract Many empirical networks have community structure, with which nodes are densely interconnected within eac...