We define Sobolev norms of arbitrary real order for a Banach representation $(\pi, E)$ Lie group, with regard to single differential operator $D=d\pi(R^2+\Delta)$. Here, $\Delta$ is Laplace element in the universal enveloping algebra, and $R>0$ depends explicitly on growth rate representation. In particular, we obtain spectral gap $D$ space smooth vectors $E$. The main tool novel factorization ...

Children and adolescents evaluated group inclusion and exclusion in the context of generic and group-specific norms involving morality and social conventions. Participants (N = 381), aged 9.5 and 13.5 years, judged an in-group member's decision to deviate from the norms of the group, whom to include, and whether their personal preference was the same as what they expected a group should do. Dev...

Let A be the automorphism group of the unit interval with its usual order relation, and let B be the embedding of the multiplicative group of positive real numbers into A given by exponentiation. Strict t-norms are in one-to-one correspondence with the right cosets of B in A: Here, we identify the normalizer N of B in A and give explicit formulas for the corresponding set of t-norms.

Two studies investigated the impact of group norms for maintaining consensus versus norms for critical thought on group decisions in a modification of the biased sampling paradigm (G. Stasser & W. Titus, 1985). Both studies showed that critical norms improved the quality of decisions, whereas consensus norms did not. This effect appeared to be mediated by the perceived value of shared and unsha...

Organizations have started to realize the economic value of virtual communities. Unfortunately, traditional management methods of control do not work on virtual communities. Often, group norms are the principal method of virtual community governance. However, it is not clear how group norms are formed in virtual communities, and how managers can shape norm evolution. This research in progress p...