Online communities are the gatherings of like-minded people, brought together in cyberspace by shared interests. The shared interest has hidden social capital aspects and can be of bridging or bonding type .Creating such communities is not a big challenge but sustaining member’s participation is. This study examines the formation and maintenance of social capital in social network sites. In add...

The venture capital industry is characterized by strong inter-organizational networks that have been shown to affect VC firm performance and the competitive supply of capital for entrepreneurs. We examine how VC firms’ observable resources are related to tie formation, and thus how networks facilitate the distribution and combination of resources across organizations. Unlike the social networks...

We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr’s inequality and present several norm inequalities. More precisely, let A be a C∗ -algebra, T be a locally compact Hausdorff space equipped with a Radon measure μ and let (At)t∈T be a continuous field of operators in A such that the function t → At is norm c...

is of Hausdorff dimension at most n− p, by a theorem of Federer-Ziemer [3]. And for functions of bounded variation, we have Hn−1 (Σ∗) = 0, see section 5.9 of [1] for more information on fine properties of BV functions. Hence our result concerning Σ, the Lebesgue set of u of the value zero makes sense because s > n− p. In order to show Theorem 1, we will need a Poincaré type inequality which wil...

The dot sign means inner product. If b is forced to be 0, the VC-dimension reduces to n. It is often the case that the VC-dimension is equal to the number of free parameters of a concept (for example, a rectangle’s parameters are its topmost, bottommost, leftmost and rightmost bounds, and its VC-dimension is 4). However, it is not always true; there exists concepts with 1 parameter but an infin...

Meteorological observing networks are nearly always irregularly distributed in space. This irregularity generally has an adverse impact on objective analysis and must be accounted for when designing an analysis scheme. Unfortunately, there has been no completely satisfactory measure of the degree of irregularity, which is of particular significance when designing artificial sampling networks fo...

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...

Abstract. In this note, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Hölder inequal...