There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in R with n ≥ 2. Besides many partial results, this conjecture has been only completely solved for n = 2. In this paper, we give a confirmed answer to this conjecture for n = 3. In order to prove this result, we e...

There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in R with n ≥ 2. Besides many partial results, this conjecture has been only completely solved for n = 2. In this paper, we give a confirmed answer to this conjecture for n = 3. In order to prove this result, we e...

Arenas et al. [1] introduced the notion of lambda-closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of lambda-locally closed sets, Lambda_lambda-closed sets and lambda_g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.

Abstract Augmented reality (AR) is a unique, hands-on tool to deliver information. However, its educational value has been mainly demonstrated empirically so far. In this paper, we present modeling approach provide users with mastery of skill, using AR learning content implement an curriculum. We illustrate the potential by applying important but pervasively misunderstood area STEM learning, el...

Skilling (2007) previously identified that the number of steps required to reach a given set is Poisson distributed. Huber and Schott suggest making this special case central, recasting all computations as finding the mass of a distribution on a set. Additional contributions are a theoretical analysis, two general ways of reducing problems to the required form and a link to annealing. The resul...