Let X and Y be independent 2-dimensional Brownian motions, X(0) = (0, 0), Y (0) = (ε, 0), and let p(ε) = P (X[0, 1] ∩ Y [0, 1] = ∅), q(ε) = {Y [0, 1] does not contain a closed loop around 0}. Asymptotic estimates (when ε → 0) of p(ε), q(ε), and some related probabilities, are given. Let F be the boundary of the unbounded connected component of R2\Z[0, 1], where Z(t) = X(t) − tX(1) for t ∈ [0, 1...

It is a well-known principle, for finite-dimensional systems, that applying sampled-and-hold in the feedback loop around a stabilizing state feedback (or dynamic) controller results in a stable sampled-data feedback control system if the sampling period is small enough. The principle extends to infinite-dimensional systems with compact state feedback if either the input operator is bounded or t...

When the saddle-center bifurcation occurs in an analytic family of area-preserving maps, rst a parabolic xed point appears at the origin and then this point bi-furcates, creating an elliptic xed point and a hyperbolic one. Separatrices of the hyperbolic xed point form a small loop around the elliptic point. In general the sep-aratrices intersect transversely and the splitting is exponentially s...

If a host is located behind a NAT, then in certain situations it can be impossible for that host to communicate directly with other hosts (peers). In these situations, it is necessary for the host to use the services of an intermediate node that acts as a communication relay. This specification defines a protocol, called TURN (Traversal Using Relays around NAT), that allows the host to control ...

In order to understand the reasons that lead individuals to practice physical activity, researchers developed the Motives for Physical Activity Measure-Revised (MPAM-R) scale. In 2010, a translation of MPAM-R to Portuguese and its validation was performed. However, psychometric measures were not acceptable. In addition, factor scores in some sports psychology scales are calculated by the mean o...

Local time processes parameterized by a circle, de ned by the occupation density up to time T of Brownian motion with constant drift on the circle, are studied for various random times T . While such processes are typically non-Markovian, their Laplace functionals are expressed by series formulae related to similar formulae for the Markovian local time processes subject to the Ray-Knight theore...