For an absolutely continuous probability measure on Rd and a nonnegative integer k, let ~ sk( ;0) denote the probability that the convex hull of k + d + 1 random points which are i.i.d. according to contains the origin 0. For d and k given, we determine a tight upper bound on ~ sk( ;0), and we characterize the measures in Rd which attain this bound. As we will see, this result can be considered...

A b-coloring of a graph G by k colors is a proper k-coloring of G such that in each color class there exists a vertex having neighbors in all the other k− 1 color classes. The b-chromatic number of a graph G, denoted by φ(G), is the maximum k for which G has a b-coloring by k colors. It is obvious that χ(G) ≤ φ(G). A graph G is b-continuous if for every k between χ(G) and φ(G) there is a b-colo...

The first point here is that convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex topological vectorspace have continuous extensions to the whole space. Proofs are for real vectorspaces. The complex versions are corollaries. A crucial corollary is that on locally convex topological vectorspaces continuous linear functionals s...

Pancreatic beta cells exhibit oscillations in electrical activity, cytoplasmic free Ca2+ concentration ([Ca2+](i)), and insulin release upon glucose stimulation. The mechanism by which these oscillations are generated is not known. Here we demonstrate fluctuations in the activity of the ATP-dependent K+ channels (K(ATP) channels) in single beta cells subject to glucose stimulation or to stimula...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Continuous K nearest neighbor queries (C-KNN) on moving objects retrieve the K nearest neighbors of all points along a query trajectory. In existing methods, the cost of retrieving the exact C-KNN data set is expensive, particularly in highly dynamic spatio-temporal applications. The cost includes the location updates of the moving objects when the velocities change over time and the number of ...

Forecasting the future states of a complex system is a complicated challenge that is encountered in many industrial applications covered in the community of Prognostics and Health Management (PHM). Practically, states can be either continuous or discrete: Continuous states generally represent the value of a signal while discrete states generally depict functioning modes reflecting the current d...

Pointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained which allow us to study the singularity of central measures. For example, we find the minimal integer k such that any continuous orbital measure convolved with itself k times belongs to L. We also prove that if k = rankG then μ ∈ L for all central, continuous measures μ. This ...

A family of compact spaces containing continuous images of Radon-Nikodým compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikodým compact K we prove: If K is totally disconnected, then it is Radon-Nikodým compact. If K is adequate, then it is even Eberl...

Given a closed (and non necessarily compact) basic semialgebraic set K ⊆ R, we solve the K-moment problem for continuous linear functionals. Namely, we introduce a weighted l1-norm lw on R[x], and show that the lw-closures of the preordering P and quadratic module Q (associated with the generators of K) is the cone Psd(K) of polynomials nonnegative on K. We also prove that P and Q solve the K-m...