This note answers one question in [1], concerning the connected allocation for the Poisson process in R. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to the halfplane. A picture of a numerically simulated example is included. 1 The problem Let X ⊂ R be a discrete set. We call the elements of X centers, the eleme...

Absfract: Let EN, be the expected number of extreme points among n i.i.d. points with a common radially symmetric distribution in the plane. We show that for any monotone sequence wn t co and for every e z 0, there exists a radially symmetric distribution for which EN,, 2 n/w,, infinitely often and EN, d 4+ E infinitely often. In addition, there exists a unimodal radially symmetric density such...

We associate to any object in the nilpotent module category of an algebra with the 2-Calabi-Yau property a character (in the sense of [11]) and prove a multiplication formula for the characters. This formula extends a multiplication formula for the evaluation forms (in particular, dual semicanonical basis) associated to modules over a preprojective algebra given by Geiss, Leclerc and Schröer [6...

The so-called first selection lemma states the following: given any set P of n points in R, there exists a point in R contained in at least cdn − O(n) simplices spanned by P , where the constant cd depends on d. We present improved bounds on the first selection lemma in R. In particular, we prove that c3 ≥ 0.00227, improving the previous best result of c3 ≥ 0.00162 by Wagner [Wag03]. This makes...

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for each pair of (not necessarily distinct) points on the circle. By putting restrictions on these points we obtain various Frobenius subcategories. The main pur...

a m i t r a z, a n i ns e c t i c i d e /a ca ri c i de of the f o r m a m i d i n e p e st i c i d e s group, is a ? 2 a d r e n e r g i c ag on i st a nd of t he a m i d i ne c h e m i ca l f a m il y generally us e d to c o n t r ol animal e c top a r a s i t e s. poisoning due to am i t r a z i s r a r e and characterized by c e nt r a l n e r v ous s y st e m a nd r e sp ir a to r y d e p ...

In this paper we consider vector fields in R that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e and e−) and their invariant manifolds: one of dimension 2 (a sphere minus the points e and e−) and one of dimension 1 (the open diameter of the sphere having endpoints e and e−). In particular, we analyze the dynamics of t...

The present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter −R ≤ r ≤ R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectra...

In this note we introduce the concept of a lacunary statistical cluster ( l.s.c.) point and prove some of its properties in finite dimensional Banach spaces. We develop the method suggested by S. Pehlivan and M.A. Mamedov [20] where it was proved that under some conditions optimal paths have the same unique stationary limit point and stationary cluster point. We also show that the set Γx of l.s...

If there is a Sidon subset of the integers Z which has a member of Z as a cluster point in the Bohr compactification of Z, then there is a Sidon subset of Z which is dense in the Bohr compactification. A weaker result holds for quasiindependent and dissociate subsets of Z. It is a long standing open problem whether Sidon subsets of Z can be dense in the Bohr compactification of Z ([LR]). Yitzha...