An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy)−1 = x−1y−1 holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if and only if every element of Q has order a power of p. The loop Q decomposes as a direct product of a loop of odd order and a loop of order a ...

We show that the number of halving sets of a set of n points in R is O ( n ) , improving the previous bound of [9] with a simpler (albeit similar) proof.

In this paper a testbed for development and verification of hybrid localization systems is presented. It allows for systematic analysis of hybrid localization methods and speed up the development of new schemes. The proposed testbed platform is composed of subsystem for sequential data collection and testing infrastructure that can be used for investigating the localization mechanisms in contro...

We show, with an elementary proof, that the number of halving simplices in a set of n points in R4 in general position is O(n4−2/45). This improves the previous bound of O(n4−1/13 4 ). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.

We consider the following searching game: there are two players, say Questioner and Responder. Responder chooses a number x ∈ Sn = {1, 2, . . . , n}, Questioner has to find out the number x by asking bi-interval queries and Responder is allowed to lie at most two times throughout the game. The minimal number q(n) of bi-interval queries sufficient to find the unknown integer x is determined for ...

A. For f > g ∈ ω let c∀f ,g be the minimal number of uniform trees with g-splitting needed to ∀-cover the uniform tree with f -splitting. c∃f ,g is the dual notion for the ∃ cover. Assuming CH and given א1 many (sufficiently different) pairs ( f2 , g2 ) and cardinals κ2 such that κ0 2 = κ2 , we construct a partial order forcing that c∃f2 ,g2 = c ∀ f2 ,g2 = κ2 . For this, we introduce a c...

We propose to explain the recent observations of GRB early X-ray afterglows with SWIFT by the dissipation of energy in the reverse shock which crosses the ejecta as it is decelerated by the burst environment. We compute the evolution of the dissipated power and discuss the possibility that a fraction of it can be radiated in the X-ray range. We show that this reverse shock contribution behaves ...

Here we shall introduce the concept of harmonic balls in subdomains of Rn, through a mean value property for a sub-class of harmonic functions on such domains. In the complex plane, and for analytic functions, a similar concept fails to exist due to the fact that analytic functions can not have prescribed data on the boundary. Nevertheless, a two-phase version of the problem does exists, and gi...

The field distribution, dielectric constant, and loss in a two-phase composite, in which phase A is distributed inside a square matrix of phase B, have been calculated using the finite-element method ~FEM!. The calculation was carried out by taking into account different shapes for phase A, such as circles, triangles, and rings with different sizes. The modeling by FEM in the dielectric composi...