Triangle in a brick

In this paper we shall investigate the following problem: Which is the largest regular triangle in a brick with volume 1 and having edge lengthes greater than $\frac{1}{\sqrt{2}}$? We prove that there are three optimal cases in all which the edge lengthes of the triangles are $\sqrt{2}$, respectively.Comment: 6 pages, 4 figure

Cosmological Brightness Distribution Fits of Gamma Ray Burst Sources

We discuss detailed fits of the BATSE and PVO gamma-ray burst peak-flux distributions with Friedman models taking into account possible density evolution and standard candle or power law luminosity functions. A chi-square analysis is used to estimate the goodness of the fits and we derive the significance level of limits on the density evolution and luminosity function parameters. Cosmological models provide a good fit over a range of parameter space which is physically reasonable.Comment: Ap.J. in press, uuencoded .ps file, 9 pages manuscript plus 5 figure

On the probability of hitting the boundary for Brownian motions on the SABR plane

Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models–related to the SABR model in mathematical finance–which can be obtained by geometry-preserving transformations, and show how to translate the properties of the hyperbolic Brownian motion (density, probability mass, drift) to each particular model. Our main result is an explicit expression for the probability of any of these models hitting the boundary of their domains, the proof of which relies on the properties of the aforementioned transformations as well as time-change methods

Strings in plane-fronted gravitational waves

Brinkmann's plane-fronted gravitational waves with parallel rays --~shortly pp-waves~-- are shown to provide, under suitable conditions, exact string vacua at all orders of the sigma-model perturbation expansion.Comment: 7 pages, no figure

Polyethylene imine-based receptor immobilization for label free bioassays

Polyethylene imine (PEI) based immobilization of antibodies is described and the concept is proved on the label free assay of C-Reactive Protein (CRP). This novel immobilization method is composed of a hyperbranched PEI layer which was deposited at a high pH (9.5) on the sensor surface. The free amino groups of PEI were derivatized with neutravidin by Biotin N-hydroxysuccinimide ester and the biotinylated anti-CRP antibody immobilized on this layer. Direct binding assay of recombinant CRP was successfully performed in the low μg/ml concentrations using a label free optical waveguide biosensor