SIMPLE ENTRAPMENT OF ALCALASE IN DIFFERENT SILICA XEROGELS USING THE TWO STEPS SOL-GEL METHOD

The present study has focused on the entrapment of Alcalase in different xerogels obtained by using various molar ratios of methyltriethoxysilane, dimethyldietoxisilane and tetraethoxysilane. Silica and their derivatives were characterized with regard to specific surface area (nitrogen adsorbtion), chemical composition (Fourier transform infrared spectroscopy (FT-IR)), weight loss upon heating (thermogravimetric analysis (TGA)) and catalytic activity

Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

Analytic solutions of the Madelung equation

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.Comment: 10 pages, 3 figure

Random Matrix Filtering in Portfolio Optimization

We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may be misleading. In this paper we investigate a recently introduced filtering procedure, and demonstrate the applicability of this method in a controlled, simulation environment.Comment: 9 pages with 3 EPS figure