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

Scattering and transport statistics at criticality

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.Comment: 10 pages, 11 figure

On the generalized dimensions of multifractal eigenstates

Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, $D_q$ and $D_{q'}$, of the eigenstates of critical random matrix ensembles: $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q, q' \le 2$. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to $q<1/2$ but also to deterministic models producing multifractal eigenstates and to generic multifractal structures. We also demonstrate, for the scattering version of the power-law banded random matrix model at criticality, that the scaling exponents $\sigma_q$ of the inverse moments of Wigner delay times, \bra \tau_{\tbox W}^{-q} \ket \propto N^{-\sigma_q} where $N$ is the linear size of the system, are related to the level compressibility $\chi$ as $\sigma_q\approx q(1-\chi)[1+q\chi]^{-1}$ for a limited range of $q$; thus providing a way to probe level correlations by means of scattering experiments.Comment: 12 pages, 15 figures. Minor corrections made. arXiv admin note: text overlap with arXiv:1201.635

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

Simulation Studies of Nanomagnet-Based Architecture

We report a simulation study on interacting ensembles of Co nanomagnets that can perform basic logic operations and propagate logic signals, where the state variable is the magnetization direction. Dipole field coupling between individual nanomagnets drives the logic functionality of the ensemble and coordinated arrangements of the nanomagnets allow for the logic signal to propagate in a predictable way. Problems with the integrity of the logic signal arising from instabilities in the constituent magnetizations are solved by introducing a biaxial anisotropy term to the Gibbs magnetic free energy of each nanomagnet. The enhanced stability allows for more complex components of a logic architecture capable of random combinatorial logic, including horizontal wires, vertical wires, junctions, fanout nodes, and a novel universal logic gate. Our simulations define the focus of scaling trends in nanomagnet-based logic and provide estimates of the energy dissipation and time per nanomagnet reversal

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