Tracy-Widom distribution, Airy2 process and its sample path properties

Tracy-Widom distribution was rst discovered in the study of largest eigenvalues of high dimensional Gaussian unitary ensembles(GUE),and since then it has appeared in a number of apparently distinct research elds.It is believed that Tracy-Widom distribution have a universal feature like classic normal distribution.Airy2 process is de ned through nite dimensional distributions with Tracy-Widom distribution as its marginal distributions.In this introductory survey,we will briey review some basic notions,intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process.For sake of reading,the paper starts with some simple and well-known facts about normal distributions,Gaussian processes and their sample path properties.

Dimension Properties of Sample Paths of Self-Similar Processes

The Hansdorff dimensions of the image and the graph of random fields are given under general conditions.The results can be used to a wider class of self-similar random fields and processes,including Brownian motion,Brownian sheet,fractional Brownian motion,processes with stable or(α,β)-fractional stable components.

Region stepwise reconstruction method based on two source–detector-separation groups for reconstructing background optical properties of two-layered slab sample

The accuracy of the background optical properties has a considerable effect on the quality of reconstructed images in near-infrared functional brain imaging based on continuous wave diffuse optical tomography（CW-DOT）. We propose a region stepwise reconstruction method in CW-DOT scheme for reconstructing the background absorption and reduced scattering coefficients of the two-layered slab sample with the known geometric information. According to the relation between the thickness of the top layer and source– detector separation, the conventional measurement data are divided into two groups and are employed to reconstruct the top and bottom background optical properties, respectively. The numerical simulation results demonstrate that the proposed method can reconstruct the background optical properties of two-layered slab sample effectively. The region-of-interest reconstruction results are better than those of the conventional simultaneous reconstruction method.

A facile and green synthetic approach toward fabrication of starch-stabilized magnetite nanoparticles

A facile and green synthetic approach for fabrication of starch-stabilized magnetite nanoparticles was implemented at moderate temperature. This synthesis involved the use of iron salts, potato starch,sodium hydroxide and deionized water as iron precursors, stabilizer, reducing agent and solvent respectively. The nanoparticles（NPs） were characterized by UV-vis, PXRD, HR-TEM, FESEM, EDX, VSM and FT-IR spectroscopy. The ultrasonic assisted co-precipitation technique provides well formation of highly distributed starch/Fe3O4-NPs. Based on UV–vis analysis, the sample showed the characteristic of surface plasmon resonance in the presence of Fe3O4-NPs. The PXRD pattern depicted the characteristic of the cubic lattice structure of Fe3O4-NPs. HR-TEM analysis showed the good dispersion of NPs with a mean diameter and standard deviation of 10.68 4.207 nm. The d spacing measured from the lattice images were found to be around 0.30 nm and 0.52 nm attributed to the Fe3O4 and starch, respectively. FESEM analysis confirmed the formation of spherical starch/Fe3O4-NPs with the emission of elements of C, O and Fe by EDX analysis. The magnetic properties illustrated by VSM analysis indicated that the as synthesized sample has a saturation magnetization and coercivity of 5.30 emu/g and 22.898 G respectively.Additionally, the FTIR analysis confirmed the binding of starch with Fe3O4-NPs. This method was cost effective, facile and eco-friendly alternative for preparation of NPs.