A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general . 相似文献
A single-polarization filter comprising a gold-coated photonic crystal fiber based on surface plasmon resonance is designed and investigated. The pattern matching and coupled polarization characteristics analyzed by the full-vector finite element method (FEM) and losses at 1,540 nm are achieved to 1,016.01739 dB/cm (x-pol core mode) and 33.81917 dB/cm (y-pol core mode). The crosstalk (CT) value of the 1,540 nm band is ?853.12653 dB for fiber length and the bandwidth is 850 nm. The working wavelength of the filter ranges from 1,280 nm to 1,540 nm by varying the diameter of outer air holes (), the diameter of inner air holes (), the metal film thickness (t), as well as the liquid refractive index (n). 相似文献
JETP Letters - Relatively low crossover temperature suggests that chiral symmetry restoration in Quantum Chromodynamics may well be described within the low-energy effective theory. The shape of... 相似文献
Prostate cancer is a highly prevalent disease and ranks second among malignant neoplasms that affect men around the world, behind lung cancer alone. Trace elements are very important and are involved in many cellular processes. The X-ray microfluorescence technique is an advanced tool of high spatial resolution, sensitivity, multielemental analysis, and nondestructiveness for trace element study. This study aimed to investigate the elemental distribution in spheroids obtained through the following human prostate cell lines using synchrotron X-ray microfluorescence: tumor cell line androgen independent (DU145), tumor cell line androgen dependent (LNCaP), and normal cell line (RWPE-1). The measurements were performed with a standard geometry of 45° of incidence, excited by a white beam using a pixel of 25 μm and an acquisition time of 300 ms/pixel at the X-ray fluorescence beamline at the Synchrotron Light National Laboratory (Campinas, Brazil). The synchrotron X-ray microfluorescence results showed differences between groups in all elements analyzed and suggested that further studies should be performed to understand the relationship of these trace elements with the progression and development of the disease. 相似文献
The diffusive behavior of nanoparticles inside porous materials is attracting a lot of interest in the context of understanding, modeling, and optimization of many technical processes. A very powerful technique for characterizing the diffusive behavior of particles in free media is dynamic light scattering (DLS). The applicability of the method in porous media is considered, however, to be rather difficult due to the presence of multiple sources of scattering. In contrast to most of the previous approaches, the DLS method was applied without ensuring matching refractive indices of solvent and porous matrix in the present study. To test the capabilities of the method, the diffusion of spherical gold nanoparticles within the interconnected, periodic nanopores of inverse opals was analyzed. Despite the complexity of this system, which involves many interfaces and different refractive indices, a clear signal related to the motion of particles inside the porous media was obtained. As expected, the diffusive process inside the porous sample slowed down compared to the particle diffusion in free media. The obtained effective diffusion coefficients were found to be wave vector-dependent. They increased linearly with increasing spatial extension of the probed particle concentration fluctuations. On average, the slowing-down factor measured in this work agrees within combined uncertainties with literature data.
Copper oxide decorated multi‐walled carbon nanotube (MWCNT) modified glassy carbon electrode (GCE) was prepared for determination of isoniazid (INZ) in various matrices. The electrochemical behavior of INZ was tested with the aid of Cyclic Voltammetry (CV) and quantitative experiments were performed by using Linear Sweep Voltammetry (LSV). Morphological and structural characterization of the modified electrode was performed by utilizing Scanning Electron Microscopy (SEM), X‐Ray Photoelectron Spectroscopy (XPS) while electrochemical characterization was performed by using CV and Electrochemical Impedance spectroscopy (EIS). The proposed sensor exhibited well defined anodic peak at 0.30 V for INZ at pH 6.0 medium. Under the optimum conditions, a linear relation between INZ concentration and peak current was observed in the range of 2.0×10?7 to 5.0×10?5 M. Limit of detection was calculated as 1.0×10?8 M and repeatability and accuracy was found as 5.60 % and 91.0 % for 5.0 10?7 M INZ by using 3 successive measurement, respectively. Then, the analytic performance of the electrode developed was tested by analyzing commercial tablets, artificial human serum and urine samples. The results indicated that satisfactory recoveries was observed for all issue. 相似文献