Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values.     

Distribution of some major and trace elements in Danube Delta lacustrine sediments and soil

Sediment cores collected from lakes Mesteru and Furtuna (eastern part), Sontea channel and soil samples collected from Caraorman bar, all located in the Danube Delta, were analyzed for 42 elements (Ag, Al, As, Be, Na, Mg, P, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, As, Se, Br, Rb, Sr, Y, Mo, Ag, Cd, In, Sn, Sb, Cs, Ce, Hf, Hg, Tl. Pb, Bi, Th. U) by instrumental neutron activation analysis (INAA), thick target proton induced X-ray emission (TT-PIXE) and inductively coupled plasma-mass spectrometry (ICP-MS). The INAA and TTPIXE yielded total concentrations whereas the ICP-MS data reflected the fractions soluble in 14M HNO₃. The ICP-MS data exhibited surface enrichment relative to the lower part of the sediment core of Cu, Zn, As, Ag, Cd, In, Sn, Sb, Hg, Tl, Pb, and Bi, most prominently by Cd and Hg. Their vertical distribution in the investigated cores generally reflected the pollution history of recent sediments in Danube delta, showing a steady increase until the end of the 1980s followed by a slow decrease after 1990. The vertical profiles of most remaining elements were characterized by a relatively uniform distribution along the cores. In some cases, the concentrations of As, Cd, Cu, Cr, Mn, Ni and Pb exceeded minimum thresholds of safety, as defined by the Romanian regulations. The elemental composition of the sediment below 20 cm depth (total concentrations) was similar to that of the upper continental crust (UCC) for most elements. Values distinctly higher than UCC were observed for As, Sb (factor ~5) and Cr, Ni, Cu (factor 2 to 3). The nitric acid soluble element concentrations in the soil samples in some cases showed increased values at the surface as compared to 30 cm depth, either due to air pollution or to the action of plants. In no case a large contribution to the topsoil from atmospheric deposition was evident, indicating that the surface contamination of the sediments was mainly by riverine transport. This revised version was published online in July 2006 with corrections to the Cover Date.     

Acid properties of semicrystalline zeolitic mesoporous UL-ZSM-5 materials

UL-ZSM-5 materials have been prepared by templated solid-state crystallization of zeolites starting from the amorphous mesostructured aluminosilicate Al-Meso. Microcalorimetry and FTIR have been employed to characterize their surface acidity. In good agreement with ²⁷Al MAS NMR data, UL-ZSM-5 displayed an improved density and strength of Brönsted acid sites, as compared to Al-Meso, owing to the incorporation of aluminium in a tetrahedral environment similar to that of zeolite ZSM-5. Moreover, they showed an enhanced Brönsted/Lewis relative acid ratio. However, Al-Meso showed the highest concentration of strong Lewis acid sites due to its largest amount of aluminium in extraframework positions.     

Calorimetric determination of the acidic character of amorphous and crystalline aluminosilicates

Aluminosilicates can present different structures such as crystalline true zeolite molecular sieves or amorphous silica–aluminas. With a large surface area available, both can be involved as catalysts, adsorbents or catalyst supports, and the determination of their surface acidic properties is an important parameter in the study of such materials.

The number, strength and strength distribution of the acidic sites were determined using microcalorimetry linked to a volumetric line. Ammonia was used as a basic probe molecule. The adsorption temperatures ranged from 353 K up to 473 K. The samples consisted of two amorphous silica–aluminas (Si/Al ≈ 6.5) and three microporous zeolites H-β, H-ZSM-5 and H-MCM-22 with similar Si/Al ratios (Si/Al ≈ 13).

The differential heats of ammonia adsorption versus coverage and the corresponding isotherms are given. The H-ZSM-5, H-MCM-22, H-β samples display a plateau of constant adsorption heats near 150 kJ mol⁻¹, while the silica–alumina samples present continuously decreasing heats from 150 kJ mol⁻¹ at zero coverage to 40 kJ mol⁻¹ at high coverage, due to their surface heterogeneity. For amorphous silica–aluminas, the number of acid sites is dependent of the aluminum distribution at the surface.

The differences observed in the adsorption behavior of ammonia over the three zeolites arise from differences in their morphology, i.e. the total free volumes, pore geometries and electric field gradients at the adsorption sites. The adsorption isosteres have also been calculated from the adsorption isotherms, and the isosteric heats of adsorption have been compared with the heats measured by calorimetry.     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Chemoenzymatic synthesis of highly enantiomerically enriched secondary alcohols with a thiazolic core

Stereoselective preparative enzymatic acylation and hydrolysis/methanolysis of various C-substituted rac-thiazol-2-yl-methanols were achieved for the preparation of enantiopure or enantiomerically enriched, naturally occurring 2-hydroxymethylthiazoles. The absolute configurations of the resulting secondary alcohols were determined by a detailed ¹H NMR study of Mosher’s derivatives.     

Bioactive Polymers. XXVI. Immobilization of Pepsin on Biozan R

Pepsin was immobilized on BIOZAN R (Hercules) with dicyclohexylcarbodiimide as activator. The reaction product obtained has a protein content of 35–110 mg/g of polymer and a proteolytic activity between 20.85–28.75 μmol tyrosine/L·min·g of polymer). The coupling reaction rate is maximum under the following conditions: pepsin/BIOZAN R ratio = 0.52 g/g, DCCI/BIOZAN R ratio = 0.2 g/g, pH = 3.4, reaction time = 4 h.     

Gold internal standard correction for elemental imaging of soft tissue sections by LA-ICP-MS: element distribution in eye microstructures

Laser ablation coupled to inductively coupled plasma mass spectrometry has been developed for the elemental imaging of Mg, Fe and Cu distribution in histological tissue sections of fixed eyes, embedded in paraffin, from human donors (cadavers). This work presents the development of a novel internal standard correction methodology based on the deposition of a homogeneous thin gold film on the tissue surface and the use of the ¹⁹⁷Au⁺ signal as internal standard. Sample preparation (tissue section thickness) and laser conditions were carefully optimized, and internal normalisation using ¹⁹⁷Au⁺ was compared with ¹³C⁺ correction for imaging applications. ²⁴Mg⁺, ⁵⁶Fe⁺ and ⁶³Cu⁺ distributions were investigated in histological sections of the anterior segment of the eye (including the iris, ciliary body, cornea and trabecular meshwork) and were shown to be heterogeneously distributed along those tissue structures. Reproducibility was assessed by imaging different human eye sections from the same donor and from ten different eyes from adult normal donors, which showed that similar spatial maps were obtained and therefore demonstrate the analytical potential of using ¹⁹⁷Au⁺ as internal standard. The proposed analytical approach could offer a robust tool with great practical interest for clinical studies, e.g. to investigate trace element distribution of metals and their alterations in ocular diseases.