Absolute configuration determination of 2-(2-oxo-3-indolyl)acetamide derivatives

We describe a reliable method for determining the absolute configuration of 2-(2-oxo-3-indolyl)acetamides based on analysis of the ¹H NMR spectra of their phenylethylamide diastereomers. The conformational preferences for two diastereomeric amides were calculated by DFT, which matched well with the experimental results. X-ray diffraction analysis allowed us to validate the method.     

On the spectra of certain rooted trees

Let T be an unweighted tree with vertex root v which is the union of two trees T₁=(V₁,E₁), T₂=(V₂,E₂) such that V₁ ∩ V₂ = {v} and T₁ and T₂ have the property that the vertices in each of their levels have equal degree. We characterize completely the eigenvalues of the adjacency matrix and of the Laplacian matrix of T. They are the eigenvalues of symmetric tridiagonal matrices whose entries are given in terms of the vertex degrees. Moreover, we give some results about the multiplicity of the eigenvalues. Applications to some particular trees are developed.     

Spectra of generalized Bethe trees attached to a path

A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let P_m be a path of m vertices. Let {B_i:1?i?m} be a set of generalized Bethe trees. Let P_m{B_i:1?i?m} be the tree obtained from P_m and the trees B₁,B₂,…,B_m by identifying the root vertex of B_i with the i-th vertex of P_m. We give a complete characterization of the eigenvalues of the Laplacian and adjacency matrices of P_m{B_i:1?i?m}. In particular, we characterize their spectral radii and the algebraic conectivity. Moreover, we derive results concerning their multiplicities. Finally, we apply the results to the case B₁=B₂=…=B_m.     

Multielemental analysis of dried residue from metal-bearing waters by wavelength dispersive X-ray fluorescence spectrometry

The purpose of this work was evaluation of instrumental sensitivity and detection limits for determination of elemental composition (20 different elements ranging from Na to Pb) of liquid mining samples by using conventional Wavelength Dispersive X-Ray Fluorescence (WDXRF) instrumentation. Preconcentration of elements from liquid samples was performed by means of a simple dried residue process, and spectral evaluation was carried out by integration of the peak area (using WinQXAS/AXIL package software, International Atomic Energy Agency (IAEA)) instead of the common net peak line intensity traditionally used in conventional WDXRF systems. With the proposed methodology, the calculated detection limits were in the µg L^− 1 range (from 0.005 to 0.1 mg L^− 1 level depending on the element) in all cases, which is suitable for element determination in most liquid samples involved in environmental studies such as metal mining liquid effluents. The detection limits are also below the established limits of the TCLP 1311 (United States Environmental Protection Agency (US-EPA)) and DIN 38414-S4 (German Standard legislation) procedures, which are commonly used to evaluate the leaching of metals from landfill disposal.     

On certain curves of genus three in characteristic two

We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties. – Dedicated to the treasured memory of our coauthor, Paulo Henrique Viana     

Sulla caratterizzazione delle curve di diramazione dei piani tripli

Sunto Si studiano e si caratterizzano, dal punto di vista aritmetico e funzionale, le curve di diramazione dei piani tripli. Nel presente lavoro la suddetta caratterizzazione è limitata al caso dei piani tripli ottenuti per proiezione di una superficie di ordinen (≥3), sprovvista di curva multipla, da un suo punto multiplo secondon−3. Si dimostra l'unicità birazionale del piano triplo avente una data curva di diramazione e si dà l'equazione effettiva di un suo modello proiettivo. Giunto alla Redazione nel gennaio 1946.     

Well Posed Constraint-Preserving Boundary Conditions for the Linearized Einstein Equations

In this paper we address the problem of specifying boundary conditions for Einstein's equations when linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. The boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial-boundary value formulation. We consider the case of a manifold with a non-smooth boundary, as is the usual case of the cubic boxes commonly used in numerical relativity. The techniques discussed should be applicable to more general cases, as linearizations around more complicated backgrounds, and may be used to establish well posedness in the full non-linear case.     

A characterization of Hering's plane of order 27

Hering's translation plane of order 27 has been characterized by its order and the fact that it admits SL(2, 13) in its translation complement (see [1]). We show that, aside from the Desarguian plane and a Generalized, André plane, it is the only plane of order 27 which admits a subgroup of SL(2, 13) of order 13×12.Partially supported by FONDECYT 0343 and ANDES FOUNDATION.