A reparametrization of Triangular Distribution based on the Skew-Symmetric Distributions

In this paper a new approach is considered for studying the triangular distribution using the theoretical development behind Skew distributions. Triangular distribution are obtained by a reparametrization of usual triangular distribution. Main probabilistic properties of the distribution are studied, including moments, asymmetry and kurtosis coefficients, and an stochastic representation, which provides a simple and efficient method for generating random variables. Moments estimation is also implemented. Finally, a simulation study is conducted to illustrate the behavior of the estimation approach proposed.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

Triangular ruthenium acetate clusters containing the bis(pyridyl)propane ligand and their inclusion chemistry with beta-cyclodextrin

The triruthenium carboxylate cluster [Ru(3)O(OAc)(6)(py)(2)(bpp)](+) (OAc = acetate) containing the bridging 1,3-bis(4-pyridyl)propane (bpp) ligand, and its dimeric species [{Ru(3)O(OAc)(6)(py(2))}(2)(mu-bpp)](2+) were synthesized in order to investigate their inclusion compounds with beta-cyclodextrin (beta-CD). Characterization of the complexes was carried out based on spectroscopic, electrochemical and spectroelectrochemical techniques, while the formation of inclusion complexes was evaluated using (1)H NMR/NOESY spectroscopy. Since bpp is a flexible ligand, a DFT study was carried out in order to characterize its conformational isomers and their possible role in the host-guest chemistry with beta-CD. Instead of observing the formation of inclusion compounds with different stoichiometries, we observed the formation of 1:1 bpp/beta-CD compounds in which the bpp ligand assumes different conformations. The assembly of polymetallic rotaxane species was successfully demonstrated by monitoring the (1)H NMR spectra of the monomeric cluster species in the presence of aquapentacyanoferrate(II) ions and beta-CD.