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Hierarchical Principal Component Analysis (HPCA) is a multiblock method which is designed to reveal covariant patterns between and within several multivariate datasets. The computation of the parameters of this method, namely block scores, block loadings, global loadings and global scores, is based on an iterative procedure. However, very few properties are known regarding the convergence of this iterative procedure. The paper discloses a monotony property of HPCA and exhibits an optimization criterion for which HPCA algorithm provides a monotonic convergent solution. This makes it possible to shed a new light on this method of analysis by showing new properties and pinpointing its relation to existing methods such as Common Component and Specific weights Analysis (CCSWA), INDSCAL and PARAFAC Models. Copyright (C) 2010 John Wiley & Sons, Ltd.

Three pyrazole-3-carboxylic acid (H(2)pca) complexes, Cr(Hpca)(3)center dot 2H(2)O (1), Ni-2(pca)(2)(H2O)(6)center dot 2H(2)O (2) and [Pb-2(Hpca)(4)](n) (3), have been synthesized and fully characterized. The single crystal X-ray diffraction indicate that the mononuclear Cr(III) cation in complex 1 and binuclear Ni(II) cations in complex 2 are coordinated by pyrazole-3-carboxylic acid ligands and water molecules in a distorted octahedral geometry and the binuclear Pb(II) cations in complex 3 presents a distorted seven-coordinated {PbN2O5} pentagonal-bipyramid geometry. Notably, these complexes as effective heterogeneous catalysts show efficient catalytic activities for Knoevenagel condensation (yield up to 97%) and the catalyst can be recycled without losing activity. (C) 2017 Published by Elsevier B.V.