THERMAL DECOMPOSITIONS OF SOME BIOINORGANIC COMPLEXES OF EUROPIUM

Thermogravimetric and derivative thermogravimetric investigations for three kinds of bioinorganic complexes of europium with N-acetyl-DL-alanine, N-acetyl-DL-valine and DL-alanyl-DL-alanine have been performed. It was found that the water molecules in these solid state complexes are not directly coordinated to the europium ion and that there may be three or four steps in the thermal decomposition process of these complexes after dehydration. The possible thermal decomposition reactions of these bioinorganic complexes have been suggested and discussed.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

New techniques for enhanced medial axis based decompositions in 2-D

New techniques are presented for using the medial axis to generate high quality decompositions for generating block-structured meshes with well-placed mesh singularities away from the surface boundaries. Established medial axis based meshing algorithms are highly effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometry concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Methods for directly constructing the corresponding decompositions are also put forward.

THE SYNTHESIS OF BRIDGED-RING CARBOCYCLES AND HETEROCYCLES VIA PALLADIUM CATALYZED REGIOSPECIFIC CYCLIZATION REACTIONS

A catalyst system comprising 10 mol % (Pd(OAc) and 20 mol % PPh3 effects the cyclisation of aryl halides onto proximate alkenes via 5-, 6-, and 7-exo-trig, and 7-endo-trig processes giving a variety of bridged-ring carbo- and hetero-cycles in excellent yield. Double bond isomerisation in the product is rarely encountered and may be suppressed by the addition of Tl(1) salts. One example of diastereospecific bis-cyclisation is given and the crystal structure of 1-aza-2-sulphonyl-3,4-benzobicyclo[3.2.1]nona-6-ene is reported.