Synthesis and Structure of K[Cd(O2N‐C6H4‐NNN‐C6H4‐NO2)3], an Anionic 1, 3‐Bis(4‐nitrophenyl)triazenido Complex of Cadmium

The reaction of cadmium acetate in methanol with 1, 3‐bis(4‐nitrophenyl)triazene in THF in the presence of KOH yields K[Cd(O₂NC₆H₄NNNC₆H₄NO₂)₃] in form of hexagonal prismatic, red crystals with the trigonal space group R3¯ and a = 12.229(2), c = 48.988(10) Å and Z = 6. In the anionic cadmium complexes, which are located along the threefold axis, the Cd atoms are coordinated in a trigonal prismatic arrangement by the atoms N(1) and N(3) of three triazenido ligands. The potassium cations are coordinated icosahedrally by oxygen atoms of each one nitro group of six neighbouring anionic complexes. The Cd‐N distances are 2.376(4) and 2.350(4) Å, and the K‐O distances are in the range of 2.833(6) to 3.365(6) Å.     

Index abstracts

Abstract List

Index abstracts     

Rigidity Theorems for Manifolds with Boundary and Nonnegative Ricci Curvature

In this paper, we obtain some rigidity theorems for compact Riemannian manifolds Ω with boundary M and nonnegative Ricci curvature; for instance, we prove that the existence of certain functions on M together with a lower bound c > 0 on the principal curvtures of M imply that Ω is an euclidean ball of radius $ {1\over c} $ .     

One‐pot Preparation,Spectroscopic and Structural Characterization of Mercury(II) Complexes of Bulky Diimines with Halides and Pseudohalides

The preparation and characterization of two novel HgCl₂ and Hg(SCN)₂ complexes with bis[N‐(2‐tert‐butylphenyl)imine]acenaphthene is here described. One‐pot reaction techniques were used, leading to high yields of 75 % and 81 %, respectively. The complexes were characterized by microanalysis, i.r. and ¹HNMR spectroscopy, and by single crystal X‐ray diffraction. The structures of the complexes present similar characteristics, the most outstanding being the formation of dimers via intermolecular interaction. Whereas the HgCl₂ complex shows a unidimensional network due to strong π–π interactions, its Hg(SCN)₂ counterpart displays a supramolecular arrangement resulting from non classical hydrogen bond formation.     

Multivalent Complex Salts of Copper: Synthesis and X‐Ray Structural Analysis of [CuII(en)3][CuI4{(NNNPh)2C6H4}3] (en = ethylendiamine), an anionic Tris‐1,3‐bis(phenyltriazenide)benzene Complex of Tetrakis‐Copper(I)

An ethanolic solution of CuCl / ethylendiamine reacts with 1.3‐bis‐ (phenyltriazene)benzene in THF leading to the deprotonation of the bis triazene ligand to give orange crystals of [Cu^II(en)₃][Cu^I₄{(NNN‐Ph)₂C₆H₄}₃], an example of a rare complex salt of copper with mixed valence states. In the anion complex [Cu^I₄{(NNNPh)₂C₆H₄}₃]^2? the copper(I) ions are disposed linearly as single, bridged pairs in the two extremes of an axis, each of them presenting a trigonal bipyramidal alike coordination arrangement.     

Polymeric bidimensional self-assembling of [Hg(RC6H4NNNC6H4R)2Py] (R = m-acetyl) through metal-η,η-arene π-interactions and non classical C-H?O bonding: Synthesis and X-ray characterization of a bis diaryl symmetric-substituted triazenide complex of Hg(II)

Deprotonated 1,3-bis(3-acetylphenyl)triazene reacts with Hg(CH₃COO)₂ and pyridine to give light-yellow crystals of {[Hg^II(RC₆H₄NNNC₆H₄R)₂Py]}_n (R = acetyl). The tectons [Hg^II(RC₆H₄NNNC₆H₄R)₂Py] [R = CH₃C(O)] are linked to pairs as centrosymmetric dimers through reciprocal metal-η²-arene π-interactions. The dimeric units are operated by a screw axis 2₁ parallel to the crystallographic direction [0 1 0], also through a reflection-translation plane parallel to the c-axis, resulting a supramolecular bidimensional (2D) assembling of the dimeric tectons through non classical C-H?(O)CCH₃ bonding.     

Operatori estremanti e problemi ai limiti

Suuto Si studiano particolari operatori differenziali del secondo ordine con proprietà massimali e si impiegano per riottenere con un procedimento costruttivo la dimostrazione del teorema di esistenza e unicità degli autovalori per un problema ai límiti.

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Summary A particular kind of second order differential operators with maximal properties is studied, and used to obtain constructively the proof of the existence and uniqueness theorem for eigenvalues of a boundary problem.

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Lavoro eseguito nell'ambito dell'attività del Gruppo di Ricerca N. 23. del Comitato per la Matematica del CNR.     

On the compactness of constant mean curvature hypersurfaces with finite total curvature

In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature c ￡ 0c\leq 0. If M has finite total curvature and |H|² > -c|H|^2>-c, we prove that M must be compact.     

Eigenvalue estimate on complete noncompact Riemannian manifolds and applications

We obtain some sharp estimates on the first eigenvalues of complete noncompact Riemannian manifolds under assumptions of volume growth. Using these estimates we study hypersurfaces with constant mean curvature and give some estimates on the mean curvatures.