How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Ultrastructural analysis of Wuchereria bancrofti (Nematoda: Filarioidea) body wall

Bancroftian filariasis constitutes the principal mosquito-borne nematode infection of humans and the surface of adult of Wuchereria bancrofti seems to be especially important in the intricate interplay between host and parasite. The study of the parasite's surface structure might help to understand the localization and function of various organelles. W. bancrofti adult worms were recovered from untreated patients during hydrocele repair surgery and studied by transmission electron microscopy. The body wall of adult parasite is composed of cuticle, hypodermis and muscular layer. Cuticle is the external layer and shows transverse cuticular striation. It is composed by an epicuticle, cortical layers, median layer, fibrous layers and basal layer. The epicuticle is the most external cuticular layer and appears as a single laminar electron-dense layer. The cortical external region is more electron-dense and granular in appearance than the inner cortical layer. Electron-dense structures, called bosses are randomly distributed filling the cuticular striation. The median layer is formed by an electron-dense and continuous thick line. The fibrous layer is subdivided in inner and external layers connected by projections. The basal layer includes a large quantity of membranous projections directed toward the hypodermis. The hypodermis is a syncytium where some cellular organelles are observed. The somatic musculature is meromyarian. The muscle fibers consist of contractile and non-contractile regions and the contractile region is composed of myofilaments separated by dense body. This is the first study of W. bancrofti adult worms obtained from untreated patients and studied by transmission electron microscopy.     

Partial and Gradual Hydrolysis of 2,2′-Biimidazoline upon Coordination to Metal Ions,yielding New Chelating Ligands - Synthesis,Characterization and X-ray Structure of two Examples with Cobalt(III) and Copper(II)

The synthesis, a full structural characterization of two transition-metal compounds obtained by in-situ hydrolysis and partly hydrolysis of the ligand 2, 2′-biimidazoline (abbreviated as biz) is reported. When the biz ligand is completely hydrolysed the compound, N, N′-bis(2-aminoethyl)oxamide (abbreviated as H₂oxen) is obtained, while the partial hydrolysis results in the ligand N-(2-aminoethyl)imidazoline-2-carboxamide (abbreviated as Hoxim). The Co^III ion in the mononuclear Co^III compound, [Co(biz)(oxim)(NCS)](ClO₄)(C₂H₅OH)_1/6(H₂O)_1/6 ( 1 ), has an octahedral coordination consisting of 6 nitrogen atoms with a distance varying from 1.889(6) to 1.950(5) Å. Two nitrogen atoms originating from a biz molecule, 3 nitrogen atoms are from the oxim ligand and one nitrogen is from the thiocyanate anion. Each Cu^II ion in the dinuclear Cu^II compound, [Cu₂(H₂oxen)(oxim)₂(C₂H₅OH)₂] (ClO₄)₂ ( 2 ), has a slightly distorted square-pyramidal structure of which the basal plain consists of3 nitrogen atoms of the oxim ligand and one nitrogen atom of the H₂oxen ligand, which is used as a “spacer” connecting the second Cu^II atom, with Cu-N distances which vary from 1.944(2) to 2.037(2) Å. The apical position is formed by the oxygen atom of a semi-coordinating ethanol molecule with a Cu-O distance of 2.446(2) Å. The compounds are characterized by elemental analysis, ligand field, infrared and, for the Cu^II ion, also by EPR spectroscopy.