Size Functions from a Categorical Viewpoint

A new categorical approach to size functions is given. Using this point of view, it is shown that size functions of a Morse map, f: M can be computed through the 0-dimensional homology. This result is extended to the homology of arbitrary degree in order to obtain new invariants of the shape of the graph of the given map.     

The influence of the boat-to-chair conversion on the demetallation of the nickel(II) complex of an open-chain tetramine containing a piperazine fragment

The nickel(II) complex with an open chain tetramine containing a piperazine fragment (1) displays an unusual resistance to demetallation in acidic solution and exhibits a lifetime of about five minutes in a solution 0.1 M in HClO4 and 7.0 M in NaClO4. Sluggishness with respect to the demetallation is ascribed to the occurrence of the boat-to-chair conformational conversion of the piperazine fragment, which implies the passage through the highly energetic half-boat transition state. The use of a high concentration of the inert electrolyte induces a 'salting out' effect on both thermodynamics (stability of metal complexes is enhanced) and kinetics (resistance to demetallation is increased).     

Mannich reaction as a new route to pyridine-based polyaminocarboxylic ligands

The Mannich reaction was successfully employed to obtain two pyridine-based ligands 1 and 2. The latter represents the first example of a Mannich reaction leading to a 12-membered pyridine-containing macrocycle. [reaction: see text]     

Smoothness of the density of states in the Anderson model at high disorder

We prove smoothness of the density of states in the Anderson model at high disorder for a class of potential distributions that include the uniform distribution.Research partially supported by the NSF under grants DMS 83-01889 and INT 85-03418Research partially supported by the CNPq     

Tubular-shaped stoichiometric chrysotile nanocrystals

Stoichiometric chrysotile tubular nanocrystals have been synthesized as possible starting materials for applications toward nanotechnology, and as a standard reference sample for the investigation of the molecular interactions between chrysotile, the most utilized asbestos, and biological systems. Chrysotile nanocrystals have been synthesized under controlled hydrothermal conditions, and have been characterized by chemical, morphological, structural, spectroscopic and microcalorimetric analyses. They show a constant "cylinder-in-cylinder" morphology constituted by two or three concentric subunits. Each single nanocrystal has a tubular shape of about 49+/-1 nm in outer maximum diameter, and a hollow core of about 7+/-1 nm. Structural investigation carried out on an X-ray powder pattern allowed to improve the structural model proposed for chrysotile mineral samples. Synthetic chrysotile crystallizes in the monoclinic Cc space group with a=0.5340(1) nm, b=0.9241(1) nm, and c=1.4689(2) nm, beta=93.66(3) degrees.     

Anion receptors containing -NH binding sites: hydrogen-bond formation or neat proton transfer?

When the amide-containing receptor 1(+) is in a solution of dimethyl sulfoxide (DMSO) in the presence of basic anions (CH(3)COO(-), F(-), H(2)PO(4) (-)), it undergoes deprotonation of the -NH fragment to give the corresponding zwitterion, which can be isolated as a crystalline solid. In the presence of less basic anions (Cl(-), Br(-), NO(3) (-)), 1(+) establishes true hydrogen-bond interactions of decreasing intensity. The less acidic receptor 2(+) undergoes neat proton transfer with only the more basic anions CH(3)COO(-) and F(-), and establishes hydrogen-bond interactions with H(2)PO(4) (-). An empirical criterion for discerning neutralisation and hydrogen bonding, based on UV/Vis and (1)H NMR spectra, is proposed.     

Langmuir-Shäfer transfer of fullerenes and porphyrins: formation, deposition, and application of versatile films

Thin films consisting of a fulleropyrrolidine derivative 1 and a novel water-soluble porphyrin 2 were prepared by the Langmuir-Sh?fer (LS, horizontal lifting) method. In particular, a solution of 1 in chloroform and dimethyl sulfoxide was spread on the water surface, while porphyrin 2 (bearing peripheral anionic groups) was dissolved into the aqueous subphase. To the best of our knowledge, such a versatile method of film fabrication for fullerene/porphyrin mixed composite films has never been used before. Evidence of the effective interactions between the two moieties at the air-water interface was obtained from the analysis of the floating layers by means of surface pressure versus area per molecule Langmuir curves, Brewster angle microscopy and UV-visible reflection spectroscopy. The characterisation of the LS films by UV-visible spectroscopy reveals that the two constituents behave as discrete and weakly interacting pi systems. The use of polarised light suggests the existence of a preferential direction of the macrocyclic rings with an edge-on arrangement with respect to the substrate surface. Finally, photoaction spectra were recorded from films deposited by only one horizontal lifting onto indium-tin-oxide (ITO) electrodes and the observed photocurrent increased notably with increasing transfer surface pressure.     

Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity

In this paper we give asymptotic estimates of the least energy solution of the functional

as goes to infinity. Here is a smooth bounded domain of . Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that .

     

Origin of network connectivity and structural units in amorphous SiSe2

We elucidate the structural properties of amorphous SiSe2 by first-principles molecular dynamics. The calculated structure factor is in very good agreement with experiments, as well as the number of corner- and edge-sharing tetrahedra. By focusing on the sequences of Si atoms linked via intra- and intertetrahedral bonds, we identify the predominant structural motifs. The sequences involving both corner- and edge-sharing connections are significantly more frequent than those formed exclusively by edge-shared Si atoms. Our results clarify a longstanding controversy on the structure of this prototypical disordered network-forming material.