Local Łojasiewicz exponents,Milnor numbers and mixed multiplicities of ideals

Let be a finite analytic map. We give an expression for the local Łojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals I ₁,..., I _n . We give an effective method to compute Łojasiewicz exponents based on the computation of mixed multiplicities. As a consequence of our study, we give a numerical characterization of a class of functions that includes semi-weighted homogenous functions and Newton non-degenerate functions. Work supported by DGICYT Grant MTM2006-06027.     

Exohedral reactivity of trimetallic nitride template (TNT) endohedral metallofullerenes

[structures: see text] Fullerenes containing a trimetallic nitride template (TNT) within the cage are a particularly interesting class of endohedral metallofullerenes. Recently two exohedral derivatives of the Sc3N@C80 fullerene have been synthesized: a Diels-Alder and a fulleropyrrolidine cycloadduct. The successful isolation, purification, and structural elucidation of these metallofullerenes derivatives have encouraged us to understand how the chemical reactivity is affected by TNT encapsulation. First of all, we predicted the most reactive exohedral sites, taking into account the double bond character and the pyramidalization angle of the C-C bonds. For this purpose, a full characterization of all different types of C-C bonds of the following fullerenes was carried out: I(h)-C60:1, D3-C68:6140, D3-Sc3N@C68, D(5h)-C70:1, D(3h')-C78:5, D(3h)-Sc3N@C78, I(h)-C80:7 and several isomers of Sc3N@C80. Finally the exohedral reactivity of these TNT endohedral metallofullerenes, via [4 + 2] cycloaddition reactions of 1,3-butadiene, was corroborated by means of DFT calculations.     

Singular Solutions of a Boussinesq System for Water Waves

Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a model for small-amplitude, long-crested water waves. The issue addressed is whether or not the initial-value problem for this system of equations is globally well posed.The investigation proceeds by way of numerical simulations using a computer code based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes or velocities do seem to lead to singularity formation in finite time, indicating that the problem is not globally well posed.     

Polystyrene-supported (2S)-(-)-3-exo-piperazinoisoborneol: an efficient catalyst for the batch and continuous flow production of enantiopure alcohols

A polystyrene-supported analog (PS-PIB) of 3-exo-morpholinoisoborneol (MIB), designed for increased chemical stability, has been synthesized and used as a ligand in the asymmetric alkylation of aldehydes with Et(2)Zn. The supported ligand turned out to be highly active and enantioselective for a broad scope of substrates (92-99% ee), allowing repeated recycling. A single-pass, continuous flow process implemented with PS-PIB shows only a marginal decrease in conversion after 30 h of operation.     

A journey inside the U28 nanocapsule

Anionic uranyl-peroxide U(28) nanocapsules trap cations and other anions inside, whose structures cannot be resolved by X-ray diffraction, owing to crystallographic disorder. DFT calculations enabled the complete characterization of the geometry of these complex systems and also explained the origin of the disorder. The stability of the capsules was strongly influenced by the entrapped cations. Excellent agreement between experiment and theory was also obtained for the electronic character and redox properties.     

Efficient γ-amino-proline-derived cell penetrating peptide-superparamagnetic iron oxide nanoparticle conjugates via aniline-catalyzed oxime chemistry as bimodal imaging nanoagents

Aniline-catalyzed oxime chemistry was employed to conjugate a γ-amino-proline-derived cell penetrating peptide to superparamagnetic iron oxide nanoparticles (SPIONs). Internalization of the novel nanoconjugate into HeLa cells was found to be remarkably higher compared to the analogous TAT-SPION conjugate.     

Localized growth and in situ integration of nanowires for device applications

Simultaneous localized growth and device integration of inorganic nanostructures on heated micromembranes is demonstrated for single crystalline germanium and tin oxide nanowires. Fully operating CO gas sensors prove the potential of the presented approach. With this simple CMOS compatible technique, issues of assembly, transfer and contact formation are addressed.     

Synthesis and Characterization of Acetone Hydrazones

1‐Isopropylidene‐2‐methylhydrazine ( 1 ), 1‐isopropylidene‐2‐hydroxyethylhydrazine ( 2 ) and 1‐isopropylidene‐2‐formylhydrazine ( 3 ) were synthesized by reaction of the corresponding hydrazine with an excess of acetone in the presence of a drying agent (anhydrous sodium sulfate or barium oxide). All compounds 1 – 3 were characterized by elemental analysis, coupled gas chromatography‐mass spectrometry (GC–MS), multinuclear NMR spectroscopy (¹H, ¹³C and ¹⁵N) and vibrational spectroscopy (infrared and Raman). Compounds 1 and 2 are liquid at room conditions and their density was measured by means of a picnometer, however, (at room conditions) compound 3 is a solid and its crystal density and structure were determined by low temperature X‐ray diffraction techniques (monoclinic, P2₁/n, Z = 4, a = 5.666(1) Å, b = 6.254(1) Å, c = 15.277(4) Å, β = 91.30(2)°, V = 541.2(2) ų). The structure of hydrazone 3 is discussed in detail and compared to that of monoformylhydrazine. Finally, the (gas phase) structure of compound 3 was optimized using DFT calculations (B3LYP/6‐31+G(d, p)) and its NBO charges are reported.     

Geometric Optics and Long Range Scattering¶for One-Dimensional Nonlinear Schrödinger Equations

With the methods of geometric optics used in [2], we provide a new proof of some results of [10], to construct modified wave operators for the one-dimensional cubic Schr?dinger equation. We improve the rate of convergence of the nonlinear solution towards the simplified evolution, and get better control of the loss of regularity in Sobolev spaces. In particular, using the results of [9], we deduce the existence of a modified scattering operator with small data in some Sobolev spaces. We show that in terms of geometric optics, this gives rise to a “random phase shift” at a caustic. Received: 23 May 2000 / Accepted: 8 January 2001