On Lusin's condition for the inverse function

Sia ? una funzione invertibile, continua e quasi ovunque differenziabile, da un aperto di IR ⁿ in IR ⁿ . Allora ?^?1soddisfa alla condizione di Lusin (N) se e solo se lo Jacobiano di ? è quasi ovunque diverso da zero.     

Strong displacement convexity on Riemannian manifolds

Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in Lott and Villani (Ann of Math, to appear). C. Villani is member of the Institut Universitaire de France.     

Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit

Summary. In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann equation in the spirit of [21,23]. We show that the kernel modes that define the spectral method have the correct grazing collision limit providing a consistent spectral method for the limiting Fokker-Planck-Landau equation. In particular, for small values of the scattering angle, we derive an approximate formula for the kernel modes of the non cut-off Boltzmann equation which, similarly to the Fokker-Planck-Landau case, can be computed with a fast algorithm. The uniform spectral accuracy of the method with respect to the grazing collision parameter is also proved. Received July 10, 2001 / Revised version received October 12, 2001 / Published online January 30, 2002     

High-performance liquid chromatography chiral stationary phases based on low-molecular-mass selectors

A review of HPLC chiral stationary phases (CSPs) based on low molecular mass selectors is given. The review is focused on brush- and monomeric-type CSPs obtained by covalent linkage of chiral selectors, with emphasis on those obtained by total synthesis. Emphasis is given to new, emerging aspects like enantioseparations on receptor-like chiral stationary phases and dynamic enantioselective chromatography of stereolabile compounds.     

Synthesis and conformational studies of a beta-turn mimetic incorporated in Leu-enkephalin

A beta-turn mimetic in which the four amino acids of a beta-turn have been replaced by a 10-membered ring has been designed, synthesized, and subjected to conformational studies. In the mimetic, the intramolecular CO(i)-HN(i)(+3) hydrogen bond that is often found in beta-turns has been replaced by an ethylene bridge. In addition, the amide bond between residues i and i + 1 was exchanged for a methylene ether isoster. Such a beta-turn mimetic, based on the first four residues of Leu-enkephalin (Tyr-Gly-Gly-Phe-Leu), was prepared in 15 steps. The synthesis relied on a beta-azido alcohol prepared in five steps from Cbz-Tyr(tBu)-OH as a key, i-position building block. tert-Butyl bromoacetate, glycine, and a Phe-Leu dipetide were then used as building blocks for positions i + 1, i + 2, and i + 3, respectively. Conformational studies based on (1)H NMR data showed that the beta-turn mimetic was flexible, but that it resembled a type-II beta-turn at low temperature. This low energy conformer closely resembled the structure determined for crystalline Leu-enkephalin.     

Derivatives of 10,11-dihydro-5H-dibenzo[a,d] cycloheptene and related compounds. III. Azaketones

The preparation and properties of four isomeric azadibenzoeycloheptenones 3 and their 10,11-dihydro derivatives 2 are described. The ketones 2 were prepared by cyclization of appropriately substituted phenethylpyridine carboxylic acids and dehydrogenated to 3 . Four monochloro derivatives 24 of the 4-azaketone 2d are also described.     

On the structure and desorption dynamics of DNA bases adsorbed on gold: a temperature-programmed study

The structure and desorption dynamics of mono- and multilayer samples of adenine, cytosine, guanine, and thymine on polycrystalline gold thin films are studied using temperature-programmed desorption-infrared reflection absorption spectroscopy (TPD-IRAS) and temperature-programmed desorption-mass spectroscopy (TPD-MS). It is shown that the pyrimidines, adenine and guanine, adsorb to gold in a complex manner and that both adhesive (adenine) and cohesive (guanine) interactions contribute the apparent binding energies to the substrate surface. Adenine displays at least two adsorption sites, including a high-energy site (210 degrees C, approximately 136 kJ/mol), wherein the molecule coordinates to the gold substrate via the NH2 group in an sp3-like, strongly perturbed, nonplanar configuration. The purines, cytosine and thymine, display a less complicated adsorption/desorption behavior. The desorption energy for cytosine (160 degrees C, approximately 122 kJ/mol) is similar to those obtained for adenine and guanine, but desorption occurs from a single site of dispersed, nonaggregated cytosine. Thymine desorbs also from a single site but at a significantly lower energy (100 degrees C, approximately 104 kJ/mol). Infrared data reveal that the monolayer architectures discussed herein are structurally very different from those observed for the bases in the bulk crystalline state. It is also evident that both pyrimidines and purines adsorb on gold with the plane of the molecule in a nonparallel orientation with respect to the substrate surface. The results of this work are discussed in the context of improving the understanding of the design of capturing oligonucleotides or DNA strands for bioanalytical applications, in particular, for gold nanoparticle-based assays.     

Poly(dimethylsiloxane) microchip: microchannel with integrated open electrospray tip

A polymer microchip with an open tip for electrospray mass spectrometry is presented. The tip consists of a groove with parallel walls where a droplet can form at the end surface. A lid covers the whole chip except at the microchannel tip, which is left open. Poly(dimethylsiloxane) (PDMS) microchips were cast using a nickel mould which in turn was replicated from a dry etched silicon wafer. Tips with microchannel widths of around 50 microm could easily be replicated. Since the tip had no cover, the assembly of microchip and cover was simplified. A total ion current variation of 5% during 300 s was achieved for a 1 microM myoglobin solution. The non-complex design of the cover makes it suitable for versatile tests of chip prototypes. The nickel mould was found to be useful for PDMS microstructure fabrication. Also, such a robust mould allows casting electrospray tips in more rigid thermoset materials.     

On the Ma–Trudinger–Wang curvature on surfaces

We investigate the properties of the Ma–Trudinger–Wang nonlocal curvature tensor in the case of surfaces. In particular, we prove that a strict form of the Ma–Trudinger– Wang condition is stable under C ⁴ perturbation if the nonfocal domains are uniformly convex; and we present new examples of positively curved surfaces which do not satisfy the Ma–Trudinger–Wang condition. As a corollary of our results, optimal transport maps on a “sufficiently flat” ellipsoid are in general nonsmooth.     

Silicate-Phenolic Networks: Coordination-Mediated Deposition of Bioinspired Tannic Acid Coatings

Surface modification with polyphenolic molecules has been pursued in biomedical materials owing to their antioxidant, anti-inflammatory, and antimicrobial characteristics. Recently, the use of silicic acid (Si_aq) as a mediator for efficient surface deposition of tannic acid (TA) was reported, but the postulated Si-TA polymeric networks were not characterized. Herein, we present unambiguous evidence for silicate-TA networks that involve Si−O−C motifs by using solid-state NMR spectroscopy, further supported by XPS and ToF-SIMS. By using QCM-D we demonstrate the advantages of Si_aq, compared to using transition-metal ions, to improve the coating efficiency under mildly acidic conditions. The presented homogenous coating buildup and validated applicability in inorganic buffers broadens the use of TA for surface modifications in technological and biomedical applications.