Kato's inequality when Δu is a measure

We extend the classical version of Kato's inequality in order to allow functions u∈L¹_loc such that Δu is a Radon measure. This inequality has been recently applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation ?Δu+g(u)=μ, where μ is a measure and $\text{g}\text{:}\text{R}\text{→}\text{R}$ is a nondecreasing continuous function. To cite this article: H. Brezis, A.C. Ponce, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.     

Limits on the cosmological abundance of supermassive compact objects from a search for multiple imaging in compact radio sources

Using very long baseline interferometry we have searched a sample of 300 compact radio sources for examples of multiple imaging produced by gravitational lensing; no multiple images were found with separations in the angular range 1.5--50 milliarcsec. This null result allows us to place a limit on the cosmological abundance of intergalactic supermassive compact objects in the mass range approximately 10(6)M( middle dot in circle) to approximately 10(8)M( middle dot in circle); such objects cannot make up more than approximately 1% of the closure density ( 95% confidence). A uniformly distributed population of supermassive black holes forming soon after the big bang does not, therefore, contribute significantly to the dark matter content of the Universe.     

Inferring topological features of proteins from amino acid residue networks

Topological properties of native folds are obtained from statistical analysis of 160 low homology proteins covering the four structural classes. This is done analyzing one, two and three-vertex joint distribution of quantities related to the corresponding network of amino acid residues. Emphasis on the amino acid residue hydrophobicity leads to the definition of their center of mass as vertices in this contact network model with interactions represented by edges. The network analysis helps us to interpret experimental results such as hydrophobic scales and fraction of buried accessible surface area in terms of the network connectivity. Moreover, those networks show assortative mixing by degree. To explore the vertex-type dependent correlations, we build a network of hydrophobic and polar vertices. This procedure presents the wiring diagram of the topological structure of globular proteins leading to the following attachment probabilities between hydrophobic–hydrophobic 0.424(5), hydrophobic-polar 0.419(2) and polar–polar 0.157(3) residues.     

Reaction of 3-methylindole and 2,3-dimethylindole with dimethyl acetylenedicarboxylate using boron trifluoride-diethyl ether catalysis

Reactions of dimethyl acetylenedicarboxylate with 3-methylindole and 2,3-dimethylindole under boron trifluoride-diethyl ether catalysis were carried out at low temperature (0–25°). Thermally unstable cyclobutenes were isolated, mainly in apolar solvents, which isomerized to benzazepines. The other compounds isolated were Michael adducts and dihydro-2-oxocarbazoles.     

Optimization of nisin production by Lactococcus lactis

Applied Biochemistry and Biotechnology - The production of nisin by batch culture of Lactococcus lactis ATCC 11454 in MRS broth (pH 6.5), as treated in 30 assays, that were set up by a fractional...     

Nematic and smectic mesophases in a new series of Cu(II) organometallic complexes

The synthesis and the phase behaviour of a homologous series of copper, bis[N-[[4-[4-(alkoxy)benzoyloxy],2-hydroxyphenyl]methylene]-methanamino] complexes is reported. They all exhibit thermotropic mesomorphism. The thermal stability range of the mesophase decreases slightly with increasing length of the alkoxy terminals. With the onset of smectic mesomorphism, for alkoxy groups containing ten carbon atoms, the stability interval of the nematic phase decreases progressively so that the compound containing 14 carbon atoms in the alkoxy terminal chains exhibits only smectic mesomorphism. Optical texture analysis suggests the smectic C nature of the phase in all cases. The enthalpies for the liquid crystal-isotropic transition have been measured and they are comparatively low. Remarkably low values have also been measured for the melting enthalpies of the smectogenic members of the series. These are associated with solid phase polymorphism which is discussed briefly.     

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana’s (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to J, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.      

On Some Classical Methods to Improve Algebraic Curves and Surfaces

First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves.