Triplets spectraux en géométrie d'ArakelovSpectral triples in Arakelov geometry

In this Note, we use Connes' theory of spectral triples to provide a connection between Manin's model of the dual graph of the fiber at infinity of an Arakelov surface and the cohomology of the mapping cone of the local monodromy. To cite this article: C. Consani, M. Marcolli, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 779–784.     

Analysis of barbiturates in human serum and urine by high-performance capillary electrophoresis-micellar electrokinetic capillary chromatography with on-column multi-wavelength detection

The analysis of barbiturates in human serum (or plasma) and urine by high-performance capillary electrophoresis-electrokinetic capillary chromatography with on-column fast-scanning multi-wavelength detection is discussed. The use of a buffer of ca. pH 8 and containing sodium dodecyl sulphate provides a medium suitable for fast and high-resolution separations of barbiturates. Seven barbiturates are characterized by their retention and absorption spectra between 195 and 320 nm. Comparison of these computer-stored data with those of unknown samples is shown to allow the identification of barbiturates in samples of patients undergoing pharmacotherapy and in toxicological urine and serum specimens. Three-dimensional electropherograms provide reliable information on the requirement and suitability of sample pretreatment procedures. With urine, extraction of barbiturates prior to analysis is necessary. With human serum several barbiturates, including phenobarbital, are shown to elute in an interference-free window in front of uric acid and the proteins, allowing these substances to be determined by direct sample injection. The need for multi-wavelength detection over a relatively wide wavelength range as a means of peak confirmation in electrokinetic capillary analyses is demonstrated and limitations of this technique for compounds with similar retention behaviour and absorption spectra are discussed.     

Heterogeneous ice nucleation in aqueous solutions: the role of water activity

Heterogeneous ice nucleation experiments have been performed with four different ice nuclei (IN), namely nonadecanol, silica, silver iodide and Arizona test dust. All IN are either immersed in the droplets or located at the droplets surface. The IN were exposed to various aqueous solutions, which consist of (NH4)2SO4, H2SO4, MgCl2, NaCl, LiCl, Ca(NO3)2, K2CO3, CH3COONa, ethylene glycol, glycerol, malonic acid, PEG300 or a NaCl/malonic acid mixture. Freezing was studied using a differential scanning calorimeter and a cold finger cell. The results show that the heterogeneous ice freezing temperatures decrease with increasing solute concentration; however, the magnitude of this effect is solute dependent. In contrast, when the results are analyzed in terms of the solution water activity a very consistent behavior emerges: heterogeneous ice nucleation temperatures for all four IN converge each onto a single line, irrespective of the nature of the solute. We find that a constant offset with respect to the ice melting point curve, Deltaaw,het, can describe the observed freezing temperatures for each IN. Such a behavior is well-known for homogeneous ice nucleation from supercooled liquid droplets and has led to the development of water-activity-based ice nucleation theory. The large variety of investigated solutes together with different general types of ice nuclei studied (monolayers, ionic crystals, covalently bound network-forming compounds, and a mixture of chemically different crystallites) underlines the general applicability of water-activity-based ice nucleation theory also for heterogeneous ice nucleation in the immersion mode. Finally, the ice nucleation efficiencies of the various IN, as well as the atmospheric implication of the developed parametrization are discussed.     

Motives and periods in Bianchi IX gravity models

We show that, when considering the anisotropic scaling factors and their derivatives as affine variables, the coefficients of the heat-kernel expansion of the Dirac–Laplacian on SU(2) Bianchi IX metrics are algebro-geometric periods of motives of complements in affine spaces of unions of quadrics and hyperplanes. We show that the motives are mixed Tate and we provide an explicit computation of their Grothendieck classes.     

In Situ Characterization of Polymorphic Forms: The Potential of Raman Techniques

The use of hot-stage Raman microscopy — the direct coupling of Raman spectroscopy and thermomicroscopy — is demonstrated for the drug substances paracetamol and lufenuron.Paracetamol is a well-known analgesic and antipyretic drug, for which three polymorphic forms are currently known. Lufenuron is a benzoylphenyl urea derivative that has been classified as a chitin synthesis inhibitor. It is indicated for the use in pets for the prevention and control of flea population and used in crop protection for the control of Lepidoptera, Western Flower thrips and rust mites. It is the first time that the polymorphism of lufenuron is addressed. All known modifications of paracetamol and lufenuron were produced and identified by hot-stage Raman microscopy. A close correlation of thermal and spectroscopic information was achieved by this combination of techniques.For lufenuron a series of new polymorphic forms were found and characterized. Raman spectroscopy allowed to identify the thermodynamic stable form A as the one which is marketed in tablets.This revised version was published online in November 2005 with corrections to the Cover Date.     

Twisted spectral triples and quantum statistical mechanical systems

Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of twisted spectral triple, introduced recently by Connes and Moscovici, provides a natural bridge between them. We investigate explicit examples, related to the Bost-Connes quantum statistical mechanical system and to Riemann surfaces and graphs.     

Cyclotomy and endomotives

We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes (BC) quantum statistical mechanical system and the second on the Habiro ring, where the Habiro functions have, in addition to evaluations at roots of unity, also full Taylor expansions. Both have compatible endomorphisms actions of the multiplicative semigroup of positive integers. As a higher dimensional generalization, we consider a crossed product ring obtained using Manin’s multivariable generalizations of the Habiro functions and an action by endomorphisms of the semigroup of integer matrices with positive determinant. We then construct a corresponding class of multivariable BC endomotives, which are obtained geometrically from self maps of higher dimensional algebraic tori, and we discuss some of their quantum statistical mechanical properties. These multivariable BC endomotives are universal for (torsion free) Λ-rings, compatibly with the Frobenius action. Finally, we discuss briefly how Habiro’s universal Witten-Reshetikhin-Turaev invariant of integral homology 3-spheres may relate invariants of 3-manifolds to gadgets over and semigroup actions on homology 3-spheres to endomotives. The text was submitted by the author in English.