Isogénie minimale entre modules de Drinfel'd

Résumé. Nous majorons le degré d'une isogénie minimale entre deux modules de Drinfel'd. Il s'agit d'un analogue d'un résultat démontré tout d'abord sur les courbes elliptiques, puis généralisé aux variétés abéliennes par Masser et Wüstholz. Comme dans le cas abélien, la majoration dépend uniquement de la hauteur de l'un des modules et du degré d'un corps de définition commun aux deux modules. Cette dépendance est polyn?miale.

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We give a bound for the degree of a minimal isogeny between two Drinfel'd modules. This result is an anlogue of a theorem first proved on elliptic curves and then extended to abelian varieties by Masser and Wüstholz. This upper bound, as in the abelian case depends only on the height of one of the modules and on the degree of a field over which both modules are defined. We get a polynomial bound.

Received: 4 October 1994 / in final form: 30 July 1998     

Shock Layers Interactions for a Relaxation Approximation to Conservation Laws

We consider the interaction between shock waves in a semilinear relaxation approximation to N×N systems of conservation laws. This interaction is described by proving the existence of a particular solution to the relaxing system, with a certain asymptotic as Received July 1998     

Odds and Trends: Recent Developments in the Chemistry of Odorants

Fragrance chemistry is, together with the closely related area of flavor chemistry, one of the few domains, if not the only one, in which chemists can immediately experience structure–activity relationships. This review presents structure–odor correlations and olfactophore models for the main odor notes of perfumery: “fruity”, “marine”, “green”, “floral”, “spicy”, “woody”, “amber”, and “musky”. New trendsetters and so‐called captive odorants of these notes are introduced, and recent activities and highlights in fragrance chemistry are summarized. The design of odorants, their chemical synthesis, and their use in modern perfumery is discussed. Our selection is guided and illustrated by creative fragrances, and features new odorants which encompassed current trends in perfumery. New odorants for grapefruit and blackcurrant, for galbanum, and leafy top notes are presented. Compounds with fashionable marine, ozonic, and aquatic facets are treated, as well as new odorants for classical lily‐of‐the‐valley, rose, and jasmine accords. Compounds with sweet and spicy tonalities are also discussed, as are the most recent developments for woody notes such as sandalwood and vetiver. We conclude with musky and ambery odorants possessing uncommon or unusual structural features. Some odor trends and effects are illustrated by microencapsulated fragrance samples, and areas where there is need for the development of new synthetic materials and methodologies are pointed out. Thus, chemists are invited to explore fragrance chemistry and participate in the design and synthesis of new odorants. This review gives the latest state of the art of the subject.     

Polarization Switching along a Substrate in Thin Bi4Ti3O12 Films under Different Deformation Stresses

Technical Physics - Single-crystal Bi4Ti3O12 films deposited on a 4-nm-thick Ba0.4Sr0.6TiO3 sublayer covering an MgO(001) substrate have been investigated. It has been found that the unit cells of...     

Reduced-order model of a reacting,turbulent supersonic jet based on proper orthogonal decomposition

Theoretical and Computational Fluid Dynamics - The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent jet. A flowfield dataset is first obtained from a LES...     

Correlation between static mechanical properties of starch-glycerol materials and low-temperature relaxation

Mechanical, calorimetric, dynamic mechanical and dielectric properties were measured in starch and amylose films plasticized by different glycerol contents. Low-temperature relaxation was found to be highly dependent on plasticizer level and related to unusual mechanical properties.     

Formation of Catalytically Active Nanoparticles under Thermolysis of Silver Chloroplatinate(II) and Chloroplatinate(IV)

The thermal behaviour of Ag₂[PtCl₄] and Ag₂[PtCl₆] complex salts in inert and reducing atmospheres has been studied. The thermolysis of compounds in a helium atmosphere is shown to occur in two stages. At the first stage, the complexes decompose in the temperature range of 350–500 °C with the formation of platinum and silver chloride and the release of chlorine gas. At the second stage, silver chloride is sublimated in the temperature range of 700–900 °C, while metallic platinum remains in the solid phase. In contrast to the thermolysis of Ag₂[PtCl₆], the thermal decomposition of Ag₂[PtCl₄] at 350 °C is accompanied by significant heat release, which is associated with disproportionation of the initial salt to Ag₂[PtCl₆], silver chloride, and platinum metal. It is confirmed by DSC measurements, DFT calculations of a suggested reaction, and XRD. The thermolysis of Ag₂[PtCl₄] and Ag₂[PtCl₆] compounds is shown to occur in a hydrogen atmosphere in two poorly separable steps. The compounds are decomposed within 170–350 °C, and silver and platinum are reduced to a metallic state, while a metastable single-phase solid solution of Ag_0.67Pt_0.33 is formed. The catalytic activity of the resulting nanoalloy Ag_0.67Pt_0.33 is studied in the reaction of CO total (TOX) and preferential (PROX) oxidation. Ag_0.67Pt_0.33 enhanced Pt nano-powder activity in CO TOX, but was not selective in CO PROX.     

Water as the Key to Proto‐Aragonite Amorphous CaCO3

Temperature and pH value can affect the short‐range order of proto‐structured and additive‐free amorphous calcium carbonates (ACCs). Whereas a distinct change occurs in proto‐vaterite (pv) ACC above 45 °C at pH 9.80, proto‐calcite (pc) ACC (pH 8.75) is unaffected within the investigated range of temperatures (7–65 °C). IR and NMR spectroscopic studies together with EXAFS analysis showed that the temperature‐induced change is related to the formation of proto‐aragonite (pa) ACC. The data strongly suggest that the binding of water molecules induces dipole moments across the carbonate ions in pa‐ACC as in aragonite, where the dipole moments are due to the symmetry of the crystal structure. Altogether, a (pseudo‐)phase diagram of the CaCO₃ polyamorphism in which water plays a key role can be formulated based on variables of state, such as the temperature, and solution parameters, such as the pH value.