Two classes of conformally flat contact metric 3-manifolds

We give a classification of 3—dimensional conformally flat contact metric manifolds satisfying: =0(=L g) orR(Y, Z)=k[(Z)Y–(Y)Z]+[(Z)hY]–(Y)hZ] wherek and are functions. It is proved that they are flat (the non-Sasakian case) or of constant curvature 1 (the Sasakian case).     

Synthesis of 8-dipropylamino-7,8,9,10-tetrahydrophenanthridines as potential serotoninergic agonists

A number of 8-dipropylamino-7,8,9,10-tetrahydrophenanthridines have been prepared as analogs of the known serotoninergic agonist 8-hydroxy-2-(dipropylamino)tetralin (8-OH-DPAT) and their affinity for the 5-HT_1A receptor subtype evaluated by radioligand binding assay.     

Pressure effect on the magnetic properties of CeSb

Changes in the magnetic field-temperature phase diagram of CeSb with pressure have been determined up to 6kbar by magnetization measurements on a single crystal. High magnetic fields up to 70 kOe have been applied along a four fold axis of the rock-salt type structure. The features of the phase diagram are not changed by pressure except for a shift towards high temperature. The saturated magnetic moment and the hysteresis of the transition fields are independent of pressure. Variation of exchange energy with volume is deduced from the experimental results. It is shown that the effect of pressure and the magnetic volume anomaly at 0 K are essentially due to the variation of the exchange energy in the ferromagnetic (001) planes.     

2-Groupe des classes positives d'un corps de nombres et noyau sauvage de la K-théorie

We compute the 2-rank of the wild kernel WK₂(F) of a number field by constructing a 2-class group ad hoc. The main result generalizes in the more intricate case the canonical isomorphism established for odd primes under the assumption in a previous article (cf. (Acta. Arith. 67 (1994) 335; Math. Z. 238 (2001) 335)). It involves a criterium of triviality for the 2-part of the wild kernel of Galois number fields and, in the particular case of quadratic fields, it leads to a logarithmic interpretation of the diophantine conditions obtained by other authors.     

On conformally flat contact metric manifolds

In the present paper we classify the conformally flat contact metric manifolds of dimension satisfying . We prove that these manifolds are Sasakian of constant curvature 1.     

Nonlinear synthesis of input signals in ultrasonic experimental setups

A method is proposed to find the digital input signals to enter in nonlinear acoustical systems (power amplifiers, transducers, etc.) in order to obtain desired arbitrary response signals. The searched input signals are found by performing a Monte Carlo search guided by a simulated annealing process applied to a hidden model with a small number of parameters. The physical system is actually used in the optimization procedure, in a real-time manner, so that no theoretical model of the system response is required. The main aspects of the algorithm are described and illustrated with several examples.     

On the essential dimension of cyclic <Emphasis Type="Italic">p</Emphasis>-groups

Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r≥1 be an integer. We compute the essential dimension of ℤ/p ^r ℤ over K (Theorem 4.1). In particular, i) We have ed_ℚ(ℤ/8ℤ)=4, a result which was conjectured by Buhler and Reichstein in 1995 (unpublished). ii) We have ed_ℚ(ℤ/p ^r ℤ)≥p ^r-1.     

Kinetic 12C/13C isotope fractionation by invertase: evidence for a small in vitro isotope effect and comparison of two techniques for the isotopic analysis of carbohydrates

The natural ¹³C/¹²C isotope composition (δ¹³C) of plants and organic compounds within plant organs is a powerful tool to understand carbon allocation patterns and the regulation of photosynthetic or respiratory metabolism. However, many enzymatic fractionations are currently unknown, thus impeding our understanding of carbon trafficking pathways within plant cells. One of them is the ¹²C/¹³C isotope effect associated with invertases (EC 3.2.1.26) that are cornerstone enzymes for Suc metabolism and translocation in plants. Another conundrum of isotopic plant biology is the need to measure accurately the specific δ¹³C of individual carbohydrates. Here, we examined two complementary methods for measuring the δ¹³C value of sucrose, glucose and fructose, that is, off‐line high‐performance liquid chromatography (HPLC) purification followed by elemental analysis and isotope ratio mass spectrometry (EA‐IRMS) analysis, and gas chromatography‐combustion (GC‐C)‐IRMS. We also used these methods to determine the in vitro ¹²C/¹³C isotope effect associated with the yeast invertase. Our results show that, although providing more variable values than HPLC～EA‐IRMS, and being sensitive to derivatization conditions, the GC‐C‐IRMS method gives reliable results. When applied to the invertase reaction, both methods indicate that the ¹²C/¹³C isotope effect is rather small and it is not affected by the use of heavy water (D₂O). Copyright © 2009 John Wiley & Sons, Ltd.