Rhodium-catalyzed asymmetric arylative ring opening of bicyclic hydrazines

The development of a novel asymmetric ring opening of bi- and polycyclic hydrazines with aryl organometallic reagents is presented. The application of this reaction to the most simple bicyclic hydrazine 1a gives a straightforward regio- and diastereoselective access to synthetically useful trans 3,4-disubstituted hydrazinocyclopentenes in an enantioenriched form.     

A well-posedness result for hyperbolic operators with Zygmund coefficients

In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space. In particular, this estimate implies the well-posedness for the related Cauchy problem. On the one hand, this result is quite surprising, because it allows to consider coefficients which are not Lipschitz continuous in time. On the other hand, it holds true only in the very special case of initial data in H^1/2×H^−1/2$H^{1/2}\times H^{-1/2}$. Paradifferential calculus with parameters is the main ingredient to the proof.     

Synthesis and cyclodehydration of hydroxyphenols: a new stereoselective approach to 3-aryl-2,3-dihydrobenzofurans

A novel and simple method for the stereoselective synthesis of substituted 3-aryl-2,3-dihydrobenzofurans by intramolecular cyclization of hydroxyphenols is described. The stereoselective ortho-C-alkylation of phenols allows a novel and stereoselective access to a diverse array of polyfunctionalized products containing a diarylmethane stereogenic center without the need for time-consuming protection-deprotection steps.     

Rhodium-catalyzed enantioselective desymmetrization of bicyclic hydrazines with alkynylboronic esters

The first successful asymmetric transfer of rhodium-alkynyl species to symmetrical strained alkenes has been realized starting from bicyclic hydrazines and alkynylboronic esters.     

On the regularity of the roots of hyperbolic polynomials

We prove that a hyperbolic monic polynomial whose coefficients are functions of class C ^r of a parameter t admits roots of class C ¹ in t, if r is the maximal multiplicity of the roots as t varies. Moreover, if the coefficients are functions of t of class C ^2r , then the roots may be chosen two times differentiable at every point in t. This improves, among others, previous results of Bronšteĭn, Mandai, Wakabayashi and Kriegl, Losik and Michor.     

Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem

We deal with the Cauchy problem for a strictly hyperbolic second-order operator with non-regular coefficients in the time variable. It is well-known that the problem is well-posed in L² in case of Lipschitz continuous coefficients and that the log-Lipschitz continuity is the natural threshold for the well-posedness in Sobolev spaces which, in this case, holds with a loss of derivatives. Here, we prove that any intermediate modulus of continuity between the Lipschitz and the log-Lipschitz one leads to an energy estimate with arbitrary small loss of derivatives. We also provide counterexamples to show that the following classification:

     

Creatinine determination in serum by capillary electrophoresis

Creatinine in human serum was separated in a fused-silica capillary with H3PO4 (75 mmol/L, pH 2.5) as BGE, followed by UV detection at 200 nm. Serum with methylimidazole added as internal standard was deproteinized with acetonitrile and the supernatant, after dilution with water was injected at pressure mode. Creatinine and methylimidazole were baseline-resolved in 6.5 min. Linearity in the 0-880 micromol/L range gave an r2 > or = 0.998, recovery was 102 +/- 2.8% (n = 6). Enzymatic breakdown with creatininase confirmed that serum does not interfere. The within-day and between-days coefficient of variation (CV) were < or = 2.16 and 2.7%, respectively. The accuracy, determined for lyophilized samples by isotope dilution gas chromatography-mass spectrometry was < or = +/- 2.0%. The results were compared with HPLC for 32 lyophilized samples and on 27 serum pools. Capillary electrophoresis, rapid and inexpensive, seems a promising alternative to high-performance liquid chromatography (HPLC) for creatinine determination in human serum.