Stabilité du fibré tangent des surfaces de Del Pezzo

Sans résumé     

One‐step synthesis of aminopyrimidines from 5‐Oxo‐4H‐benzopyrans

Novel 4‐amino‐6‐aryl‐2‐phenylpyrimidine‐5‐carbonitriles have been prepared in one step procedure from the readily available 4‐aryl‐2‐amino‐3‐cyano‐5,6,7,8‐tetrahydro‐7,7‐dimethyl‐5‐oxo‐4H‐benzopyrans. The mass spectroscopy study under EI conditions shows molecular peaks with high intensity corresponding to the loss of benzonitrile from the C2 position of the pyrimidine ring. Semiempirical (AMI and PM3) and ab initio HF/6–31G* calculations reveal a favored distorted geometry where the three rings are not in the same plane.     

A short and efficient synthesis of 2′-deoxybenzo- and pyridoimidazole C-nucleosides

A short route to a series of 2′-deoxy-C-nucleosides featuring substituted nucleobases has been developed. The key step is the formation of the cyclized products following Mukaiyama's type amide coupling and a simple dehydration, starting from readily accessible synthons. The epimerization of the C1′-stereogenic center was avoided under mild and controlled conditions.     

A short and highly stereoselective synthesis of α-(2-aminothiazolyl)-C-nucleosides

A short route to novel α-(2-aminothiazolyl)-C-nucleosides has been developed. The key step was the high diastereoselective reduction of the hemiacetal intermediates using L-Selectride, which afforded the corresponding R-diols in quantitative yields. These diols were converted, after C4-C1 ring closure and protecting groups cleavage, to their corresponding free α-C-nucleosides.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.