Summary We study precise estimates for on hypersurfaces the Levi matrix of which has certain form. In particular, we give and simple proof of the so-called maximal estimates, using the microlocal analysis. In fact, we obtain a refined version (inequality 3.17), which permits the study of more general cases. Finally, from such estimates, we deduce optimal subelliptic estimates for .
Oblatum 3-IX-1990 相似文献
Most high voltage circuit breakers in operation use SF6 as the arc interruption medium because of its high dielectric strength and good arc interruption properties. However SF6 also displays a high global warming potential which motivates the investigation of possible alternatives such as CO2–Novec?4710 and N2–Novec?5110 mixtures proposed by different HVCB manufacturers. CB power test comparison between pure CO2 and CO2–Novec?4710 mixture shows that the latter created a large amount of graphite and reduced CB performances after several current breaking shots. Using Gibbs free energy method, a theoretical study has been conducted on SF6 replacement candidates listed above. Aiming to understand graphite formation, several parameters impact were discussed: carrier gas such as CO2 and N2, pressure and O2 initial mixture proportions. The study focuses on graphite condensation temperature and graphite production amount evolutions in respect to the study parameters as well as in respect to CB inter-contacts space condition in terms of pressure and temperature at current-zero. It has been shown that a high percentage of CO2 in the mixture reduces graphite condensation temperature by 2600 K while adding N2 do not make such an impact. Pressure increases graphite condensation temperature and O2 reduces it. The amount of graphite produced is pressure independent but decreases with the increase of O2 proportion in the initial mixture. It has been shown that adding a sufficient O2 amount can prevent graphite production at all.
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