negative Gaussian curvature, by manipulating the tensorial expressions of the problem the main equation reads (cy^{2 n-1)}sigma _{yy,xx}-sigma_{yy,yy}=0) in ((0,a times -b,0)) with some (a,a times -b,0 an integer greater than 1, exactly degenerating for (y=0).
Darek's spinal cord was just degenerating".
Moreover, the rightmost expression of d nk in eq 5.18 does not hold at conical intersections, which are defined as points where the adiabatic electronic PESs are exactly degenerate (and thus the denominator of this expression vanishes).
For one thing, it is unclear exactly how degenerate the pld are; according to one early estimate, an impressive 99.7% of utterances of mothers to their children are grammatically impeccable (Newport, Gleitman and Gleitman 1977).
"We don't exactly know why, but at the time France had some serious problems, like a low birth rate, and questions over whether the country was degenerating.
Tent life is degenerating".
Lately, though, that relationship has been degenerating.
But the film, by Carol Stein and Susan Wittenberg, quickly degenerates into cheerleading, serving up exactly the names you'd expect and only the most obvious of insights.
A variant of the filter-diagonalization method, using targeted excitation to filter out unwanted modes, can extract exactly or nearly degenerate eigenmodes and frequencies from time-domain simulations.
In particular we prove that, for non-zero photon mass, the ground state is exactly two-fold degenerate and separated by a gap, uniformly in P, from the rest of the spectrum.
The embedding (overline{Delta } rightarrow Delta ) canonically lifts to an embedding (gamma :overline{Delta } rightarrow Delta P in fact, (Delta P) has exactly one non-degenerate simplex in any degree, and (overline{Delta } subset Delta P) is the full subcategory spanned by these non-degenerate simplices.
