And that defined-number list suddenly has me checking Mr DeLong's site with great interest and regularity to see if I've made the cut.I'm not sure what it is about set-number lists that people find so engrossing.
We first prove Lp (p≥2) estimates for gradients of weak solutions by using a priori estimates and a known reverse Hölder inequality, and consider regularity to the corresponding nondiagonal homogeneous degenerate elliptic systems.
"If one's gambling activity is pursued full-time, in good faith and with regularity, to the production of income for a livelihood, and is not a mere hobby, it is a trade or business," Justice Harry Blackmun declared.
Mr. Hussein, now 63, is as firmly in power in this nation of 23 million people as ever, and just as harsh in defense of his power, according to human rights reports chronicling the parade of opponents, would-be assassins and "traitors" into Iraq's prisons, and on with chilling regularity to the firing squad or gallows.
No computationally simulated dynamos have yet been constructed to operate in this regime, though Hori et al. (2012) note that volumetric buoyancy sources, which could characterize exsolution-driven dynamos, yield more multipolar fields and hence less spatial regularity to the field, perhaps mimicking Mars' surface magnetism.
Kohn's work, which should be viewed as the starting point for the Hodge Theorem on manifolds with boundary, provided (L^2) estimates and regularity up to the boundary for the solution of the Cauchy Riemann equations having minimal (L^2) norm.
The FSHG/BSHG is highly dependent upon the fibril diameter, the packing density and regularity relative to the size-scale of the SHG wavelength[ 23].
Specifically, repetition and regularity lends to the perception of tonality [ 59], rhythm and meter [ 60, 61] and the structural use of musical themes.
We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems.
