Katz and Pavlovic recently proposed a dyadic model of the Euler equations for which they proved finite time blow-up in the H3/2+ǫ Sobolev norm. It is shown that their model can be reduced to the dyadic inviscid Burgers equation where nonlinear interactions are restricted to dyadic wavenumbers. The inviscid Burgers equation exhibits finite time blow-up in Hα, for α ≥ 1/2, but its dyadic restrict...

The Friedlander–Milnor Conjecture [1] asserts that if G is a reductive algebraic group over an algebraically closed field k, then the comparison map H ét(BGk,Z/p) −→ H (BG,Z/p) is an isomorphism for all primes p not equal to the characteristic of k. Gabber’s rigidity theorem [2] implies that this map is indeed an isomorphism for the stable general linear group GL (this is due to Suslin [6] for ...

Motivated by an equation arising in magnetohydrodynamics, we address the well-posedness theroy for non-diffusive magneto-geostrophic equation. Namely, active scalar which divergence-free drift velocity is one derivative more singular than scalar. In Friedlander and Vicol (Nonlinearity 24(11)::3019–3042, 2011), authors prove that ill-posed sense of Hadamard Sobolev spaces, but locally well posed...

a simple and efficient method for the synthesis of quinolines and polycyclic quinolines using li+ modified nanoporous na+-montmorillonite is described. this new nanocatalyst proceeds via friedlander annulation under solvent-free conditions. it describes our observations about a trend of catalytic activity of lithium cation in nanoporous na+-montmorillonite. in this study, several types of 1,3-d...

The Friedlander{Milnor Conjecture 1] asserts that if G is a reductive algebraic group over an algebraically closed eld k, then the comparison map H et (BG k ; Z=p) ?! H (BG; Z=p) is an isomorphism for all primes p not equal to the characteristic of k. Gabber's rigidity theorem 2] implies that this map is indeed an isomorphism for the stable general linear group GL (this is due to Suslin 6] for ...

In a recent preprint, [CGJ], we showed that for the Dirichlet Laplacian ∆ on the unit disk, the wave trace Tr(eit √ ∆), which has complicated singularities on 2π − ε < t < 2π, is, on the interval 2π < t < 2π+ ε, the restriction to this interval of a C∞ function on its closure. In this paper we prove the analogue of this somewhat counter-intuitive result for the Friedlander model. The proof for ...

Previous blast injury prediction criteria have been based on exposure to classic Friedlander or ideal blast waves. An ideal waveform is characterized by an instantaneous rise to a peak overpressure that decays exponentially to ambient pressure followed by a negative phase. The prediction criteria did not address injuries resulting from exposure to complex blast waves. It was difficult to establ...

developed their genocidal methods, inventing and refining the techniques of transportation, selection and gassing, and the schemes of subterfuge used to hide these atrocities from relatives and potential pockets of opposition. To demonstrate the "intimate connections" between these two programmes, Friedlander chronicles the various stages in the Nazi campaigns against their most helpless victim...