Quillen [7] defines an algebraic A -̂functor from the category of associative rings to that of positively graded abelian groups, with Kf(R) = ÏI^BGLR ") for i > 1. Kx and K2 correspond respectively to the 'classical' Bass and Milnor definitions. The /^-images of finite fields and their algebraic closures were computed by Quillen in [8]. Since then, there has been only a handful of complete calcu...

The standard approach to applying ray theory solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have ( i ) an oscillatory exponential with a phase term is linear and ii has amplitude profile expressed terms of inverse powers wave-number. Friedlander–Keller modification includes additional power this wave structure, crucial when analysing certain phenomena...

With Fq a finite field of characteristic p, let F(q) be the category whose objects are functors from finite dimensional Fq–vector spaces to F̄p– vector spaces. Extension groups in F(q) can be interpreted as MacLane (or Topological Hochschild) cohomology with twisted coefficients. Furthermore, evaluation on an m dimensional vector space Vm induces a homorphism from Ext F(q) (F, G) to finite group...

A four-step route for the synthesis of 5-azatetracene (benzo[b]acridine) has been developed, employing a base-catalysed Friedlander condensation reaction between 3-amino-2-napthaldehyde and cyclohexanone as key step followed by dehydrogenation intermediate. The optical electrochemical properties were investigated UV-vis photoluminescence spectroscopy, cyclic voltammetry compared with those tetr...

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...

If Ω is any compact Lipschitz domain, possibly in a Riemannian manifold, with boundary Γ = ∂Ω, the Dirichlet-to-Neumann operator Dλ is defined on L2(Γ) for any real λ. We prove a close relationship between the eigenvalues of Dλ and those of the Robin Laplacian ∆μ, i.e. the Laplacian with Robin boundary conditions ∂νu = μu. This is used to give another proof of the Friedlander inequalities betwe...

Let q denote a large prime number, a be any integer. Let N(q, a) denote the smallest positive integer n for which φ(n) ≡ a (mod q). The number N(q, a) exists. Indeed, if a+1 ≡ 0 (mod q) then one can take n = q. Otherwise, one can take n to be a prime from the arithmetical progression a + 1 (mod q). The problem of upper bound estimates for N(q, a) has been a subject of study of the work of Fried...