We show that every separable $C^$-algebra of real rank zero tensorially absorbs the Jiang–Su algebra contains a dense set generators. It follows that, in classifiable, simple, nuclear $C^$-algebra, generic element is generator.

We study the thermalization, injection, and acceleration of ions with different mass/charge ratios, A/Z, in nonrelativistic collisionless shocks via hybrid (kinetic ions-fluid electrons) simulations. In general, ions thermalize to a postshock temperature proportional to A. When diffusive shock acceleration is efficient, ions develop a nonthermal tail whose extent scales with Z and whose normali...

For functions p analytic in the open unit disc U = {z : |z|< 1} with the normalization p(0)= 1, we consider the families [A,−1], −1 0, consisting of p, which have the disc formulation |p−1|< b in U . We then introduce subordination criteria for the choice of p(z)= zf ′(z)/f(z), where f is analytic in U and n...

We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane. Astala [1] proved the following theorem conjectured by Gehring and Reich in [3]: Theorem A. Let f be a K-quasiconformal mapping of D = {z: \z\ < 1} onto itself with f(0) = 0. Then for any measurable E c D we have \f(E)\<C(K)\E\xlK, where \ • \ stands for the area. The first author [2] obtaine...

It is shown that for AR(D) functions f1 and f2 with inf z∈D (|f1(z)|+ |f2(z)|) ≥ δ > 0 and f1 being positive on real zeros of f2 then there exists AR(D) functions g2 and g1, g −1 1 with and g1f1 + g2f2 = 1 ∀z ∈ D. This result is connected to the computation of the stable rank of the algebra AR(D) and to Control Theory.

We give conditions on the rational numbers a, b, c which imply that there are infinitely many triples (x, y, z) of rational numbers such that x+ y + z = a+ b+ c and xyz = abc. We do the same for the equations x + y + z = a + b + c and x + y + z = a + b + c. These results rely on exhibiting families of positive-rank elliptic curves.

I here propose an index that links the number of papers a researcher has published with impact factors (IFs) of the journals that publish these papers. A researcher is said to have an index z if totally z of his/her papers are published in journals with IFs of at least z/2. The z-index, not meant to evaluate, compare and rank scientists, is a number that hopefully conveniently summarizes the nu...

In this article, we consider the family of functions f analytic in unit disk $$|z|<1$$ with normalization $$f(0)=0=f'(0)-1$$ and satisfying condition $$\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $$ for some $$0<\lambda \le 1$$ . We denote class by $$\mathcal {U}(\lambda )$$ are interested relations between other families holomorphic or harmonic disk. Our first example direction is convex...

We reanalyze deep inelastic scattering data of BCDMS Collaboration by including proper cuts of ranges with large systematic errors. We perform also the fits of high statistic deep inelastic scattering data of BCDMS, SLAC, NM and BFP Collaborations taking the data separately and in combined way and find good agreement between these analyses. We extract the values of both the QCD coupling constan...