This paper addresses the sharpness of a weighted L2-estimate for the Fourier extension operator associated to the circle, obtained by J. Bennett, A. Carbery, F. Soria and A. Vargas in 2006. A point left open in their paper was the necessity of a certain logR-factor in the bound. Here, I show that the factor is necessary for all 1/2 -Ahlfors–David regular weights on the circle, but it can be r…

Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of the density properties of rational points on the Kummer variety Km(Ar) of the r-fold product of A with itself. One consequence of our results is the following. Fix an abelian variety A over k, and suppose that for so…

Adult somatic cells can be reprogrammed into pluripotent stem cells, which can indefinitely proliferate in a dish and differentiate into almost all the cell types that constitute the human body. These cells hold great promise for cell therapy and regenerative medicine, as well as drug screening and disease modeling. Theoretically, we can create a source of versatile, therapeutic cells that coul…

Let G be a locally compact group, and let B(G) denote its Fourier–Stieltjes algebra. We show that B(G) is Connes-amenable if and only if G is almost abelian.

Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g ∈ Hol(D) such that the sum |f| + |g| is equivalent to w. Also, we obtain similar results in several complex variables for circular, strictly convex domains with smooth boundary.

Let {φt}t >= 0 be a semigroup of holomorphic self-maps of the unit disk. We assume that the Denjoy–Wolff point of the semigroup is the point 1; so 1 is the unique attractive boundary fixed point of the semigroup. We further assume that for all t > 0, φt(1) < 1 (angular derivative), namely the semigroup is hyperbolic. We prove then that the rate of convergence of the semigroup to t…

We use the Dandelin–Gallucci theorem to give a proof of Wedderburn’s little theorem that every finite division ring is commutative, and the proof is geometric in the sense that the non-geometric concepts employed are of an elementary nature. As a consequence, we obtain a geometric proof that a finite Desarguesian projective space is Pappian.

We prove partial regularity of minimizers u for p(x)-energy functionals of the following type: E(u) =Ω(Aαβij (x, u)DαuiDβuj)p(x)/2 dx, assuming that Aαβ ij (x, u) and p(x) are sufficiently smooth and that p(x) is subquadratic. We prove that u ∈ C0,α(Ω0) for some α ∈ (0,1) and an open set Ω0 ⊂Ω with Hm−γ…

Tahun Terbit

2010

Noise shapes the efficacy and evolution of biological communication systems. Although examined in auditory and visual communication, the effects of noise on olfactory communication remains poorly known. We propose using information theory as a tool for analyzing noise in one type of olfactory signaling: between plants and insects. Plants and insects are cornerstones of terrestrial ecosystems, a…