Astala’s conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane

Let \( E \subset \mathbb{C} \) be a compact set, \( g:\mathbb{C} \to \mathbb{C} \) be a K-quasiconformal map, and let 0 < t < 2. Let \( {\mathcal{H}^t} \) denote t-dimensional Hausdorff measure. Then

$ {\mathcal{H}^t}(E) = 0\quad \Rightarrow \quad {\mathcal{H}^{t'}}\left( {gE} \right) = 0,\quad t' = \frac{{2Kt}}{{2 + \left( {K - 1} \right)t}}. $

This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala in [2] and answers in the positive a conjecture of K. Astala in op. cit.     

Examining the acute effects of cediranib (RECENTIN, AZD2171) treatment in tumor models: a dynamic contrast-enhanced MRI study using gadopentate

Cediranib (RECENTIN, AZD2171) is a highly potent inhibitor of the tyrosine kinase activity associated with all three vascular endothelial growth factor (VEGF) receptors and is currently in Phase II/III clinical trials. Preclinically, cediranib inhibits VEGF signaling and angiogenesis in vivo and impedes solid tumor growth significantly. Clinically, changes observed using dynamic contrast-enhanced MRI (DCE-MRI) with gadopentate suggest that acute cediranib treatment compromises tumor hemodynamics. In this study, a DCE-MRI baseline scan using gadopentate was performed in nude rats bearing Lovo (human colorectal carcinoma) or C6 (rat glioma) tumors. Cediranib (3 mg/kg per day) or vehicle was then dosed orally (2, 26 and 50 h after the baseline scan; 12 rats per group) and a second scan acquired 2 h after the final dosing event. Mean values for K(trans) (Tofts and Kermode-derived) [Magn Reson Med 17 (1991) 357-67] and the initial area under the gadolinium concentration curve over the first 60 s (iAUC) were reduced significantly following cediranib treatment: K(trans) by 33% (P<.05) in both tumor models and iAUC by 23% (P>.05) and 33% (P>.005) in Lovo and C6, respectively. This is the first preclinical investigation to examine the effect of cediranib treatment on tumors by DCE-MRI with gadopentate.     

Longitudinal flow of protons from (2-8)A GeV central Au+Au collisions

Rapidity distributions of protons from central 197Au+197Au collisions measured by the E895 Collaboration in the energy range from (2-8)A GeV at the Brookhaven AGS are presented. Longitudinal flow parameters derived using a thermal model including collective longitudinal expansion are extracted from these distributions. The results show an approximately linear increase in the longitudinal flow velocity, (L), as a function of the logarithm of beam energy.     

Microcavities combining a semiconductor with a fused-silica microsphere

We report studies of a novel microcavity system that combines a semiconductor quantum well with a fused-silica microsphere. We show that excitonic photoluminescence from the quantum well couples efficiently into whispering-gallery modes. Using a resonant light-scattering technique, we demonstrate that the Q factor of the combined system exceeds 10(5) . Our studies also point to the necessity of using semiconductor nanostructures with a capping layer no more than a few nanometers thick.     

Labelling studies of hydrogen rearrangements in the chemical ionization mass spectra of cyclohexanone and its derivatives

Deuterium labelling studies indicate that loss of water from the protonated molecular ion of cyclohexanone involves competitive site-specific eliminations. Loss of alcohol from the protonated molecular ions of 4-alkoxycyclohexanones involves competition between a direct cleavage, a 1,3-hydrogen rearrangement and consecutive losses of alkene and water.     

An elementary proof of the <Emphasis Type="Italic">A</Emphasis><Subscript>2</Subscript> bound

A martingale transform T, applied to an integrable locally supported function f, is pointwise dominated by a positive sparse operator applied to |f|, the choice of sparse operator being a function of T and f. As a corollary, one derives the sharp A _p bounds for martingale transforms, recently proved by Thiele-Treil-Volberg, as well as a number of new sharp weighted inequalities for martingale transforms. The (very easy) method of proof (a) only depends upon the weak-L ¹ norm of maximal truncations of martingale transforms, (b) applies in the vector valued setting, and (c) has an extension to the continuous case, giving a new elementary proof of the A ² bounds in that setting.     

Has the QCD critical point been signaled by observations at the BNL relativistic heavy ion collider?

The shear viscosity to entropy ratio (eta/s) is estimated for the hot and dense QCD matter created in Au+Au collisions at BNL Relativistic Heavy Ion Collider (square root[s_{NN}]=200 GeV). A very low value is found; eta/s approximately 0.1, which is close to the conjectured lower bound (1/4pi). It is argued that such a low value is indicative of thermodynamic trajectories for the decaying matter which lie close to the QCD critical end point.     

Novel side-chain liquid crystalline polymer architectures produced by the Wittig-Horner reaction

We have investigated the use of the Wittig-Horner reaction in the preparation of novel side-chain liquid crystalline (SCLC) polymers. The simplicity and versatility of the Wittig-Horner methodology makes it another useful synthetic route in preparing SCLC polymers with polar groups being positioned along the polymer backbone. This new methodology will now be used to synthesise a range of novel ferroelectric SCLC polymers.