Growth conditions for entire functions with only bounded Fatou components

Let f be a transcendental entire function of order less than 1/2. Denote the maximum and minimum modulus of f by M(r, f) = max{|f(z)|: |z| = r} and m(r, f) = min{|f(z)|: |z| = r}. We obtain a minimum modulus condition satisfied by many f of order zero that implies all Fatou components are bounded. A special case of our result is that if

Influence of atmospheric turbulence on states of light carrying orbital angular momentum

We have experimentally studied the degradation of mode purity for light beams carrying orbital angular momentum (OAM) propagating through simulated atmospheric turbulence. The turbulence is modeled as a randomly varying phase aberration, which obeys statistics postulated by Kolmogorov turbulence theory. We introduce this simulated turbulence through the use of a phase-only spatial light modulator. Once the turbulence is introduced, the degradation in mode quality results in crosstalk between OAM modes. We study this crosstalk in OAM for 11 modes, showing that turbulence uniformly degrades the purity of all the modes within this range, irrespective of mode number.     

Faster first-order primal-dual methods for linear programming using restarts and sharpness

Mathematical Programming - First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high...     

Comparing π-complexation capabilities of ionic liquids containing silver(I) and copper(I) ions by headspace single drop microextraction in combination with high-performance liquid chromatography

Selective π-complexation capabilities of silver(I) and copper(I) ions can be effectively facilitated in ionic liquids. To understand the effects of environmental factors that influence the π-complexation of these metal ions with analytes, techniques that employ small volumes of ionic liquid that can be readily analyzed are desired. In this study, headspace single drop microextraction coupled with HPLC is used to investigate a diverse set of environmental factors on the metal ion-mediated complexation with aromatic compounds in ionic liquid media. Silver(I) and copper(I) bis[(trifluoromethyl)sulfonyl]imide salts were both studied by dissolving them in the 1-decyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ionic liquid and employing the mixture as extraction media for aromatic compounds. Water and acetonitrile within the sample solution were observed to interfere with the complexation of silver(I) ions and aromatic compounds, while ethylene glycol and triethylene glycol did not. The temperature and extraction times were optimized to fully facilitate the π-complexation capabilities of metal ions in ionic liquid media. Partition coefficients between the sample headspace and metal ion were determined using a three-phase equilibria model. Although no discernable difference in analyte partitioning between the headspace and ionic liquid solvent was observed, analyte partition coefficients to silver(I) ion tended to be greater compared to copper(I) ion.     

Some recent developments in SPM of crystalline polymers

Some recent advances in the application of atomic force microscopy to crystalline polymers are detailed. Ultra‐high resolution imaging of crystal surfaces, combined with the analysis of computer generated Connolly surfaces, enables the unambiguous identification of features on the cellulose crystal surface at near‐atomic resolution. The electronic enhancement of the quality factor of the cantilever when tapping in liquids enables a considerable improvement in force sensitivity to be obtained, allowing the fully saturated surface of an isotactic polystyrene gel to be imaged under the solvating molecule, at nanometre resolution. A series of experiments are detailed in which processes such as crystallization, crystal thickening and crystal deformation are followed in situ, in real time, providing significant new insights into long standing problems in polymer science.