Die Verteilung der schlichten Funktionen in einem Funktionenraum

We consider the set of regular functions . We construct a Borel measure and a class of outer measures _h onH. With these and _h we show that: (HS)=0 and _h (HS)=0, (S is the set of normed univalent functions). From _h (HS)=0 follows—forh=t —that the Hausdorff—Billingsley-dimension ofHS is zero.     

The exponent of convergence of poincaré series

This paper continues the systematic study of the exponent of convergence (G) of a Fuchsian groupG begun byA. F. Beardon. The object is to show that in various senses (G) is a continuous function ofG. In view of the incompleteness of our knowledge about (G) considerable attention is paid to illustrative examples.     

Three theorems on σ-m-expandable spaces

Results concerning the connections between -m-expandability and compact-m-expandability, as well as the connections between -m-normality and compact-m-normality. Two problems are proposed.     

Imaging cellular distribution of fluorescent supramolecular nanofibers

In this study, we used the 4-nitro-2,1,3-benzoxadiazole (NBD) as an aromatic capping group for a peptide to construct the supramolecular nanofibers. Taking the advantage of the fluorescence property of NBD, we could directly observe the cellular distribution of the self-assembled nanofibers. We found that the distributions of the nanofibers of NBD-FFETIGGY are different in four mammalian cells and two plant cells. The nanofibers are mainly located at the surface of two mammalian cells and one plant cell, while in the intracellular space of other cells. Different distributions of nanofibers lead to different protein binding patterns of the nanofibers in two different cell lines. We believe that a useful and versatile platform has been offered to the image cellular distribution of nanofibers, which can provide useful information to the biological functions of the self-assembled nanostructures.     

Seed‐Mediated Synthesis of Gold Tetrahedra in High Purity and with Tunable,Well‐Controlled Sizes

We report a facile synthesis of Au tetrahedra in high purity and with tunable, well‐controlled sizes via seed‐mediated growth. The success of this synthesis relies on the use of single‐crystal, spherical Au nanocrystals as the seeds and manipulation of the reaction kinetics to induce an unsymmetrical growth pattern for the seeds. In particular, the dropwise addition of a precursor solution with a syringe pump, assisted by cetyltrimethylammonium chloride and bromide at appropriate concentrations, was found to be critical to the formation of Au tetrahedra in high purity. Their sizes could be readily tuned in the range of 30–60 nm by simply varying the amount of precursor added to the reaction solution. The current strategy not only enables the synthesis of Au tetrahedra with tunable and controlled sizes but also provides a facile and versatile approach to reducing the symmetry of nanocrystals made of a face‐centered cubic lattice.