Zur Theorie der endlichen Gruppen topologischer Abbildungen von geschlossenen Flächen in sich

Ohne Zusammenfassung     

Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. II

Ohne Zusammenfassung     

Voltammetric analysis of Pb(II) in natural waters using a carbon paste electrode modified with 5-mercapto-1-methyltetrazol grafted on hexagonal mesoporous silica

A hexagonal mesoporous silica (HMS) functionalized with a 5-mercapto-1-methyltetrazole derivative was employed to prepare a chemically modified carbon paste electrode for Pb(II) detection in aqueous solution by square wave adsorptive stripping voltammetry. The optimal operating conditions were 5 min preconcentration time at pH 6.5, and 120 s electrolysis time in 0.2 mol L^?1 HCl. Under these conditions, the voltammetric signal increased linearly with the preconcentration time in the range 1 to 10 min and with the Pb(II) concentration in the range 1 to 100?µg L^?1. The electrode was reproducible and sensitive. Simultaneous determination of Pb, Cd and Cu was also carried out with the electrode. The accuracy of the method was validated by analysing Pb(II) in tap water and groundwater samples.     

Entropically Driven Self‐Assembly of Lysinibacillus sphaericus S‐Layer Proteins Analyzed Under Various Environmental Conditions

S‐Layer proteins are an example of bionanostructures that can be exploited in nanofabrication. In addition to their ordered structure, the ability to self‐assembly is a key feature that makes them a promising technological tool. Here, in vitro self‐assembly kinetics of SpbA was investigated, and found that it occurs at a rate that is dependent on temperature, its concentration, and the concentration of calcium ions and sodium chloride. The activation enthalpy (120.81 kJ · mol^?1) and entropy (129.34 J · mol^?1 · K^?1) obtained infers that the incorporation of monomers incurs in a net loss of hydrophobic surface. By understanding how the protein monomers drive the self‐assembly at different conditions, the rational optimization of this process was feasible.

     

On globally generated vector bundles on projective spaces II

Extending the main result of Sierra and Ugaglia (2009)  [12], we classify globally generated vector bundles on Pⁿ${\mathbb{P}}^n$ with first Chern class equal to 3.     

Identification of Structure–Activity Relationships from Screening a Structurally Compact DNA‐Encoded Chemical Library

Methods for the rapid and inexpensive discovery of hit compounds are essential for pharmaceutical research and DNA‐encoded chemical libraries represent promising tools for this purpose. We here report on the design and synthesis of DAL‐100K, a DNA‐encoded chemical library containing 103 200 structurally compact compounds. Affinity screening experiments and DNA‐sequencing analysis provided ligands with nanomolar affinities to several proteins, including prostate‐specific membrane antigen and tankyrase 1. Correlations of sequence counts with binding affinities and potencies of enzyme inhibition were observed and enabled the identification of structural features critical for activity. These results indicate that libraries of this type represent a useful source of small‐molecule binders for target proteins of pharmaceutical interest and information on structural features important for binding.     

Dirichlet product for boolean functions

Boolean functions play an important role in many symmetric cryptosystems and are crucial for their security. It is important to design boolean functions with reliable cryptographic properties such as balancedness and nonlinearity. Most of these properties are based on specific structures such as Möbius transform and Algebraic Normal Form. In this paper, we introduce the notion of Dirichlet product and use it to study the arithmetical properties of boolean functions. We show that, with the Dirichlet product, the set of boolean functions is an Abelian monoid with interesting algebraic structure. In addition, we apply the Dirichlet product to the sub-family of coincident functions and exhibit many properties satisfied by such functions.     

Water structure and dynamics at a silica surface: Pake doublets in 1H NMR spectra

Detailed knowledge about the dynamics and structure of liquids in the vicinity of a solid surface is important in several fields of research. In this study a homogeneous model system of colloidal and nonporous silica particles with a narrow particle size distribution was used to examine such properties of adsorbed water and 1-heptanol. Doublet (1)H water resonances ("Pake doublets") indicate a preferred spatial orientation for the water molecules, as well as a lower molecular density in the surface-induced water structures compared to bulk water. These surface-induced structures are found to extend at least 8 nm from the silica surface. T(1) relaxation measurements at several temperatures indicate weaker H-bonding in the adsorbed water compared to bulk water. T(2) relaxation measurements at several temperatures reveal the presence of two water phases and give quantitative information on the mobility of water molecules and proton exchange processes. The presence of 1-heptanol changes the water characteristics, primarily in the water phase closer to the surface, where water molecules experience decreased translational and increased rotational freedom. In the absence of water, adsorbed 1-heptanol forms surface aggregates encompassing several molecular layers, where the first adsorbed layer shows severe restrictions in mobility and subsequent layers are more mobile.