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

Ohne Zusammenfassung     

Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. II

Ohne Zusammenfassung     

Host-guest-driven copolymerization of tetraphosphonate cavitands

The outstanding complexing properties of tetraphosphonate cavitands towards N‐methylpyridinium salts were exploited to realise a new class of linear and cyclic AABB supramolecular polymers through host–guest interactions. The effectiveness of the selected self‐association processes was tested by ¹H NMR studies, whereas microcalorimetric analyses clarified the binding thermodynamics and revealed the possibility of tuning entropic contributions by acting on the flexibility of the guest linker. Although the formation of linear polymeric chains for a rigid system was demonstrated by X‐ray analysis, the presence of a concentration‐dependent ring–chain equilibrium was indicated by solution viscosity measurements in the case of a very flexible ditopic BB guest co‐monomer.     

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.     

Morniga G: a plant lectin as an endocytic ligand for photosensitizer molecule targeting toward tumor-associated T/Tn antigens

Porphyrins are used as photosensitizer (PS) in photodynamic therapy in cancer treatment. Nevertheless, the development of photochemotherapy in oncology remains limited, because of the low selectivity of PSs. In order to allow PS targeting toward tumor-associated antigens, for the first time a white-light activatable porphyrin, [5-(4-(5-carboxy-1-butoxy)-phenyl)-10,15,20-tris(4-N-methyl)-pyridiniumyl)-porphyrin] (TrMPyP) was covalently linked to Morniga G (MorG), a galactose-specific binding plant lectin, known to recognize with high-affinity tumor-associated T/Tn antigen in cell-free systems. Firstly, using fluorescein-labeled MorG, the sugar-dependent binding and uptake of lectin by Tn-positive (Jurkat lymphoid leukemia) cells was demonstrated. Secondly, the TrMPyP-MorG conjugate was molecularly characterized. Cytometric and confocal microscopic analysis demonstrated that PS covalent linking to MorG preserved sugar-dependent specific binding and uptake of lectin by Jurkat leukemia lymphocytes. Thirdly, the conjugate (with a 1:1 PS:lectin ratio) that was bound and quickly (5 min) taken-up, induced greater than 90% cytotoxicity upon irradiation at 10 nm concentration, whereas the free PS was absolutely nontoxic. On the contrary, normal lymphocytes strongly resisted to the conjugate-mediated phototoxicity. Thus, owing to their binding and endocytosis capacities, plant lectins represent promising molecules for targeting of tumor glycan alteration and to enhance the efficiency of specific delivery of PSs to tumor cells.     

Hybrid nanoparticle design based on cationized gelatin and the polyanions dextran sulfate and chondroitin sulfate for ocular gene therapy

We describe the development of hybrid nanoparticles composed of cationized gelatin and the polyanions CS and DS for gene therapy in the ocular surface. The physicochemical properties of the nanoparticles that impact their bioperformance, such as average size and zeta potential, can be conveniently modulated by changing the ratio of polymers and the crosslinker. These systems associate plasmid DNA and are able to protect it from DNase I degradation. We corroborate that the introduction of CS or DS in the formulation decreases the in vitro toxicity of the nanoparticles to human corneal cells without compromising the transfection efficiency. These nanoparticles are potential candidates for the development of safer and more effective nanomedicines for ocular therapy.     

Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994