On the geometry of the coefficient body (a 2 , a 3 ) for bounded univalent functions and some related coefficient problems

Journal d'Analyse Mathématique -     

Fluorescent small molecule probe to modulate and explore α2β1 integrin function

Collagen binding integrins are an important family of cell surface receptors that mediate bidirectionally signals between the interior of the cell and the extracellular matrix. The protein-protein interactions between cells and collagen are necessary for many physiological functions, but also promote diseases. For example, the interaction of α2β1 integrin and collagen has been shown to have an important role in thrombus formation and cancer spread. The fact that the discovery of small molecules that can block such protein-protein interactions is highly challenging has significantly hindered the discovery of pharmaceutical agents to treat these diseases. Here, we present a rationally designed novel fluorescent molecule that can be synthesized in just a few minutes from commercially available starting materials. This molecule blocks the protein-protein interaction between α2β1 integrin and collagen, and due to its fluorescent properties, it can be employed in wide variety of biological applications.     

Übergangsmetallketen-verbindungen: XXIII. Röntgenstrukturanalyse von α-[Dicarbonyl(η5-cyclopentadienyl)trimethylphosphinwolframa]α-(4-methylphenyl)essigsäuremethylester

Transition-metal-substituted η¹-ketenes react with methanol to form methyl acetate with the metal in the α-position. X-Ray analysis proves the trans-position of the two carbonyl ligands.     

A reduction technique for weighted grouping problems

Weighted grouping problems are shown to have an equivalent reduced form, which is often considerably smaller than the original problem. Although the reduction may be small for randomly generated problems, real-life problems often contain non-random properties that greatly increase the effect of reduction. We give an efficient algorithm to build the reduced problem instance, and analyse the expected amount of reduction for certain statistical distributions and real-life data. In addition, we briefly discuss the effect of reduction on traditional solving methods of the grouping problem. The results show clearly the usefulness of problem reduction: it is computationally cheap to apply and may make the reduced problem solvable in a practical time whilst the original one is not. The method is readily applicable to the job grouping problem of printed circuit board (PCB) printing industry.