Some remarks on multilinear exponential sums with an application

A sum-product equation is considered in prime fields. We bound a multilinear exponential sum with an additional requirement for some sets.     

Limiting the Number of Potential Binding Modes by Introducing Symmetry into Ligands: Structure‐Based Design of Inhibitors for Trypsin‐Like Serine Proteases

In the absence of X‐ray data, the exploration of compound binding modes continues to be a challenging task. For structure‐based design, specific features of active sites in different targets play a major role in rationalizing ligand binding characteristics. For example, dibasic compounds have been reported as potent inhibitors of various trypsin‐like serine proteases, the active sites of which contain several binding pockets that can be targeted by cationic moieties. This results in several possible orientations within the active site, complicating the binding mode prediction of such compounds by docking tools. Therefore, we introduced symmetry in bi‐ and tribasic compounds to reduce conformational space in docking calculations and to simplify binding mode selection by limiting the number of possible pocket occupations. Asymmetric bisbenzamidines were used as starting points for a multistage and structure‐guided optimization. A series of 24 final compounds with either two or three benzamidine substructures was ultimately synthesized and evaluated as inhibitors of five serine proteases, leading to potent symmetric inhibitors for the pharmaceutical drug targets matriptase, matriptase‐2, thrombin and factor Xa. This study underlines the relevance of ligand symmetry for chemical biology.     

Integrated Density of States for Ergodic Random Schrödinger Operators on Manifolds

We consider the Riemannian universal covering of a compact manifold M = X/ and assume that is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrödinger operators on X.     

Synthesis of 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylic acid derivatives, doubly constrained ACC derivatives, by a remarkable cyclopropanation process

Reaction of N-benzoyl-1,2,3,4-tetrahydroquinoline-2-carboxylic acid with acetic anhydride resulted in 1H,3H,5H-oxazolo[3,4-a]quinolin-3-one derivative 13. Different cyclopropanation processes were applied to 13, but only diazomethane in the presence of water furnished the hitherto unknown methyl 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylate 14, which can be considered as a doubly constrained 1-aminocyclopropane-1-carboxylic acid system. The mechanism of the cyclopropanation was studied in detail. The new ACC ester 14 was transformed into fused tetracyclic hydantoin derivatives, which comprised a new type of heterocyclic system.