Microwave-assisted synthesis of a triazole-linked 3′-5′ dithymidine using click chemistry

Synthesis of a triazole-linked 3′-5′ thymidine dimer making use of 1,3-dipolar cycloaddition is described. The azido-precursor was obtained by regioselective chlorination of thymidine, followed by azidation. The second precursor, a propargyl derivative, was obtained by selective 3′-O-alkylation of thymidine. Two ‘click systems’ were compared to obtain the desired dimer. These reactions were performed by microwave irradiation.     

Random walks on finite volume homogeneous spaces

Extending previous results by A. Eskin and G. Margulis, and answering their conjectures, we prove that a random walk on a finite volume homogeneous space is always recurrent as soon as the transition probability has finite exponential moments and its support generates a subgroup whose Zariski closure is semisimple.     

Sequential functionalization of janus‐type dendrimer‐like poly(ethylene oxide)s with camptothecin and folic acid

Janus‐type dendrimer‐like poly(ethylene oxide)s (PEOs) of 1st, 2nd, and 3rd generation carrying terminal hydroxyl functions on one side and cleavable ketal groups on the other were used as substrates to conjugate folic acid as a folate receptor and camptothecin (CPT) as a therapeutic drug in a sequential fashion. The conjugation of both FA and CPT was accomplished by “click chemistry” based on the 1,3 dipolar cycloaddition coupling reaction. First, the hydroxyl functions present at one face of Janus‐type dendrimer‐like PEOs were transformed into alkyne groups through a simple Williamson‐type etherification reaction. Next, the ketals carried by the other face of the dendrimer‐like PEOs were hydrolyzed, yielding twice as many hydroxyls which were subsequently subjected to an esterification reaction using 2‐bromopropionic bromide. Before substituting azides for the bromide of 2‐bromopropionate esters just generated in the presence of NaN₃, an azido‐containing amidified FA derivative was reacted through click chemistry with alkyne functions introduced on the other face of the dendrimer‐like PEOs. A purposely designed alkyne‐functionalized biomolecule derived from CPT was conjugated to the azido functions carried by the dendritic PEOs by a second “click reaction.” In this case, twice as many CPT as FA moieties were finally conjugated to the two faces of the Janus‐type dendrimer‐like PEOs, the numbers of folate and CPT introduced being 2 and 4, 4 and 8, and 8 and 16 for samples of 1st, 2nd, and 3rd generation, respectively (route A). An alternate route for functionalizing the dendrimer‐like PEO of 1st generation consisted, first, in conjugating the azido‐containing CPT onto the alkyne groups present on one face of the dendritic PEO scaffold. The alkyne‐functionalized FA was further introduced by click chemistry after the bromides of 2‐bromopropionate esters were chemically transformed into azido groups. The corresponding prodrug thus contains 2 CPT and 4 FA external moieties (route B). Every reaction step product was thoroughly characterized by ¹H NMR spectroscopy. A preliminary investigation into the water solution properties of these functionalized dendritic PEOs is also presented. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Clarkson's algorithm for violator spaces

Clarkson's algorithm is a three-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems such as computing the smallest enclosing ball of a set of points in Rd. In 2006, it has been shown that the algorithm in its original form works for violator spaces too, which are a proper generalization of LP-type problems. It was not clear, however, whether previous simplifications of the algorithm carry over to the new setting.In this paper we show the following theoretical results: (a) It is shown, for the first time, that Clarkson's second stage can be simplified. (b) The previous simplifications of Clarkson's first stage carry over to the violator space setting. (c) The equivalence of violator spaces and partitions of the hypercube by hypercubes.