On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

$$\left( {\mathop \Sigma \limits_{i = 1}^\infty \mathop \Sigma \limits_{j = 1}^\infty a_{ij}^{(n)} \mu ^i *v^j ,n \in \mathbb{N}} \right)$$     

A Note on Some Inequalities for Finite Sums and an Application to Entropies of Probability Distributions

In this paper we prove some inequalities for finite sums with positive terms. As a consequence of these results we obtain an inequality for entropies of discrete probability distributions.     

Synthesis of 5-, 6- and 7-substituted-2-aminoquinolines as SH3 domain ligands

The Src homology 3 (SH3) domains are small protein-protein interaction domains that mediate a range of important biological processes and are considered valuable targets for the development of therapeutic agents. We have been developing 2-aminoquinolines as ligands for SH3 domains--so far the only reported examples of entirely small-molecule ligands for the SH3 domains. The highest affinity 2-aminoquinolines so far identified are 6-substituted compounds. In this article, the synthesis of several new 2-aminoquinolines, including 5-, 6- and 7-substituted compounds, for Tec SH3 domain ligand binding studies is presented. As a part of the synthetic investigation, the utility of different methods for the synthesis of 2-aminoquinolines was explored and potentially powerful methods were identified for the synthesis of 2-aminoquinolines with diverse functionality. Of the compounds prepared, the 5-substituted-2-aminoquinolines generally bound with similar affinities to unsubstituted 2-aminoquinoline, whilst the 7-substituted compounds generally bound with similar or lower affinity than unsubstituted 2-aminoquinoline. However, the 6-substituted-2-aminoquinolines generally bound with significantly higher affinity than unsubstituted 2-aminoquinoline. In addition, one 6-substituted-N-benzylated-2-aminoquinoline was also tested for SH3 binding and some evidence for the formation of additional contacts at other regions of the SH3 domain was found. These results provide new and useful SAR information that should greatly assist with the challenge of developing high affinity small-molecule ligands for the SH3 domains.