INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Scale Up of PLA Nanoparticle Synthesis by Solvent Displacement and Functionalization of the Particles with a Silica Shell for Targeted Drug Delivery Applications

Biodegradable polymer nanoparticles have the properties necessary to address many of the issues associated with current drug delivery techniques including targeted and controlled delivery. A novel drug delivery vehicle is proposed consisting of a poly(lactic acid) nanoparticle core, with a functionalized, mesoporous silica shell. In this study, the production of PLA nanoparticles is investigated using solvent displacement in both a batch and continuous manner, and the effects of various system parameters are examined. Using Pluronic F-127 as the stabilization agent throughout the study, PLA nanoparticles are produced through solvent displacement with diameters ranging from 200 to 250 nm using two different methods: dropwise addition and in an impinging jet mixer. The impinging jet mixer allows for easy scale-up of particle production. The concentration of surfactant and volume of quench solution is found to have minimal impact on particle diameter; however, the concentration of PLA is found to significantly impact the diameter mean and polydispersity. In addition, the stability of the PLA nanoparticles is observed to increase as residual THF is evaporated. Lastly, the isolated PLA nanoparticles are coated with a silica shell using the Stöber Process. It is found that functionalizing the silica with a phosphonic silane in the presence of excess Pluronic F-127 decreases coalescence of the particles during the coating process. Future work should be conducted to fine-tune the PLA nanoparticle synthesis process by understanding the effect of other system parameters and in synthesizing mesoporous silica shells.