An explicit expression is obtained for the perimeter and area generating function G(y, z) = ∑ n>=2 ∑ m>=1 cn,my z, where cn,m is the number of row-convex polygons with area m and perimeter n. A similar expression is obtained for the area-perimeter generating function for staircase polygons. Both expressions contain q-series.

We study the conformal capacity by using novel computational algorithms based on implementations of fast multipole method, and analytic techniques. Especially, we apply domain functionals to capacities condensers $(G,E)$ where $G$ is a simply connected in complex plane $E$ compact subset $G$. Due invariance, our main tools are hyperbolic geometry such as perimeter $E$. Our experiments demonstra...

BACKGROUND Adjuvants can improve pesticide application efficiency and effectiveness. However, quantifications of the adjuvant-amended pesticide droplet actions on foliage, which could affect application efficiencies, are largely unknown. RESULTS Droplet evaporation rates and spread on waxy or hairy leaves varied greatly with the adjuvant types tested. On waxy leaves, the wetted areas of dropl...

Hydrophobic poly(methyl methacrylate) (PMMA) colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image-charge effects lead to strong binding of colloidal particles to the interface, even though the particles are wetted very little by the aqueous phase. We study both the...

Particles that are partially wetted by oil and water are known to adsorb at oil/water interfaces. By the same mechanism, particles that are partially wetted by two immiscible polymers should adsorb at the interface between those two polymers. However, since chemical differences between immiscible polymers are relatively modest, particle adsorption at polymer/polymer interfaces may be expected t...

Obstructive sleep apnea (OSA) is a medical condition characterized by repetitive obstructions in the human upper airways during sleep. Recent estimates from United States show that impacts 15% to 20% of adult population. OSA treatment can be subdivided into surgical and non-surgical approaches. Non-surgical approaches such as continuous positive airway pressure (CPAP) devices have highest succe...