Abstract.e Osgood-Carathéodory theorem asserts that conformal mappings between Jordan domains extend to homeomorphisms between their closures. For multiplyconnected domains on Riemann surfaces, similar results can be reduced to the simplyconnected case, but we nd it simpler to deduce such results using a direct analogue of the Carathéodory re ection principle.
The inhibition of gas hydrate (clathrate hydrate) formation plays an important role in petroleum industries. A way to prevent this problem is injecting chemical inhibitors to the transportation pipelines. Two typical kinds of chemical inhibitors are thermodynamic and kinetic inhibitors. The main goal of the current work is to provide a thermodynamic model without using any adjustable parameters for prediction of the dissociation conditions of hydrate for pure and mixed gases including several thermodynamic inhibitors of ethylene glycol (EG), methanol (MeOH), potassium chloride (KCl), calcium chloride (CaCl 2 ), and sodium chloride (NaCl). For this purpose, application of the extended UNIQUAC activity coefficient model along with the van der Waals-Platteuw solid solution theory has been proposed. A comprehensive literature survey has been performed to provide a complete set of experimental data, and 1455 data points have been provided. Comparing the current model results with the experimental data reported in literature, the average absolute deviations (AAD) is 0.50 K which shows the accuracy of the results of the model developed in the current study.
We study the problem of tracking multiple diffusing particles using a laser scanning fluorescence microscope. The goal is to design trajectories for the laser to maximize the information contained in the measured intensity signal about the particles' trajectories. Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it. In the higher level controller, we decide which particle should be observed at each instant, with the goal of efficiently estimating each particle position while not losing track of any of them. Using simulations, we show that this technique is able to collect photons efficiently and to track multiple particles with low position estimation error.
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