Computer‐Aided Estimation of Diffusion Coefficients in Non‐Solvent/Polymer Systems

A novel method for estimating the mutual and self‐diffusion coefficients of a non‐solvent/polymer system is proposed in this work. The idea is to study the evaporation process from non‐solvent/solvent/polymer systems as a one‐dimensional numerical experiment and to use polymer solution weight versus time data to fit the unknown parameters of the diffusion‐coefficient correlations based on free‐volume theory. For this purpose, the evaporation process is modeled as a coupled heat‐ and mass‐transfer problem with a moving boundary, and the Galerkin finite‐element method is used to solve simultaneously the non‐linear governing equations. This method is successfully applied to the estimation of water–cellulose acetate diffusion coefficients and is valid over the whole range of temperatures and concentrations for practical applications in membrane technology. Additionally, there is a detailed discussion on if water affects the morphology of the final cellulosic membrane by studying the concentration profiles of the constituents of the casting solution.     

The fractional porous medium equation on manifolds with conical singularities II

This is the second of a series of two papers that studies the fractional porous medium equation, ${\partial }_{t}u+{(-\mathrm{\Delta })}^{\sigma }{(|u|}^{m-1}u)=0$ with $m>0$ and $\sigma \in (0,1]$, posed on a Riemannian manifold with isolated conical singularities. The first aim of the article is to derive some useful properties for the Mellin–Sobolev spaces including the Rellich–Kondrachov theorem and Sobolev–Poincaré, Nash and Super Poincaré type inequalities. The second part of the article is devoted to the study the Markovian extensions of the conical Laplacian operator and its fractional powers. Then based on the obtained results, we establish existence and uniqueness of a global strong solution for $L_{\infty }-$initial data and all $m>0$. We further investigate a number of properties of the solutions, including comparison principle, $L_p-$contraction and conservation of mass. Our approach is quite general and thus is applicable to a variety of similar problems on manifolds with more general singularities.     

An Efficient Opal-Suppressor Tryptophanyl Pair Creates New Routes for Simultaneously Incorporating up to Three Distinct Noncanonical Amino Acids into Proteins in Mammalian Cells**

Site-specific incorporation of multiple distinct noncanonical amino acids (ncAAs) into proteins in mammalian cells is a promising technology, where each ncAA must be assigned to a different orthogonal aminoacyl-tRNA synthetase (aaRS)/tRNA pair that reads a distinct nonsense codon. Available pairs suppress TGA or TAA codons at a considerably lower efficiency than TAG, limiting the scope of this technology. Here we show that the E. coli tryptophanyl (EcTrp) pair is an excellent TGA-suppressor in mammalian cells, which can be combined with the three other established pairs to develop three new routes for dual-ncAA incorporation. Using these platforms, we site-specifically incorporated two different bioconjugation handles into an antibody with excellent efficiency, and subsequently labeled it with two distinct cytotoxic payloads. Additionally, we combined the EcTrp pair with other pairs to site-specifically incorporate three distinct ncAAs into a reporter protein in mammalian cells.     

Positive solutions for singular p(z)$p(z)$-equations

We consider a Dirichlet problem driven by the anisotropic p-Laplacian, with a reaction having the competing effects of a singular term and a parametric superlinear perturbation. We prove a bifurcation-type theorem describing the changes of the set of positive solutions as the parameter varies. We also prove the existence of minimal positive solutions.