Interpolation of bilinear operators and compactness

The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some gaps in the original proof of Theorem 4.3, Here we give a new proof. For this, we change the Lemma 4.

The bacterial hydrophobin BslA is a switchable ellipsoidal Janus nanocolloid

BslA is an amphiphilic protein that forms a highly hydrophobic coat around <i>Bacillus subtilis</i> biofilms, shielding the bacterial community from external aqueous solution. It has a unique structure featuring a distinct partition between hydrophilic and hydrophobic surfaces. This surface property is reminiscent of synthesized Janus colloids. By investigating the behavior of BslA variants at water-cyclohexane interfaces through a set of multiscale simulations informed by experimental data, we show that BslA indeed represents a biological example of an ellipsoidal Janus nanoparticle, whose surface interactions are, moreover, readily switchable. BslA contains a local conformational toggle, which controls its global affinity for, and orientation at, water–oil interfaces. This adaptability, together with single-point mutations, enables the fine-tuning of its solvent and interfacial interactions, and suggests that BslA could be a basis for biotechnological applications

Cation Ordering and Exsolution in Copper-Containing Forms of the Flexible Zeolite Rho (Cu,M-Rho; M=H, Na) and Their Consequences for CO₂ Adsorption

Funding: UK Engineering and Physical Sciences Research Council. Grant Numbers: EP/N024613/1, EP/N032942/1, EP/L017008/1.The flexibility of the zeolite Rho framework offers great potential for tunable molecular sieving. The fully copper-exchanged form of Rho and mixed Cu,H- and Cu,Na-forms have been prepared. EPR spectroscopy reveals that Cu2+ ions are present in the dehydrated forms and Rietveld refinement shows these prefer S6R sites, away from the d8r windows that control diffusion. Fully exchanged Cu-Rho remains in an open form upon dehydration, the d8r windows remain nearly circular and the occupancy of window sites is low, so that it adsorbs CO2 rapidly at room temperature. Breakthrough tests with 10 % CO2/40 % CH4 mixtures show that Cu4.9-Rho is able to produce pure methane, albeit with a relatively low capacity at this pCO2 due to the weak interaction of CO2 with Cu cations. This is in strong contrast to Na-Rho, where cations in narrow elliptical window sites enable CO2 to be adsorbed with high selectivity and uptake but too slowly to enable the production of pure methane in similar breakthrough experiments. A series of Cu,Na-Rho materials was prepared to improve uptake and selectivity compared to Cu-Rho, and kinetics compared to Na-Rho. Remarkably, Cu,Na-Rho with >2 Cu cations per unit cell exhibited exsolution, due to the preference of Na cations for narrow S8R sites in distorted Rho and of Cu cations for S6R sites in the centric, open form of Rho. The exsolved Cu,Na-Rho showed improved performance in CO2/CH4 breakthrough tests, producing pure CH4 with improved uptake and CO2/CH4 selectivity compared to that of Cu4.9-Rho.Publisher PDFPeer reviewe

Just in case it rains:building a hydrophobic biofilm the <i>Bacillus subtilis</i> way

Over the millennia, diverse species of bacteria have evolved multiple independent mechanisms to structure sessile biofilm communities that confer protection and stability to the inhabitants. The Gram-positive soil bacterium Bacillus subtilis biofilm presents as an architecturally complex, highly hydrophobic community that resists wetting by water, solvents, and biocides. This remarkable property is conferred by a small secreted protein called BslA, which self-assembles into an organized lattice at an interface. In the biofilm, production of BslA is tightly regulated and the resultant protein is secreted into the extracellular environment where it forms a very effective communal barrier allowing the resident B. subtilis cells to shelter under the protection of a protein raincoat