Nanofibrillar Peptide Hydrogels for the Immobilization of Biocatalysts for Chemical Transformations

Enzymes are attractive, “green” alternatives to chemical catalysts within the industrial sector, but their robustness to environmental conditions needs optimizing. Here, an enzyme is tagged chemically and recombinantly with a self‐assembling peptide that allows the conjugate to spontaneously assemble with pure peptide to form β‐sheet‐rich nanofibers decorated with tethered enzyme. Above a critical concentration, these fibers entangle and form a 3D hydrogel. The immobilized enzyme catalyzes chemical transformations and critically its stability is increased significantly where it retains activity after exposure to high temperatures (90 °C) and long storage times (up to 12 months).

     

Design of hierarchical porous aluminas by using one-pot synthesis and different calcination temperatures

Hierarchical aluminas with pore sizes ranging from a few nanometers to micrometers were obtained using an one-pot sol?Cgel synthesis. The aluminas were synthesized under acid conditions from aluminum isopropoxide in presence of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer template and decahydronaphthalene as emulsifier agent. High-resolution transmission electron microscopy, small-angle X-ray scattering, nitrogen physisorption isotherms and mercury intrusion porosimetry provided evidences of porous structure at different hierarchical levels. The produced aluminas possess hierarchical structure composed of different family of pores that coexist in form of cylinders, pyramids and stacking of platelets. The morphology observed by electron microscopy suggests that the cylindrical pores result from the stacking platelets and that the cylinders and pyramidal pores form the walls of macropores of circular section. These aluminas with hierarchical porous architecture present large surface areas (ca. 435?m² g^?1) and pore volumes (ca. 2.1?cm³ g^?1), tunable pore-size distributions and good thermal stability.     

In Vitro Degradation of Poly(lactic-co2-glycolic) Acid Random Copolymers

We have investigated the in vitro degradation of poly(lactic-co-glycolic) acid copolymer with a lactic to glycolic ratio of 65/35. The degradation studies were performed on solvent-cast films of controlled thickness and shape. The samples were then incubated at 37 °C in phosphate buffered saline solution. The degradation was followed using potentiometry, light microscopy, gravimetry, gel permeation chromatography and differential scanning calorimetry. Water was found to diffuse inside the film as soon as the sample was placed in the degradation media. Wrinkles formed on the upper layer while degradation took place via chain scission in the bulk of the film. After 10 days, this led to the creation of a vesicle where liquid low molecular weight oligomers were trapped inside a thin film of high molecular weight polymer. This thin film acted as a membrane allowing only low molecular weight compounds to diffuse out of the film.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Gaps in the number of generators of monomial Togliatti systems

Let $I_{d,n}?k[x_0,?,x_n]$ be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators $\mu (I_{d,n})$ of $I_{d,n}$ lies in the interval $[2n+1,\left(\begin{array}{c}n+d?1\\ n?1\end{array}\right)]$. In this paper, we prove that for $n\ge 4$ and $d\ge 3$, the integer values in $[2n+3,3n?1]$ cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{d,n})=2n+2$ or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for $n=4$, $d\ge 3$ and $\mu \in [9,\left(\begin{array}{c}d+3\\ 3\end{array}\right)]?\{11\}$ there exists a minimal monomial Togliatti system $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{n,d})=\mu$.     

A bound on the treewidth of planar even-hole-free graphs

The class of planar graphs has unbounded treewidth, since the k×k grid, ∀k∈N, is planar and has treewidth k. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.     

Characterizing Extremal Digraphs for Identifying Codes and Extremal Cases of Bondy’s Theorem on Induced Subsets

An identifying code of a (di)graph G is a dominating subset C of the vertices of G such that all distinct vertices of G have distinct (in)neighbourhoods within C. In this paper, we classify all finite digraphs which only admit their whole vertex set as an identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well-known theorem of Bondy on set systems, we classify the extremal cases for this theorem.