Random Walk on Surfaces with Hyperbolic Cusps

We consider the operator associated with a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated with this operator and deduce some rate of convergence of the iterated kernel towards its stationary distribution.     

Drawing Disconnected Graphs on the Klein Bottle

We prove that two disjoint graphs must always be drawn separately on the Klein bottle in order to minimize the crossing number of the whole drawing.     

Effect of X-ray $$mu$$ μ CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils

Transport in Porous Media - X-ray micro-computed tomography ( $$mu$$ CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of...     

Grafting of Lanthanum Complexes on a Functionalized Graphene Surface: Theoretical Investigation on Ethylene and 1,3-Butadiene Homo- and Co-Polymerization

In this contribution, we describe the use of graphene as an efficient catalyst support and the role it plays in increasing the Lewis acidity of the supported metal complexes. By a density functional theory study, we show that the [La(N(SiMe₃)₂)₃] complex can be easily grafted on graphene-OH and -COOH functionalized surfaces. Two stable mono-grafted compounds, (gO)-[La(N(SiMe₃)₂)₂] and (gOO)-[La(N(SiMe₃)₂)₂], are formed, behaving as stronger Lewis acids than the previously reported silica grafted analogues. To study the role of the graphene support in catalysis, we also computed the catalytic activity of the alkylated (gO)-[La(CH₃)₂] and (gOO)-[La(CH₃)₂] complexes in the ethylene and 1,3-butadiene homo- and co-polymerization reactions. Both compounds are efficient catalysts for the homo-polymerization of the ethylene and 1,3-butadiene. For the 1,3-butadiene homo-polymerization, the stereoselectivity outcome of the reaction differs according to the grafting site. The results computed for the co-polymerization reaction, finally, show that the high stability of the allylic products leads to the formation of block copolymers.     

Anchoring Supramolecular Polymers to Human Red Blood Cells by Combining Dynamic Covalent and Non-Covalent Chemistries

Understanding cell/material interactions is essential to design functional cell-responsive materials. While the scientific literature abounds with formulations of biomimetic materials, only a fraction of them focused on mechanisms of the molecular interactions between cells and material. To provide new knowledge on the strategies for materials/cell recognition and binding, supramolecular benzene-1,3,5-tricarboxamide copolymers bearing benzoxaborole moieties are anchored on the surface of human erythrocytes via benzoxaborole/sialic-acid binding. This interaction based on both dynamic covalent and non-covalent chemistries is visualized in real time by means of total internal reflection fluorescence microscopy. Exploiting this imaging method, we observe that the functional copolymers specifically interact with the cell surface. An optimal fiber affinity towards the cells as a function of benzoxaborole concentration demonstrates the crucial role of multivalency in these cell/material interactions.     

Stabilization of the Oxidation State +IV in Siloxide-Supported Terbium Compounds

The synthesis of lanthanides other than cerium in the oxidation state +IV has remained a desirable but unmet target until recently, when two examples of Tb^IV with saturated coordination spheres were isolated. Here we report the third example of an isolated molecular complex of terbium(IV), where the supporting siloxide ligands do not saturate the coordination sphere. The fully characterized six-coordinate complex [Tb^IV(OSiPh₃)₄(MeCN)₂], 2 -Tb^Ph, shows high stability and the labile MeCN ligands can be replaced by phosphinoxide ligands. Computational studies suggest that the stability is due to a strong π(O−Tb) interaction which is stronger than in the previously reported Tb^IV complexes. Cyclic-voltammetry experiments demonstrate that non-binding counterions contribute to the stability of Tb^IV in solution by destabilizing the +III oxidation state, while alkali ions promote Tb^IV/Tb^III electron transfer.     

Regioselective Hydrosilylation of Olefins Catalyzed by a Molecular Calcium Hydride Cation

Chemo‐ and regioselectivity are often difficult to control during olefin hydrosilylation catalyzed by d‐ and f‐block metal complexes. The cationic hydride of calcium [CaH]⁺ stabilized by an NNNN macrocycle was found to catalyze the regioselective hydrosilylation of aliphatic olefins to give anti‐Markovnikov products, while aryl‐substituted olefins were hydrosilyated with Markovnikov regioselectivity. Ethylene was efficiently hydrosilylated by primary and secondary hydrosilanes to give di‐ and monoethylated silanes. Aliphatic hydrosilanes were preferred over other commonly employed hydrosilanes: Arylsilanes such as PhSiH₃ underwent scrambling reactions promoted by the nucleophilic hydride, while alkoxy‐ and siloxy‐substituted hydrosilanes gave isolable alkoxy and siloxy calcium derivatives.     

Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions

Efficient recovery of smooth functions which are s-sparse with respect to the basis of so-called prolate spheroidal wave functions from a small number of random sampling points is considered. The main ingredient in the design of both the algorithms we propose here consists in establishing a uniform L ^∞ bound on the measurement ensembles which constitute the columns of the sensing matrix. Such a bound provides us with the restricted isometry property for this rectangular random matrix, which leads to either the exact recovery property or the “best s-term approximation” of the original signal by means of the ? ¹ minimization program. The first algorithm considers only a restricted number of columns for which the L ^∞ holds as a consequence of the fact that eigenvalues of the Bergman’s restriction operator are close to 1 whereas the second one allows for a wider system of PSWF by taking advantage of a preconditioning technique. Numerical examples are spread throughout the text to illustrate the results.