Static bending of granular beam: exact discrete and nonlocal solutions

Meccanica - This study is an attempt towards a better understanding of the length scale effects on the bending response of the granular beams. To this aim, a unidimensional discrete granular chain...     

Unusual sum rule for Clebsch–Gordan coefficients

Letters in Mathematical Physics - We present a new sum rule for Clebsch–Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is...     

Two-Photon Absorption and Cell Imaging of Fluorene-Functionalized Epicocconone Analogues

Epicocconone 1 is a natural chromophore isolated from the fungus Epicoccum nigrum that has shown applications in proteomics and fluorescent microscopy thanks to its unique pro-fluorescence properties. The modification of the skeleton of the natural product by replacing the triene side chain by a fluorenyl scaffold can noticeably increase the fluorophore's absorption coefficient. The synthesis of the analogues of the natural product has been made possible by the use of a palladium-catalyzed carbonylation reaction, allowing the construction of the β-keto-dioxinone key intermediate. Two-photon absorption cross-section measurements of the fluorenyl epicocconone analogues show a structure dependency with values ranging from 60 to 280 GM and live cell imaging show intense staining of intracellular vesicle-like structures around the nucleus.     

Optimization of Experimental Parameters to Explore Small‐Ligand/Aptamer Interactions through Use of 1H NMR Spectroscopy and Molecular Modeling

Aptamers constitute an emerging class of molecules designed and selected to recognize any given target that ranges from small compounds to large biomolecules, and even cells. However, the underlying physicochemical principles that govern the ligand‐binding process still have to be clarified. A major issue when dealing with short oligonucleotides is their intrinsic flexibility that renders their active conformation highly sensitive to experimental conditions. To overcome this problem and determine the best experimental parameters, an approach based on the design‐of‐experiments methodology has been developed. Here, the focus is on DNA aptamers that possess high specificity and affinity for small molecules, L ‐tyrosinamide, and adenosine monophosphate. Factors such as buffer, pH value, ionic strength, Mg²⁺‐ion concentration, and ligand/aptamer ratio have been considered to find the optimal experimental conditions. It was then possible to gain new insight into the conformational features of the two ligands by using ligand‐observed NMR spectroscopic techniques and molecular mechanics.     

Poly(N-vinylimidazole/ethylene glycol dimethacrylate) for the purification and isolation of phenolic acids

In this study we report the novel polymeric resin poly(N-vinyl imidazole/ethylene glycol dimethacrylate) for the purification and isolation of phenolic acids. The monomer to crosslinker ratio and the porogen composition were optimized for isolating phenolic acids diluted in acetonitrile at normal phase chromatography conditions, first. Acetonitrile serves as polar, aprotic solvent, dissolving phenolic acids but not interrupting interactions with the stationary phase due to the approved Hansen solubility parameters. The optimized resin demonstrated high loading capacities and adsorption abilities particularly for phenolic acids in both, acetonitrile and aqueous solutions. The adsorption behavior of aqueous standards can be attributed to ion exchange effects due to electrostatic interactions between protonated imidazole residues and deprotonated phenolic acids. Furthermore, adsorption experiments and subsequent curve fittings provide information of maximum loading capacities of single standards according to the Langmuir adsorption model. Recovery studies of the optimized polymer in the normal-phase and ion-exchange mode illustrate the powerful isolation properties for phenolic acids and are comparable or even better than typical, commercially available solid phase extraction materials. In order to prove the applicability, a highly complex extract of rosemary leaves was purified by poly(N-vinyl imidazole/ethylene glycol dimethacrylate) and the isolated compounds were identified using UHPLC–qTOF-MS.     

Turning it off! Disfavouring hydrogen evolution to enhance selectivity for CO production during homogeneous CO2 reduction by cobalt–terpyridine complexes

Understanding the activity and selectivity of molecular catalysts for CO₂ reduction to fuels is an important scientific endeavour in addressing the growing global energy demand. Cobalt–terpyridine compounds have been shown to be catalysts for CO₂ reduction to CO while simultaneously producing H₂ from the requisite proton source. To investigate the parameters governing the competition for H⁺ reduction versus CO₂ reduction, the cobalt bisterpyridine class of compounds is first evaluated as H⁺ reduction catalysts. We report that electronic tuning of the ancillary ligand sphere can result in a wide range of second-order rate constants for H⁺ reduction. When this class of compounds is next submitted to CO₂ reduction conditions, a trend is found in which the less active catalysts for H⁺ reduction are the more selective towards CO₂ reduction to CO. This represents the first report of the selectivity of a molecular system for CO₂ reduction being controlled through turning off one of the competing reactions. The activities of the series of catalysts are evaluated through foot-of-the-wave analysis and a catalytic Tafel plot is provided.     

Convergence of the Two‐Dimensional Dynamic Ising‐Kac Model to

The Ising‐Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighborhood of radius γ ^{? 1} for around its base point. We study the Glauber dynamics for this model on a discrete two‐dimensional torus for a system size and for an inverse temperature close to the critical value of the mean field model. We show that the suitably rescaled coarse‐grained spin field converges in distribution to the solution of a nonlinear stochastic partial differential equation. This equation is the dynamic version of the quantum field theory, which is formally given by a reaction‐diffusion equation driven by an additive space‐time white noise. It is well‐known that in two spatial dimensions such equations are distribution valued and a Wick renormalization has to be performed in order to define the nonlinear term. Formally, this renormalization corresponds to adding an infinite mass term to the equation. We show that this need for renormalization for the limiting equation is reflected in the discrete system by a shift of the critical temperature away from its mean field value.© 2016 by the authors. Communications on Pure and Applied Mathematics is published by Wiley Periodicals, Inc., on behalf of the Courant Institute of Mathematics.     

Positive block matrices and numerical ranges

Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality $6M6\le 6M_{1,1}+M_{2,2}+\omega I6$, where ω is the width of the numerical range of $M_{1,2}$. Some related inequalities and a reverse Lidskii majorization are given.     

Chemical Processes Involving 18-Crown-6-Ether in Activated Noncovalent Complexes with Protonated Peptides

These last decades, it has been widely assumed that 18-crown-6-ether (CE) plays a spectator role during the chemical processes occurring in isolated host-guest complexes between peptides or proteins and CE after activation in mass spectrometers. Our present experimental and theoretical results challenge this hypothesis by showing that CE can abstract a proton or a protonated molecule from protonated peptides after activation by collisions in argon or electron capture/transfer. Furthermore, thanks to comparison between experimental and calculated values of collision cross-sections, we demonstrate that CE can change binding site after electron transfer. We also propose detailed mechanisms for these processes.