Layered solutions with multiple asymptotes for non autonomous Allen–Cahn equations in {\mathbb {R}^{3}}

We consider a class of semilinear elliptic equations of the form $$ \label{eq:abs}-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\mathbb {R}^{3},$$ where ${a:\mathbb {R} \to \mathbb {R}}$ is a periodic, positive, even function and, in the simplest case, ${W : \mathbb {R} \to \mathbb {R}}$ is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W^{\prime}(q(x))=0,\ x\in\mathbb {R},\quad q(x)\to\pm1\,{\rm as}\, x\to \pm\infty,$$ we show, via variational methods the existence of infinitely many geometrically distinct solutions u of (0.1) verifying u(x, y, z) → ± 1 as x → ± ∞ uniformly with respect to ${(y, z) \in \mathbb {R}^{2}}$ and such that ${\partial_{y}u \not \equiv0, \partial_{z}u \not\equiv 0}$ in ${\mathbb {R}^{3}}$ .     

The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

Subcellular Duplex DNA and G‐Quadruplex Interaction Profiling of a Hexagonal PtII Metallacycle

Metal‐driven self‐assembly afforded a multitude of fascinating supramolecular coordination complexes (SCCs) with applications as catalysts, host–guest, and stimuli‐responsive systems. However, the interest in the biological applications of SCCs is only starting to emerge and thorough characterization of their behavior in biological milieus is still lacking. Herein, we report on the synthesis and detailed in‐cell tracking of a Pt₂L₂ metallacycle. We show that our hexagonal supramolecule accumulates in cancer cell nuclei, exerting a distinctive blue fluorescence staining of chromatin resistant to UV photobleaching selectively in nucleolar G4‐rich regions. SCC co‐localizes with epitopes of the quadruplex‐specific antibody BG4 and replaces other well‐known G4 stabilizers. Moreover, the photophysical changes accompanying the metallacycle binding to G4s in solution (fluorescence quenching, absorption enhancement) also take place intracellularly, allowing its subcellular interaction tracking.     

Optimizing the Size of Platinum Nanoparticles for Enhanced Mass Activity in the Electrochemical Oxygen Reduction Reaction

High oxygen reduction (ORR) activity has been for many years considered as the key to many energy applications. Herein, by combining theory and experiment we prepare Pt nanoparticles with optimal size for the efficient ORR in proton‐exchange‐membrane fuel cells. Optimal nanoparticle sizes are predicted near 1, 2, and 3 nm by computational screening. To corroborate our computational results, we have addressed the challenge of approximately 1 nm sized Pt nanoparticle synthesis with a metal–organic framework (MOF) template approach. The electrocatalyst was characterized by HR‐TEM, XPS, and its ORR activity was measured using a rotating disk electrode setup. The observed mass activities (0.87±0.14 A mg_Pt^?1) are close to the computational prediction (0.99 A mg_Pt^?1). We report the highest to date mass activity among pure Pt catalysts for the ORR within similar size range. The specific and mass activities are twice as high as the Tanaka commercial Pt/C catalysis.     

Atomic scale design and control of cation distribution in hexagonal ferrite

Using a novel alternating target laser ablation deposition technique, Mn cations were placed in specific interstitial sites of BaFe12O19 thin films as opposed to being distributed throughout the unit cell as in conventional bulk materials. The distribution of Mn cations has been confirmed experimentally and predicted theoretically. As a result of site selection, the saturation magnetization increased 12%-22%, and the Néel temperature increased by 40-60 K compared to bulk materials. This technique implies a new methodology to design and process a new generation of ferrite, oxide, and alloy materials.     

Statistical approach to the analysis of cell desynchronization data

Experimental measurements on semi-synchronous tumor cell populations show that after a few cell cycles they desynchronize completely, and this desynchronization reflects the intercell variability of cell-cycle duration. It is important to identify the sources of randomness that desynchronize a population of cells living in a homogeneous environment: for example, being able to reduce randomness and induce synchronization would aid in targeting tumor cells with chemotherapy or radiotherapy. Here we describe a statistical approach to the analysis of the desynchronization measurements that is based on minimal modeling hypotheses, and can be derived from simple heuristics. We use the method to analyze existing desynchronization data and to draw conclusions on the randomness of cell growth and proliferation.     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.