Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

The electrochemical manipulation of apolar solvent drops in aqueous electrolytes by altering the surface polarity of polypyrrole architectures

We demonstrate an electrochemically assisted three-dimensional robotic system for the pickup, transport and release of dichloromethane drops in electrolytes using polypyrrole-coated O-rings. Changing the oxidation state of the polymer by means of cyclic voltammetry, pickup, transport and release of drops is demonstrated. Also, the drop manipulation is evaluated as a function of different doping agents in the polypyrrole coatings. Moreover, other polypyrrole-coated architectures such as chips and meshes are utilized to manipulate dichloromethane drops to successfully trap and release them on demand in moving electrolytes. These architectures are envisioned for use as microfluidic tools such as microreactors or microseparators.     

Periodic Solutions of the Duffing Differential Equation Revisited via the Averaging Theory

We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations $\ddot y+ a \sin y= b \sin t$ and $\ddot y+a y-c y^3=b\sin t$, where $a$, $b$ and $c$ are real parameters.     

Negatively Charged Metallacarborane Redox Couples with Both Members Stable to Air

The metallacarborane [3,3′‐Co(1,2‐closo‐C₂B₉H₁₁)₂]^? has been synthesized. This species allows the formation of redox couples in which both partners are negatively charged. The E_1/2 potential can be tuned by adjusting the nature and number of substituents on B and C. The octaiodinated species [3,3′‐Co(1,2‐closo‐C₂B₉H₇I₄)₂]^? is the most favorable, as it is isolatable and stable in air. A DFT study on stability and redox potentials of complexes has been performed.     

Metallacarboranes as Photoredox Catalysts in Water

Metallacarboranes with the shape of the Greek letter θ, such as [Co(C₂B₉H₁₁)₂]⁻, were tested, for the first time, as efficient photoredox catalysts in the oxidation of aromatic and aliphatic alcohols in water. Their efficiency is linked to their high solubility in water, their high oxidizing power (Co^4+/3+), and their absence of fluorescence on excitation, among others. In most of the studied examples, using a catalyst load of 0.4 mol % gave high yields of 90–95 % with selectivity greater than 99 %. By reducing the catalyst load to 0.01 mol %, quantitative conversion of reactants to products was achieved, in some cases with greater than 99 % yield, high catalyst efficiency reaching a turnover number of 10 000, and a higher yield with a 45 times lower concentration of catalyst. The metallacarboranes can be recovered easily by precipitation on addition of [NMe₄]Cl. A pathway for the photoredox-catalyzed oxidation of alcohols is proposed.     

Highlights on the Binding of Cobalta-Bis-(Dicarbollide) with Glucose Units

Metalla-bis-dicarbollides, such as the cobalta-bis-dicarbollide (COSAN) anion [Co(C₂B₉H₁₁)₂]⁻, have attracted much attention in biology but a deep understanding of their interactions with cell components is still missing. For this purpose, we studied the interactions of COSAN with the glucose moiety, which is ubiquitous at biological interfaces. Octyl-glucopyranoside surfactant (C8G1) was chosen as a model as it self-assembles in water and creates a hydrated glucose-covered interface. At low COSAN content and below the critical micellar concentration (CMC) of C8G1, COSAN binds to C8G1 monomers through the hydrophobic effect. Above the CMC of C8G1, COSAN adsorbs onto C8G1 micelles through the superchaotropic effect. At high COSAN concentrations, COSAN disrupts C8G1 micelles and the assemblies become similar to COSAN micelles but with a small amount of solubilized C8G1. Therefore, COSAN binds in a versatile way to C8G1 through either the hydrophobic or superchaotropic effect depending on their relative concentrations.