The small quantum group as a quantum double

We prove that the quantum double of the quasi-Hopf algebra of dimension attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] to a simple complex Lie algebra and a primitive root of unity q of order n² is equivalent to Lusztig's small quantum group (under some conditions on n). We also give a conceptual construction of using the notion of de-equivariantization of tensor categories.     

Simple Concepts

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined.     

Matrix-free interior point method for compressed sensing problems

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA, $\mathbf{\ell _1\_\ell _s}$ , PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an ${\mathcal {O}}(n^3)$ computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in $\mathbf{\ell _1\_\ell _s}$ and PDCO softwares. We go a few steps further. First, we use the matrix-free IPM, an approach which redesigns IPM to avoid the need to explicitly formulate (and store) the Newton equation systems. Secondly, we exploit the special features of the signal processing matrices within the matrix-free IPM. Two such features are of particular interest: an excellent conditioning of these matrices and the ability to perform inexpensive (low complexity) matrix–vector multiplications with them. Computational experience with large scale one-dimensional signals confirms that the new approach is efficient and offers an attractive alternative to other state-of-the-art solvers.     

Phase behaviour,structural properties and intermolecular interactions of systems based on substituted thiacalix[4]arene and nonionic surfactants

Supramolecular organised materials were prepared from nonionic surfactants and the following macrocyclic ionic liquids: n-tert-butylthiacalix[4]arenes containing quaternary ammonium fragments with amino acid substituents. Tetraethylene glycol monododecyl ether and decadiethylene glycol monododecyl ether were used as nonionic surfactants. They form lamellar and hexagonal mesophases in aqueous media, respectively. Liquid crystal and structural properties of these systems were studied. Intermolecular interactions of system components leading to formation of lyomesophases were estimated. Molecular structure of thiacalixarene contributes to the formation of a hydrogen bonding with surfactants. This process, in turn, initiates formation of a denser packed hexagonal structure.     

The unusual stability of H-bonded complexes in solvent caused by greater solvation energy of complex compared to those of isolated fragments

Here, the effect of solvent on the stability of non-covalent complexes, was studied. These complexes were from previously published S22, S66, and X40 datasets, which include hydrogen-, halogen- and dispersion-bonded complexes. It was shown that the charge transfer in the complex determines whether the complex is stabilized or destabilized in solvent.     

Conformations of polyolefins on platinum catalysts control product distribution in plastics recycling

The design of catalysts for the chemical recycling of plastic waste will benefit greatly from an intimate knowledge of the interfacial polymer–catalyst interactions that determine reactant and product distributions. Here, we investigate backbone chain length, side chain length, and concentration effects on the density and conformation of polyethylene surrogates at the interface with Pt(111) and relate them to experimental product distributions resulting from carbon–carbon bond cleavage. Using replica-exchange molecular dynamics simulations, we characterize the polymer conformations at the interface by the distributions of trains, loops, and tails and their first moments. We find that the preponderance of short chains, in the range of 20 carbon atoms, lies entirely on the Pt surface, whereas longer chains exhibit much broader distributions of conformational features. Remarkably, the average length of trains is independent of the chain length but can be tuned via the polymer–surface interaction. Branching profoundly impacts the conformations of long chains at the interface as the distributions of trains become less dispersed and more structured, localized around short trains, with the immediate implication of a wider carbon product distribution upon C–C bond cleavage. The degree of localization increases with the number and size of the side chains. Long chains can adsorb from the melt onto the Pt surface even in melt mixtures containing shorter polymer chains at high concentrations. We confirm experimentally key computational findings and demonstrate that blends may provide a strategy to reduce the selectivity for undesired light gases.

The design of catalysts for the chemical recycling of plastic waste will benefit greatly from an intimate knowledge of the interfacial polymer–catalyst interactions that determine reactant and product distributions.     

Ultrafast excited state dynamics controlling photochemical isomerization of N-methyl-4-[trans-2-(4-pyridyl)ethenyl]pyridinium coordinated to a {Re I(CO)3(2,2'-bipyridine)} chromophore

Two multifunctional photoactive complexes [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) and [Re(MeDpe(+))(CO)(3)(bpy)](2+) (MeDpe(+)=N-methyl-4-[trans-2-(4-pyridyl)ethenyl]pyridinium, bpy=2,2'-bipyridine) were synthesized, characterized, and their redox and photonic properties were investigated by cyclic voltammetry; ultraviolet-visible-infrared (UV/Vis/IR) spectroelectrochemistry, stationary UV/Vis and resonance Raman spectroscopy; photolysis; picosecond time-resolved absorption spectroscopy in the visible and infrared regions; and time-resolved resonance Raman spectroscopy. The first reduction step of either complex occurs at about -1.1 V versus Fc/Fc(+) and is localized at MeDpe(+). Reduction alone does not induce a trans-->cis isomerization of MeDpe(+). [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) is photostable, while [Re(MeDpe(+))(CO)(3)(bpy)](2+) and free MeDpe(+) isomerize under near-UV irradiation. The lowest excited state of [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) has been identified as the Re(Cl)(CO)(3)-->MeDpe(+ 3)MLCT (MLCT=metal-to-ligand charge transfer), decaying directly to the ground state with lifetimes of approximately 42 (73 %) and approximately 430 ps (27 %). Optical excitation of [Re(MeDpe(+))(CO)(3)(bpy)](2+) leads to population of Re(CO)(3)-->MeDpe(+) and Re(CO)(3)-->bpy (3)MLCT states, from which a MeDpe(+) localized intraligand (3)pipi* excited state ((3)IL) is populated with lifetimes of approximately 0.6 and approximately 10 ps, respectively. The (3)IL state undergoes a approximately 21 ps internal rotation, which eventually produces the cis isomer on a much longer timescale. The different excited-state behavior of the two complexes and the absence of thermodynamically favorable interligand electron transfer in excited [Re(MeDpe(+))(CO)(3)(bpy)](2+) reflect the fine energetic balance between excited states of different orbital origin, which can be tuned by subtle structural variations. The complex [Re(MeDpe(+))(CO)(3)(bpy)](2+) emerges as a prototypical, multifunctional species with complementary redox and photonic behavior.     

Heterologous expression, purification, refolding, and structural-functional characterization of EP-B2, a self-activating barley cysteine endoprotease

We describe the heterologous expression in Escherichia coli of the proenzyme precursor to EP-B2, a cysteine endoprotease from germinating barley seeds. High yields (50 mg/l) of recombinant proEP-B2 were obtained from E. coli inclusion bodies in shake flask cultures following purification and refolding. The zymogen was rapidly autoactivated to its mature form under acidic conditions at a rate independent of proEP-B2 concentration, suggesting a cis mechanism of autoactivation. Mature EP-B2 was stable and active over a wide pH range and efficiently hydrolyzed a recombinant wheat gluten protein, alpha2-gliadin, at sequences with known immunotoxicity in celiac sprue patients. The X-ray crystal structure of mature EP-B2 bound to leupeptin was solved to 2.2 A resolution and provided atomic insights into the observed subsite specificity of the endoprotease. Our findings suggest that orally administered proEP-B2 may be especially well suited for treatment of celiac sprue.     

Unexpected interconversion reaction of 1,4-diaminofullerenes

A facile substitution of amine groups attached to the fullerene cage occurs when 1,4-diaminofullerenes C60[NR2]2 are allowed to react with excess of another amine R'2NH; this reaction proceeds rapidly at room temperature without any additional initiators.     

Simple electrooptical sensors for inorganic anions

[reaction: see text] Electrooptical sensors consisting of a conjugated chromophore undergoing a change in color and a redox-active moiety such as quinone fused to the chromophore were synthesized. Strong changes in colorimetric and electrochemical properties were observed in the presence of inorganic anions. A unique anion-specific response was observed for fluoride, pyrophosphate, and acetate. DFT (B3LYP/6-31G) calculations performed for both "on/off" states of a sensor-fluoride model are in good agreement with the observed electrochemical and spectroscopic data.