A(SLq(2)) at Roots of Unity is a Free Module over A(SL(2))

It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.     

Studying Natural Buckyballs and Buckybowls in Fossil Materials

Buckyballs (fullerenes) were first reported over 30 years ago, but still little is known regarding their natural occurrence, since they have so far only been found at sites of high‐energy incidents, such as lightning strikes or meteor impacts, but have not been reported in low‐energy materials like fossil fuels. Using ultrahigh‐resolution mass spectrometry, a wide range of fullerenes from C₃₀ to C₁₁₄ was detected in the asphaltene fraction of a heavy crude oil, together with their building blocks of C_10nH₁₀ stoichiometry. High‐level DLPNO‐CCSD(T) calculations corroborate their stability as spherical and hemispherical species. Interestingly, the maximum intensity of the fullerenes was found at C₄₀ instead of the major fullerene C₆₀. Hence, experimental evidence supported by calculations show the existence of not only buckyballs but also buckybowls as 3‐dimensional polyaromatic compounds in fossil materials.     

New chiral polyfunctional cyclobutane derivatives from (−)-verbenone: possible surfactant behaviour

New enantiopure cyclobutane derivatives have been synthesized from a chiral precursor derived from (?)-verbenone. The cyclobutane moiety acts as a chiral platform to afford a γ-amino acid function in a branched side-chain containing an additional stereogenic centre as well as additional C₆ or C₁₆-alkyl chains linked to the ring by means of an amine or an amide function. One of these compounds, obtained as a 1:2 mixture with its TFA salt has been investigated, suggesting behaviour as a good surfactant and its critical micellar concentration has been determined.     

Theoretical and experimental characterization of amino‐PEG‐phosphonate‐terminated Polyphosphorhydrazone dendrimers: Influence of size and PEG capping on cytotoxicity profiles

The synthesis of new series of PPH (poly(phosphorhydrazone)) dendrimers with amino‐PEG phosphonates or the corresponding amino‐PEG phosphonic acids as terminal groups is presented, from generations 1–3. The size of PEG‐terminated dendrimers is experimentally measured by diffusional NMR, and by means of dynamic light scattering. Classical molecular dynamics and well‐tempered metadynamics simulations are used to assess or confirm the formation of aggregates in some cases. The influence of PEG capping on the cytotoxicity profiles of the dendrimers is evaluated on human peripheral blood mononuclear cells by means of LIVE/DEAD assays, and confirms the importance of PEG capping to ensure low cytotoxicity. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 761–774     

Incoherence correction strategies in statistical matching

Several economic applications require to consider different data sources and to integrate the information coming from them. This paper focuses on statistical matching, in particular we deal with incoherences. In fact, when logical constraints among the variables are present incoherencies on the probability evaluations can arise. The aim of this paper is to remove such incoherences by using different methods based on distances minimization or least commitment imprecise probabilities extensions. An illustrative example shows peculiarities of the different correction methods. Finally, limited to pseudo distance minimization, we performed a systematic comparison through a simulation study.     

Counter‐Rotating Spin‐Polarised Ring Currents in Odd‐Electron Carbocycles

We propose a molecular‐orbital model to explain how majority and minority spins in odd‐π‐electron carbocycles sustain counter‐rotating magnetic‐field‐induced ring currents. The model is based on the ipsocentric approach to magnetic response, in which ring currents are dominated by frontier‐orbital contributions obeying angular‐momentum selection rules. Coupled unrestricted Hartree–Fock ab initio calculations of the ring‐current responses for singly charged benzene and planarised cyclo‐octatetraene ions confirm the predictions of the qualitative model, and are consistent with correlated MP2 spin‐polarised current calculations.