On pointed Hopf algebras associated with the symmetric groups

Let G be the symmetric group . It is an important open problem whether the dimension of the Nichols algebra is finite when is the class of the transpositions and ρ is the sign representation, with m ≥ 6. In the present paper, we discard most of the other conjugacy classes showing that very few pairs might give rise to finite-dimensional Nichols algebras. This work was partially supported by CONICET, ANPCyT and Secyt (UNC).     

Balance in Stable Categories

We study when the stable category ${\mathcal A}/\langle{\mathcal T}\rangleWe study when the stable category A/áT?{\mathcal A}/\langle{\mathcal T}\rangle of an abelian category A{\mathcal A} modulo a full additive subcategory T{\mathcal T} is balanced and, in case T{\mathcal T} is functorially finite in A{\mathcal A}, we study a weak version of balance for A/áT?{\mathcal A}/\langle{\mathcal T}\rangle. Precise necessary and sufficient conditions are given in case T{\mathcal T} is either a Serre class or a class consisting of projective objects. The results in this second case apply very neatly to (generalizations of) hereditary abelian categories.     

Protonated Bis(quinuclidine) Included in Channel Thiourea-Bromide and Ribbons Thiourea-Iodide Lattice: New Thiourea Inclusion Compounds

Host-guest supramolecular complexes are of special interest for understanding the chemistry in low dimensional spaces. The molecular recognition involved in the formation of such structures sometimes may be a relevant model for the kind of organized system usually found in living organisms. Matrix effects and anisotropic features which are habitual of the chemistry in restricted spaces also appear as useful for the development of new material of scientific and technological importance (Takemoto and Sonoda, 1984). Urea and thiourea clathrates constitute interesting systems in which the matrix being structured by hydrogen bond interactions has a relatively high liability to structural changes caused by the interaction with the host (Lehn, 1996). The syntheses and crystal structure of two novel ternary inclusion compounds having protonated bis (quinuclidine) as a guest into anionic thiourea-bromide and thiourea-iodide hosts are reported: (thiourea₂[quinuclidine₂H]⁺Br^?), 1 and (thiourea₂[(quinuclidine₂H)⁺]₂(I^?)₂), 2. In the two structures thiourea molecules interact with each other via N–H....S hydrogen bonds to produce ribbon-like arrangements. In structure 1 these ribbons do not contain the halogen and define two non intersecting sets running along the a and b axis, linked through N–H....Br hydrogen bonds having the external halide ions as acceptors. This ribbon-crossover defines a channel structure along c with a cavity cross section of ca. 5.85 × 15.50 Å. In structure 2, ribbons contain iodide anions as well, bridging thiourea dimers into parallel 1D structures which align their flat side parallel to the (110) set of planes leaving a free spacing of ca. 8.25 Å.     

Cu(I) dinuclear complexes with tripodal ligands vs monodentate donors: triphenylphosphine, thiourea, and pyridine. A 1H NMR titration study

Complexes [PPh3Cu(Tr(Mes,Me))] (1), [PPh3Cu(Tr(Me,o-Py))] (2), and [PPh3Cu(Br(Mes)pz(o-Py))] (3) (Tr(Mes,Me) = hydrotris[1,4-dihydro-3-methyl-4-mesityl-5-thioxo-1,2,4-triazolyl]borate; Tr(Me,o-Py) = hydrotris[1,4-dihydro-4-methyl-3-(2-pyridyl)-5-thioxo-1,2,4-triazolyl]borate; Br(Mes)pz(o-Py) = hydro[bis(thioxotriazolyl)-3-(2-pyridyl)pyrazolyl]borate; PPh3 = triphenylphosphine) were synthesized by the reaction of dinuclear complexes [Cu(Tr(Mes,Me))]2, [Cu(Tr(Me,o-Py))]2, [Cu(Br(Mes)pz(o-Py))]2, and PPh3. 1-3 were characterized by 1H, 13C, and 31P NMR spectroscopy and ESI-mass spectrometry. Crystal structure analyses were performed for 1 and 2. Both complexes crystallize in the triclinic P space group with the metal in a slightly distorted tetrahedral geometry (S3P coordination) bound by a kappa3-S3 ligand and a PPh3 molecule. The solution molecular structures were investigated by means of variable-temperature (210-310 K, CDCl3, 1-2; 200-310 K, CD2Cl2, 3) and NOESY NMR spectroscopy. The solution structures of 1-2 are in accordance with the X-ray structures, and the complexes do not exhibit fluxional behavior. On the other hand, 3 is subject to an equilibrium between two species with a coalescing temperature of approximately 260 K. DFT geometry optimizations suggest that the major species of 3 consists of the Br(Mes)pz(o-Py) ligand bound to Cu(I) in the kappa3-S2H fashion with two C=S groups and a [Cu...H-B] interaction. A PPh3 completes the copper coordination (S2HP coordination). The complex [TuCu(Tr(Mes,Me))] (4) (Tu = thiourea) was crystallized using an excess of Tu with respect to [Cu(Tr(Me,2-Py))]2 (approximately a 6:1 ratio). The metal adopts a distorted tetrahedral geometry with an overall S3H coordination determined by the bound kappa3-S2H ligand (two C=S groups and a [B-H...Cu] interaction) and by a Tu. The reactivity of dinuclear complexes [Cu(Tr(Mes,Me))]2, [Cu(Tr(Me,o-Py))]2, and [Cu(Br(Mes)pz(o-Py))]2 with monodentate ligands was investigated by means of NMR titrations with PPh3, Tu. and pyridine (Py), and formation constants for the adducts [DCu(L)] (D = monodentate donor, L = tripodal ligand) were determined.     

Five-to-six membered ring-rearrangements in the reaction of 5-perfluoroalkyl-1,2,4-oxadiazoles with hydrazine and methylhydrazine

The hydrazinolysis reaction of 5-perfluoroalkyl-1,2,4-oxadiazoles with hydrazine or methylhydrazine as bidentate nucleophiles has been investigated. The reaction occurred through the addition of the bidentate nucleophile to the C(5)-N(4) double bond of the 1,2,4-oxadiazole followed by ring-opening and ring-closure (ANRORC) involving the second nucleophilic site of the reagent. This ring-closure step could involve either the original C(3) of the 1,2,4-oxadiazole (giving a five-to-five membered ring rearrangement) or an additional electrophilic center linked to it (exploiting a five-to-six membered ring rearrangement). An alternative initial nucleophilic attack may involve the additional electrophilic center linked at C(3), that is the carbonyl group, leading to the formation of the hydrazones which undergo the Boulton-Katritzky rearrangement (BKR). The chosen reaction path is a function of the used nucleophile and of the nature of the substituent at C(3). At variance with previous hypotheses, when methylhydrazine was used, the observed regiochemistry always showed the preferred initial attack by the less hindered NH(2) end of the nucleophile on C(5). Moreover, new spectroscopic evidence allowed the assignment of correct structures to the products formed by reaction of 5-perfluoroalkyl-3-phenyl-1,2,4-oxadiazoles with methylhydrazine.     

Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

The observation of the inspiral and merger of compact binaries by the LIGO/Virgo collaboration ushered in a new era in the study of strong-field gravity. We review current and future tests of strong gravity and of the Kerr paradigm with gravitational-wave interferometers, both within a theory-agnostic framework (the parametrized post-Einsteinian formalism) and in the context of specific modified theories of gravity (scalar–tensor, Einstein–dilaton–Gauss–Bonnet, dynamical Chern–Simons, Lorentz-violating, and extra dimensional theories). In this contribution we focus on (i) the information carried by the inspiral radiation, and (ii) recent progress in numerical simulations of compact binary mergers in modified gravity.     

Spin-flip limited exciton dephasing in CdSe/ZnS colloidal quantum dots

The dephasing time of the lowest bright exciton in CdSe/ZnS wurtzite quantum dots is measured from 5 to 170 K and compared with density dynamics within the exciton fine structure using a sensitive three-beam four-wave-mixing technique unaffected by spectral diffusion. Pure dephasing via acoustic phonons dominates the initial dynamics, followed by an exponential zero-phonon line dephasing of 109 ps at 5 K, much faster than the ~10 ns exciton radiative lifetime. The zero-phonon line dephasing is explained by phonon-assisted spin flip from the lowest bright state to dark-exciton states. This is confirmed by the temperature dependence of the exciton lifetime and by direct measurements of the bright-dark-exciton relaxation. Our results give an unambiguous evidence of the physical origin of the exciton dephasing in these nanocrystals.     

Structural influences on preferential oxazolone versus diketopiperazine b(2+) ion formation for histidine analogue-containing peptides

Studies of peptide fragment ion structures are important to aid in the accurate kinetic modeling and prediction of peptide fragmentation pathways for a given sequence. Peptide b(2)(+) ion structures have been of recent interest. While previously studied b(2)(+) ions that contain only aliphatic or simple aromatic residues are oxazolone structures, the HA b(2)(+) ion consists of both oxazolone and diketopiperazine structures. The structures of a series of histidine-analogue-containing Xxx-Ala b(2)(+) ions were studied by using action infrared multiphoton dissociation (IRMPD) spectroscopy, fragment ion hydrogen-deuterium exchange (HDX), and density functional theory (DFT) calculations to systematically probe the influence of different side chain structural elements on the resulting b(2)(+) ion structures formed. The b(2)(+) ions studied include His-Ala (HA), methylated histidine analogues, including π-methyl-HA and τ-methyl-HA, pyridylalanine (pa) analogues, including 2-(pa)A, 3-(pa)A, and 4-(pa)A, and linear analogues, including diaminobutanoic acid-Ala (DabA) and Lys-Ala (KA). The location and accessibility of the histidine π-nitrogen, or an amino nitrogen on an aliphatic side chain, were seen to be essential for diketopiperazine formation in addition to the more typical oxazolone structure formation, while blocking or removal of the τ-nitrogen did not change the b(2)(+) ion structures formed. Linear histidine analogues, DabA and KA, formed only diketopiperazine structures, suggesting that a steric interaction in the HisAla case may interfere with the complete trans-cis isomerization of the first amide bond that is necessary for diketopiperazine formation.     

Convex Quantum Logic

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. These differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement and it provides a new entanglement criteria.