Gradings on Modules Over Lie Algebras of E Types

For any grading by an abelian group G on the exceptional simple Lie algebra \(\mathcal {L}\) of type E ₆ or E ₇ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple finite-dimensional modules, thus completing the computation of these invariants for simple finite-dimensional Lie algebras. This yields the classification of finite-dimensional G-graded simple \(\mathcal {L}\)-modules, as well as necessary and sufficient conditions for a finite-dimensional \(\mathcal {L}\)-module to admit a G-grading compatible with the given G-grading on \(\mathcal {L}\).     

Simulation of heterogeneous end-coupling reactions in polydisperse polymer blends

The influence of polydispersity on the interfacial kinetics of end-coupling and microstructure formation in the melt of immiscible polymers was studied using dissipative particle dynamics simulations. The irreversible reaction started at a flat interface between two layers, each of which contained polymer chains of two different lengths with functionalized or unreactive end groups. As in the case of fully functionalized monodisperse reactants [A. V. Berezkin and Y. V. Kudryavtsev, Macromolecules 44, 112 (2011)], four kinetic regimes were observed: linear (mean field coupling at the initial interface), saturation (decreasing the reaction rate due to the copolymer brush formation or reactant depletion near the interface), autocatalytic (loss of the initial interface stability and formation of a lamellar microstructure), and terminal (microstructure ripening under diffusion control). The interfacial instability is caused by overcrowding the interface with the reaction product, and it can be kinetically suppressed by increasing chain length of the reactants. Main effects of polydispersity are as follows: (i) the overall end-coupling rate is dominated by the shortest reactive chains; (ii) the copolymer concentration at the interface causing its instability can be not the same as in the lamellas formed afterwards; (iii) mean length of the copolymer product considerably changes with conversion passing through a minimum when a microstructure is just formed.     

Local coordination of Fe3+ in Li[Co(0.98)Fe(0.02)]O2 as cathode material for lithium ion batteries-multi-frequency EPR and Monte-Carlo Newman-superposition model analysis

The local coordination of the Fe(3+)-centers in Li[Co(0.98)Fe(0.02)]O(2) cathode materials for lithium-ion batteries has been investigated by means of XRD and multi-frequency EPR spectroscopy. EPR clearly showed the Fe(3+) being in a high-spin state with S = 5/2. The set of spin-Hamiltonian parameters obtained from multi-frequency EPR experiments with Larmor frequencies ranging between 9.8 and 406 GHz was transformed into structural information by means of an expansion to standard Newton-superposition modeling, termed as Monte-Carlo Newman superposition modeling. Based on this analysis, an isovalent incorporation of the Fe(3+)-ions on the Co(3+)-sites, i.e. Fe(x)(Co), has been shown. With that respect, the positive sign of the axial second-order fine-structure interaction parameter B(0)(2) is indicative of an elongated oxygen octahedron, whereas B(0)(2) < 0 points to a compressed octahedron coordinated about the Fe(3+)-center. Furthermore, the results obtained here suggest that the oxygen octahedron about the Fe(3+)-ion is slightly distorted as compared to the CoO(6) octahedron, which in turn may impose mechanical strain to the cathode material.     

Evidence for a high mass enhancement in K+K− photoproduction

The reaction γp → K⁺K^? p has been investigated with tagged photons in the energy range of 20 < E_γ < 70 GeV. A structure in the 1.7 GeV mass region is observed and interpreted in terms of a recurrence of the ø.     

Thermal accommodation coefficients by high speed vibration of solid samples: VI. O2 and N2 on As(111) and Sb(111) single crystal surfaces

Translational γ_t and rotational γ_r energy accommodation coefficients are measured using a high speed vibrational method described earlier. For N₂ on cleaved As(111) single crystal surfaces γ_t = 0.34 ± 0.03, γ_r = 0.03 ± 0.03; on cleaved Sb(111) single crystal surfaces γ_t = 0.49 ± 0.02, γ_r = 0.06 ± 0.04. For O₂ on As(111) γ_t = 0.39 ± 0.02, γ_r = 0.02 ± 0.02; on Sb(111) γ_t = 0.56 ± 0.05, γ_r = 0.07 ± 0.06. (Uncertainties are statistical estimates of precision. In addition, it is possible that the results are systematically low by up to 10%.) Comparison with N₂ and O₂ accommodation coefficients measured by the same method on other metal substrates suggests that the antimony surface is covered by chemisorbed oxygen but that the arsenic surface is somewhat cleaner. The results are consistent with oxidation of these semimetals occurring by way of physisorbed gas precursor states.     

A journey through quality control

The Euroanalysis VII conference in Vienna included a two-day session: Quality Assurance in Analytical Chemistry. The contributions comprised 15 lectures devoted to: intra-laboratory quality measures, inter-laboratory control, formal aspects and accreditation and implementation. The paper presents an overview of the main items developed by the contributors.A survey on the session on Quality Assurance in Analytical Chemistry of Euroanalysis VIIThe authors thank the organizers of EUROANALYSIS VII and in particular Dr. B. Griepink and Dr. E. Maier of the Community Bureau of Reference (BCR) of the CEC for their support and considerable contributions.     

Transition quadrupole moments of superdeformed states in194Pb

Lifetimes of superdeformed states in¹⁹⁴Pb were measured by the Doppler-shift attenuation method. Quadrupole moments around 20 eb, that are constant over the observed frequency range, are derived. The results rule out large centrifugal stretching effects.     

Extending the nitrogen-heterosuperbenzene family: the spectroscopic, redox, and photophysical properties of "half-cyclized" N-1/2HSB and Its Ru(II) complex

Oxidative cyclodehydrogenation is an important process in the formation of the new graphene, N-(1)/(2)HSB 2. This heteropolyaromatic results from the FeCl(3)-catalyzed oxidative cyclodehydrogenation of 1,2-dipyrimidyl-3,4,5,6-tetra-(4-tert-butylphenyl)benzene. Three new C-C bonds are formed that lock the two pyrimidines in a molecular platform comprising eight fused aromatic rings flanked by two remaining "uncyclized" phenyl rings. Mechanistically intriguing is the fact that N-HSB 1, the product of six C-C bond fusions, is co-synthesized with its "half-cyclized" daughter in this reaction. 1 and 2 have the same bidentate N-atom arrangement. This facilitates formation of the heteroleptic Ru(II) complexes, [Ru(bpy)(2)(2)](PF(6))(2) 4 and [Ru(bpy)(2)(1)](PF(6))(2) 3, which differ in the size and planarity of their aromatic ligands. The new ligand 2 and its complex 4 are characterized by (1)H NMR, IR, ESI-MS, and accurate mass methods. 2 exhibits photophysical properties that are consistent with a reduction of the pi/pi framework, a concomitant increase in the energy of the LUMO, and a blue-shift of the solvent-dependent fluorescence (lambda(em) = 474 nm, phi(F) = 0.55, toluene) as compared to its parent. Complex 4 absorbs throughout the visible region and borders on near-IR emitter character, exhibiting a slightly blue-shifted (3)MLCT emission (868 nm, CH(3)CN) as compared to that of [Ru(bpy)(2)(1)](PF(6))(2) 3 (880 nm, CH(3)CN). Electrochemical analyses permit further elucidation of the intermolecular interactions of 3 and 4. These and the concentration and temperature-dependent NMR spectra of 4 confirm it to be nonaggregating, a direct result of the two uncyclized and rotatable phenyl rings in 2.     

On nonlinear integral equations and Λ-bounded variation

Summary We discuss the existence or the existence and uniqueness of global and local -bounded variation (BV) solutions as well as continuous BV-solutions of nonlinear Hammerstein and Volterra-Hammerstein integral equations formulated in terms of the Lebesgue integral. Since the space of functions of bounded variation in the sense of Jordan is a proper subspace of functions of -bounded variation and for some class of functions , the space of functions of bounded -variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.