On a singular minimizing problem

We investigate the non-homogeneous modular Dirichlet problem Δ _p (·)u(x) = f (x) (where Δ _p (·)u(x) = div(|?u|^p(x-2)?u(x)) from the functional analytic point of view and we prove the stability of the solutions \({\left( {{u_{{p_i}}}} \right)_i}\) of the equation \({\Delta _{{p_i}\left( \cdot \right)}}{u_{{p_i}\left( \cdot \right)}} = f\) as p _i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals.     

Die Pasteursche Methode zur Bestimmung der Bernsteins?ure neben anderen bei der G?rung entstehenden S?uren hat

Ohne Zusammenfassung     

Disulfide bond isomerization in basic pancreatic trypsin inhibitor: multisite chemical exchange quantified by CPMG relaxation dispersion and chemical shift modeling

Conformational changes occurring on the microsecond-millisecond time scale in basic pancreatic trypsin inhibitor (BPTI) are investigated using nuclear magnetic resonance spectroscopy. The rczz CPMG experiment (Wang, C.; Grey, M. J.; Palmer, A. G. J. Biomol. NMR 2001, 21, 361-366) is used to record (15)N spin relaxation dispersion data, R(ex)(1/tau(cp)), in which 1/tau(cp) is the pulsing rate in the CPMG sequence, at two static magnetic fields, 11.7 and 14.1 T, and three temperatures, 280, 290, and 300 K. These data are used to characterize the kinetics and mechanism of chemical exchange line broadening of the backbone (15)N spins of Cys 14, Lys 15, Cys 38, and Arg 39 in BPTI. Line broadening is found to result from two processes: the previously identified isomerization of the Cys 38 side chain between chi(1) rotamers (Otting, G.; Liepinsh, E.; Wüthrich, K. Biochemistry 1993, 32, 3571-3582) and a previously uncharacterized process on a faster time scale. At 300 K, both processes contribute significantly to the relaxation dispersion for Cys 14 and an analytical expression for a linear three-site exchange model is used to analyze the data. At 280 K, isomerization of the Cys 38 side chain is negligibly slow and the faster process dominates the relaxation dispersion for all four spins. Global analysis of the temperature and static field dependence of R(ex)(1/tau(cp)) for Cys 14 and Lys 15 is used to determine the activation parameters and chemical shift changes for the previously uncharacterized chemical exchange process. Through an analysis of a database of chemical shifts, (15)N chemical shift changes for Cys 14 and Lys 15 are interpreted to result from a chi(1) rotamer transition of Cys 14 that converts the Cys 14-Cys 38 disulfide bond between right- and left-handed conformations. At 290 K, isomerization of Cys 14 occurs with a forward and reverse rate constant of 35 s(-1) and 2500 s(-1), respectively, a time scale more than 30-fold faster than the Cys 38 chi(1) isomerization. A comparison of the kinetics and thermodynamics for the transitions between the two alternative Cys 14-Cys 38 conformations highlights the factors that affect the contribution of disulfide bonds to protein stability.     

Bond length alternation in cyclic polyenes. II. Unrestricted hartree–fock method

The problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π-electron Hamiltonian, together with an empirical quasi harmonic σ-core potential is investigated using the unrestricted Hartree–Fock wave function employing different spatial orbitals for different spins. It is shown that in contrast to the restricted Hartree–Fock method, which favors bond alternation in large cyclic polyenes, the unrestricted Hartree–Fock method stabilizes the symmetric structures with equidistant internuclear separation. An assessment of the amount of correlation error recovered by the unrestricted Hartree–Fock procedure is examined and the qualitatively different behavior of the cyclic polyene models when described by restricted and unrestricted Hartree–Fock wave functions is discussed from this viewpoint.     

Short- and long-range order in the positive electrode material, Li(NiMn)0.5O2: a joint X-ray and neutron diffraction, pair distribution function analysis and NMR study

The local environments and short-range ordering of LiNi(0.5)Mn(0.5)O(2), a potential Li-ion battery positive electrode material, were investigated by using a combination of X-ray and neutron diffraction and isotopic substitution (NDIS) techniques, (6)Li Magic Angle Spinning (MAS) NMR spectroscopy, and for the first time, X-ray and neutron Pair Distribution Function (PDF) analysis, associated with Reverse Monte Carlo (RMC) calculations. Three samples were studied: (6)Li(NiMn)(0.5)O(2), (7)Li(NiMn)(0.5)O(2), and (7)Li(NiMn)(0.5)O(2) enriched with (62)Ni (denoted as (7)Li(ZERO)Ni(0.5)Mn(0.5)O(2)), so that the resulting scattering length of Ni atoms is null. LiNi(0.5)Mn(0.5)O(2) adopts the LiCoO(2) structure (space group Rm) and comprises separate lithium layers, transition metal layers (Ni, Mn), and oxygen layers. NMR experiments and Rietveld refinements show that there is approximately 10% of Ni/Li site exchange between the Li and transition metal layers. PDF analysis of the neutron data revealed considerable local distortions in the layers that were not captured in the Rietveld refinements performed using the Bragg diffraction data and the LiCoO(2) structure, resulting in different M-O bond lengths of 1.93 and 2.07 Angstroms for Mn-O and Ni/Li-O, respectively. Large clusters of 2400-3456 atoms were built to investigate cation ordering. The RMC method was then used to improve the fit between the calculated model and experimental PDF data. Both NMR and RMC results were consistent with a nonrandom distribution of Ni, Mn, and Li cations in the transition metal layers; both the Ni and Li atoms are, on average, close to more Mn ions than predicted based on a random distribution of these ions in the transition metal layers. Constraints from both experimental methods showed the presence of short-range order in the transition metal layers comprising LiMn(6) and LiMn(5)Ni clusters combined with Ni and Mn contacts resembling those found in the so-called "flower structure" or structures derived from ordered honeycomb arrays.     

Structural Study of Li1+x−yNb1−x−3yTix+4yO3 Solid Solutions

The structures of Li_1+x−yNb_1−x−3yTi_x+4yO₃ solid solutions within the so-called M-phase field in the Li₂O-Nb₂O₅-TiO₂ system were investigated using high-resolution transmission electron, microscope (HRTEM) and single-crystal X-ray diffraction. The results demonstrated that the phase field is not a solid solution but rather a homologous series of commensurate intergrowth structures with LiNbO₃-type (LN) slabs separated by single [Ti₂O₃]²⁺ corundum-type layers. The thickness of the LN slab decreases with increasing Ti-content from ∼55 to 3 atomic layers in the metastable H-Li₂Ti₃O₇ end-member. The LN slabs accommodate a wide range of Ti⁴⁺/Nb⁵⁺ substitution, and for a given homolog the distribution of Ti and Nb is not uniform across the slab. A single-crystal X-ray diffraction study of a structure composed of nine-layer LN slabs revealed preferential segregation of Ti to the slab surfaces which apparently provides partial compensation for the charge on the adjacent [Ti₂O₃]²⁺ corundum layers. The extra cations in phases with x>0 are accommodated through the formation of Li-rich Li₂MO₃-type layers in the middle of the LN slabs. The fraction of layers with extra cations increases with increasing Ti-content in the structure.     

The crystal chemistry of L-Ta2O5 and related structures

Single crystals of a new form of L-Ta₂O₅ with a 19×b superstructure have been synthesised by flux growth. The phase is most likely stabilised by the incorporation of a small amount of lithium (0.14 wt% Li) from the flux. The phase has C-centred monoclinic symmetry with , (), , γ=90.00(1)°. The structure was refined in space group C112/m to R₁=0.044 for 814 unique reflections with F>4σ(F). The structure can be described as comprising chains of edge-shared TaO₇ pentagonal bipyramids that are regularly folded at (010) planes to give sinusoidal chains along [010]. These chains are interconnected along [100] and [001] by corner sharing, creating inter-chain regions that are occupied by isolated TaO₆ octahedra and pairs of corner-shared octahedra. A comparison with published data for high-quality refinements of related structures has led to the development of a general model that can explain the structural chemistry variations in the known L-Ta₂O₅-related structures. A shorthand notation is presented for representing the structures, based on the sequence along [010] of the interchain octahedra.     

Untersuchung von Wasser und Abwasser

Ohne Zusammenfassung     

Mechanism of THz emission from asymmetric double quantum wells

Impulsive interband optical excitation of the lowest two conduction subbands of a suitably engineered GaAs/AlGaAs double quantum well can lead to coherent THz emission. We demonstrate that, contrary to previous expectations, the dominant emission mechanism can involve the beating of either continuum or exciton states, depending on excitation conditions. The coherence of the continuum beats persists for several picoseconds even for excitation an optical phonon energy above the band edge. We attribute this to the small energy difference between the component eigenstates, which substantially reduces the number of relevant scattering events.