Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N−H⋅⋅⋅O and C−H⋅⋅⋅O Hydrogen Bond Networks**

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C₁₂H₃₀N₈)]³⁺ ⋅ 3 NO₃⁻ is reported to undergo a disorder-order phase transition at T_c1 ≈133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T_c1. The modulation wave vector varies as function of temperature and locks in at T_c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T_c1<T<T_c3. Distinctive levels of competitions: trade-off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.     

Artificial Splitting of a Non‐Ribosomal Peptide Synthetase by Inserting Natural Docking Domains

The interaction in multisubunit non‐ribosomal peptide synthetases (NRPSs) is mediated by docking domains that ensure the correct subunit‐to‐subunit interaction. We introduced natural docking domains into the three‐module xefoampeptide synthetase (XfpS) to create two to three artificial NRPS XfpS subunits. The enzymatic performance of the split biosynthesis was measured by absolute quantification of the products by HPLC‐ESI‐MS. The connecting role of the docking domains was probed by deleting integral parts of them. The peptide production data was compared to soluble protein amounts of the NRPS using SDS‐PAGE. Reduced peptide synthesis was not a result of reduced soluble NRPS concentration but a consequence of the deletion of vital docking domain parts. Splitting the xefoampeptide biosynthesis polypeptide by introducing docking domains was feasible and resulted in higher amounts of product in one of the two tested split‐module cases compared to the full‐length wild‐type enzyme.     

Size‐Mediated Recurring Spinel Sub‐nanodomains in Li‐ and Mn‐Rich Layered Cathode Materials

Li‐ and Mn‐rich layered oxides are among the most promising cathode materials for Li‐ion batteries with high theoretical energy density. Its practical application is, however, hampered by the capacity and voltage fade after long cycling. Herein, a finite difference method for near‐edge structure (FDMNES) code was combined with in situ X‐ray absorption spectroscopy (XAS) and transmission electron microscopy/electron energy loss spectroscopy (TEM/EELS) to investigate the evolution of transition metals (TMs) in fresh and heavily cycled electrodes. Theoretical modeling reveals a recurring partially reversible LiMn₂O₄‐like sub‐nanodomain formation/dissolution process during each charge/discharge, which accumulates gradually and accounts for the Mn phase transition. From the modeling of spectra and maps of the valence state over large regions of the cathodes, it was found that the phase change is size‐dependent. After prolonged cycling, the TMs displayed different levels of inactivity.     

High‐Tc Enantiomeric Ferroelectrics Based on Homochiral Dabco‐derivatives (Dabco=1,4‐Diazabicyclo[2.2.2]octane)

1,4‐Diazabicyclo[2.2.2]octane (dabco) and its derivatives have been extensively utilized as building units of excellent molecular ferroelectrics for decades. However, the homochiral dabco‐based ferroelectric remains a blank. Herein, by adding a methyl (Me) group accompanied by the introduction of homochirality to the [H₂dabco]²⁺ in the non‐ferroelectric [H₂dabco][TFSA]₂ (TFSA=bis(trifluoromethylsulfonyl)ammonium), we successfully designed enantiomeric ferroelectrics [R and S‐2‐Me‐H₂dabco][TFSA]₂. The two enantiomers show two sequential phase transitions with transition temperature (T_c) as high as 405.8 K and 415.8 K, which is outstanding in both dabco‐based ferroelectrics and homochiral ferroelectrics. To our knowledge, [R and S‐2‐Me‐H₂dabco][TFSA]₂ are the first examples of dabco‐based homochiral ferroelectrics. This finding opens an avenue to construct dabco‐based homochiral ferroelectrics and will inspire the exploration of more eminent enantiomeric molecular ferroelectrics.     

The equivalence between the TE,TM model and the Darwin models

In this paper,we study the TE,TM model by using the decompositions of the vector fields in 2-D bounded multiply connected domains and 2-D unbounded domains,respectively.We find that the TE,TM model and the Darwin models are equivalent if we assume some regularity of the initial data.     

Magnetic domain structures of precipitation-hardened SmCo 2：17-type sintered magnets： Heat treatment effect

The typical magnetic domains of Sm（CObalFe0.25Cuo.07Zr0.02）7.4 magnets quenched through various heattreatment steps have been revealed by using magnetic force microscopy （MFM）. For the specimens in which the nominal c-axis is perpendicular to the imaging plane, the domain configurations change from plate-like for the as-sintered magnet to corrugation and spike-like for the homogenized one, and then to a coarse and finally to a finer domain structure when isothermally aged at 830℃ and then annealed at 400℃. However, only plate-like domains can be detected on the surfaces with the nominal c-axis parallel to the imaging plane. The finer domain （so-called interaction domain） is a characteristic magnetic domain pattern of the SmCo 2：IT-type magnets with high coercivities. Domain walls in a zigzag shape are revealed by means of MFM in final bulk SraCo 2：17-type sintered magnets.     

Stability and Attraction to Normality for Lévy Processes at Zero and at Infinity

We prove some limiting results for a Lévy process X _t as t0 or t, with a view to their ultimate application in boundary crossing problems for continuous time processes. In the present paper we are mostly concerned with ideas related to relative stability and attraction to the normal distribution on the one hand and divergence to large values of the Lévy process on the other. The aim is to find analytical conditions for these kinds of behaviour which are in terms of the characteristics of the process, rather than its distribution. Some surprising results occur, especially for the case t0; for example, we may have X _t /t ^P + (t0) (weak divergence to +), whereas X _t /t a.s. (t0) is impossible (both are possible when t), and the former can occur when the negative Lévy spectral component dominates the positive, in a certain sense. Almost sure stability of X _t , i.e., X _t tending to a nonzero constant a.s. as t or as t0, after normalisation by a non-stochastic measurable function, reduces to the same type of convergence but with normalisation by t, thus is equivalent to strong law behaviour. Boundary crossing problems which are amenable to the methods we develop arise in areas such as sequential analysis and option pricing problems in finance.