Castelnuovo-Mumford regularity for complexes and weakly Koszul modules

Let A be a noetherian AS-regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and the category of finitely generated graded left A-modules. Following Jørgensen, we define the Castelnuovo-Mumford regularity of a complex in terms of the local cohomologies or the minimal projective resolution of M^•. Let A^! be the quadratic dual ring of A. For the Koszul duality functor , we have . Using these concepts, we interpret results of Martinez-Villa and Zacharia concerning weakly Koszul modules (also called componentwise linear modules) over A^!. As an application, refining a result of Herzog and Römer, we show that if J is a monomial ideal of an exterior algebra E=?〈y₁,…,y_d〉, d≥3, then the (d−2)nd syzygy of E/J is weakly Koszul.     

Irreversibility lines of layered Fe-based superconductors with thick blocking layers

Irreversibility lines of the layered iron-arsenide superconductors with thick perovskite-type oxide blocking layers have been systematically studied. Five compounds with different interlayer distance between iron layers from 1.5 to 3.0 nm were selected for the magnetization measurements. These compounds showed very large magnetically reversible region. The irreversibility lines of these compounds were found to locate at very low fields compared to the other iron-based superconductors and shift towards lower fields with an increase in the thickness of the blocking layer. In addition, the analysis on the irreversibility line suggested that the change of dimensionality of the vortex system occurs at $T/T_c～0.6$. These results indicate that the electromagnetic anisotropy originated from the layered crystal structure plays a crucial role to determine the irreversibility line and magnetic phase diagram of layered iron arsenides as is the case in the layered cuprates.     

Supramolecular Structure of N,N-Bis(2-hydroxy-benzyl)alkylamine: From Hydrogen Bond Assembly to Coordination Network in Guest Acceptance

N,N-Bis(2-hydroxybenzyl)alkylamine ( HBA ) was described as a model to simplify the supramolecular system of polybenzoxazines. The single crystal X-ray analysis revealed that HBA forms a dimeric assembly based on its simultaneous inter- and intramolecular hydrogen bond network. When the HBA accepted the copper ion, the dimeric assembly HBA changed its primary hydrogen bond network to charge transfer coordination as clarified by the single crystal analysis as well as the superimposed structure based on DMol³ calculation. The supramolecular structure of HBA and copper also exhibited the role of solvent molecules in the packing structure which is a rare example showing the host accepts not only the metal ions but also the neutral molecules in the same time. The cyclization of HBA with esters or ethers to macrocyclic compounds was also an important model reaction to show how the backbone molecules self-stabilized with the hydrogen bond network initiate the simple, effective and efficient macrocyclic reaction.