Free reflection multiarrangements and quasi-invariants

To a complex reflection arrangement with an invariant multiplicity function one can relate the space of logarithmic vector fields and the space of quasi-invariants, which are both modules over invariant polynomials. We establish a close relation between these modules. Berest-Chalykh freeness results for the module of quasi-invariants lead to new free complex reflection multiarrangements. K. Saito's primitive derivative gives a linear map between certain spaces of quasi-invariants. We also establish a close relation between non-homogeneous quasi-invariants for root systems and logarithmic vector fields for the extended Catalan arrangements. As an application, we prove the freeness of Catalan arrangements corresponding to the non-reduced root system $BC_N$.Comment: 26 pages; small change

Optimization of electrochemical synthesis conditions for dense and doped ceria thin films

In the present study, the appropriate electrolysis conditions were determined for attaining doped ceria thin films with a high density and adhesion in an aqueous solution containing of Ce3+ and Sm3+ ions. Based on a comparison of the anodic and cathodic polarizations, while the former only induced the deposition of Ce3+, the latter accomplished the simultaneous deposition of Ce and Sm species. Under an applied cathodic bias below the hydrogen evolution potential, the Ce3+ and Sm3+ were reacted with OH- ions generated by the reduction of water molecules, and then were deposited on the electrode as a hydroxide. The hydroxide was subsequently oxidized and dehydrated to form the ceria-based thin layer. The morphologies of the as-deposited films were significantly altered on the basis of the applied potential. Moreover, the addition of acetic acid to the electrolysis bath caused the production of a transparent, dense, and adherent film. The XRD pattern and Raman spectrum of the thin film revealed that the film was crystallized as the fluorite structure without any heat treatment, and Sm3+ is substituted at the Ce4+ site. Moreover, the Sm content in the film could be easily controlled by the metal concentration in the solution

Surface micromachining via solid electrochemical reaction on oxide ion conductors

We propose a simple and novel route for the surface microstructuring of tough materials (glassy carbon, SiC, W and Mo) through a solid electrochemical reaction at a microcontact between the oxide ion conductor and target substrate. More specifically, the surface of materials was locally oxidized by an anodic electrochemical reaction with the oxide ion conductor via the microcontact under a dc bias. Since the oxidation products of the targets were gaseous or sublimable, a fine-patterned surface was obtained as a result of the continuous consumption of the oxidation products formed at the microcontact. The success of the proposed method may stimulate such conventional applications of oxide ion conductors