Torsion divisors of plane curves with maximal flexes and Zariski pairs

There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves that include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper, we consider curve arrangements that contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples, which show the interplay between topology, geometry, and arithmetic.      

Supported Noble Metal Catalysts and Adsorbents with Soft Lewis Acid Functions

Heterogeneous noble metal catalysts exhibit various functions. Although their redox functions have been extensively studied, we focused on their soft Lewis acid functions. Supported Au, Pt, and Pd catalysts electrophilically attack the π-electrons of soft bases such as alkynes, alkenes, and aromatic compounds to perform addition and substitution reactions. Hydroamination, intramolecular cyclization of alkynyl carboxylic acids, isomerization of allylic esters, vinyl exchange reactions, Wacker oxidation, and oxidative homocoupling of aromatics are introduced based on a discussion of the active species and reaction mechanisms. Furthermore, the adsorption of sulfur compounds, which are soft bases, onto the supported AuNPs is discussed. The adsorption and removal of 1,3-dimethyltrisulfane (DMTS), which is the compound responsible for the stale odor of “hine-ka” in alcoholic beverages, particularly Japanese sake, is described.