The strong Lefschetz property in codimension two

Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. Using this we classify when both bounds are sharp. Moreover, we prove that the artinian quotient of a monomial ideal in $K[x,y]$ always has the strong Lefschetz property, regardless of the characteristic of the field, exactly when the ideal is lexsegment. As a consequence we describe a family of non-monomial complete intersections that always have the strong Lefschetz property.Comment: 18 pages, 1 figure; v2: Updated history and reference

Nauty in Macaulay2

We introduce a new Macaulay2 package, Nauty, which gives access to powerful methods on graphs provided by the software nauty by Brendan McKay. The primary motivation for accessing nauty is to determine if two graphs are isomorphic. We also implement methods to generate families of graphs restricted in various ways using tools provided with the software nauty.Comment: 4 pages; second updated for clarit

C. malvarum spore concentrate, formulation, and agricultural process

Describes the preparation of C. malvarum spores, spore concentrates and agricultural formulations for use as a mycoherbicide by application onto undesired vegetation, e.g. teaweed, or to the situs of the undesirable vegetation, controlling the undesired vegetation in cropland and other locales where the presence of the vegetation is undesired

Fate of Some Common Radionuclides Found in Dardanelle Lake

Four factors influence the concentrations of radionuclides in Dardanelle Lake water: injections due to fallout and discharge from Nuclear I coupled with losses due to decay, to dilution and to sedimentation. It is possible to estimate the first three factors and to measure monthly changes in the concentrations of Sr-89, Ce-141, Cs-137, Co-38, Ce-144, and Sr-90 - Y-90 during periods when the concentrations of these nuclides are abnormally high (after large releases or the Chinese weapons tests) or abnormally low (during reactor refueling)