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

Damages for a Decedent’s Pre-Impact Fear: An Element of Damages under Alaska’s Survivorship Statute

  This study is formed with respect to finding a suitable optimization method of the total costs for the number of jobs that are executed in a FEM solver at Scania. FEM (Finite Element Method) is a solution method for solid mechanic problems. It is good to withhold the calculation speed with GPU, CPU and licenses taken into consideration. Computer clusters are usable for the purpose of optimizing the solving speed. Several factors are involved and it is appropriate to consider many parameters to finally end up in a consequent method. The total cost ΣiNi . ( licence cost + hardware cost) was minimized and simulated with respect to the parameters: core number and number of GPU. N is the number of jobs executed. Linear constraints were added to further precise the model though the primary task was to formulate the optimization problem.Denna studie är utformad med avseende på att en lämplig optimeringsmetod för optimering av total kostnad hos ett antal jobb som körs i en FEM lösare på Scania. FEM (Finita elementmetoden) är en lösningsbaserad metod för hållfasthetsberäkningar. Det är bra att upprätthålla en hög beräkningshastighet med avseende på GPU, CPU och antal licenser. Beräkningskluster är användbart för att i syfte att minimera beräkningstiden. Många faktorer är involverade och man bör titta på flera parametrar för att slutligen hitta en konsekvent metod. Man sökte minimera totala kostnaden ΣiNi .  (licens kostnad + hårdvaru kostnad ) och simuleringar utfördes med avseende på parametrarna antal kärnor och antal GPU. N är antalet jobb som kördes. Vidare tillsattes linjära bivillkor för att ytterligare förbättra noggrannheten i modellen, dock var huvudsyftet att konstruera ett optimeringsproblem

Distribution and biological notes for some Cerambycidae (Coleoptera) occurring in the southeastern United States

New distribution records and new host records are provided for 33 species of Cerambycidae in Florida and Georgia