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

Combined calculi for photon orbital and spin angular momenta

Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital angular momentum (POAM), completely describe the state of a photon or an electric field (an ensemble of photons). Wavelength relates directly to energy and linear momentum, the corresponding kinetic quantities. PSAMand POAM, themselves kinetic quantities, are colloquially known as polarization and optical vortices, respectively. Astrophysical sources emit photons that carry this information. Aims. PSAM characteristics of an electric field (intensity) are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I created calculi to represent POAM characteristics of electric fields and intensities in an astrophysical context. Adding wavelength dependence to all of these calculi is trivial. The next logical steps are to 1) form photon total angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using operators and expectation values; and 3) show that instrumental PSAM can affect measured POAM values for certain types electric fields. Methods. I derive the PTAM calculi of electric fields and intensities by combining the POAM and PSAM calculi. I show how these quantities propagate from celestial sphere to image plane. I also form the PTAMoperator (the sum of the POAMand PSAMoperators), with and without instrumental PSAM, and calculate the corresponding expectation values. Results. Apart from the vector, matrix, dot product, and direct product symbols, the PTAM and POAM calculi appear superficially identical. I provide tables with all possible forms of PTAM calculi. I prove that PTAM expectation values are correct for instruments with and without instrumental PSAM. I also show that POAM measurements of "unfactored" PTAM electric fields passing through non-zero instrumental circular PSAM can be biased. Conclusions. The combined PTAM calculi provide insight into how to mathematically model PTAM sources and calibrate POAMand PSAM- induced POAM measurement errors

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

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)