Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

Let $I$ be a homogeneous Artinian ideal in a polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic 0. We study an equivalent condition for the generic initial ideal \gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fr\"{o}berg conjecture. And for the case \Codim I \le 3, we show that $R/I$ has the strong Lefschetz property if and only if \gin(I) is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that \gin(I) is almost reverse lexicographic if $d_i > \sum_{j=1}^{i-1} d_j - i + 1$ for each $i \ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr\"{o}berg conjecture.Comment: 10 page

A GIS-Based Approach for Determining Potential Runoff Coefficient and Runoff Depth for the Indian River Lagoon, Florida, USA

The Indian River Lagoon system (IRL), spanning ~40% of Florida’s east coast, is one of the nation’s biggest and most biodiverse estuaries. In 2011, a super algal bloom event occurred in the IRL with total nitrogen and phosphorus levels that exceeded historical levels. Scientists suspect that nonpoint source pollution through surface runoff may have had a significant impact on the recent recurring algal blooms. Digital Elevation Model, land cover/land use, and soil data were used to calculate a runoff coefficient for the IRL drainage basin. Rainfall data were used to calculate runoff depth for the study area between the years of 2006–2016. When the monthly runoff depth data for 2011 were compared to a previous study on the 2011 super algal bloom in the lagoon, areas with high runoff visually matched the areas with higher chlorophyll a concentrations. Land development was a significant variable for determining runoff depth (p < 0.0001), and although used to derive runoff depths, the influence of precipitation was marginally significant (p = 0.06). Significant spatial autocorrelation indicated local trends between land development and runoff depth (p < 0.0001). Outputs will aid with decisions on stormwater management to more sustainable land development planning

Competing Magnetic Orderings and Tunable Topological States in Two-Dimensional Hexagonal Organometallic Lattices

The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using first-principles calculations, we show that a 2D hexagonal triphenyl-lead lattice composed of only main group elements is susceptible to a magnetic instability, characterized by a considerably more stable antiferromagnetic (AFM) insulating state rather than the topologically nontrivial quantum spin Hall state proposed recently. Even though this AFM phase is topologically trivial, it possesses an intricate emergent degree of freedom, defined by the product of spin and valley indices, leading to Berry curvature-induced spin and valley currents under electron or hole doping. Furthermore, such a trivial band insulator can be tuned into a topologically nontrivial matter by the application of an out-of-plane electric field, which destroys the AFM order, favoring instead ferrimagnetic spin ordering and a quantum anomalous Hall state with a non-zero topological invariant. These findings further enrich our understanding of 2D hexagonal organometallic lattices for potential applications in spintronics and valleytronics.Comment: 9 pages, 8 figure