5,562 research outputs found
Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic
Let be a homogeneous Artinian ideal in a polynomial ring
over a field 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 has the strong Lefschetz property if and
only if \gin(I) is almost reverse lexicographic. Finally for a monomial
complete intersection Artinian ideal , we prove
that \gin(I) is almost reverse lexicographic if for each . 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
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