We consider the role of supersymmetric flat directions in reheating the Universe after inflation. One or more flat directions can develop large vevs during inflation, which can potentially affect reheating by slowing down scattering processes among inflaton decay products or by coming to dominate the energy density of the Universe. Both effects occur only if flat directions are sufficiently lon...

We construct a Π2 enumeration degree which is a strong minimal cover.

We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on boundary domain $ \Omega can be extended, under suitable conditions, to case in which forcing term f(x) is changing sign. In addition, for solutions normal derivative may also vanish (definition flat solutions). This leads examples unique continuation property fails....

Coral reefs are built of calcium carbonate (CaCO3) produced biogenically by a diversity of calcifying plants, animals, and microbes. As the ocean warms and acidifies, there is mounting concern that declining calcification rates could shift coral reef CaCO3 budgets from net accretion to net dissolution. We quantified net ecosystem calcification (NEC) and production (NEP) on Dongsha Atoll, northe...

The optimal path cover problem is to find a minimum number of vertex disjoint paths which together cover all the vertices of the graph. Finding an optimal path cover for an arbitrary graph is known to be NP-complete [3]. However, polynornial-time algorithms exist for trees [4], cacti [4] and for interval graphs [9]. The solution presented in [2] For circular-arc graphs is known to be wrong. In ...

We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier–Stokes equations in terms of diffusion processes.

Macroalgal forests dominate shallow hard bottom areas along the northern portion of Western Antarctic Peninsula (WAP). biomass and diversity are known to be dramatically lower in southern WAP at similar latitudes around Antarctica, but few reports detail distributions macroalgae or associated macroinvertebrates central WAP. We used satellite imagery identify 14 sites differing sea ice coverage ...

Evaluating and improving snow models and outflow predictions for hydrological applications is hindered by the lack of continuous data on bulk volumetric liquid water content (θw) and storage capacity of the melting snowpack. The combination of upward looking ground-penetrating radar and conventional snow height sensors enable continuous, nondestructive determinations of θw in natural snow cover...

This study, in a broad sense, fills in the missing parts in previous efforts at pullback stripping mode design with a dipping coal seam. Three different spoiling procedures have been developed: the normal mode, where the coal seam is flat/nearly flat; the uphill mode, where the coal seam is dipping and the dragline spoils uphill; and the downhill mode, where the coal seam is again dipping but t...