A thorough understanding of the dynamics of cirrus cloud formation is needed in order to parameterize these clouds accurately in numerical models. The scales at which cirrus clouds develop affect their treatment within the coarse resolution climate models, which typically have grid-point separations on The model used for this experiment is the non-hydrostatic verthe order of 200 km. There is a ...

We determine the simplicial complexes ∆ whose Stanley-Reisner ideals I∆ have the following property: for all n ≥ 1 the powers In ∆ have linear resolutions and finite length local cohomologies.

Abstract Let Δ be a one‐dimensional simplicial complex. the Stanley–Reisner ideal of Δ. We prove that for all and intermediate ideals J generated by some minimal generators , we have

When studying a graded module $M$ over the Cox ring of smooth projective toric variety $X$, there are two standard types resolutions commonly used to glean information: free and vector bundle its sheafification. Each approach comes with own challenges. There is geometric information that fail encode, while can resist study using algebraic combinatorial techniques. Recently, Berkesch, Erman, Smi...

Using certain finite-dimensional stable range of the nonlinear terms, we obtain large families of exact solutions parameterized by functions for the equation of nonstationary transonic gas flows discovered by Lin, Reisner and Tsien, and its three-dimensional generalization.

Let Σ be a finite regular cell complex with ∅ ∈ Σ, and regard it as a poset (i.e., partially ordered set) by inclusion. Let R be the incidence algebra of the poset Σ over a field k. Corresponding to the Verdier duality for constructible sheaves on Σ, we have a dualizing complex ω ∈ Db(modR⊗kR) giving a duality functor from Db(modR) to itself. This duality is somewhat analogous to the Serre dual...