We study the behavior of generic initial ideals with respect to fibre products. In our main result we determine the generic initial ideal of the fibre product with respect to the reverse lexicographic order. As an application we compute the symmetric algebraic shifted complex of two disjoint simplicial complexes as was conjectured by Kalai. This result is the symmetric analogue of a theorem of ...

LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...

Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-produc...

Yellow-poplar (also called tulip poplar and American tulip) has shown a resurgence in popularity in recent years due to its cost and greater abundance. Unfortunately, decay in yellow-poplar lumber can be a serious issue in just a few years (Figures 1 and 2). This publication will discuss the positive and negative attributes of yellow-poplar as an exterior millwork product and describe ongoing e...

The purpose of the present paper is to establish the local energy decay estimates and dispersive estimates for 3-dimensional wave equation with a potential to the initial-boundary value problem on exterior domains. The geometrical assumptions on domains are rather general, for example non-trapping condition is not imposed in the local energy decay result. As a by-product, Strichartz estimates i...

We use Grayson’s binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a λ-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial f...

the contraposition (musāmita) argument is among the arguments for proving the finitude of dimensions that has received attention in discussing physics and has yielded some philosophical consequences. contraposition argument is based on the two concepts of motion and contraposition, and by proving the impossibility of the motion of circle in case of the infinitude of dimensions, it deals with th...

Given a digraph G = (V,E) with the set of vertices V and the set of edges E, let d : F → Ω be the exterior derivative map from the space of complex-valued functions on V to the complex vector space spanned by E. We introduce the Laplacian ∆ : F → F and the label difference map d̂ : F → (Ω1)∗ of F into the dual space (Ω1)∗ of Ω and establish their connections with d. In particular, we prove that,...

The language of modern mechanics is calculus on manifolds, and exterior calculus is an important part of that. It consists of objects like differential forms, general tensors and vector fields on manifolds, and operators that act on these. While the smooth exterior calculus has a long history going back to Cartan, Lie, Grassmann, Hodge, de Rham and many others, the need for a discrete calculus ...

This paper will prove the generalized Stokes Theorem over kdimensional manifolds. We will begin from the definition of a k-dimensional manifold as well as introduce the notion of boundaries of manifolds. Using these, we will construct the necessary machinery, namely tensors, wedge products, differential forms, exterior derivatives, and integrals over manifolds, in order to prove the main result...