Events
Department of Mathematics and Statistics
Texas Tech University
The Auslander bound of a module can be thought of as a generalization
of projective dimension. For a finitely generated module \(M\) with finite
projective dimension over a Noetherian local ring \(R\),
\(Ext_{R}^{n}(M,N)=0\) for \(n>pdim_{R}M\) and \(Ext_{R}^{pdim_{R}M}(M,N)\neq 0\)
for all finitely generated modules \(N\). We say that the Auslander bound
of \(M\) is finite if for all finitely generated modules \(N\), there exists
an integer \(b\) that only depends on \(M\) so that \(Ext_{R}^{n}(M,N)=0\) for \(n>b\)
whenever \(Ext_{R}^{n}(M,N)=0\) for \(n\gg 0\). The Auslander bound is the
least such \(b\). In this talk we give an introduction to the Auslander
bound of a module and share some related results. We will then see
that we can define an Auslander bound for complexes and extend the
module results to complexes.
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Meeting ID: 913 0074 4693
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Abstract. Abstract. We consider sewing machinery between finite difference and analytical solutions defined at different scales: far away and near the source of the perturbation of the flow. One of the essences of the approach is that coarse problem and boundary value problem in the proxy of the source model two different flows. In his remarkable paper Peaceman propose a framework how to deal with solutions defined on different scale for linear time independent problem by introducing famous, Peaceman well block radius. In this article we consider novel problem how to solve this issue for transient flow generated by compressiblity of the fluid. We are proposing method to glue solution via total fluxes, which is predefined on coarse grid and
changes in the pressure, due to compressibility, in the block containing production(injection) well. It is important to mention that the coarse solution "does not see" boundary.
From industrial point of view our report provide mathematical tool for analytical interpretation of simulated data for compressible fluid flow around a well in a porous medium. It can be considered as a mathematical "shirt" on famous Peaceman well-block radius formula for linear (Darcy) transient flow but can be applied in much more general scenario. In the article we use Einstein approach to derive Material Balance equation, a key instrument to define R0. We will enlarge Einstein approach for three regimes of the Darcy and non-Darcy flows
for compressible fluid (time dependent): I.Stationary; II.P seudo Stationary(P SS); III.Boundary Dominated(BD).
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
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* Meeting ID: 968 6501 7586
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We will review various models and definitions for K-theory, including differential K-theory and twisted K-theory.abstract 2 PM CDT (UT-5)