1 Exterior Algebras 2 1.1 The exterior algebra of a module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Free modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Determinants done right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 The trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

This paper is devoted to some mathematical questions related to the stationary Navier-Stokes problem in three-dimensional exterior domains. Our approach is based on a combination of properties of Oseen problems in R and in exterior domains of R.

We survey and compare invariants of modules over the polynomial ring and the exterior algebra. In our considerations, we focus on the depth. The exterior analogue of depth was first introduced by Aramova, Avramov and Herzog. We state similarities between the two notion of depth and exhibit their relation in the case of squarefree modules. Work of Conca, Herzog and Hibi and Trung, respectively, ...

| A new symmetric formulation of the Hybrid Finite Element Method(HFEM) is described which combines elements of the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE) for the exterior region along with the nite element solution for the interior problem. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in...

A pedagogical application-oriented introduction to the calculus of exterior differential forms on differential manifolds is presented. Stokes’ theorem, the Lie derivative, linear connections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their traditional vector counterparts. In pa...

We prove wavenumber-explicit bounds on the Dirichlet-to-Neumann map for the Helmholtz equation in the exterior of a bounded obstacle when one of the following three conditions holds: (i) the exterior of the obstacle is smooth and nontrapping, (ii) the obstacle is a nontrapping polygon, (iii) the obstacle is star-shaped and Lipschitz. We prove bounds on the Neumann-to-Dirichlet map when one of c...

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and...

There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus. However, we are not aware of any numerical experiments where mixed finite elements derived from discretizations of exterior calculus are used for a surface do...

For a Hopf algebra A, we define the structures of differential complexes on two dual exterior Hopf algebras: 1) an exterior extension of A and 2) an exterior extension of the dual algebra A. The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on A. The first differential complex is an analog of the de Rham complex. In t...

The paper presents the combined ridge-stein estimator (CRS) for linear pushbroom imagery exterior orientation, which is severely ill-conditioned for the strong correlation among exterior orientation elements of linear pushbroom imagery. The estimator is a new biased method combining the ridge estimator and the stein estimator. It can effectively change the ill-conditioned state of linear pushbr...