We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate systems and also uses the exterior algebra techniques of Eisenbud and Schreyer.

In this article, we give an explicit formula to compute the non-abelian twisted sign-determined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot.

We prove existence and a representation formula for solutions to the equations describing steady flows of an isothermal, viscous, compressible gas having a positive infimum for the density ̺, moving in an exterior domain, when the speed of the obstacle and the external forces are sufficiently small.

We prove a version of the Stokes formula for differential forms on locally convex spaces announced in [10]. The main tool used for proving this formula is the surface layer theorem proved in the paper [6] by the author. Moreover, for differential forms of a Sobolev-type class relative to a differentiable measure [1], we compute the operator adjoint to the exterior differential in terms of stand...

After casting Euler-$\alpha$ equations into vorticity-stream function formula, we obtain some very useful estimates from the properties of vorticity formula in exterior domain. Basing on these estimates, one can have got global existence and uniqueness solutions to 2D domain provided that initial data is regular enough.

1 2 Contents 0. One-variable calculus 1. The derivative 2. Inverse function and implicit function theorem 3. Fundamental local existence theorem for ODE 4. The Riemann integral in n variables 5. Integration on surfaces 6. Differential forms 7. Products and exterior derivatives of forms 8. The general Stokes formula 9. The classical Gauss, Green, and Stokes formulas 10. Holomorphic functions and...

Let EC denote the complexified adjoint Lie-algebra bundle associated to P . For the purposes of this summary, we will assume that E = EC; the more general case will be dealt with in section 7. Let dt : Ω (M ;EC)→Ω (M ;EC) denote the exterior derivative corresponding to At for each t. At t = 0, we wish to calculate the dimension of ker(D0), which gives the number of eigenvalues λα(t) of Dt passi...

Let M̃ be a (2m+ 1)-dimensional almost contact manifold with almost contact structure (φ,ξ,η), that is, a global vector field ξ, a (1,1) tensor field φ, and a 1-form η on M̃ such that φ2X =−X +η(X)ξ, η(ξ) = 1 for any vector field X on M̃. We consider a product manifold M̃×R, whereR denotes a real line. Then a vector field on M̃×R is given by (X , f (d/dt)), where X is a vector field tangent to M̃, t ...

Princeton University, Princeton, NJ This paper desribes a technique for finding the numerical solution of the Full Potential equation for steady transonic flow about airfoils. The exterior but finite domain is discretized by breaking it up into triangles. Difference equations are formulated using variational principle and a formula for the derivative in an arbitrary polygon. The iterative schem...