Physical Sciences and Mathematics Commons^™

Computer Assistance In Discovering Formulas And Theorems In System Engineering Ii, J. W. Helton, Mark Stankus, Kurt Schneider

Mathematics

[HSWcdc94] focused on procedures for simplifying complicated expressions automatically. [HScdc95] turned to the adventurous pursuit of developing a highly computer assisted method for “discovering” certain types of formulas and theorems.

It is often the case that some variables in the formulation of a problem are not the natural “coordinates” for solution of the problem. Gröbner Basis Algorithms, which lie at the core of our method, are very good at eliminating unknowns, but have no way of finding good changes of variables. This paper gives a way of incorporating changes of variables into our method.

As an example, we “discover” the …

M-Isometric Transformations Of Hilbert Space, Iii, Jim Alger, Mark Stankus

Mathematics

No abstract provided.

An Existence Result For Linear Partial Differential Equations With C∞ Coefficients In An Algebra Of Generalized Functions, Todor D. Todorov

Mathematics

We prove the existence of solutions for essentially all linear partial differential equations with C^∞-coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy’s equation has solutions whenever its right-hand side is a classical C^∞-function.

The Closed Geodesic Problem For Compact Riemannian 2-Orbifolds, Joseph E. Borzellino, Benjamin G. Lorica

Mathematics

In this paper it is shown that any compact Riemannian 2-orbifold whose underlying space is a (compact) manifold without boundary has at least one closed geodesic.