An elementary proof of Lubeseder's theorem

Dedicated to Professor B. Huppert on his 60th birthday     

An elementary proof of the Jordan-Kronecker theorem

This paper presents a proof of the Jordan-Kronecker theorem on the reduction to canonical form of a pair of skew-symmetric bilinear forms on a finite-dimensional linear space over an algebraically closed field.     

An elementary proof of the restricted invertibility theorem

We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace.     

An elementary proof of a theorem of tacon

In this Note we give an elementary proof (based on a simple, seemingly new, characterization of compact operators) of a Theorem of Tacon [3].Partially supported by a grant from the National Science Foundation.     

An elementary proof of the local central limit theorem

We give an elementary proof of the local central limit theorem for independent, non-identically distributed, integer valued and vector valued random variables.Support by a NSF Grant.Supported by an NSERC Grant     

An elementary proof of a converse mean-value theorem

We present a new converse mean value theorem, with a rather elementary proof.     

An elementary geometric nonstandard proof of the Jordan curve theorem

We give an elementary proof, using nonstandard analysis, of the Jordan curve theorem. We also give a nonstandard generalization of the theorem. The proof is purely geometrical in character, without any use of topological concepts and is based on a discrete finite form of the Jordan theorem, whose proof is purely combinatorial.Some familiarity with nonstandard analysis is assumed. The rest of the paper is self-contained except for the proof a discrete standard form of the Jordan theorem. The proof is based on hyperfinite approximations to regions on the plane.Research of the first author partially supported by FONDECYT Grant # 91-1208 and of the second author, by FONDECYT Grant # 90-0647.     

An elementary proof of the duality theorem of linear programming

A constructive and elementary proof of the duality theorem of linear programming is presented. The proof utilizes the new concept of an embedded core program, which is a program generated from a linear program with finite optimum by successively removing constraints until no remaining constraints can be deleted without changing the optimal solution.     

An elementary proof of the Petersson-Knopp theorem on Dedekind sums

A brief and elementary proof of Petersson and Knopp's recent theorem on Dedekind sums is given. The proof is based on a result of Subrahmanyam.