A Short Proof of a Gauss Problem
نویسندگان
چکیده
The traversal of a self crossing closed plane curve, with points of multiplicity at most two, deenes a double occurrence sequence. C.F. Gauss conjectured 2] that such sequences could be characterized by their interlacement properties. This conjecture was proved by P. Rosenstiehl in 1976 15]. We shall give here a simple self-contained proof of his characterization. This new proof relies on the D-switch operation.
منابع مشابه
A geometric approach for convexity in some variational problem in the Gauss space
In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.
متن کاملA SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS
In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.
متن کاملGroups with one conjugacy class of non-normal subgroups - a short proof
For a finite group $G$ let $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. We give a short proof of a theorem of Brandl, which classifies finite groups with $nu(G)=1$.
متن کاملA Brief Determination of Certain Class of Power Semicircle Distribution
In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).
متن کاملConvergence of a Short-step Primal-dual Algorithm Based on the Gauss-newton Direction
We prove the theoretical convergence of a short-step, approximate pathfollowing, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict complementarity and uniqueness of the ...
متن کامل