We give a full proof of the two dimensional Jacobian conjecture.

We give a shorter proof to a recent result by Neuberger [11], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results presented in [11].

The paper is devoted to the proof of equivalence of Jacobian and Dixmier conjectures. We show that 2n-dimensional Jacobian conjecture implies Dixmier conjecture for Wn. The proof uses “antiquantization”: positive characteristics and Poisson brackets on the center of Weyl algebra in characteristic p. 2000 Math. Subj. Class. 16S32, 16S80, 14R15.

‎‎we investigate graham higman's paper emph{enumerating }$p$emph{-groups}‎, ‎ii‎, ‎in which he formulated his famous porc conjecture‎. ‎we are able to simplify some of the theory‎. ‎in particular‎, ‎higman's paper contains five pages of homological algebra which he uses in‎ ‎his proof that the number of solutions in a finite field to a finite set of‎ ‎emph{monomial} equations is porc‎. ‎it turn...

Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and continuous (discrete) Lyapunov matrix equation. Also, modifications of the existing sufficient conditions of convergence of Traub and Bernoilli algorithms for computing the dominant solvent of the matrix polynomial equation are derived. These results have been extended to large scale systems as well...

Operations research/management contributions to emergency department patient flow optimization: Review and research prospects Soroush Saghafian, Garrett Austin & Stephen J. Traub a Industrial Engineering, School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ, 85281, USA b Department of Emergency Medicine, Mayo Clinic, Phoenix, AZ, 85054, USA Publ...

We present a derivation of a regular language recognizing circuit originally developed by Foster and Kung [4]. We make use of pointfree relation algebra, in a style combining elements from earlier work in the Eindhoven Mathematics of Program Construction group [0], and from Ruby [6]. First we derive non-systolic recognizers, much in the same way as functional programs are derived. Then we make ...