Jintai DingDepartment of Mathematical Sciences, University of CincinnatiJason E. GowerDepartment of Mathematical Sciences, University of CincinnatiDieter S. SchmidtDepartment of Electrical & Computer Engineering and Computer Science, University of Cincinnati
We present the Zhuang-Zi algorithm, a new method for solving multivariate polynomial equations over a finite field. We describe the algorithm and present examples, some of which cannot be solved with the fastest known algorithms.
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Luca BaraccoDipartimento di Matematica Pura ed Applicata, Università degli Studi di PadovaAlexander TumanovDepartment of Mathematics, University of IllinoisGiuseppe ZampieriDipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova
Let$D$be a convex domain with smooth boundary in complex space and let$f$be a continuous function on the boundary of$D$. Suppose that$f$holomorphically extends to the extremal discs tangent to a convex subdomain of$D$. We prove that f holomorphically extends to$D$. The result partially answers a conjecture by Globevnik and Stout of 1991.