Now showing items 1-5 of 5

    • A Polynomial Blossom for the Askey–Wilson Operator 

      Simeonov, Plamen; Goldman, Ron (2018)
      We introduce a blossoming procedure for polynomials related to the Askey–Wilson operator. This new blossom is symmetric, multiaffine, and reduces to the complex representation of the polynomial on a certain diagonal. This ...
    • q-Blossoming for analytic functions 

      Goldman, Ron; Simeonov, Plamen (2018)
      We construct aᅠq-analog of the blossom for analytic functions, the analyticᅠq-blossom. Thisᅠq-analog also extends the notion ofᅠq-blossoming from polynomials to analytic functions. We then apply this analyticᅠq-blossom to ...
    • Rational curves over generalized complex numbers 

      Du, Juan; Goldman, Ron; Wang, Xuhui (2019)
      Complex rational curves have been used to represent circular splines as well as many classical curves including epicycloids, cardioids, Joukowski profiles, and the lemniscate of Bernoulli. Complex rational curves are known ...
    • Strong $\mu$-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity 

      Shen, Li-Yong; Goldman, Ron (2017)
      We investigate conditions under which the resultant of a $\mu$-basis for a rational tensor product surface is the implicit equation of the surface without any extraneous factors. In this case, we also derive a formula for ...
    • Syzygies for translational surfaces 

      Wang, Haohao; Goldman, Ron (2018)
      A translational surface is a rational tensor product surface generated from two rational space curves by translating one curve along the other curve. Translational surfaces are invariant under rigid motions: translating ...