The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of along illustrated. numerical algorithm provided based collocation method and Tikhonov regularization. estimates parabolic hyperbolic are demonstrated by examples respectively.

The dynamics of all quadratic Newton maps rational functions is completely described. Julia set such a map found to be either Jordan curve or totally disconnected. It proved that no with degree at least three any function conformally conjugate unicritical polynomial (i.e., exactly one finite critical point). However, there are cubic which other polynomials. shown closed curve. whenever the has ...

In this paper, we determine theWalsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Göloğlu is affine equivalent to Gold functions.