A C1 piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of deve...

A piecewise rational cubic spline [5] has been used to visualize the positive data in its natural form. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of a rational cubic have been constrained in such a way that they preserve the shape of the positive data in the view of positive curve. As far as visual smoothness is ...

1. PROLOGUE. Late in the last millennium, the second author ran a seminar course for undergraduates that was intended to introduce them to problem-solving and question-asking in the context of mathematical research. He led them through the classic " difficult " equation x y = y x (x, y > 0), (1) whose solution is much easier than one would think at first glance. Solutions were sought, first ove...

We study mainly connected conngurations of irreducible curves r i=1 C i on a nonsingular rational projective complex surface X such that the Euler characteristic (X n r i=1 C i) 0, hereby continuing a former conjecture of the author and work of Gurjar and Parameswaran. Roughly we show that any such connguration can be extended to another connguration s i=1 C i (r s) with still (X n s i=1 C i) 0...

Late in the last millennium, the second author ran a seminar course for undergraduates which was intended to introduce them to problem-solving and questionasking in the context of mathematical research. He led them through the classic “difficult” equation x = y, x, y > 0, (1) whose solution is much easier than one would think at first glance. Solutions were sought, first over R, then over Z and...

Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.

In this paper, an attempt has been made to construct a shape preserving rational bi-cubic interpolant (cubic/quadratic) with twelve free parameters to depict a more pleasant and smooth display of positive surface through positive data. Simple data dependent constraints are derived for four free parameters to preserve the positivity of data while the remaining eight are left free for designer’s ...

We consider notions of freeness and ambiguity for the acceptance probability Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). study injectivity problem determining if function a MO-QFA is injective over all input words, i.e., giving distinct each word. show that undecidable 8 state MO-QFA, even when unitary matrices projection matrix are rational initial vector real algebraic. a...