We highlight a new algorithm for evaluating the surface intersection curve using a matrix formulation. The projection of the intersection curve is represented as the singular set of a bivariate matrix polynomial. The resulting algorithm for evaluating the intersection curve is based on matrix computations like eigendecomposition and singular value decomposition. Furthermore, at each stage of th...

Regression analysis is used to predict the dependent variables individually concerning the explanatory available variables and find out the “best fit” line or curve through a series of data in a graph. It is also minimizing the sum of the squares deviations of any experimental data points from the theoretical curve. An important aspect of this analysis is to ensure that the x values are as accu...

An algorithm is presented to approximate planar ooset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an ooset radius r, the circle of radius r is rst approximated by piecewise quadratic B ezier curve segments within the tolerance. The exact ooset curve C r (t) is then approximated by the convolution of C(t) with the quadratic B ezier curve segments. For a pol...

We investigate the separation of irreducible characters by blocks at different primes and the covering of irreducible characters by blocks (viewed as sets of characters); these notions are used to prove results on the group structure. The covering of all characters of a group by principal blocks is only possible when already one principal block suffices or the generalized Fitting subgroup has a...

In this paper, methods of mechanical deriving of formulas from a set of differential polynomial equations and a set of differential polynomial inequations are presented. The methods have been used successfully to many problems in space curve theory and mechanics. In particular, a mechanical derivation of Newton’s gravitational law from Kepler’s laws has been given without knowing Newton’s laws ...

Article history: Received 9 March 2007 Received in revised form 16 June 2008 Accepted 20 October 2008 Available online 1 November 2008

We study finiteness (and vanishing) properties of the higher order degrees associated to complements complex affine plane curves with mild singularities at infinity. Our results impose new obstructions on class groups that can be realized as fundamental curve complements. also clarify relationship between and multivariable Alexander polynomial a non-irreducible curve.

The motive associated to the second Symanzik polynomial of double-box two-loop Feynman graph with generic masses and momenta is shown be an elliptic curve.