1 By using the effective notion of the approximate roots of a polynomial, we describe the equisingularity classes of irreducible curve singularities with a given Milnor number.

The present study introduces a novel curve-fitting algorithm for surface plasmon resonance (SPR) curves using a self-constructed, wedge-shaped beam type angular interrogation SPR spectroscopy technique. Previous fitting approaches such as asymmetric and polynomial equations are still unsatisfactory for analyzing full SPR curves and their use is limited to determining the resonance angle. In the...

We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can be adapted to yield the discriminant of the endomorphism ring of the curve.

In this talk, it is shown that a space curve in $\R^d$ can be approximated by a piecewise polynomial curve of degree $m$ with order $ (m+1)+ \lfloor (m+1)/(2d-1) \rfloor$ rather than $m+1$. Moreover, we show that the optimal order $(m+1)+\lfloor (m-1)/(d-1)\rfloor$ is possible for a particular set of curves.

GB-spline curves can be considered as the generalization of B-spline curve incorporating a shape parameter into the polynomial basis functions. The geometric effect of the alteration of the shape parameter is discussed in this paper, including constrained shape control of the curve.

Wepresent ternary six-point interpolating subdivision schemewith one shape parameter for curve design. The behavior of the limit curve defined by the scheme is analyzed in terms of the Laurent polynomial and attains C degree of smoothness. 2000 Mathematics Subject Classification: 65D17, 65D07, 65D05 DOI: 10.1134/S1995080208030062

In this research paper, an experimental breakthrough curve for citric acid in an adsorption recovery process was determined by an ion-exchange resin in 20, 35, 55 °C. Also, a mathematical model for breakthrough curve was presented. Among ion exchange resins that have been experienced, many weak and strong basic anionic resins are available such as, IRA-92, IRA-93, IRA-420 and IRA-458 and all of...

We give a new algorithm to simplify a given triangulation with respect to a given curve. The simplification uses flips together with powers of Dehn twists in order to complete in polynomial time in the bit-size of the curve. keywords. triangulations of surfaces, flip graphs, Dehn twists Mathematics Subject Classification (2010): 57M20

We reprove the result of Stone and DeRose, which gives the geometric classification of the affine type of an untrimmed Bézier curve, using classical algebraic geometry. We show how to derive the characterization of Stone and DeRose from three classical results: Bézout theorem, polynomial parametrization criterion and classification of the singularity type of an algebraic curve given in Weierstr...

In this thesis we will have a look at algebraic curves in the projective plane over an arbitrary algebraically closed field k. Using the resultant of polynomial rings over k we define intersection multiplicities and prove Bézout’s Theorem for effective divisors. We define singularities and inflexion points and count their number depending on the degree of the curve, using the Hessian of a curve.