In this paper we introduce the D-resultant of two rational functions f(t), g(t) ∈ K(t) and show how it can be used to decide if K(f(t), g(t)) = K(t) or if K[t] ⊂ K[f(t), g(t)] and to find the singularities of the parametric algebraic curve define by X = f(t), Y = g(t). In the course of our work we extend a result about implicitization of polynomial parametric curves to the rational case, which ...

Let P be a system of n linear nonhomogeneous generic sparse ordinary differential polynomials in n − 1 differential indeterminates. In this paper, differential resultant formulas are presented to compute, whenever it exists, the sparse differential resultant ∂Res(P) introduced by Li, Gao and Yuan in [12], as the determinant of the coefficient matrix of an appropriate set of derivatives of diffe...

The antibiotic streptomycin was discovered soon after penicillin was introduced into medicine. Selman Waksman, who was awarded the Nobel Prize for the discovery, has since generally been credited as streptomycin's sole discoverer. However, one of Waksman's graduate students, Albert Schatz, was legally recognized as streptomycin's co-discoverer and received a share of the royalties from the drug...

We describe properties of the Resultant polytope of a given set of polynomial equations towards an outputsensitive algorithm for enumerating its vertices. In principle, one has to consider all regular fine mixed subdivisions of the Minkowski sum of the Newton polytopes of the given equations. By the Cayley trick, this is equivalent to computing all regular triangulations of another point set in...

We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .

The multipolynomial resultant of a set of equations is fundamental in quantiier elimination over the elementary theory of real and algebraically closed elds. Earlier algorithms for resultant computation and symbolic elimination are considered slow in practice. In this paper we present eecient algorithms to compute multi-polynomial resultants and demonstrates their use for polynomial manipulatio...

OBJECTIVETo determine the pregnaflcy outcome with letrozole as an ovulation inducing agent in infertile pa tients. METHOD A Randomized clinical trial was conducted on 250infertile patients attending the outpatient department. Letrozole wa s administered as 5 mg tablets from day 3 to 7 of menstruation after a preliminary day 2 LH level and baseline ultrasound. RESULTS Letrozole given alone had a...