The study of Newton polytopes of resultants and discriminants has its orgin in the work of Gelfand, Kapranov, and Zelevinsky on generalized hypergeometric functions (see e.g., [8]). Central to this theory is the notion of the A-discriminant AA, which is the discriminant of a Laurent polynomial with specified support set A (see [6, 7]). Two main results of Gelfand, Kapranov, and Zelevinsky are c...

It is well known that Euclid's algorithm for computing the greatest common divisor (gcd) of two integer numbers is more than two thousand years old and, as it turns out, it is the oldest known algorithm. Interest in computing a gcd of two polynomials first appeared only in the sixteenth century and the problem was solved by Simon Stevin [13] simply by applying Euclid's algorithm (for integers) ...

The resultant is an algebraic expression, computable in a finite number of arithmetic operations from the coefficients of two univariate polynomials, that vanishes if, and only if, the two polynomials have common zeros. The paper considers formal resultant for degree-deficient polynomials (polynomials whose actual degree is lower than their assumed degree). Some key properties of the resultant ...

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the ...

The paper concerns the thermoelastic problems in a thermosensitive elliptical plate subjected to the activity of a heat source which changes its place on the plate surface with time. The solution of conductivity equation and the corresponding initial and boundary conditions is obtained by employing a new integral transform technique. In addition, the intensities of bending moments, resultant fo...