In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into irreducible factors of several constructions involving two times iterated univariate resultants and discriminants over the integer universal ring of coe cien...

A statistically stationary and nearly homogeneous turbulent shear flow is established by an additional volume forcing in combination with stress-free boundary conditions in the shear direction. Both turbulent energy and enstrophy are stationary to a much better approximation than in previous simulations that use remeshing. The temporal fluctuations decrease with increasing Reynolds number. Ener...

The Cayley-Dixon formulation for multivariate resultants have been shown to be efficient (both experimentally and theoretically) for computing resultants by simultaneously eliminating many variables from a polynomial system. In this paper, the behavior of Cayley-Dixon resultant construction and the structure of Dixon matrices is analyzed for composed polynomial systems constructed from a multiv...

Abstract The interaction of slender bodies with fluid flow plays an important role in many industrial processes and biomedical applications. numerical modeling problems involving such rod‐like structures classical continuum‐based finite elements poses a challenge because it promptly leads to locking effects as well very large system sizes. An alternative approach leading rather well‐posed is th...

This paper selects from a longer chapter which recapitulates and extends discussions on anti administration (anti-admin) from the perspective of discourse theory. First, it discusses discourse theory, explaining that the discourses of anti-admin aim toward the inclusion of marginalized or excluded perspectives. Second, it outlines some anti-admin theory. Parallel to the action of anti matter an...

The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1, . . . , fn be homogeneous sparse polynomials in the variables y1, . . . , yn and g1, . . . , gn be homogeneous sparse polynomials in the variables x1, . . . , xn. Let fi ◦ (g1, . . . , gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj . Naturally a quest...

The main question of this paper is: What is the dense (Macaulay) resultant of composed polynomials? By a composed polynomial f ◦ (g1, . . . , gn), we mean the polynomial obtained from a polynomial f in the variables y1, . . . , yn by replacing yj by by some polynomial gj . Cheng, McKay and Wang and Jouanolou have provided answers for two particular subcases. The main contribution of this paper ...

Introduction: Resultants of multi-variate polynomials are fundamental for solving systems of polynomial equations and have numerous applications. Thus they are being intensely studied. Macaulay [3] showed that the projective resultant of a list of multi-variate polynomials is the quotient of two determinants. The numerator of this quotient is the determinant of a (sparse) matrix containing the ...