We describe a method, based on the rational univariate reduction (RUR), for computing roots of systems of multivariate polynomials with rational coefficients. Our method enables exact algebraic computations with the root coordinates and works even if the underlying set of roots is positive dimensional. We describe several applications, with special emphasis on geometric modeling. In particular,...

Increased attention is being paid to students who demonstrate difficulty in learning and applying mathematics concepts. The purpose of this special series was to address issues related to students and mathematics learning disabilities (LD). We identify Response to Intervention (Rtl) as it relates to early mathematics instruction and a multi-tiered service delivery system. Further, because Rtl h...

The recent increase in oil price and environmental concerns has attracted various research efforts on hybrid electric vehicles (HEVs) which provide promising alternatives to conventional engine-powered vehicles with better fuel economy and fewer emissions. To speed up the design and prototyping processes of new HEVs, a method that automatically generates mathematics equations governing the vehi...

Schoute (1911) introduced the permutahedron on an n-element set N= { 1, . . . , n} as follows. With any permutation n of N we associate an incidence vector x(71) = (n(I), *.., n(n)) E IR”. The permutahedron is the polytope Perm(N) = conv{x(rr): rr is a permutation of N}. Independently, several authors (cf., e.g., Rado [4], Balas [l], Gaiha and Gupta [2], Young [6]) studied the permutahedron and...

This paper is a very brief introduction to idempotent mathematics and related topics. It appears as an introductory paper in the volume Idempotent Mathematics and Mathematical Physics (G. L. Litvinov and V. P. Maslov, eds; AMS Contemporary Mathematics Proceedings Series, 2005) [73]. This paper is a very brief introduction, without exact theorems and proofs, to the Maslov dequantization and idem...

This paper is a very brief introduction to idempotent mathematics and related topics. It appears as an introductory paper in the volume Idempotent Mathematics and Mathematical Physics (G. L. Litvinov and V. P. Maslov, eds; AMS Contemporary Mathematics Proceedings Series, 2005) [73]. This paper is a very brief introduction, without exact theorems and proofs, to the Maslov dequantization and idem...

This paper is a very brief introduction to idempotent mathematics and related topics. It appears as an introductory paper in the volume Idempotent Mathematics and Mathematical Physics (G. L. Litvinov and V. P. Maslov, eds; AMS Contemporary Mathematics Proceedings Series, 2005) [73]. This paper is a very brief introduction, without exact theorems and proofs, to the Maslov dequantization and idem...