Motivated by practical numerical issues in a number of modeling and simulation problems, we introduce the notion of a compatible dual complex to a primal triangulation, such that a simplicial mesh and its compatible dual complex (made out of convex cells) form what we call a primal-dual triangulation. Using algebraic and computational geometry results, we show that compatible dual complexes exi...

This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group...

In this section we will define the sheaf of relative differential forms of one scheme over another. In the case of a nonsingular variety over C, which is like a complex manifold, the sheaf of differential forms is essentially the same as the dual of the tangent bundle in differential geometry. However, in abstract algebraic geometry, we will define the sheaf of differentials first, by a purely ...

Dual quaternion algebra and its application to robotics have attracted considerable interest in the last two decades. quaternions great geometric appeal easily capture physical phenomena inside an algebraic framework, which is useful for both robot modeling control. Mathematical objects, such as points, lines, planes, infinite cylinders, spheres, coordinate systems, twists, wrenches, are all we...

This paper describes the interaction between classical Algebraic Geometry, General Algebra, and Formal Concept Analysis. The mathematical foundations of Formal Concept Analysis can be found in ([GW99]). Its goal is to elaborate the general core of the basic results of Algebraic Geometry using this interaction. We start from a general polynomial context of the form Kn,A := (A, Fn(X,A) × Fn(X,A),...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

In this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we ...

Here G is considered as an algebraic group defined over F . The Lie algebra g may be identified with Mn(F ), with Lie bracket [X,Y ] = XY − Y X . The group T is isomorphic to the algebraic torus Gm, T (F ) is isomorphic to (F), and the Lie algebra t is isomorphic to F. The character group X(T ) is the lattice of algebraic homomorphisms T → Gm, the cocharacter group that of algebraic homomorphis...

To integer programming, a ideals have been problems, which Hiroki Nakayama The University of Tokyo (Received October 27, 2003) Hiroshi Imai jases and standard pairs via toric ilgebraic approaches using Grobner k studied in recent years. In this paper, we consider a unimodular case, e.g., network flow enables us to analyze primal and dual problems in an equal setting. By combining existing resul...