This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent cons...

It has been recently argued that knowledge is the norm of practical reasoning. A way of formulating this norm is the following bi-conditional: it is rational to treat p as a reason for acting if and only if you know that p. In my talk, I provide three new counterexamples to this claim. I show cases of rational action: i) motivated by imagining, ii) grounded in acceptance, and iii) performed in ...

We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be applied for a finitely generated group which is an HNN extension with certain properties.

In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant–Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space of maps from Zn to GL(n,R) endowed with a structure of a pair of Lie-algebroids.

In this paper we provide a constructive version of Tits alternative for a broad class of quaternions with algebraic coefficients. Our result is a generalization of that contained in the paper [1], concerning groups of rational quaternions. Indeed, the tools developed in [1] can be extended to arbitrary number fields by translating them in the corresponding Dedekind domain, as the techniques inv...

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce finite automata and rational expressions for these words. We prove that for countable scattered linear orderings, these two notions are equivalent. This result extends Kleene’s theorem.

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork execution into parallel threads, upon completion join to resume as a single thread. We characterize fragment pomset admits decision procedure for language equivalence. Furthermore, we prove this corresponds precisely series-rational expressions, i.e., rational expressions with additional o...

We present a new approach to the construction of piecewise polynomial or rational C k-spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions, and to solve the well known problems at extraordinary points by admitting singular parametrizations. The smoothness of the spline surfaces is guaranteed by specifying a regular smooth re-p...

Compatible Poisson-Lie structures on the loop group of SL 2. Abstract. We define a 1-parameter family of r-matrices on the loop algebra of sl 2 , defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin triples associated to them. Introduction. The concept of bi-(or multi-)Hamiltonian structures on ...