Search results for "Birkhoff"

Dehn surgeries and smooth structures on 3-dimensional transitive Anosov flows.

2020

The present thesis is about Dehn surgeries and smooth structures associated with transitive Anosov flows in dimension three. Anosov flows constitute a very important class of dynamical systems, because of its persistent chaotic behaviour, as well as for its rich interaction with the topology of the ambient space. Even if a lot is known about the dynamical and ergodic properties of these systems, there is not a clear understanding about how to classify its different orbital equivalence classes. Until now, the biggest progress has been done in dimension three, where there is a family of techniques intended for the construction of Anosov flows called surgeries.During the realization of this th…

Applications of the Connection between Approximation Theory and Algebra

2009

The aim of this paper is to illustrate a possibility of obtaining various theoretical results using the connection between multivariate interpolation and reduction process with respect to a H-basis of an ideal. Using this connection we can switch between interpolation theory and the theory of ideals. As a application of this connection, we found and proved an interesting identity, which is satisfied for all polynomials in d variables from an interpolation polynomial subspace.

Properties of Generalized Polynomial Spaces in Three Variables

2009

Multivariate interpolation is a topic which often appears in practical modeling problems. Different type of spaces of functions are used for solving interpolation problems. When the interpolation conditions are of different kind, by example, spacial and temporal, one possibility for modeling the problem is to use a generalize degree, in which the monomials exponents are weighted with a weight vector with integer components. In order to use such a generalize polynomial space as interpolation space, it is necessary to know the dimension and a basis of it. The aim of this article is to study and prove many properties of the generalize polynomial spaces in three variables.

The Linear Ordering Polytope

2010

So far we developed a general integer programming approach for solving the LOP. It was based on the canonical IP formulation with equations and 3-dicycle inequalities which was then strengthened by generating mod-k-inequalities as cutting planes. In this chapter we will add further ingredients by looking for problem- specific inequalities. To this end we will study the convex hull of feasible solutions of the LOP: the so-called linear ordering polytope.

Vortex layers of small thickness

2020

We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is $O(1/epsilon)$ on the curve while it decays on an $O(epsilon)$ distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time which does not depend on $epsilon$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.

On the integration of Riemann-measurable vector-valued functions

2016

We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.

High order normal form construction near the elliptic orbit of the Sitnikov problem

2011

We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.

MR2569913: Rodríguez, José. Some examples in vector integration. Bull. Aust. Math. Soc. 80 (2009), no. 3, 384–392. (Reviewer: Luisa Di Piazza),

2009

The paper deals with some classical examples in vector integration due to Phillips, Hagler and Talagrand, revisited from the point of view of the Birkhoff and McShane integrals. More precisely, the author considers: - Phillips' example of a Pettis integrable function f which is not Birkhoff integrable [R. S. Phillips, Trans. Amer. Math. Soc. 47 (1940), 114--145; MR0002707 (2,103c)]. It is proved here that f is universally McShane integrable. - Hagler's example of a scalarly measurable l∞-valued function g which is not strongly measurable. The function g is proved to be universally Birkhoff integrable. - Talagrand's example of a bounded Pettis integrable function φ having no conditional expe…

The completely distributive lattice of machine invariant sets of infnite words

2007

Posets That Locally Resemble Distributive Lattices

2000

Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.