The Lindstedt-Poincare technique in perturbation theory can be turned into a quadratically convergent algorithm for computing periodic orbits of differential equations. Most of the computational work is done in solving linear systems of the form ż(τ) =A(τ)z+g(τ), A(τ)2Rd;d , z2Rd , g(τ)2Rd , where A(τ) and g(τ) are 2π periodic. The method given here for solving such linear systems, while not th...

This paper presents a convenient graphical tool for encoding visual patterns (such as image patches and image atoms) as point constellations in a space spanned by perceptual features and with a clear geometrical interpretation. General theory and a practical pattern encoding scheme are presented, inspired by encoding polarization states of a light wave on the Poincaré sphere. This new pattern e...

Anders Björner characterized which finite graded partially ordered sets arise as the closure relation on cells of a finite regular CW complex. His characterization of these “CW posets” required each open interval (0̂, u) to have order complex homeomorphic to a sphere of dimension rk(u)− 2. Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The...

In the pattern matching approach to imaging science, the process of “metamorphosis” is template matching with dynamical templates (Trouvé and Younes, Found. Comp. Math., 2005). Here, we recast the metamorphosis equations of that paper into the Euler-Poincaré variational framework of Holm, Marsden, and Ratiu, Adv. in Math., 1998 and show that the metamorphosis equations contain the equations for...

Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.

Some basic mathematical tools such as convex sets, polytopes and combinatorial topology are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed as a tutorial and a set of notes on convex sets, polytopes, polyhedra, combinatorial topology, Voronoi Diagrams and Delaunay Triangulations. It is intended fo...

We consider the deformed Poincare group describing the space-time symmetry of noncommutative field theory. It is shown that the deformed symmetry is equivalent to explicit symmetry breaking. PACS number(s): 11.10-z, 11.30Cp

The κ−Poincare group and its algebra in an arbitrary basis are constructed. The κ−deformation of the Weyl group and its algebra in any dimentions and in the reference frame in which g00 = 0 are discussed.

Relativistic Gamow vectors were originally obtained from the Smatrix pole term for resonance formation experiments. They furnish an irreducible representation of the Poincare semi-group in the forward light cone and are characterized by spin and the complex pole position, very much like stable relativistic particles are labeled by spin and mass, and defined by Wigner’s basis vectors of unitary ...

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...