Following on from our previous study of the geodesic flow on three dimensional ellipsoid with equal middle semi-axes, here we study the remaining cases: Ellipsoids with two sets of equal semi-axes with SO(2) × SO(2) symmetry, ellipsoids with equal larger or smaller semi-axes with SO(2) symmetry, and ellipsoids with three semi-axes coinciding with SO(3) symmetry. All of these cases are Liouville...

In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this paper, we deal with linear codes of Fnq invariant under a semi-linear map T : F q → F q for some n ≥ 2. In particular, we study three kind of their dual codes, some relations between them and we focus on codes which are products of module skew codes in the non-commutative polynomial ring as a subca...

In this paper a theoretical framework for Bayesian adaptive learning of discrete HMM and semi continuous one with Gaussian mixture state observation densities is presented Corre sponding to the well known Baum Welch and segmental k means algorithms respectively for HMM training formulations of MAP maximum a posteriori and segmental MAP estima tion of HMM parameters are developed Furthermore a c...

We use a decimation procedure in order to obtain the dynamical renormalization group transformation (RGT) properties of random walk distribution in a 1+1 lattice. We obtain an equation similar to the Chapman-Kolmogorov equation. First we show the existence of invariants through the RGT. We also show the existence of functions which are semi-invariants through the RGT. Second, we show as well th...

Let G be a finite group having an order preserving and rank preserving action on a finite ranked poset P. Let P/G denote the quotient poset. A well known result in algebraic Sperner theory asserts that an order raising G-linear map on V (P) (the complex vector space with P as basis) satisfying the full rank property induces an order raising linear map on V (P/G), also satisfying the full rank p...

The purpose of this paper is twofold. First we show that the dynamics of a Sun-Jupiter-Comet system and under some simplifying assumptions has a semi-infinite region of instability. This is done by reducing the dynamics to the study of a certain exact area preserving (EAP) map and showing applicability of Aubry–Mather theory. Second, we give a sufficient “cumulative twist” condition to verify t...