The existence of a Hamiltonian vector field in which trajectories of the invariant set of a dissipative hyperbolic chaotic system are embedded will be proved (see notation below). Evidence of this with an example concerning the Lorenz system will be provided. Also, a constructive method of designing a Hamiltonian for the Lorenz attractor with a universal approximator will be introduced. The pre...

We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero.

When examining the structure of a finite group G, a typical question is the determination of the conjugacy classes of subgroups. For this problem a well-known algorithm – the cyclic extension method (Neubüser 1960, Mnich 1992) – has been in use for over 30 years. For practical purposes this algorithm is limited to groups of size a few thousand. If the subgroup lattice is very thin the possible ...

Let G be a connected linear Lie group which finitely covers the isometry group of X. Furthermore, let Γ ⊂ G be a discrete subgroup. We assume that Γ is geometrically finite. We refer to Definition 2.1 for a precise explanation of this notion. If X is a real hyperbolic space, then Γ is geometrically finite iff it admits a fundamental domain with finitely many totally geodesic faces. In the other...

In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support...

Title of thesis: BLUR AND ILLUMINATIONINVARIANT FACE RECOGNITION VIA SET-THEORETIC CHARACTERIZATION Priyanka Vageeswaran, Master of Science, 2013 Thesis directed by: Professor Rama Chellappa Department of Electrical and Computer Engineering In this thesis we address the problem of unconstrained face recognition from remotely acquired images. The main factors that make this problem challenging a...

Given a continuous dynamical system f on a compact metric space X and a continuous potential Φ : X → R, the generalized rotation set is the subset of R consisting of all integrals of Φ with respect to all invariant probability measures. The localized entropy at a point in the rotation set is defined as the supremum of the measuretheoretic entropies over all invariant measures whose integrals pr...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...