Optimal tracking is considered for a linear time-invariant plant in data space. The proposed control strategy does not employ any traditional mathematical model such as a transfer function or a state-space equation. Instead, the plant dynamics is represented as a set of basis vectors whose elements are inputoutput data of the plant. Using this system representation, an optimal tracking problem ...

Székely, Rizzo and Bakirov (2007) and Székely and Rizzo (2009), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets of random variables. We study in this paper an affinely invariant version of the distance correlation and an empirical version of that distance correlation, and we establish the consistency of the empirical quantit...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

We construct the coordinate Bethe ansatz for all eigenstates of open $\mathrm{spin}\text{\ensuremath{-}}\frac{1}{2}$ XXZ chain that fulfill phantom roots criterion (PRC). Under PRC, Hilbert space splits into two invariant subspaces and there are sets homogeneous equations (BAE) to characterize in each case. propose vectors with chiral shocks span expand corresponding eigenstates. All factorized...

1 Basic notions 4 1.1 ⊕, ⊗ and Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Invariant vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Invariant subspaces and irreducible representations . . . . . . . . . . . . . . . . . . . 5 1.4 The group algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We introduce the notion of the geometrically equivalent quantum systems (GEQS) as quantum systems that lead to the same geometric phases for a given complete set of initial state vectors. We give a characterization of the GEQS. These systems have a common dynamical invariant, and their Hamiltonians and evolution operators are related by symmetry transformations of the invariant. If the invarian...

In recent years many deterministic parabolic equations have been shown to possess global attractors which, despite being subsets of an infinite-dimensional phase space, are finite-dimensional objects. Debussche showed how to generalize the deterministic theory to show that the random attractors of the corresponding stochastic equations have finite Hausdorff dimension. However, to deduce a param...

Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on the point set surface, is sampled by farthest point samp...