It is shown that the support of an irreducible weight module over the SchrödingerVirasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite-dimensional. As a side-product, it is obtained that every simple weight module over the Schrödinger-Virasoro Lie algebra with a nontrivial finite-dime...

Abstract We consider the controllability problem for finite-dimensional linear autonomous control systems with nonnegative controls. Despite Kalman condition, unilateral nonnegativity constraint may cause a positive minimal time. When this happens, we prove that, if matrix of system has real eigenvalue, then there is time in space Radon measures, which consists finite sum Dirac impulses. all ei...

Let X be an n-dimensional compact complex manifold, L → X a positive holomorphic line bundle, and H the space of positively curved hermitian metrics on L. The purpose of this article is to prove that geodesics in the infinite-dimensional symmetric space H can be uniformly approximated by geodesics in the finite-dimensional symmetric spaces Hk = GL(Nk + 1,C)/U(Nk + 1,C), where Nk + 1 = dim(H(L))...

Congruence and symmetry testing in 3-dimensional space seems an old and well-studied problem, but it is optimally solved only for (labelled) finite point sets and convex polytopes. In this paper we present a very general class of geometric objects in 3-dimensional space and give algorithms to test congruence or symmetry of such objects, also in O(n logn) time. For this we use the classification...

Two approaches for optimal control of diffusion-convection-reaction processes based on reduced-order models are presented. The approaches differ in the way spatial discretization is carried out to compute a reduced-order model suitable for controller design. In the first approach, the partial differential equation (PDE) that describes the process is first discretized in space and time using the...

In this paper we consider a class of distributed parameter systems governed by the heat equation on bounded domains in Rn. We consider two types of boundary inputs (actuators) and two types of boundary outputs (sensors). Allowing for any possible pairing of these, we consider a total of four possible arrangements of our system. The first type of input (control) is through the Neumann boundary c...

We investigate the distribution of eigenvalues of completely nuclear maps on an operator space. We prove that eigenvalues of completely nuclear maps are square-summable in general and summable if the underlying operator space is Hilbertian and homogeneous. Conversely, if eigenvalues are summable for all completely nuclear maps, then every finite dimensional subspace of the underlying operator s...

The problem of estimation of a regression curve in an infinite dimensional space is considered. Such problems arise in the statistics of random processes. Observation data in such processes is a pair whose one component is an element of an infinite dimensional space. It is shown that the finite dimensional projections of observations and the regression curve estimators constructed on their basi...

Let T be a continuous linear operator on a Hausdorff topological vector space X over the field C. We show that if T is N -supercyclic, i.e., if X has an N dimensional subspace whose orbit under T is dense in X , then T ∗ has at most N eigenvalues (counting geometric multiplicity). We then show that N -supercyclicity cannot occur nontrivially in the finite dimensional setting: the orbit of an N ...