ID: A083 Abstract Boticelli is a mobile robot, designed and built for testing new approaches in stereo vision, world modeling, data fusion, map extraction, reinforcement learning and navigation planning. A single camera is used to capture depth information by taking advantage of camera movements. The main thrust of the new approaches is to replace well-known techniques, that depend upon grids o...

Let Y = μ∗(X)+ε, where μ∗ is unknown and E[ε|X] 6= 0 with positive probability but there exist instrumental variables W such that E[ε|W ] = 0 w.p.1. It is well known that such nonparametric regression models are generally “ill-posed” in the sense that the map from the data to μ∗ is not continuous. In this paper, we derive the efficiency bounds for estimating certain linear functionals of μ∗ wit...

The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables reduction of linearization problem to a system of first order partial differential equations. By means of inverse of the Poincaré map one can relate symmetries in ...

Let A be a Hermitian matrix, let be a normalized positive linear map and let f be a continuous real valued function. Real constants and such that (f(A)) f(((A)) (f(A)) are determined. If f is matrix convex then can be taken to be 1. A uniied approach is proposed so that the problem of determining and is reduced to solving a single variable convex minimization problem. As an illustration, the re...

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of longrange interactions are considered. The discrete equations of...

[11.1] For T : V → V a continuous (=bounded) linear map of a Banach space V to itself, show that the operator norm is an upper bound for absolute values of all eigenvalues λ: |λ|C ≤ |T |op. Further, show that |T |op is an upper bound for all of the spectrum, that is, T − λ is invertible for |λ|C > |T |op. Discussion: First, for Tv = λ · v for 0 6= v ∈ V , without loss of generality take |v| = 1...

Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability are extended to such systems. The main problem is to find criteria for an abstract input/output map to have a realization as a system on the time scale. Two different characterizations of realizability are proved. They extend the classical results o...

Let X be a topological vector space, Y = IR n , n 2 IN, A a continuous linear map from X to Y , C X, B a convex set dense in C, and d 2 Y a data point. We derive conditions which guarantee that the set B \ A ?1 (d) is nonempty and dense in C \ A ?1 (d). Some applications to shape preserving interpolation and approximation are described.

We prove the existence of a continuous selection of the multivalued map ) η , ξ ( → AF ) η , ξ ( , where AF ) η , ξ ( is the set of all mild solutions of the Cauchy problem x” ∈ Ax + F(t, x) , x (0) = ξ , x (0) = η assuming that F is Lipschitzian with respect to x and A is the infinitesimal generator of a strongly cosine family of linear operators on a Banach space E. AMS 2000 Subject Classific...