The ARTEMIS-project R3-COP aims at providing European industry with methodologies and technologies to enable production of advanced robust and safe cognitive, reasoning autonomous and co-operative robotic systems at reduced cost. Three major topics are addressed: advanced robotic capabilities, methodologies for design and development of robotic systems, and new V&V technologies for robotic feat...

We study the use of cubic spline interpolation to represent the centerline of a road, for curves in both R2 and R3 . We look at algorithms to create a representation based on arc length and evenly spaced nodes along the centerline. We also consider methods for moving between rectangular coordinates and coordinates based on distance along the centerline and the offset from that centerline (in R2...

Let V (t) = etGb , t ≥ 0, be the semigroup generated by Maxwell’s equations in an exterior domain Ω ⊂ R3 with dissipative boundary condition Etan − γ(x)(ν ∧ Btan) = 0, γ(x) > 0, ∀x ∈ Γ = ∂Ω. We study the case when Ω = {x ∈ R3 : |x| > 1} and γ 6= 1 is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of Gb.

In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in R3. Following the idea of Strichartz estimates based on [3, 10], we also show that the energy of the whole evolution is bounded independently of time without using the phase space method, as for example, in [5]. One can easily generalize our arguments to Rn for n ≥ 3. We also discuss the extens...

We consider the following nonlinear Schrödinger system in R3 {− u + P(|x |)u = μu3 + βv2u, x ∈ R3, − v + Q(|x |)v = νv3 + βu2v, x ∈ R3, where P(r) and Q(r) are positive radial potentials, μ > 0, ν > 0 and β ∈ R is a coupling constant. This type of system arises, in particular, in models in Bose– Einstein condensates theory. We examine the effect of nonlinear coupling on the solution structure. ...

Based on a reverse genetics approach, we previously reported that bovine leukemia virus (BLV) mutants harboring deletions in the accessory R3 and G4 genes persist at very low proviral loads and are unable to induce leukemia or lymphoma in sheep, indicating that these R3 and G4 gene sequences are required for pathogenesis. We now show that lymphoma can occur, albeit infrequently (1 case of 20) a...

We present techniques of compiling a reflective concurrent object-oriented language, ABCL/R3, by using partial evaluation. Although the compilation framework is based on the first Futamura projection, mere application of partial evaluation cannot improve performance due to concurrent, object-oriented, and dynamically modifiable design in ABCL/R3. Instead of developing a dedicated partial evalua...

The connection of curves and surfaces in R3 to some nonlinear partial differential equations is very well known in differential geometry [1], [2]. Motion of curves on two dimensional surfaces in differential geometry lead to some integrable nonlinear differential equations such as nonlinear Schrödinger (NLS) equation [3], Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations [...

1.1 Topology Let us first recall some basic Euclidean topology. For x0 = (x0, y0, z0) ∈ R3 and r > 0 we define the open ball of radius r > 0 centered at x0 to be B(x0, r) = {x ∈ R | ‖x− x0‖ < r}. Recall that ‖x‖ = √ x2 + y2 + z2 is the Euclidean norm, or length, of the vector x. Definition 1 (Open set). We say a set D ⊂ R3 is open if for every x0 ∈ D, there exists a radius r > 0 such that B(x0,...

This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.