'Spindles' in symmetric spaces

We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric

Almost Extrinsically Homogeneous Submanifolds of Euclidean Space

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = T M ⊗ ν M is equipped with an almost metric connection ~ ∇ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂~∇ with the usual derivative ∂ in Rm is almost ~∇-parallel. Then M admits an extrinsically homogeneous immersion into Rm. Mathematics Subject Classifications (2000): 53C20, 53C24, 53C30, 53C42, 53C4

A pinching theorem for extrinsically symmetric submanifolds of Euclidean space

Abstract.: We show that a compact connected manifold which can be immersed into ℝm with almost parallel second fundamental form, admits an extrinsically symmetric immersion into ℝ

ADDENDUM TO: MAXIMAL TORI OF EXTRINSIC SYMMETRIC SPACES AND MERIDIANS

Improving a theorem in [1] we observe that a maximal torus of an extrinsic symmetric space in a euclidean space V is itself extrinsic symmetric in some affine subspace of V

The MANTA: An RPV design to investigate forces and moments on a lifting surface

The overall goal was to investigate and exploit the advantages of using remotely powered vehicles (RPV's) for in-flight data collection at low Reynold's numbers. The data to be collected is on actual flight loads for any type of rectangular or tapered airfoil section, including vertical and horizontal stabilizers. The data will be on a test specimen using a force-balance system which is located forward of the aircraft to insure an undisturbed air flow over the test section. The collected data of the lift, drag and moment of the test specimen is to be radioed to a grand receiver, thus providing real-time data acquisition. The design of the mission profile and the selection of the instrumentation to satisfy aerodynamic requirements are studied and tested. A half-size demonstrator was constructed and flown to test the flight worthiness of the system

A novel framework to harmonise satellite data series for climate applications

Fundamental and thematic climate data records derived from satellite observations provide unique information for climate monitoring and research. Since any satellite operates over a limited period of time only, creating a climate data record requires the combination of space-borne measurements from a series of several (often similar) satellite sensors. A simple combination of calibrated measurements from several sensors, however, can produce an inconsistent climate data record. This is particularly true of older, historic sensors whose behavior in space was often different from their behavior during pre-launch calibration in the laboratory. More scientific value can be derived from considering the series of historical and present satellites as a whole. Here we consider harmonisation as a process that obtains new calibration coefficients for revised sensor calibration models by comparing calibrated measurements over appropriate satellite-to-satellite match-ups, such as simultaneous nadir overpasses. When we perform a comparison of two sensors, however, we must consider that those sensors are not observing exactly the same Earth radiance. This is in part due to differences in exact location and time tolerated by the match-up process itself, but also due to differences in the spectral response functions of the two instruments, even when nominally observing the same spectral band. To derive a harmonised data set we do not aim to correct for spectral response function differences, but to reconcile the calibration of different sensors given their estimated spectral response function differences. Here we present the concept of a framework that establishes calibration coefficients and their uncertainty and error covariance for an arbitrary number of sensors in a metrologically-rigorous manner. We describe harmonisation and its mathematical formulation as an inverse problem. Solving this problem is challenging when some hundreds of millions of match-ups are involved and the errors of fundamental sensor measurements are correlated. We solve the harmonisation problem as marginalised errors in variables regression. The algorithm involves computation of first and second order partial derivatives, for which the corresponding computer source code is generated by Automatic Differentiation. Finally we present re-calibrated AVHRR radiances from a series of 10 sensors. It is shown that the new time series have much less match-up differences while being consistent with uncertainty statistics