We investigate the properties of a special kind of frame, which we call the Euler–Rodrigues frame (ERF), defined on the spatial Pythagorean-hodograph (PH) curves. It is a frame that can be naturally constructed from the PH condition. It turns out that this ERF enjoys some nice properties. In particular, a close examination of its angular velocity against a rotation-minimizing frame yields a cha...

The purpose of this white paper is to present discussion and findings that conclude that Cisco MPLS-based VPNs are as secure as their layer 2 counterparts such as FrameRelay and ATM. This document details a series of tests were carried out on a Cisco router test bed validating that MPLS based VPNs (MPLS-VPN) provide the same security as Frame-Relay or ATM. ATM and Frame-Relay have a reputation ...

Experimental results for quasi-static cyclic tests on reinforced concrete (RC) walls have shown that shear deformations can constitute a significant ratio of the total deformations when the wall is loaded beyond the elastic regime. For walls, which form a stable flexural hinge at their base, the ratio of shear to flexural deformations remains approximately constant over the entire range of impo...

In J. T. Wilson’s doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L. Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame. In this paper it is shown that for algebraic frames L wit...

Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...

Nomenclature SF a , SFx a , SF y a , SFz a = specific force acceleration vector (sensed by accelerometers) and components in frame B B = sensor (body) coordinate frame aligned with strapdown inertial sensor axes 1 m B  = frame B orientation at computer cycle 1 m  () Bt = frame B orientation at time t k r c = combination, k elements selected from a set of r elements without regard to the order...

Both standard formulations of the frame problem and standard solutions implicitly assume that the re-identification of objects as persisting individuals between pre-and post-action contexts is unproblematic. In the case of human beings, this assumption is false; humans dedicate considerable cognitive resources to object re-identification. An analysis of both the phenomenology and neurocognitive...

This paper deals with the time-optimal problem for a class of underwater vehicles. We prove that if two configurations at rest can be joined by a horizontal or a vertical translation in the body frame coordinates, then there exists a shorter path. Our computations are based on the maximum principle and use that translations in the body frame coordinates are time-equivalent to paths formed by co...

This paper shows how the Gauss-Mainardi-Codazzi equations can be reinterpreted in terms of variations of curvature with respect to arc-length along lines of curvature. Secondly, it reviews the frame-and-position matching method for surface synthesis. Thirdly, it brings these two ideas together to show that frame and position matching for an infinitesimal patch are exactly equivalent to the Gaus...

We prove fourteen equivalent conditions for a set of time-frequency shifts on a lattice Λ, {e2g(t − λ1) : (λ1, λ2) ∈ Λ} ⊆ L (R), to be a frame for L(R). Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L(R), it suffices to verify that it is one-to-one on a certain subspace of tempered d...