this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a representation of a further generalized Weierstrass relations for a general k-s...

Title of Dissertation: BINORMAL MOTION OF CURVES AND SURFACES IN A MANIFOLD Hector Hernando Gomez, Doctor of Philosophy, 2004 Dissertation directed by: Dr. Manoussos Grillakis Department of Mathematics In the present work we consider a curve embedded in a three-dimensional Riemannian manifold moving in the binormal direction proportional to its curvature. We study how an appropriate orthonormal...

In this paper, modal analysis is carried out by using a Frenet frame-based shape measurement algorithm. This algorithm is validated through experiments conducted with a long slender, aluminum cantilever structure (65.625′′×2.0′′×0.125′′), which is instrumented with eight serially multiplexed fiber Bragg grating (FBG) sensors. The multiplexed FBG sensors measure the bending strain distribution a...

Through two diierent approaches, this report proposes two general controllers for unicycle-type and two-steering-wheels mobile robots. For both systems, conditions for asymptotical convergence to a predeened path are established and simulation results are presented. Rather than writing the systems' equations with respect to a xed reference frame, the robot state is here parametrized relative to...

BACKGROUND This study introduces two novel outcomes that could be used to identify people with knee osteoarthritis from healthy controls. These outcomes examine the lengths of paths on a sphere derived from knee angle and knee position during gait. METHODS Participants with moderate knee osteoarthritis (n=47) and no knee pathology (n=51) walked overground. The time-varying orientation matrice...

Kinney et al [PPL 1,(1994)] have investigated plasma filamentary structure dynamics. More recently, Wilkin et al [Phys Rev Lett 99:134501,(2007)] have shown that kinetic energy spectrum of magnetic structures in small-scale dynamos, are predominantly fila-mentary. Kirilov et al [PRE (2009)] have shown that use of the boundary values of the mean-field isotropic helical turbulent α 2-dynamo, coul...

We present algorithms for computing the differential geometry properties of Frenet apparatus and higher-order derivatives of intersection curves of implicit and parametric surfaces in 3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given an...