The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on space curve in E³. differential geometric properties soliton surface accociated with Nonlinear Schrödinger (NLS) equation, called NLS or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature found terms curvatures k_{n}, ...

We introduce a new 2D visual tracking algorithm that utilizes an approximate nearest neighbour search to estimate per-frame state updates. We experimentally demonstrate that the new algorithm capable of estimating larger per-frame motions than the standard registration-based algorithms and that it is more robust in a vision-controlled robotic alignment task.

This work develops a quantitative framework for describing the overcompleteness of a large class of frames. A previous article introduced notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. This article shows that those ab...

Frames for Hilbert spaces were first introduced by Duffin and Schaeffer [10] in 1952 to study some problems in nonharmonic Fourier series, reintroduced in 1986 by Daubechies, Grossmann and Meyer [8]. Frames are very useful in characterization of function spaces and other fields of applications such as filter bank theory, sigmadelta quantization, signal and image processing and wireless communic...

This paper studies the problem of sequence-to-sequence alignment, namely establishing correspondences in time and in space between two di erent video sequences of the same dynamic scene. The sequences are recorded by uncalibrated video cameras, which are either stationary or jointly moving, with xed (but unknown) internal parameters and relative inter-camera external parameters. Temporal variat...

motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces  has a series expansion.

Introduction Formulation of spatial RF pulse design in a gradient-dependent rotating frame is introduced. This work was motivated by the need for a fast RF design algorithm for use in a high-field parallel transmit system where dielectric effect creates transmit field distribution with significant patientdependent variability. The new reference frame, called a “local rotating frame”, transforms...