The notion of upper distortion for graded submonoids embedded in groups and monoids is introduced. A finitely generated monoid M is graded if every element of M can be written in only finitely many ways in terms of some fixed system of generators. Examples of such monoids are free monoids, Artin monoids, and monoids satisfying certain small cancellation conditions. Whenever such a monoid is emb...

We prove that distortion of a knotted curve in R is great than 4.76. This improves a result obtained by John M. Sullivan and Elizabeth Denne in [DS]. 1 The definition and results M. Gromov introduced the notion of distortion for submanifolds of R in [G], p.113-114. In the case of a simple closed curve K (closed 1-dimensional submanifold of R) distortion is U(K) = max P,Q∈K |PQ|K |PQ| , where |P...

We establish upper and lower bounds on the distortion bit-cost function for incremental firstorder Σ∆ ADC with constant input signal U that is uniformly distributed on (0, 1) and additive white Gaussian (AWG) input noise. It is shown, under mild conditions, that the mean squared-error distortion D scales with the number of index bits m roughly as 1/m. This is in sharp contrast to the 1/m scalin...

We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective. Low-distortion embeddings of a metric space into the line, or into some other “simple” metric space, (that is, a mapping that preserves distances, up to some small multiplicative factor called the distortion) ...

We study the problem of computing low-distortion embeddings in the streaming model. We present streaming algorithms that, given an n-point metric space M , compute an embedding of M into an n-point metric space M ′ that preserves a (1−σ)-fraction of the distances with small distortion (σ is called the slack). Our algorithms use space polylogarithmic in n and the spread of the metric. Within suc...

In this paper stator current during crawling of induction motor has been assessed. Three phase current signals have been transformed into Clarke plane. Specific reference signals having sinusoidal nature and different frequencies have been defined and then areas formed by the real system data with the reference signal have been determined, wherefrom individual contributions of fundamental wavef...

In H.264/AVC, the concept of rate-distortion optimization (RDO) mode decision has proven to be an important coding tool. However, this mode decision method makes the encoding process extremely complex, especially in the computation of the rate-distortion cost function, which includes the computations of the sum of squared difference (SSD) between the original and reconstructed image blocks and ...

The M-channel maximally decimated lter bank is considered, where, except in the ideal case of perfect reconstruction, aliasing distortion, magnitude distortion, and phase distortion are present. It is shown how these can be controlled if the lter bank is designed by the method of 1] that optimizes the gain of an error system.

The topographic mapping products of airborne light detection and ranging (LiDAR) are usually required in the national coordinates (i.e., using the national datum and a conformal map projection). Since the spatial scale of the national datum is usually slightly different from the World Geodetic System 1984 (WGS 84) datum, and the map projection frame is not Cartesian, the georeferencing process ...