Torus knots that cannot be untied by twisting

We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.Comment: LaTeX, 12 pages, to appear in Revista Matem\'{a}tica Complutens

Generalized Analysis of Elastic Wave Dispersion Asymmetries in Moving Periodic Media

This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the newly adopted paradigm provides an eloquent take on the dispersion problem and, in the process, highlights discrepancies between both schemes. Equations governing the motion of an elastic rod with a prescribed moving velocity observed from a stationary reference frame are used to predict propagation patterns and asymmetries in wave velocities induced as a result of the induced linear momentum bias. Three distinct scenarios corresponding to a moving rod with a constant modulus, a spatially varying one, and one that varies in space and time are presented. These cases are utilized to extract and interpret correlations pertaining to directional velocities, dispersion patterns, as well as nature of band gaps between moving periodic media and their stationary counterparts with time-traveling material properties. A linear vertical shear transformation is derived and utilized to thoroughly neutralize the effect of the moving velocity on the resultant dispersion characteristics. Finally, dispersion contours associated with the transient response of a finite moving medium are used to validate the entirety of the presented framework

A Method to determine Partial Weight Enumerator for Linear Block Codes

In this paper we present a fast and efficient method to find partial weight enumerator (PWE) for binary linear block codes by using the error impulse technique and Monte Carlo method. This PWE can be used to compute an upper bound of the error probability for the soft decision maximum likelihood decoder (MLD). As application of this method we give partial weight enumerators and analytical performances of the BCH(130,66), BCH(103,47) and BCH(111,55) shortened codes; the first code is obtained by shortening the binary primitive BCH (255,191,17) code and the two other codes are obtained by shortening the binary primitive BCH(127,71,19) code. The weight distributions of these three codes are unknown at our knowledge.Comment: Computer Engineering and Intelligent Systems Vol 3, No.11, 201