Substitution Delone Sets

This paper addresses the problem of describing aperiodic discrete structures that have a self-similar or self-affine structure. Substitution Delone set families are families of Delone sets (X_1, ..., X_n) in R^d that satisfy an inflation functional equation under the action of an expanding integer matrix in R^d. This paper studies such functional equation in which each X_i is a discrete multiset (a set whose elements are counted with a finite multiplicity). It gives necessary conditions on the coefficients of the functional equation for discrete solutions to exist. It treats the case where the equation has Delone set solutions. Finally, it gives a large set of examples showing limits to the results obtained.Comment: 34 pages, latex file; some results in Sect 5 rearranged and theorems reformulate

An algorithm to design finite field multipliers using a self-dual normal basis

Finite field multiplication is central in the implementation of some error-correcting coders. Massey and Omura have presented a revolutionary design for multiplication in a finite field. In their design, a normal base is utilized to represent the elements of the field. The concept of using a self-dual normal basis to design the Massey-Omura finite field multiplier is presented. Presented first is an algorithm to locate a self-dual normal basis for GF(2 sup m) for odd m. Then a method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function base on a self-dual basis is simpler than that based on an arbitrary normal base

Long period pseudo random number sequence generator

A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0)

Experimental investigation of the properties of electrospun nanofibers for potential medical application

Copyright © 2015 Anhui Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Polymer based nanofibers using ethylene-co-vinyl alcohol (EVOH) were fabricated by electrospinning technology. The nanofibers were studied for potential use as dressing materials for skin wounds treatment. Properties closely related to the clinical requirements for wound dressing were investigated, including the fluid uptake ability (FUA), the water vapour transmission rate (WVTR), the bacteria control ability of nanofibers encapsulated with different antibacterial drugs, and Ag of various concentrations. Nanofibre degradation under different environmental conditions was also studied for the prospect of long term usage. The finding confirms the potential of EVOH nanofibers for wound dressing application, including the superior performance compared to cotton gauze and the strong germ killing capacity when Ag particles are present in the nanofibers