A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code

Controlling chaos in the quantum regime using adaptive measurements

The continuous monitoring of a quantum system strongly influences the emergence of chaotic dynamics near the transition from the quantum regime to the classical regime. Here we present a feedback control scheme that uses adaptive measurement techniques to control the degree of chaos in the driven-damped quantum Duffing oscillator. This control relies purely on the measurement backaction on the system, making it a uniquely quantum control, and is only possible due to the sensitivity of chaos to measurement. We quantify the effectiveness of our control by numerically computing the quantum Lyapunov exponent over a wide range of parameters. We demonstrate that adaptive measurement techniques can control the onset of chaos in the system, pushing the quantum-classical boundary further into the quantum regime

A Note on Allowed and Realized Rates of Return in the Electric Utility Industry

Most empirical investigations of electric utility behavior use the realized rate of return as a proxy for the allowed rate of return, We examine the validity of this assumption and investigate the relationship of the allowed and realized rates to the cost of capital between 1973 and 1982, We use two measures of the cost of capital: one based on returns to book equity, the other derived from a market price of equity. While realized and allowed rates were generally higher than the book measure throughout the period, both of the rates of return were less than the market price of capital after 1979. We also find firms did not earn their allowed rate of return after 1974. Therefore, the use of the realized rate as a proxy for the allowed rate in empirical models will lead to biased parameter estimates. To help correct this bias, we give data for allowed rates

Soil erosion in Iowa

Soil erosion is the carrying away of soil thru the free movement of water over the surface of the land. If all the rain falling on the soil were absorbed, erosion could not occur. But the precipitation is sometimes so rapid and so great and such a small portion is taken up by the soil, that many cultivated fields are subject to extensive losses by the washing action of water. Bare bluffs and hillsides are particularly in danger of erosion and gullies formed in such locations may extend for miles and render large areas partially or wholly unfit for cultivation. Loess soils are apt to be injured by erosion when the topography is hilly or rough and it is these soils which are affected to the greatest extent in Iowa. Large acreages in the Missouri loess, the Mississippi loess and the Southern Iowa loess soil areas are frequently rendered untillable or even entirely useless because of excessive erosion. The adoption of proper methods of preventing or controlling the washing away of valuable land is therefore important

Importance of book-keeping

The introduction of A Practical System of Book-Keeping, Sixth Edition, Revised, by Levi S. Fulton and Geo. W. Eastman in 1852 provides comments that may be of some general interest to accounting historians. Obviously the authors\u27 comments on pages 5-6 are intended, at least partially, to promote the book. However, one should note the definition of book-keeping, comments on the importance of records to people in various lines of work and particularly to the merchant, recommendations that book-keeping be more extensively taught at various levels of schools, identification of the value of book-keeping to female education and its importance along with reading, writing, and arithmetic, and the assertion that the schoolroom is the place to learn book-keeping

TB99: Flora of Oxford County, Maine

This is a study of the vascular plants occurring in Oxford County, Maine. Plants with vascular or conductive tissue (kingdom Plantae, division Tracheophyta) include the ferns and their allies (horsetails and lycopods) and the seed-bearing plants. Our aim has been to determine which plants occur in the county and, based on herbarium collections and observations, their habitat preferences, frequency of occurrence, and geographic distribution. We have also endeavored to explain the nature of the flora first in terms of the various factors which influence its composition and second by grouping the plants into the most important natural associations.https://digitalcommons.library.umaine.edu/aes_techbulletin/1106/thumbnail.jp