Download Algebraic Coding: First French-Soviet Workshop Paris, July by A. Tietäväinen (auth.), Gérard Cohen, Antoine Lobstein, PDF

By A. Tietäväinen (auth.), Gérard Cohen, Antoine Lobstein, Gilles Zémor, Simon Litsyn (eds.)

This quantity provides the court cases of the 1st French-Soviet workshop on algebraic coding, held in Paris in July 1991. the assumption for the workshop, born in Leningrad (now St. Petersburg) in 1990, used to be to collect the very best Soviet coding theorists. Scientists from France, Finland, Germany, Israel, Italy, Spain, and the USA additionally attended. The papers within the quantity fall relatively certainly into 4 different types: - functions of exponential sums - protecting radius - buildings -Decoding.

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Additional info for Algebraic Coding: First French-Soviet Workshop Paris, July 22–24, 1991 Proceedings

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When I say that the harmonic series adds up to infinity, what I really mean is that given any number S, no matter how large, the sum of the harmonic series eventually exceeds S. ” The 16 PRIME OBSESSION whole of analysis was rewritten in this kind of language in the middle third of the nineteenth century. Any statement that can’t be so rewritten is not allowed in modern mathematics. Nonmathematical people sometimes ask me, “You know math, huh? ” I can only reply, “The words you just uttered do not make sense.

If you look closely at the list of primes, you’ll see that they thin out as you go along. Between 1 and 100 there are 25 primes; between 401 and 500, 17; and between 901 and 1,000, only 14. The number of primes in any block of 100 whole numbers seems to decline. , from 999,901 to 1,000,000). If I took it to a trillion, there would be just four in the last hundred-block. ) 34 PRIME OBSESSION II. The question naturally arises, Do the primes eventually thin out to nothing? If I continued the list into the trillions of trillions, and trillions of trillions of trillions of trillions, would I eventually reach a point beyond which there are no more primes, so that the last prime on my list would be the last prime, the biggest prime?

To get the N-th member of that sequence: if N is even, multiply the previous member by NN+1 , if N is odd, multiply the previous member by NN+1 . That converges to π . 972154… (this se2 3 quence converges very slowly). Here is yet another: 11 , (1 12 ) , (1 13 ) , 4 5 (1 14 ) , (1 51 ) , …. If you work them out, these come to 1, 2 14 , 113 1526 2 10 27 , 2 256 , 2 3125 ,... 718281828459. This is an exceedingly important number—I shall use it later. Notice that all of these are sequences, just strings of numbers separated by commas.

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