Matematica (गणितम् ) si (च ) Dharma (धर्म )
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luni, 6 ianuarie 2020
Palindromic arrangement and alchemical summation.
De ce palindrom ?
https://www.google.com/url?sa=t&source=web&rct=j&url=https://ictp.acad.ro/anisiu/papers/2006-Anisiu-A-K-Properties.pdf&ved=2ahUKEwislLbaz-_mAhUDY1AKHZF7CFwQFjAFegQIAhAB&usg=AOvVaw1BxjiLMfCi3La8TVUEcZAc
De ce palindrom ? https://www.google.com/url?sa=t&source=web&rct=j&url=https://ictp.acad.ro/anisiu/papers/2006-Anisiu-A-K-Properties.pdf&ved=2ahUKEwislLbaz-_mAhUDY1AKHZF7CFwQFjAFegQIAhAB&usg=AOvVaw1BxjiLMfCi3La8TVUEcZAc
Properties of palindromes in nite words Mira-Cristiana Anisiu Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy, Cluj-Napoca e-mail: mira@math.ubbcluj.ro and Valeriu Anisiu Department of Mathematics Faculty of Mathematics and Computer Science Babe³-Bolyai University of Cluj-Napoca e-mail: anisiu@math.ubbcluj.ro and Zoltán Kása Department of Computer Science Faculty of Mathematics and Computer Science Babe³-Bolyai University of Cluj-Napoca e-mail: kasa@cs.ubbcluj.ro (Received: July 1215, 2006) Abstract. We present a method which displays all palindromes of a given length from DeBruijn words of a certain order, and also a recursive one which constructs all palindromes of length n + 1 from the set of palindromes of length n. We show that the palindrome complexity function, which counts the number of palindromes of each length contained in a given word, has a dierent shape compared with the usual (subword) complexity function. We give upper bounds for the average number of palindromes contained in all words of length n, and obtain exact formulae for the number of palindromes of length 1 and 2 contained in all words of length n. Mathematics Subject Classi cations (2000). 68R15 1 Introduction The palindrome complexity of innite words has been studied by several authors (see [1], [3], [14] and the references therein). Similar problems related to the number of palindromes are important for nite words too. One of the reasons is that palindromes occur in DNA sequences (over 4 letters) as well as in protein description (over 20 letters), and their role is under research ([9]). Let an alphabet A with card(A) = q 1 be given. The set of the words of length n over A will be denoted by An. Given a word w = w1w2:::wn; the reversed of w is w = wn:::w2w1. Denoting by " the empty word, we put by convention " = ". The word w is a palindrome if w = w. We denote by ak the word a:::a . The set of the subwords of a k times word w which are nonempty palindromes will be denoted by PAL (w). The (in nite) set of all palindromes over the alphabet A is denoted by PAL (A), while PALn(A) = PAL(A)\An.
Plecând de la acest aranjament palindromic se poate gasi o metoda simpla de a calcula diferenta dintre doua numere ridicate la puterea 2. Practic putem afla repede care este suprafata ce rămâne dupa ce vom decupa un pătrat din alt pătrat cu suprafata mai mare decat cea a primului pătrat. Formula generala este : ... n (2a+n)=(a+n)^2-(a)^2
De ce palindrom ?
RăspundețiȘtergerehttps://www.google.com/url?sa=t&source=web&rct=j&url=https://ictp.acad.ro/anisiu/papers/2006-Anisiu-A-K-Properties.pdf&ved=2ahUKEwislLbaz-_mAhUDY1AKHZF7CFwQFjAFegQIAhAB&usg=AOvVaw1BxjiLMfCi3La8TVUEcZAc
Properties of palindromes in nite words Mira-Cristiana Anisiu Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy, Cluj-Napoca e-mail: mira@math.ubbcluj.ro and Valeriu Anisiu Department of Mathematics Faculty of Mathematics and Computer Science Babe³-Bolyai University of Cluj-Napoca e-mail: anisiu@math.ubbcluj.ro and Zoltán Kása Department of Computer Science Faculty of Mathematics and Computer Science Babe³-Bolyai University of Cluj-Napoca e-mail: kasa@cs.ubbcluj.ro (Received: July 1215, 2006) Abstract. We present a method which displays all palindromes of a given length from DeBruijn words of a certain order, and also a recursive one which constructs all palindromes of length n + 1 from the set of palindromes of length n. We show that the palindrome complexity function, which counts the number of palindromes of each length contained in a given word, has a dierent shape compared with the usual (subword) complexity function. We give upper bounds for the average number of palindromes contained in all words of length n, and obtain exact formulae for the number of palindromes of length 1 and 2 contained in all words of length n. Mathematics Subject Classi cations (2000). 68R15 1 Introduction The palindrome complexity of innite words has been studied by several authors (see [1], [3], [14] and the references therein). Similar problems related to the number of palindromes are important for nite words too. One of the reasons is that palindromes occur in DNA sequences (over 4 letters) as well as in protein description (over 20 letters), and their role is under research ([9]). Let an alphabet A with card(A) = q 1 be given. The set of the words of length n over A will be denoted by An. Given a word w = w1w2:::wn; the reversed of w is w = wn:::w2w1. Denoting by " the empty word, we put by convention " = ". The word w is a palindrome if w = w. We denote by ak the word a:::a . The set of the subwords of a k times word w which are nonempty palindromes will be denoted by PAL (w). The (in nite) set of all palindromes over the alphabet A is denoted by PAL (A), while PALn(A) = PAL(A)\An.
RăspundețiȘtergerePlecând de la acest aranjament palindromic se poate gasi o metoda simpla de a calcula diferenta dintre doua numere ridicate la puterea 2.
RăspundețiȘtergerePractic putem afla repede care este suprafata ce rămâne dupa ce vom decupa un pătrat din alt pătrat cu suprafata mai mare decat cea a primului pătrat.
Formula generala este :
...
n (2a+n)=(a+n)^2-(a)^2