Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Lluís Bibiloni"'
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 9, Pp 559-567 (2002)
The approximants to regular continued fractions constitute best approximations to the numbers they converge to in two ways known as the first and the second kind. This property of continued fractions provides a solution to Gosper's problem of the bat
Externí odkaz:
https://doaj.org/article/25eeaabba39d46b5accb9174dbcf6cbf
Publikováno v:
Journal of Mathematical Analysis and Applications. 362:401-414
What do the three names in the title have in common? The purpose of this paper is to relate them in a new and, hopefully, interesting way. Starting with the Fibonacci numeration system — also known as Zeckendorff's system — we will pose ourselves
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ff079370f7a8f520c1ed4e91a3b85b2a
https://doi.org/10.1016/j.jmaa.2009.08.004
https://doi.org/10.1016/j.jmaa.2009.08.004
Publikováno v:
Journal of Mathematical Analysis and Applications. 329(1):592-602
In 1952 F. Riesz and Sz.-Nagy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eee3a57214e8868ff39d42cf8ae302f8
Publikováno v:
Scopus-Elsevier
Theorem 1 of Euler's paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d7858ee804b748a416c58221ab8904e
https://doi.org/10.1080/00029890.2006.11920299
https://doi.org/10.1080/00029890.2006.11920299
Publikováno v:
Journal of Mathematical Analysis and Applications. 253:107-125
Minkowski's ?( x ) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it enables us to prove that its derivative, when it exists in a wide sense, can o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43d3ee1be592abdb7205cdd1f20f5448
https://doi.org/10.1006/jmaa.2000.7064
https://doi.org/10.1006/jmaa.2000.7064
Publikováno v:
The American Mathematical Monthly. 106:241-251
2. STARTING POINT: THE THREE-DOOR PROBLEM. Mathematics has always been enriched by a- diversity of games and intellectual curiosities. These have provided an endless supply of problems that have acquired a life of their own, far removed from the recr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::88ec7a301e943e40dd1f1281edc56a9f
https://doi.org/10.1080/00029890.1999.12005034
https://doi.org/10.1080/00029890.1999.12005034
Publikováno v:
Order. 16:207-220
A ‘next’ operator, σ, is built on the set R 1 =(0, 1] − {1 − 1 / e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R 1. In addition, the orbits {σ n (α)} n ∈ Z are all dense in R
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79da10b985b9fd99bc94b6f1fb21f190
https://doi.org/10.1023/a:1006441703404
https://doi.org/10.1023/a:1006441703404
Publikováno v:
SSRN Electronic Journal.
In 1952 F. Riesz and Sz. Nagy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d23cc7e1036e9703544f69dae2260252
https://doi.org/10.2139/ssrn.1001890
https://doi.org/10.2139/ssrn.1001890
We start with a generalization of the well-known three-door problem: the n-door problem. The solution of this new problem leads us to a beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______645::22908b690d72282f5e5dbefdfe117c09
https://econ-papers.upf.edu/papers/239.pdf
https://econ-papers.upf.edu/papers/239.pdf
The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d62f143c3f721de138e43a1fa747ce2
https://econ-papers.upf.edu/papers/226.pdf
https://econ-papers.upf.edu/papers/226.pdf