Results 21 to 30 of about 19,285 (99)

The distribution of spacings between the fractional parts of $n^2 \alpha$

, 2001
We study the distribution of normalized spacings between the fractional parts of an^2, n=1,2,.... We conjecture that if a is "badly approximable" by rationals, then the sequence of fractional parts has Poisson spacings, and give a number of results ...
Rudnick, Zeev, Sarnak, Peter, Zaharescu, Alexandru   +2 more
core   +1 more source

On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture

, 2004
We consider the limit periodic continued fractions of Stieltjes $$ \frac{1}{1-} \frac{g_1 z}{1-} \frac{g_2(1-g_1) z}{1-} \frac{g_3(1-g_2)z}{1-...,}, z\in \mathbb C, g_i\in(0,1), \lim\limits_{i\to \infty} g_i=1/2, \quad (1) $$ appearing as Shur--Wall $g ...
Tsygvintsev, Alexei
core   +1 more source

Continued fraction digit averages an Maclaurin's inequalities [PDF]

, 2014
A classical result of Khinchin says that for almost all real numbers $\alpha$, the geometric mean of the first $n$ digits $a_i(\alpha)$ in the continued fraction expansion of $\alpha$ converges to a number $K = 2.6854520\ldots$ (Khinchin's constant) as ...
Cellarosi, Francesco, Hensley, Doug, Miller, Steven J., Wellens, Jake L.   +3 more
core   +1 more source

Report on some recent advances in Diophantine approximation [PDF]

, 2009
A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
core   +3 more sources

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

, 2010
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions.
A. Aptekarev, A. Aptekarev, A. Bultheel, A. Bultheel, A. Kuijlaars, B. Anderson, B. Simon, D. Lubinsky, E. Miña-Díaz, E. Nikishin, E. Rakhmanov, F. Peherstorfer, G. Szegő, H. Begehr, H. Langer, H. Wall, H. Wall, I. Schur, J. Garnett, J. Geronimus, J. Geronimus, K. Astala, K. Pan, L. Baratchart, L. Baratchart, L. Baratchart, M. Džrbaŝjan, M. Krein, M. Olivi, N. Akhiezer, O. Njåstad, P. Duren, P. Faurre, P. Grisvard, P. Koosis, R. Adams, R. Killip, R. Nevanlinna, S. Campanato, S. Denisov, S. Denisov, S. Khrushchev, S. Khrushchev, S. Kupin, V. Lunot, W. P. Ziemer, Y. Matthaei   +46 more
core   +2 more sources

A Convergent Method for Calculating the Properties of Many Interacting Electrons

, 1999
A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies induced by a given ...
Andrew Gibson, B. N. Parlett, E. H. Lieb, G. Freud, H. Bethe, H. Mori, J. A. Shohat, J. Friedel, James F. Annett, M. Böhm, M. von Laue, R. Kubo, Roger Haydock, Roger Haydock, Roger Haydock, Roger Haydock, T. S. Chihara   +16 more
core   +1 more source

The hyperbolic geometry of continued fractions K(1|b_n)

, 2006
The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fraction K(1|bn) diverges. H. S. Wall asks whether just convergence, rather than absolute convergence of ∑bn is sufficient for the divergence of K(1|bn).
Short, Ian
core  

Panel Data Stochastic Convergence Analysis of the Mexican Regions [PDF]

The stochastic convergence amongst Mexican Federal entities is analyzed in panel data framework. The joint consideration of cross-section dependence and multiple structural breaks is required to ensure that the statistical inference is based on ...
Josep Lluís Carrion-i-Silvestre, Vicente German-Soto   +1 more
core  

Automated navigation of condensate phase behavior with active machine learning. [PDF]

Nat Commun
Leurs YHA, van den Hout W, Gardin A, van Dongen JLJ, Rodriguez-Abetxuko A, Erkamp NA, van Hest JCM, Grisoni F, Brunsveld L.   +8 more
europepmc   +1 more source

Open data phylometabolomics reveals turnover-dominated chemical divergence and clade-specific physicochemical regimes across angiosperms. [PDF]

Plant J
Carollo CA, Boaretto AG, Nocetti MC, Carollo ARH, Alves FM.   +4 more
europepmc   +1 more source