Results 231 to 240 of about 431,788 (272)

Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
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Simultaneous Approximation of Polynomials

2016
Let \(\mathcal{P}_d\) denote the family of all polynomials of degree at most d in one variable x, with real coefficients. A sequence of positive numbers \(x_1\le x_2\le \ldots \) is called \(\mathcal{P}_d\)-controlling if there exist \(y_1, y_2,\ldots \in \mathbb {R}\) such that for every polynomial \(p\in \mathcal{P}_d\) there exists an index i with \(
Andrei Kupavskii, János Pach
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Simultaneous Diophantine Approximation

Canadian Journal of Mathematics, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
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Simultaneous Approximation and Algebraic Independence

The Ramanujan Journal, 1997
Rappelons la notion de mesure d'approximation simultanée (MAS): soit \(\theta= (\theta_1,\dots,\theta_n)\in \mathbb{C}^n\); une application \(\varphi: \mathbb{N}\times [0,+\infty[\to [0,+\infty]\) est une MAS pour \(\theta\) si il existe \(D_0\in\mathbb{N}\) et \(h_0\geq 1\) tels que, pour tout entier \(D\geq D_0\), tout nombre réel \(h\geq h_0\) et ...
Roy, Damien, Waldschmidt, Michel
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ON SIMULTANEOUS PADÉ APPROXIMANTS

Mathematics of the USSR-Sbornik, 1982
A rather large class of systems of functions is investigated in connection with the simultaneous Pade approximants (normality, perfectness, problems of uniform convergence).Bibliography: 20 titles.
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Simultaneous Approximation in Positive Characteristic

Monatshefte f�r Mathematik, 2000
The authors generalise Diophantine approximation results of Voloch and de Mathan in positive characteristic to higher dimensions. Let \(k\) be field of characteristic \(p>0\) and put \(R=k[X]\), \(K=k(X)\), \({\mathcal K}=k((X^{-1}))\). We endow \({\mathcal K}\) with a non-archimedean absolute value \(|\cdot |\), such that for \(\alpha =\sum_{n=t ...
Caulk, Stephen, Schmidt, Wolfgang M.
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Saturation in multivariate simultaneous approximation

Mathematics and Computers in Simulation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. Cárdenas-Morales, A. Fraguela, P. Garrancho   +2 more
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On Simultaneously Badly Approximable Numbers

Journal of the London Mathematical Society, 2002
For any \(i,j>0\) with \(i+j=1\) define the set \(B(i,j)\) to be the set of pairs of reals \((\alpha,\beta)\) with \[ \max\{\|q\alpha\|^{1/i}\|q\beta \|^{1/j}\}>C(\alpha,\beta)/q \] for all \(q\geq 1\) and some positive constant \(C(\alpha,\beta)\). For \(i=0\) set \(B(0,1)\) to be the set of pairs \((\alpha,\beta)\) where \(\alpha\) is any real and \(\
Pollington, Andrew, Velani, Sanju
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Simultaneous approximation with neural networks

Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium, 2000
In this paper we use a "uniformity" property of Riemann integration to obtain a single-hidden-layer neural network of fixed translates of a (not necessarily radial) basis function with a fixed "width" that approximates a (possibly infinite) set of target functions arbitrarily well in the supremum norm over a compact set.
Ajit T. Dingankar, Dhananjay S. Phatak
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Simultaneous Diophantine Approximation To Series

Journal of the London Mathematical Society, 1959
Es sei \(\mathfrak K\) die Menge aller formalen Laurentreihen \(x = \alpha_d z^d + \alpha_{d-1}z^{d-1}+ \ldots\) mit Koeffizienten aus einem Körper \(\mathfrak k\). Es werde ferner \(\mathfrak T = \mathfrak k [z]\) und \(\mathfrak R = \mathfrak k(z)\) gesetzt.
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