Results 211 to 220 of about 51,771 (253)

Suitable Norms for Simultaneous Approximation

Acta Mathematica Hungarica, 1997
The most common way to study simultaneous approximation of two points \(x,y\) of a normed linear space \(E\) from a subset \(M\) of \(E\), is to consider a suitable norm in \(E\times E\) (for instance, \(\| (u,v)\| =\sup(\| u\| ,\| v\|)\), \(\| (u,v)\| =\| u\| +\| v\|)\) and to reduce this problem to the ordinary approximation of the single point \((x ...
Benítez, Carlos, Fernández, Manuel, Soriano, María L.   +2 more
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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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On simultaneous approximation

Numerical Functional Analysis and Optimization, 1998
In this exposition, we investigate in an extended framework the problem of simultaneous best approximation. Refinement of a formula for the subdifferential of restricted radius of a p-bounded set leads us to explore some interesting results on strong uniqueness of simultaneous best approximants. In particular, we also.
LAURENT, PJ, PAI, D
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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 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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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 \(
Kupavskii, Andrei, Pach, Janos
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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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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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