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Density functional theory-accelerated design of perovskite quantum dots: unlocking atomic-level control for next-generation optoelectronics and sensors. [PDF]
Al Omari RH +8 more
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Uniform rational approximation
Proceedings of the American Mathematical Society, 1995Let K be a compact subset of the complex plane C \mathbb {C} , and let P ( K ) P(K) and R ( K ) R(K) be the closures in C ( K ) C(K) of polynomials and rational functions with poles
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The Mathematical Gazette, 1990
Any positive fraction can be represented by a lattice point in the positive quadrant of the coordinate plane, ( x , y ) being used to represent the fraction y/x.
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Any positive fraction can be represented by a lattice point in the positive quadrant of the coordinate plane, ( x , y ) being used to represent the fraction y/x.
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Approximation by Rational Functions
Journal of the London Mathematical Society, 1977This paper contains eight theorems on the rational approximation of \(e^{-x}\) . We cite one of them by way of an example: ''Let \(p(x)\) and \(q(x)\) be any polynomials of degress at most \(n-1\) where \(n\geq 2\). Then we have \[ \left\|e^{-x}-\frac{p(x)}{q(x)}\right\|_{l_{\infty}(N)}\geq\frac{(e-1)^ne^{-4n}2^{-7n}}{n(3+2\sqrt2)^{n-1}}.'', \] (\(N ...
Erdős, Paul +2 more
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Biased rational chebyshev approximation
BIT, 1982Chebyshev approximation on an interval [α, β] by ordinary rational functions when positive deviations (errors) are magnified by a bias factor is considered. This problem is related to one-sided Chebyshev approximation for large bias factors. Best approximations are characterized by alternation.
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An Interpolatory Rational Approximation
Canadian Mathematical Bulletin, 1978The classical Hermite-Fejér interpolation process is a positive linear mapping from C[-1, 1] into the space of polynomials of degree ≤2n-1. If Tn(x) denotes the Tchebisheff polynomial of degree n and xk = xnk(k = 1,2, …, n) its roots, then for any given f∈ C[-1, 1] the Hermite-Fejér image Hnf of f is defined by1 ...
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Rational approximations to \(\pi\)
1971Using an IBM 1130 computer, we have generated the first 20, 000 partial quotients in the ordinary continued fraction representation of pie. © 1971 American Mathematical Society.
Choong, K.Y. +2 more
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RATIONAL APPROXIMATION AND PLURIPOLAR SETS
Mathematics of the USSR-Sbornik, 1984The main result in the article isTheorem. Let be a closed set such that and is a pseudoconvex domain. If for almost every complex line passing through 0 the intersection is polar in , then is a pluripolar set in .This theorem is then applied to the analysis of sets of singularities of holomorphic functions which are rapidly approximated by rational ...
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RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS
Mathematics of the USSR-Izvestiya, 1971In this article we derive a new effective estimate of rational approximations to algebraic numbers simultaneously in an Archimedian and several non-Archimedian metrics.
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