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Multiscale Modelling, Analysis and Simulation of Cancer Invasion Mediated by Bound and Soluble Enzymes. [PDF]

Bull Math Biol
Ptashnyk M, Venkataraman C.
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Tunable optical matter: electrostatic repulsion modulates near- and far-field gold nanoparticle arrangements. [PDF]

Nanoscale Adv
Chen JJ, Olmos-Trigo J, Louis B, Huang CH, Rocha S, Masuhara H, Hofkens J, Delgado-Buscalioni R, Bresolí-Obach R, Marqués MI, Mélendez M.   +10 more
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Theoretical and experimental investigations on the performance of broad-sense quantum-well superluminescent diodes based on the concept of energy level divergence. [PDF]

Discov Nano
Wu D, Ren X, Li P, Liu H, Wang Q, Huang Y.   +5 more
europepmc   +1 more source

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Approximation by Rational Functions

Journal of the London Mathematical Society, 1977
This 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, Newman, D. J., Reddy, A. R.   +2 more
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Convex Approximation by Rational Functions

SIAM Journal on Mathematical Analysis, 1995
The first part of the paper is concerned with the convex approximation to \(| x |\) by rational functions on the interval \([- 1,1]\). By using \(H^ \infty\) quadrature the approximation order \(c_ 1 e^{- c_ 2 \sqrt n}\) is obtained, where \(n\) denotes the degree of the approximating rational function.
Gao, Bo, Newman, Donald J., Popov, V. A.
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Best approximations by rational functions

Mathematical Notes of the Academy of Sciences of the USSR, 1971
Description of a general class of real continuous functions cn a segment Δ of the real line for which a best rational approximation with complex coefficients is not unique.
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Approximation by rational functions

Applicable Analysis, 2008
The inverse problem of finding point sources from finite measurements of two-dimensional stationary field leads to the problem of interpolation by rational functions. However, unlike the polynomial interpolation, the system of equations for the polynomial coefficients appearing here is rather difficult to analyse and to solve numerically.
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Approximation of the function �x� by rational functions

Mathematical Notes of the Academy of Sciences of the USSR, 1974
We consider the problem of the approximation of the function ¦x¦ by rational functions. We make more precise the best approximation estimate obtained by A. P. Bulanov. We prove that for arbitrary positive integral n $$R_n [|x|]< Ane^{ - \pi \sqrt n } ,$$ where ...
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Approximation by rational spline functions

Calcolo, 2006
The author discusses the reproduction of linear functions by some classes of NURBS functions. The degree of approximation of continuous functions is estimated.
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Approximation by Generalized Rational Functions

1964
In recent years, certain aspects of the theory of best polynomial approximation on a real interval have been generalized. Classical theorems concerning existence and uniqueness of a polynomial of best approximation, and characterization of this polynomial by alternation properties, have found extensions and analogs when polynomials are replaced by ...
D. J. Newman, H. S. Shapiro
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