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Layered rare-earth hydroxides as multi-modal medical imaging probes: particle size optimisation and compositional exploration.

Dalton Trans
Strimaite M, Wells CJR, Prior TJ, Stuckey DJ, Wells JA, Davies GL, Williams GR.   +6 more
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Noninterpolatory Quadrature Formulas

SIAM Journal on Numerical Analysis, 1972
There are infinitely many formulas of the form \[\int_{ - 1}^1 {f(x)dx = a_{ - 1} f( - 1) + a_0 f(0) + a_1 (1) + b_{ - 1} f''( - 1)b_1 f''(1)} \] that are exact for quintic polynomials, although, in general, there is no interpolating quintic through the six pieces of data. On the other hand, there is no corresponding formula for \[\int_{0}^1 {f(x)dx} \]
Epstein, M. P., Hamming, R. W.
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On the Convergence of Quadrature Formulas

SIAM Journal on Numerical Analysis, 1971
Two fundamental theorems concerning quadratures are given here. The first theorem gives a constructive criterion for determining if a quadrature formula is convergent in the space of continuous functions on $[0,1]$ with maximum norm. The second theorem simply shows that Gregory’s method is convergent in the space of bounded Riemann integrable functions
Espinosa-Maldonado, Ruben J., Byrne, George D.   +1 more
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On Quadrature Formulas

Доклады Академии наук, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON QUADRATURE FORMULAS

Russian Academy of Sciences. Izvestiya Mathematics, 1995
See the review in Zbl 0836.41020.
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Gaussian interval quadrature formula

Numerische Mathematik, 2001
Let \(U_N=\{u_0,...,u_N\}, (V_N=\{1,v_1,...,v_N\})\) be a Chebyshev (Markov) system on the interval \([a,b],\) respectively. For a given set of ordered non-overlapping intervals \([c_k,d_k]\subseteq [a,b], k=1,...,n\) the authors consider the multiple node interval quadrature formula (with respect to \(V_N\)) \[ \int_a^b\mu(t)f(t)dt\approx \sum_{k=1}^n\
Borislav Bojanov, Petar Peynov Petrov
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ON THE ČEBYŠEV QUADRATURE FORMULA

Mathematics of the USSR-Izvestiya, 1969
In this paper we examine several weight functions for which the Cebysev quadrature formula is valid. A method is given in the general case by means of which the degree of precision of the formula may be estimated.
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On Mendeleev’s quadrature formula

Computational Mathematics and Mathematical Physics, 2012
Summary: It is well known that D. I. Mendeleev was also an outstanding numerical mathematician, but few people know that he devised and frequently applied a quadrature formula, which can be named after him.
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On chebyshev quadrature and variance of quadrature formulas

BIT, 1988
The purpose of this note is to give an example which demonstrates that one can achieve much higher algebraic precision with a quadrature rule with small but not minimal variance than with a Chebyshev rule with minimal variance.
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On quadrature formulae

Mathematical Proceedings of the Cambridge Philosophical Society, 1950
1. It is frequently required to find the numerical value of the definite integralIt is, however, often found that even if the analytical expression off(x) is given, it cannot be integrated in terms of known elementary functions. The elliptic integrals are perhaps the best known examples of functions of this type; and more common are cases wheref(x) is ...
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