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This gives us another asymptotics, also with many terms which are difficult to calculate.
This allows us to improve the remainder estimate in the full Weyl asymptotics but we need to include many terms which are difficult to calculate.
It is especially important to note that the highest-frequency spatial errors cannot be controlled from the "measurement side" since they arise precisely because of the truncation to finitely many terms, which actually stems from the inability to perform infinitely many measurements.
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This new expression exploits the presence of many repeated events and has many fewer terms, which significantly reduces the computational cost.
Similarly the integral I c may be evaluated employing the elliptic integral F. The above are an example of computations needed to evaluate one term in the BIM; there exist many such terms which are evaluated as integrals of F and E. Numerical integration is employed in evaluating the BIMs for two reasons.
One problem with input materials like the terminology systems used in this study is that they result in many term pairs which only occur once.
When you see it registering the chances of the election going a certain way at ninety per cent, or ninety-five per cent, it's easy to dismiss the other outcome as a live possibility — particularly if you haven't been schooled in how to think in probabilistic terms, which many people haven't.
But instead of accepting the old terms, which many African officials call unconditional surrender, some cash-starved African states are pushing back, showing an assertiveness unthinkable until recently and suggesting that the days of unbridled influence by the African continent's mega-investor may be waning.
He casts doubt on terms which many philosophers take for granted.
Quine makes similar remarks about "thought", "belief", "experience", "necessity" and other terms which many philosophers assume are legitimate and available for philosophical use without themselves requiring explanation and justification in other terms.
Several of these statements were cited by the judge's decision in Irving's lawsuit against Penguin Books and Deborah Lipstadt, leading the judge to conclude that Irving "had on many occasions spoken in terms which are plainly racist".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com