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Another informal such paradoxical situation is obtained if we define an integer to be the "least integer not definable in less than 100 words".
For every, define an integer sequence as.
We define an integer sequence as in Lemma 1.5.
The above representation can be used to define an integer approximation of the DCT.
In this case, we may define an integer sequence ( τ ( n ) ) as in Lemma 4.
Thus, we can define an integer sequence { τ n } for all n ≥ n 0 as follows: τ ( n ) = max { k ∈ N ∣ n 0 ≤ k ≤ n, s k ≤ s k + 1 }.
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An enzyme can use a metabolite in multiple unique reactions involving distinct subsets of other metabolites, and the number of unique reactions defines an integer-valued edge weight.
Firstly, we define a constant integer Q subject to M = LN = KQ.
In this paper we define a half-integer valued function on the simply connected covering group of the symplectic group, related to the Maslov index of curves on the Lagrangian Grassmannian and use it to write down explicitly the operators of the metaplectic or Oscillator representation.
More specifically, (2) S t = ∑ l c j 0 l φ j 0, k t + ∑ k ∑ j = j 0 ∞ d j k ψ j, k t, where c j (l) = ∫ R S t) φ j, l (t) dt and d j (k) = ∫ R S t) ψ j, k (t) dt are the low-pass and high-pass coefficients, respectively; j0 is an integer to define an interval on which S t) is a piecewise constant.
For k>x>1, recursively define an increasing sequence of integers p 1,q 1,… 2,q 2,… and a sequence of unit-vectors v 1,v 2,… as follows: Set p 0=0, and v 0=(1,0=.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com