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In other words, the matrix stands for the formula ((exists )H), where the subformula (H) is in DNF and contains no quantifiers.
However, although the formula exists and is proven for multidimensional systems, it requires that, in the singular limit, escapes take place almost surely at a finite number of discrete saddles.
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The Choquet integral of f with respect to μ on X is defined as (2) (C ) ∫ f dμ = ∫ − ∞ 0 [ μ (F α ) − μ (X ) ] dα + ∫ 0 ∞ μ (F α ) dα where F α ={ x| f(x)≥ α} for α∈, if both terms on the right-hand side of the formula exist, and not both are infinite.
"Now that that formula exists, that sector will get a ton of investment dollars flowing in".
For example, let (G) denote the following formula: (exists xexists y sim p_1 x,y) wedge p_4 a,x) wedge sim p_6 vee p_2 x) wedge sim p_5(b) vee sim p_3 y))).
In this case sX may be calculated as (16) sX = ln 1 2 × IQRX 0 medX 0 + IQRX 0 medX 0 2 + 4 z When the IQR is reported together with the mean no explicit formula exists to derive sX.
To determine the probability of a team winning any given game, a formula exists that factors the win percentage of both teams and the league's home win percentage.
Because of the complex mechanisms of hydrocarbon expulsion, no appropriate model or formula exists to explain the hydrocarbon expulsion process.
No set formula exists for the optimal number of households CHWs can feasibly serve with a minimum standard of care.
In addition to that Universal truth, the next concept required is to understand that a formula exists for everything.
"Profit has to be substantial relative to tax benefits, but no mathematical formula exists for that yet," Ms. Sheppard said.
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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