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The unknown part U of the miss-distance can be written in terms of a function which is an entire function of exponential type.
Let X be a fixed set, an HFS on X is in terms of a function that when applied to X returns a subset of [0, 1].
A generalised Brownian motion is an algebra of creation and annihilation operators acting on FV(H) for arbitrary Hilbert spaces H and having a prescription for the calculation of vacuum expectations in terms of a function t on pair partitions.
In a similar way, the extension of a set can be distinguished from an intensional description of the set in terms of a function: the set of integer squares is {1, 4, 9, 16, 25, 36, …}, and the intension could be given in terms of the one-place function f such that f(n) = n × n.
This derivation is accomplished by first solving for the saturation of water in terms of a function that is a solution to Laplace's equation to achieve a set of partial differential equations that allows some degree of latitude in the choice of boundary conditions.
Equation 14 corroborates that S depends on p ap which in terms of a function C W ap by Equation 2. An optimum value of C W ap is obtained when S is maximized using the following equation, frac{dS}{dtext{CW}_{text{ap}}} = frac{dS}{{dp}_{text{ap}}}frac{{dp}_{text{ap}}}{dtext{CW}_{text{ap}}}=0.
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In terms of a functioning government, southern Sudan is not starting from scratch.
The Green's function in the interface is given in terms of a Struve function and a Bessel function, (4).
Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss' hypergeometric function.
The zero-energy Green's function in the interface is given in terms of a Struve function and a Neumann function1, (20).
Thus, an analysis in terms of a cost function was done.
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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