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Exact(14)
By the uniqueness of the limit, we can conclude that T ϕ = ϕ ( c ). □.
In the thermodynamic limit, we can replace the sum over quasi-momenta with the integral,, which yields (28).
2stcase; Two-component e i limit(i.e., f → 1) In the contrast limit, we can consider the electron ion limit (f → 1), these limits of plasma support ordinary IA waves.
Because 'Monotone bounded sequence must have limit,' we can set lim n → ∞ x 4 n − 2, y 4 n − 2 = ( p 1, p 2 ), lim n → ∞ x 4 n − 1, y 4 n − 1 = ( p 3, p 4 ).
Thus, the metric-affine formalism is more likely to be introduced in these regions; and when considering the lower energy limit, we can make use of other formalisms, i.e., the metric and Palatiny formalisms.
Even if (lambda_{k}) has no limit, we can consider its convergent subsequence ({lambda_{k_{i}}}) and the corresponding solution sequence ({(x_{k_{i}},y_{k_{i}})}) for (3.1) because the sequence ({lambda_{k}}) is bounded.
Similar(45)
"We have specific amounts of fuel, equipment, but it is still limited, we can only carry on like this for a few weeks," he said.
By minimizing pit stops and pushing speed limits, we can cross the George Washington Bridge at 6 in the morning and fit in a swim in the Atlantic in Charleston by sunset.
By the uniqueness of limits, we can deduce that (2.32).
First, by condition (A 3), (2.4) and the property of limits, we can have.
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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