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I would rather have the raggedy brilliance of A Naked Singularity over the pursed and smirking lips of much contemporary British fiction any day of the week.
By introducing a domain transformation in the z-direction, we solve the corresponding complex difference equations containing an interface singularity over a computational space for great simplicity and efficiency.
In this manner, Śāntarakṣita analyzes a host of current claims of true singularity over the course of the first sixty stanzas of MA.
Remark 3.7 These solutions in (3.11) have a singularity on the line { ( x 1, x 2 ) | x 1 − x 2 = ( c 1 − c 2 ) t } for every t ≥ 0. In particular, we have the following result: For every given time t ≥ 0 and arbitrary line { ( x 1, x 2 ) | A x 1 − B x 2 = C, A 2 + B 2 ≠ 0 }, there exist some solutions with singularity over the line { ( x 1, x 2 ) | A x 1 − B x 2 = C, A 2 + B 2 ≠ 0 }.
Read more about singularity over at Motherboard.
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The mathematical formulation relies on the boundary-integral representation that expresses the flow in terms of distributions of Stokes-flow singularities over the interfaces.
However, the single application of this equation leads to the singularities over the final system of algebraic equations, when cracked bodies are considered.
First, the problems arising due to high dimensionality accompanied by a small sample size, such as matrix singularity and model over-fitting [ 27], in analyzing static or long time-series microarray data, become more pronounced in the case of short time-series data.
It is well known that time delayed systems, due to its own nature, has singular behavior in its dynamics and that such singularities propagate over the time.
Moreover due to the detection of singularities, an over smoothing will not really change the shape of the signal and main information about the shape of the signal has been preserved.
"It's the Singularity — the machines are taking over!" September 5, 2014.
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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
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