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We prove that this system possesses time dependent periodic solutions, bifurcating from a steady solution.
Experimental results prove that this system is effective to control the amount of slag that comes into the ladle.
Moreover, we prove that this system is complete for a reasonable notion of validity for Hoare judgments.
However, Post will prove that this system leads to the collapse of necessity to truth – alternatively, of impossibility to falsity – since from one of its theorems ((p⇒q)⇔(¬◊q⇒¬◊p)) it can be proved that (¬p⇔¬◊p).
By using an iteration procedure, combining with the classical existence theorem of global attractors, we prove that this system possesses a global attractor, which attracts any bounded set of (H_{alpha}) in (H_{alpha} -norm.
The innovation of the paper is that we not only prove that this system is globally bounded for all the parameters, but also give a family of mathematical expressions of global exponential attractive sets of this system with respect to its parameters.
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"It proves that this system does work, despite what some people have said," Testaverde said.
It is proved that this system admits global and bounded classical solutions for all (chi>0).
The empirical results proved that this system could significantly improve the overall performance of existing ant-based clustering algorithms.
According to the present design, the construction and the use in practice proved that this system is a set of outstanding roofing systems.
It is practically proved that this system can work stably, with fluctuation rate of water pressure no more than 2.0%, as well as good cutting quality and high production efficiency.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com