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It would appear unlikely that an untrained amateur could evolve a theory, work out the methodology by which to test it, conduct all the necessary research himself, & arrive at results that would revolutionize the study of Paleolithic archeology--yet this is what a number of professional archeologists believe happened in the case of Marshack, who entered the field, almost by accident, in 1963.
(10) And so, at the end of our analysis, we arrive at results which only confirm the old truth that we may perhaps prevent a crisis by checking expansion in time, but that we can do nothing to get out of it before its natural end, once it has come.
Motivated by the above discussion, we here make a first attempt to arrive at results on the invariant sets and attracting sets of impulsive stochastic difference equations.
Motivated by the above discussion, we here make a first attempt to arrive at results on the global exponential stability of impulsive difference equations with distributed delays.
Independently, analysts of the same project can arrive at results that differ by orders of magnitude, especially if uncertainties are not included.
There have indeed been attempts at such an encompassing account of human action, for example Tadeusz Kotarbinski's Praxiology (1965), but a perspective of such generality makes it difficult to arrive at results of sufficient depth.
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In picture after picture, he kept zooming in on nature, all too often arriving at results as scintillating as laboratory slides.
During the following years, Cantor explored the world of point sets, introducing several important topological ideas (e.g., perfect set, closed set, isolated set), and arrived at results such as the Cantor-Bendixson theorem.
Nonetheless, we believe that this potential residual confounding is not considerable, because a number of studies using objective measures have arrived at results similar to ours [ 11, 12, 38].
On basis of previous research which established links between increases in blood-Pb concentrations during childhood and resulting IQ-loss we arrive at our results.
In spite of this, he did not arrive at correct results—with the exception of a single character.
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