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Together with continuity, Lemma 3.1 implies that the solution (theta_{1}^{(f)}), on the fundamental interval ([0,tau]), is given as follows:7 theta_{1}^{(f)}(t)= textstylebegin{cases} alpha+(1+epsilon t&mbox{if } 0leq tleqsigma, alpha+epsilon sigma+t&mbox{if } sigmaleq tleqtau.
Third, we perform downsampling by a factor of G = f s /Ω which is equivalent to changing the periodicity of the spectrum to a fundamental interval of width ˜f s = f s /G = Ω.
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One of the most startling discoveries of early Greek science was that the fundamental intervals of music, the octave, the fourth, and the fifth, corresponded to whole number ratios of string length.
On the other hand, the inversions of addition and multiplication are fundamental in interval arithmetic, interval analysis, and the concept of interval differentiability.
The scale on the right is the fundamental pulse interval (5.882 ms) multiplication factor.
In a holographic world, they provide a direct, precise measurement of the fundamental minimum interval of time.
The latter case is impossible because it would imply that (theta_{1}) increases by more than 1 over the fundamental time interval.
Most of the data are aligned with eleven lines, which are predicted counter values of the integral multiples (from 1 to 11, shown in the right) of the fundamental pulse interval of 5.882 ms.
Fundamental classes are Interval, GenericInterval, and ChromaticInterval.
The most fundamental point and interval estimation process involves the estimation of a population mean.
Theorem 4 (The fundamental theorem of interval analysis) Consider any elementary function f ∈ E with expression f.
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