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Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two , e.g. 1 / 8 = 1 / 2 3 .
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...
Similarly, the sum of the reciprocals of the primes of the form 4n + 1 is divergent. By Fermat's theorem on sums of two squares , it follows that the sum of reciprocals of numbers of the form a 2 + b 2 , {\displaystyle \ a^{2}+b^{2}\ ,} where a and b are non-negative integers, not both equal to 0 , diverges, with or without repetition.
The conjecture can be understood by considering k = 1 and 2 as well as 3. When k = 1, Babbage's theorem implies that it holds for n = p 2 for p an odd prime, while Wolstenholme's theorem implies that it holds for n = p 3 for p > 3, and it holds for n = p 4 if p is a Wolstenholme prime.
The Shunt equation (also known as the Berggren equation) quantifies the extent to which venous blood bypasses oxygenation in the capillaries of the lung.. “Shunt” and “dead space“ are terms used to describe conditions where either blood flow or ventilation do not interact with each other in the lung, as they should for efficient gas exchange to take place.
This is defined as a left ventricular ejection fraction (LVEF) of 40% or less. About half of heart failure patients have a reduced ejection fraction. [2] Other types of heart failure are heart failure with mildly reduced ejection fraction (LVEF between 40% and 50%) and heart failure with preserved ejection fraction (LVEF 50% or higher). [1] [3]
Following the discovery of Leleākūhonua, Sheppard et al. concluded that it implies a population of about 2 million inner Oort cloud objects larger than 40 km (25 mi), with a combined total mass of 1 × 10 22 kg, about the mass of Pluto (a fraction the mass of Earth's moon but several times the mass of the asteroid belt).
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