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... cannot be represented as sums of two squares, some cannot be represented as sums of three, and all can be represented as sums of four. We also show that numbers of a certain form can be represented as sums of two squares. Though we mostly use classic methods of number theory, we venture into group t ...
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... Chapter 2 ...
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a Dual Fractional-N/Integer-N Frequency Synthesizer ADF4252
a Dual Fractional-N/Integer-N Frequency Synthesizer ADF4252

... wireless receivers and transmitters. Both the RF and IF synthesizers consist of a low noise digital PFD (phase frequency detector), a precision charge pump, and a programmable reference divider. The RF synthesizer has a ⌺-⌬-based fractional interpolator that allows programmable fractional-N division ...
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... that the discrepancy is O(log log T / log T ) unconditionally for any non-zero α. In this paper, we consider generalization of these results to a large class of Dirichlet series which includes the Selberg class. In Section 2 we define and study some elementary properties of the elements of this clas ...
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... The least common denominator, also called the LCD, is the same as the least common multiple, or LCM. The multiples of a number result from multiplying the number by the counting numbers (1, 2, 3, …). For example, the multiples of 2 are: ...


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... rotates during operation, while the stator (the dark blue block and light blue “fingers” around the rotor in Fig. 1) remains stationary during operation, relative to the motor’s casing and mounting [3]. The stator is made up of either a winding or a magnet, which creates magnetic flux in the magneti ...
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Mathematics of radio engineering



The mathematics of radio engineering is the mathematical description by complex analysis of the electromagnetic theory applied to radio. Waves have been studied since ancient times and many different techniques have developed of which the most useful idea is the superposition principle which apply to radio waves. The Huygen's principle, which says that each wavefront creates an infinite number of new wavefronts that can be added, is the base for this analysis.
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