IKBFU's Vestnik

2011 Issue №10

Subsets of prime numbers in the generalized arithmetical progressions

Abstract

The concept of the generalized arithmetical progression of the power k  and difference d is given. For k  1,7 formulas of nth member of such progressions and for k  1, 2, 3 formulas for the sum of the first n its members are obtained. Progressions ( ) , k p d M with the first member prime number p and difference being a positive even number d  2m (m  ) are considered. Such progressions define subsets ( )
, , k h p d M of h prime numbers (h  ). For k  20, p  95467, d  108 all subsets (1) h,p,d M with h  15 prime numbers are obtained. Some properties that connect the power k of generalized arithmetical progression and its difference d for 2  k  60, p  1014, h  5 are established.

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Study of the configuration of the core of the magnetization source of magnetic systems of electric propulsion

Abstract

Results of researches of influence of various forms of cores of external sources of magnetising force of magnetic systems of electric propulsion on azimuthal evenness of magnetic field distribution in an operating interpolar interval are presented.

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