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Shoda also showed that when a finite Abelian group is expressed as the direct product of primary Abelian groups whose orders are powers of distinct primes, the automorphism group of
Although Theorem 1.3 gives solutions to the same equation as Theorem 1.1 (if m is the same), the spirit is quite different: While m could take any value in Theorem 1.1 , we have here
The main theorem of this paper is the following result, which reduces level low- ering for the prime ℓ = 2 for totally real fields to a multiplicity one hypothesis, thus showing
(d) In case that part (c) is admissible for some higher power of a prime, we hope to derive an algorithm to enumerate congruences for various combinatorial numbers.. The second
So we shall prove the following theorem which as a particular case contains the answer to the problem..
Theorems such as Theorem 3, Theorem 4, Theorem 5, and Theorem 6 can also be proved for right s -unital rings by the same lines as above employing the necessary variations..
Very recently, Wang and Shen [15] investigated the anti-periodic boundary value problem for a class of second order differential equations by using Schauder’s fixed point theorem
Firstly, to derive closed solutions of the flow equation at very large length scale, i.e., to derive the velocity field, the flow pattern and the residence time of a fluid particle,
