Sentence examples for prime periods from inspiring English sources

Corollary 1 has shown that Abian theorem can be broken into two cases: (i) All periodic points have even prime periods and (ii) the negation of (i).

"These are the prime periods of evaluation," Ms. Barnett said.

The mathematical component of the explanation complements the biological claim by pointing out that prime periods minimize intersection.

The zeta function of an automorphism T on a simple graph G is the rational function ζ T ( z ) = ∏ p = 1 ∞ ( 1 − z p ) a ( p ) − b ( p ) ( 1 + z p ) c ( p ) − d ( p ). Proof Because prime periods are smaller or equal than the product of the cycle lengths of the permutation, the product is finite.

This formula is a finite product over all possible prime periods ζ T ( z ) = ∏ p = 1 ∞ ( 1 − z p ) a ( p ) − b ( p ) ( 1 + z p ) c ( p ) − d ( p ), where a ( p ) rsp. c ( p ) is the number of odd-dimensional prime periodic orbits { x, T x, …, T p − 1 x } for which T p | x has positive rsp.

Each d ∈ D is either a periodic element with an even prime period or an eventually periodic element that leads to a periodic element whose prime period is even.

(ii) Each d ∈ D is either a periodic element with an even prime period or an eventually periodic element that leads to a periodic element whose prime period is even.  .

We say that the solution is periodic with prime period p if p is the smallest positive integer for which (2) holds.

Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15.

In this paper, it is of key for us to find that the lengths of positive and negative semi-cycles of nontrivial solutions of (1.1) occur periodically with prime period 15 with the rule,,,,,,, and in a period.

Suppose D can be partitioned into two sets A and B so that A ∩ f ( A ) = B ∩ f ( B ) = ∅ and suppose that the prime period of some periodic element d is odd.f Then consider the following initial segment of the orbit of d, 〈 d, f ( d ), f 2 ( d ), …, f n − 1 ( d ), f n ( d ) 〉.