Homology of $\Omega ^{n + 1} \Sigma ^{n + 1} X$ and $C_{n + 1} X,n > 0$

On the Recursive Sequence xn 1 A x p n − 1 / x q n

A Note on the Nonlinear Recurrence xn + 1 xn − 1 − x 2 n = A Michele Elia

The existence and uniqueness of the integral solutions of xn+1xn−1− xn = A are examined and some open questions settled. Mathematics Subject Classification: 39A99, 12F05, 11B39

Evolutionary Biology Journal of I S S N 1 0 1 0 -0 6 1 X

Cover photo: A vigilant yellow-bellied marmot (Marmota flaviventris) at the Rocky Mountain Biological Laboratory, Colorado, USA. Blumstein et al. (pp. 879–887) report that the time allocated to anti-predator vigilance in marmots is heritable and is weakly correlated with locomotor performance. Interestingly, faster marmots allocate more time to vigilance while slower marmots allocate less time....

On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Note on Π 0 n + 1 - LEM , Σ 0 n + 1 - LEM and Σ 0 n + 1 - DNE

In [1] Akama, Berardi, Hayashi and Kohlenbach used a monotone modified realizability interpretation to establish the relative independence of Σ n+1-DNE from Π 0 n+1-LEM over HA, and hence the independence of Σ n+1-LEM from Π 0 n+1-LEM over HA, for all n ≥ 0. We show that the same relative independence results hold for these arithmetical principles over Kleene and Vesley’s system FIM of intuitio...