Eventual periodicity of the fuzzy max-difference equation $x_{n} = \max \{ C, \frac{x_{n-m-k}}{x_{n-m}}\}$

P M Max − Planck −

A Note on the Periodicity of the Lyness Max Equation

Correspondence should be addressed to Cengiz Cinar, [email protected] Received 24 October 2007; Accepted 21 December 2007 Recommended by Elena Braverman We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is xn 1 max{xn,A}/xn−1 . where A is a positive real parameter, x − 1 A−1 , and x0 ...

Global Behavior of the Max-Type Difference Equation xn+1=max{1/xn,An/xn-1}

and Applied Analysis 3 Lemma 2.5. Let {xn}n −1 be a positive solution of 1.1 and limn→∞Pn S. Then S lim supn→∞xn. Proof. Since Pn is a subsequence of xn, it follows that S ≤ lim sup n→∞ xn. 2.6 On the other hand, by xn 1 ≤ Pn for all n ≥ 1, we obtain lim sup n→∞ xn ≤ lim sup n→∞ Pn S. 2.7 The proof is complete. Remark 2.6. Let {xn}n −1 be a positive solution of 1.1 . By Lemma 2.2, we see that i...

P M Max − Planck − Institutfür biologische Kybernetik

P M Max − Planck − Institutfür biologische

We studied the visual features that support eecient entry-level object recognition by measuring naming latencies for diierent views of artifacts and four-legged animals that were shown as shaded images or as silhouettes. Experiment 1 revealed important diierences in performance for the two renderings. Although three-quarter views of animals were recognized relatively quickly when shaded, they w...