Nonsplitting sequences of value groups

The Jacobsthal Sequences in Finite Groups

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Bounding nonsplitting enumeration degrees

The Strongest Nonsplitting Theorem

Sacks [14] showed that every computably enumerable (c.e.) degree ≥ 0 has a c.e. splitting. Hence, relativising, every c.e. degree has a Δ2 splitting above each proper predecessor (by ‘splitting’ we understand ‘nontrivial splitting’). Arslanov [1] showed that 0′ has a d.c.e. splitting above each c.e. a < 0′. On the other hand, Lachlan [9] proved the existence of a c.e. a > 0 which has no c.e. sp...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

IRF and ISRF Sequences and their Anti-Pedagogical Value

Initiation, Response, and Feedback(IRF) sequences are the most frequent interaction network in any classroom contexts. IRF sequences have been examined profusely in previous studies and were reported to be negatively correlated with participation opportunities (Kasper, 2006; Cazden, 2001; Ellis, 1994).In all these studies, all contingent factors of any classroom context which might influence in...