On the Joint Distribution ofq-Additive Functions in Residue Classes

THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS

focus on communication in iranian high school language classes: a study of the role of teaching materials in changing the focus onto communication in language classes

چکیده ارتباط در کلاس به عوامل زیادی از جمله معلمان، دانش آموزان، برنامه های درسی و از همه مهم تر، مواد آموزشی وابسته است. در تدریس ارتباطی زبان که تاکید زیادی بر توانش ارتباطی دارد، کتاب درسی به عنوان عامل موثر بر پویایی کلاس محسوب میگردد که درس ها را از طریق فراهم آوردن متن ارتباط کلاسی و هم چنین نوع تمرین زبانی که دانش آموزان در طول فعالیت های کلاسی به آن مشغول اند، کنترل می کند. این حقیقت ک...

on the teacher-generated v.s. leaner-generated noticing-the-gap activities in language classes

abstract the purpose of this study is twofold: on the one hand, it is intended to see what kind of noticing-the –gap activity (teacher generated vs. learner generated) is more efficient in teaching l2 grammar in classroom language learning. on the other hand, it is an attempt to determine which approach of the noticing-the-gap- activity is more effective in the long- term retention of grammar...

The Distribution of Sequences in Residue Classes

We prove that any set of integers A ⊂ [1, x] with |A| (log x)r lies in at least νA(p) p r r+1 many residue classes modulo most primes p (log x)r+1. (Here r is a positive constant.) This generalizes a result of Erdős and Ram Murty, who proved in connection with Artin’s conjecture on primitive roots that the integers below x which are multiplicatively generated by the coprime integers a1, . . . ,...

On the Distribution of the Order over Residue Classes

For a fixed rational number g ∈ {−1, 0, 1} and integers a and d we consider the set Ng(a, d) of primes p such that the order of g modulo p is congruent to a (mod d). Under the Generalized Riemann Hypothesis (GRH), it can be shown that the set Ng(a, d) has a natural density δg(a, d). Arithmetical properties of δg(a, d) are described, and δg(a, d) is compared with δ(a, d): the average density of ...