Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for Macdonald function Kiτ(x). The results can be applied, instance, to study summability of divergent Kontorovich-Lebedev integrals in sense Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments class inverse transforms. Comput Math Appl. 2018;76(1):141–154.]...

The present study aims to investigate the perceptions of EFL students on Corrective Feedback (C F) and assess efficacy continuous explicit writings preparatory year female Umm Al Qura University in Saudi Arabia. sample consisted eleven from an entire class who volunteered for study. To reach study’s objectives, online survey was conducted gain insight into how felt about receiving CF. Also, obs...

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it easily follows that the ring of K-endomorphisms of J(C) coincides with Z and the real pro...

in recent years, collaborative filtering (cf) methods are important and widely accepted techniques are available for recommender systems. one of these techniques is user based that produces useful recommendations based on the similarity by the ratings of likeminded users. however, these systems suffer from several inherent shortcomings such as data sparsity and cold start problems. with the dev...

Noisy network coding is recently proposed for the general multi-source network by Lim, Kim, El Gamal and Chung. This scheme builds on compress-forward (CF) relaying but involves three new ideas, namely no Wyner-Ziv binning, relaxed simultaneous decoding and message repetition. In this paper, using the two-way relay channel as the underlining example, we analyze the impact of each of these ideas...

Recommender system plays an increasingly important role in identifying the individual’s preference and accordingly makes a personalized recommendation. Matrix factorization is currently most popular model-based collaborative filtering (CF) method that achieves high recommendation accuracy. However, similarity computation hinders development of CF-based systems. Preference obtained only depends ...

The principal result of this paper is an explicit description of the structure of ramification subgroups of the Galois group of 2-dimensional local field modulo its subgroup of commutators of order ≥ 3. This result plays a clue role in the author’s proof of an analogue of the Grothendieck Conjecture for higher dimensional local fields, cf. Proc. Steklov Math. Institute, vol. 241, 2003, pp. 2-34.