Essential extensions and p-extensions have been studied for commutative rings with identity in various articles, such as [2], [3], and [13]. The present article applies these concepts to certain subrings of C(X). Moreover, the article introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extensio...

conclusions the taping technique, as applied in this study demonstrates an impressive effect on wrist extension force and grip strength of patients with te. elbow taping also reduces pain at the lateral aspect of the elbow in these patients. background tennis elbow (te) is a common musculotendinous degenerative disorder of the extensor origin at the lateral humeral epicondyle. different modes o...

Background: Stabilization exercises can improve the performance of trunk and back muscles, which are effective in the prevention and treatment of low back pain. The four-point kneeling exercise is one of the most common types of stabilization exercises. This quasi-experimental study aimed to evaluate and compare the level of activation between abdominal and lumbar muscles in the different stage...

A minimal extension of a Π1 class P is a Π 0 1 class Q such that P ⊂ Q, Q − P is infinite, and for any Π1 class R, if P ⊂ R ⊂ Q, then either R −P is finite or Q−R is finite; Q is a nontrivial minimal extension of P if in addition P and Q have the same Cantor-Bendixson derivative. We show that for any class P which has a single limit point A, and that point of degree ≤ 0′, P admits a nontrivial ...

We study the growth of p-primary fine Selmer group, R(E/F ′ ), an elliptic curve over intermediate sub-extension F a p-adic Lie extension, ℒ/F. estimate ℤ p -corank kernel and cokernel restriction map r ℒ/F :R(E/F )→R(E/ℒ) Gal(ℒ/F ) with finite extension contained in ℒ. show that groups these is related to structure group infinite level. On specializing certain (possibly non-commutative) extens...

this research was based on primary data collected through well designed and pre-tested questionnaire, to determine awareness of farmers on extension methods used by adp in kano state of nigeria. multistage sampling technique was used, in which three local governments were randomly selected. secondly, three wards one each from the selected local governments (danbatta, gaya and madobi) were rando...

present study was conducted in the three provinces of pakistan with the objectives to study the curricula relevancy with the participatory extension, supervision and administration and its practical applicability at the field level. for this extension agents of the selected provinces were selected purposively. mail questionnaire were used as instruments for data collection form 227 respondents ...