Abstract. In this study, we shall research the fibrewise micro ideal topological spaces over Ḃ, as well as the relationship between fibrewise micro ideal topological spaces over Ḃ and fibrewise micro topological spaces over Ḃ. At first present introduces a novel notion from fibrewise micro ideal topological spaces over Ḃ, and differentiates it from fibrewise micro topological spaces over Ḃ. Some fundamental characteristics from these spaces are studied. Then show discussed the fibrewise micro ideal closed and micro ideal open topologies. Many propositions relating to these ideas are offered. In the next part will study defines and investigates novel conceptions from fibrewise micro ideal topological spaces over Ḃ, particularly f

The main purpose of this paper is to introduce a some concepts in fibrewise bitopological spaces which are called fibrewise , fibrewise -closed, fibrewise −compact, fibrewise -perfect, fibrewise weakly -closed, fibrewise almost -perfect, fibrewise ∗-bitopological space respectively. In addition the concepts as - contact point, ij-adherent point, filter, filter base, ij-converges to a subset, ij-directed toward a set, -continuous, -closed functions, -rigid set, -continuous functions, weakly ijclosed, ij-H-set, almost ij-perfect, ∗-continuous, pairwise Urysohn space, locally ij-QHC bitopological space are introduced and the main concept in this paper is fibrewise -perfect bitopological spaces. Several theorems and characterizations c

Spelling correction is considered a challenging task for resource-scarce languages. The Arabic language is one of these resource-scarce languages, which suffers from the absence of a large spelling correction dataset, thus datasets injected with artificial errors are used to overcome this problem. In this paper, we trained the Text-to-Text Transfer Transformer (T5) model using artificial errors to correct Arabic soft spelling mistakes. Our T5 model can correct 97.8% of the artificial errors that were injected into the test set. Additionally, our T5 model achieves a character error rate (CER) of 0.77% on a set that contains real soft spelling mistakes. We achieved these results using a 4-layer T5 model trained with a 90% error inject

Background: The surgical treatment of pilonidal sinus varies from wide excision and laying the wound open or excision with primary closure or excision with the use of skin graft in some special cases.
Objectives: The objectives of this study is to determine the efficacy of treating non complicated pilonidal sinus disease with minimal excision and primary closure technique, complications and recurrence rate.
Patients and methods: This is a prospective study conducted in shahid ahmed ismaiel hospital in rania – As sulaimania IRAQ during the period from December 2013 to January 2016 and was carried on one hundred (100) consecutive patients with non complicated non recurrent pilonidal sinus patients who were treated with minimal exci

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

Abstract. This study gives a comprehensive analysis of the properties and interactions of fibrewise maximal and minimal topological spaces. Fibrewise topology extends classical topological concepts to structured spaces, providing a thorough understanding of spaces that vary across different dimensions. We study the basic theories, crucial properties, and characterizations of maximal and minimal fibrewise topological spaces. We investigate their role in different mathematical contexts and draw connections with related topological concepts. By providing exact mathematical formulations and comprehensive examples, this abstract advances the fields of topology and mathematical analysis by elucidating the unique properties and implications of fib

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.