This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

Abstract

The multiple linear regression model of the important regression models used in the analysis for different fields of science Such as business, economics, medicine and social sciences high in data has undesirable effects on analysis results . The multicollinearity is a major problem in multiple linear regression. In its simplest state, it leads to the departure of the model parameter that is capable of its scientific properties, Also there is an important problem in regression analysis is the presence of high leverage points in the data have undesirable effects on the results of the analysis , In this research , we present some of

Lexicography, the art and craft of dictionary-making, is as old as writing. Since its very early stages several thousands of years ago, it has helped to serve basically the every-day needs of written communication among individuals in communities speaking different languages or different varieties of the same language. Two general approaches are distinguished in the craft of dictionary-making: the semasiological and the onomasiological. The former is represented by usually-alphabetical dictionaries as such, i.e. their being inventories of the lexicon, while the latter is manifested in thesauruses. English and Arabic have made use of both approaches in the preparation of their dictionaries, each having a distinct aim ahead. Wit

عند إطلالتنا على هذا البلد العربي لابد من التقصي ولو بعجاله عن اقتصاده وهو الاهم باعتبار ان الاقتصاد هو شريان الحياة لأي أمة فلا غنى ولا تهاون في نفس الوقت عن هذا الجانب المهم الذي يرتبط مدى تطوره بتطور البلد وهذا الاخير مرتبط بما متوفر لديه من موارد بشريه ومادية وان تفاوتت النسبة بينها فلا ضير في ذلك فالاهم هو وجود الموجه والمخطط بالاتجاه الصحيح نحو الاستغلال الامثل لهذه الموارد
(وان قلّتْ) وبالتالي

Many athletes believe that it enhances the level of performance during training and competition, in addition to compensating for fluids during exercise when the levels of temperature and humidity in the atmosphere rise during the athlete's intensive training, as it increases the requirements for fluid compensation to avoid the risk of potential thermal disorders. If training continues for more than an hour causing fatigue, athletes are advised to drink carbohydrate drinks that quickly convert to glucose in the blood, while sodium should be included in the fluids consumed during exercise or matches that last more than (1-2 hours). The effect of drinking a drink containing 12% carbohydrates and electrolytes before each half of a simul