Abstract Seven geological sections have been examined and sampled with emphasis on sedimentological & diagenetic processes within Abu Ghaylan Formation and the contact relationships with the underlying Abu Shaybah and overlying Kiklah Formations. Based on current detailed field loggings and microscope investigations, 10 facies are recognized within Abu Ghaylan Formation. The lowermost succession characterised by an overall transition from continental fluvially dominated deposits of the Abu Shaybah Formation into transitional to marginal marine, tidal flat deposits of the Abu Ghaylan Formation upward. The transitional nature of this lowermost part succession is demonstrated by interbeddings of claystone, sandstone and fossiliferous facies arranging in coarsening up cycle, in which most probably deposited in estuary / beach environment.The Abu Ghaylan Formation generally wedges laterally eastward and exposes intermittently east of Wadi Ghan area resulting of syngenetic uplift of Wadi Ghan area followed by erosion (ElHinnawy & Cheshitev, 1975). A slightly earlier uplift and greater erosion in a westward sloping basin of deposition near the close of the Early Jurassic and Early Cretaceous times is suggested by Fatmi & Sbeta (1991). The current study reveals that several exposure surfaces are demonstrated within Abu Ghaylan Formation suggesting uplifting and erosion episodes interrupted Abu Ghaylan Formation, where a restricted distribution of Abu Ghaylan may suggest a local tectonic overprint.Although the overall impression is that the base beds of Kiklah Formation starts with sandstone and red clay beds as channel infill deposits above Abu Ghaylan carbonate unit with surface of unconformity, however, based on current close investigation, a sequence characterized by interbeddings of carbonate and greenish clay overlying Abu Ghaylan Formation with surface of unconformity and gradationally overlain by sandstone beds should be introduced as separate unit attributes to Kiklah Formation.The current study emphasizes and supports a solution collapse origin for the breccias and introduces better insight into architecture and geomorphology of the breccias bodies that are exposed in the area of study. The dissolution of evaporites is considered responsible for all breccias development in this stratigraphic interval. According to the occurrence mode of breccias, the breccias intervals have been divided into two main parts; a lower section of strata that contains collapsed paleocaves and an upper section of strata that is deformed to varying degrees due to the collapse and compaction of the section of paleocave-bearing strata. The sharp flat base, inverse grading, V-shaped/ sag structures and irregular undulating top of brecciated bodies are recognized within Abu Ghaylan Formation and typically characterize solution collapse processes. Based on field study and architecture relationships, five distinctive karst facies are recognized in the area of study.The early diagenetic genetically related processes probably interrupted the deposition of Abu Ghaylan Formation is a most possible assumption for the origin and timing of breccias formation.
أحمد أبوبكر الحلو (2015)

أعداد كاتالان هي متتالية من الأعداد الطبيعية سميت نسبة إلي العالم البلجيكي يوجين شارلز كاتالان، وتدخل في حل العديد من مسائل العد مثل عدد تقسيمات مضلع محدب إلى مثلثات، عدد القمم الجبلية التي يمكن تشكيلها باستخدام n زوج من القطع المستقيمة الصاعدة والهابطة بعض المسارات الشبكة من نقطة الاصل إلي النقط ( (n,nبالإضافة إلي بعض التطبيقات في جبر المصفوفات والزمر. تهدف هذه الدراسة إلي تسليط الضوء علي بعض خواص أعداد كاتالان وتطبيقاتها في مسائل رياضية مختلفة، بالاضافة إلي دراسة لأعداد كاتالان المعممة ومثلث كاتالانالتطبيقات في التطبيقات في جبر المصفوفات والزمر Abstract Catalan numbers are a sequence of natural numbers named after the BelgianEugene Charles Catalan mathematician(1814-1894),they enumerate a lot of classes of combinatorial objects, for example the partitionings of a convex polygon, the mountain ranges that can be drawn with n upstrokes and n down strokes, some integral lattice paths and some problems in groups and matrices.The aim o this study is to highlight some properties, some applications of Catalan numbers, the generalized Catalan numbers and Catalan triangle.
اية فريد جرناز (2016)

في هذا البحث ناقشنا بعض المفاهيم ومنها وصلنا إلى مفهوم دالة التمثيل الخطي المحدودة بين جبران بوليان وأخيرا أثبتنا جبريا نظريتا كالتن للتمثيل الخطي المحدود بالأبواب التالية: الباب الأول: قدمنا في هذا الباب بعض التعريفات والقواعد والنتائج الأساسية التي نحتاجها لاحقا. مثل نظرية المجموعات ومجموعة كانتور ومجموعات بوريل. الباب الثاني: ناقشنا في الباب الثاني بعض المفاهيم المتعلقة بالجبر البولي والمؤثر الخطي المحدود بين جبران بوليان. الباب الثالث: أما الباب الثالث فقد ناقشنا فيه المفاهيم المتعلقة بالقياس والقياس المؤشروالمجموعات القابلة للقياس والدوال المقيسة والتكامل بالنسبة للقياس المؤشر وأخيرا عرفنا فضاء . الباب الرابع: قدمنا النتيجة الأساسية لهذا البحث وهي الإثبات جبريا نظريتا كالتن للتمثيل الخطي المحدود. Abstract In this thesis, we give an algebraic proof of the Kalton representation theorems. In chapter one, we give some basic standard definitions and some results we need later. In chapter two we discuss the concept of Boolean algebra, and bounded linear operators between two Boolean algebras. In chapter three, we discuss the concepts of measure, signed measure, measurable sets, measurable functions, integration with respect to signed measure; later in this chapter, we define.In the last chapter (4) we give the main result of our thesis which is the proof of KALTON representation theorems.
إيمان إسماعيل النحائسي (2010)