في منتصف القرن الثامن عشر قدم العالم السويسري ليونارد أويلر ((1787-1707 الحل للمعادلة حيث وسع حقل الاعداد الحقيقية إلى حقل جديد يكون فيه للمعادلة السابقة حل وهو ماسمي فيما بعد بحقل الأعداد المركبة, حيث صاغ أويلر العدد المركب على الصورة ولكن صيغة أويلر تطرح بعض الاسئلة المنطقية عن إشارة في صورة العدد المركب قبل تعريف عملية جمع الأعداد المركبة, إلى أن جاء العالم الايرلندي- بعد حوالى قرن من الزمان- ويليام رون هاملتون ( (1865-1805عرف جبر الاعداد المركبة على أنه مع عملية الجمع المعتادة والضرب المركب وكان لهذا الجبر نتائج هامة ضمنها تعريف الدوال الاسية والمثلثية بحيث تكون تعميم لنظائرها في التحليل الحقيقي.في هذا البحث نحاول تعميم الدوال الاسية والمثلثية في متغيرين في أنظمة جبرية غير الأعداد المركبة وندرس كيف أن هذا التعريف يعتمد على تعريف عمليات الضرب (الدوال ثنائية الخطية) على كما سنثبت أن هذه الدوال لها الخواص الأسية والمثلثية المشهورة مثل : ثم نتعرض لكيفية تعريف الاشتقاق , ,, بحيث نجد مشتقاتها تتوافق مع التصورات السابقة مثل: وسوف يتبين في هذه الدراسة أن هذا التعميم ينطبق , على الدوال الاولية المركبة كحالة خاصة. Abstract In the eighteen century the Swiss mathematician Leonard Euler introduced the solution of the equation , by that he extended the field of real numbers to the new one which make the above equation possible to solve, that field is called later the field of complex numbers. Euler wrote a complex number in the form. But Euler's notation raises logical questions about the + in the notation. A quite satisfactory definition of complex numbers is due the Irish mathematician William Rowan Hamilton. According to Hamilton the algebra of complex numbers, C is defined aswith the usual operations. That algebra has many important results includes the definition of the exponential and trigonometric functions to be generalization to its analog in the real analysis. In this thes is we try to extend the definitions of the exponential and trigonometric functions in two variables to include algebras distinct from the complex numbers and we study how this definition depends on the definition of multiplication (bilinear functions) on, and we well show that the functions have the same familiar exponential and trigonometric properties as , , , And we will present the definition of differentiation such that we find derivatives compatible with previous visions such as , And we try to prove this generalization compatible with the complex elementary functions as a special case.
محمد ابو القاسم ابو عجيلة (2010)

Swirl stabilised combustion is one of the most successful technologies for flame stabilisation in gas turbine combustors. Lean premixed combustion systems allow the reduction of NOx coupled with fair flame stability. The swirl mechanism produces an aerodynamic region known as central recirculation zone (CRZ) providing a low velocity region where the flame speed matches the flow velocity, thus anchoring the flame whilst serving to recycle heat and active chemical species to the root of the former. Another beneficial feature of the CRZ is the enhancement of the mixing in and around this region. However, the mixing and stabilisation processes inside of this zone have shown to be extremely complex. The level of swirl, burner outlet configuration and combustor expansion are very important variables that define the features of the CRZ. The complex fluid dynamics and lean conditions pose a problem for stabilization of the flame. The problem is even more acute when alternative fuels are used for flexible operation. Therefore, in this paper swirling flame dynamics are investigated using computational fluid dynamics (CFD) with commercial software (ANSYS). A new generic swirl burner operated under lean-premixed conditions was modelled. A variety of nozzles were analysed using isothermal case to recognize the the behavers of swirl . The investigation was based on recognising the size and strength of the central recirculation zones. The dimensions and turbulence of the Central Recirculation Zone were measured and correlated to previous experiments. The results show how the strength and size of the recirculation zone are highly influenced by both the shear layer surrounding the Central Recirculation Zones (CRZ) and outlet configurations. arabic 11 English 64
Adel Diyaf, Hesham Baej, Adel Akair, Salem Adeilla, Abdurahman Kraiem(9-2018)

Abstract As part of the NE-trending Mourizidie Shear Zone in south-central Libya (south of Mourizidie pass), four units representing Preccambrian basement rocks (metasediments) were mapped during field work: phyllites (metaclaystone); metapelites (metasiltstone); pasmmites (metasandstone) and Quartzites. Granitic bodies of various sizes (few meters to hundreds of meters) are found throughout the study area. The metasediments and granites are both intruded by veins and dikes having an overall NE trend. Four Palaeozoic sedimentary units were mapped within the study area. The concidence of the S1 foliation with the S0 of the original bedding of the protolith is a proof that the S1 foliation is caused by deep burial. The petrographic description of the minerals in thin section shows an assemblage of sericite, muscovite and biotite, all representing a sub-greenschist facies to greenshcist facies. This low grade metamorphism helped in preseving the original sedimentary structures of the protolith, thus helping in identifying the original bedding plane S0. Faults observed in the field or traced on aerial photograhs belong to three major trend: NE, NNE, and ENE. Folds are extremely diverse in shape, attiude and tightness, thus their classification is equally diverse. This diversity is observed in the field even within a distance of no more than few meters. The isostatic rebound of the basement could have caused this great difference in the attitude of the folds, especially at considerable depths characterised by a kinematically ductile, restricted and contained settingAt least two phases of deformation are present in the area. D1 is marked by the generation of S1, while D2 is marked by the first folding F1 caused by the isostatic rebound he generation of S2 foliation as fan cleavage is directly related to the F1 folding. Some folds underwent refolding, which lead to an F2 phase of folding.Sequential schematic structural model is proposed to explain the structural history of the study area. This model should be tested through intensive detailed field work large scale map in nearby areas.
مسعودة محمد حنبولة (2015)