PHD theses : Statistics

Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/12106

Browse

Now showing 1 - 20 of 49

The Algebraic Treatment of Symmetric Spaces
(Neelain University, 2008) Nemaat Hamed Taleb
ABSTRACT We study manifolds spaces ‘which lead to Lie group, then by deﬁnition of transitive action of a Lie group in a manifold we get homogeneous spaces. ' Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over IR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classiﬁcation of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.
The Algebraic Treatment of Symmetric Spaces A thesis submitted
(Neelain University, 2008) Nemaat Hamed Taleb
ABSTRACT We study manifolds spaces which lead to Lie group, then by deﬁnition of transitive action of a Lie group in a manifold we get homogeneous spaces. Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over DR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classiﬁcation of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.
APPLICATION OF - " THE VIRIAL METHOD TO THE SOLUTION OF SOME PROBLEMS < ' IN FLUID DYNAMICS
(Alneelain University, 2006) Mohamed Saad E1-Din Abdel Gafoor Abdel Magid
The problem of the charged spheroidal bubble is studied using the virial method. The conditions that are necessary for equilibrium are deduced and the oscillation of the bubble is studied . The frequencies belonging to the second order harmonics are found . Further extension of the virial theorem is made by studying the viscous ﬂuid sphere in an incompressible viscous ﬂuid giving the different and necessary virial equations of motion for both the exterior and the interior media and then the equilibrium state is studied.
An Appraisal of the Educational Statistical System of the Sudan
(Neelain University, 2006) Abbas Ali AAMIR
Abstract The Thesis is about improvement of the current educational statistical system. It concentrates on the deﬁciencies and shortcomings inherent in the present system and on ways and means of their alleviation and improving their contents. A good statistical database will help education authorities to assess the well-being of the system and to pinpoint areas of weaknesses. Thus, it would help to layout policies for possible remedies and improvements. This can better be done through calculation of comparative educational indicators and by building of models that single out variables or factors that have signiﬁcant effects on the progress of the educational system as a whole. Impoltant indicators are deﬁned and ways of calculating them are shown with illustrative examples that are based on the currently existing data. Limitations of the currently available educational data rendered it unattainable to calculate other important indicators. However, the purpose of an indicator is to characterize the components of a system: how they are related and how they change overtime. Indicators are descriptive tools that do not have the ability to measure the signiﬁcance of the changes that they reﬂect. Indicator systems, however, unlike a single indicator measure distinct components of the system and provide information about how the individual components work together to produce the overall effect. Models are more efﬁcient means of testing real variations. While expectations from social indicators are generally modest and, hence, can not substitute for a well designed, in-depth evaluations of social programs, models do the job. They give scientiﬁcally veriﬁable information about the different variables that are contained in them. Data collected should cover the complex variables that compose and interfere with the educational process and that are essential elements to be included in the planned models. There are different methods of data collection that can be used to suit the planned goals. Besides full coverage which, like all censuses, is limited in scope of coverage, other means of data collection like sample surveys, experimentation and case study evaluations can be applied wherever suitable. The World Conference on Education For All of 1990 and its assessment of Sub-Saharan Africa has urged the necessity of the establishment of National Educational Statistical Information Systems NESIS in all countries of Sub-Saharan Africa. Details of the ﬁndings of that conference with-respect-to NESIS program are included in the thesis with an illustration of the experience of Zambia in applying that program. Our educational system has gone through a multiplicity of changes in size, curriculum, policies and in economic, political and social conditions. The educational statistical system should be able to supply a wide variety of data that enables researchers to study the effect of those changes on the educational process. Examination results tell a lot about the quality of education students get and about the attainment of students from that education. Examinations usually comprise a number of components which may vary in the importance of their contribution to the ﬁnal assessment of the students’ academic achievement. A weighting system is thus sometimes introduced on the examination results to give more weight to some components that are considered more effective in infonning about the educational attaimnent of a student. It is also sometimes introduced for reasons the examiners think are justified by the ﬁndings of those particular examination results. Certain weighting methods are provided and discussed in the thesis and the formulae for a scientiﬁcally veriﬁable weighting system is discussed in detail. But the practice in the ﬁnal assessment of the Secondary School Certiﬁcate’s examination results of Sudan seems to differ from what has been originally meant by the introduction of the aforementioned weighting procedures. Those results were analyzed in detail throughout the years 1993-2001 for two components, Mathematics and English, being normally hypothesized to be the weakest areas of the students’ educational attaimnent. This comparative statistical analysis reﬂected that, rather than an introduction of a veriﬁable weighting system, the actual marks attained by the candidates were in fact seemingly adjusted to cover up the apparently weak student attainment. The true examinations results are one mean for the education system to hold itself accountable for whatever weaknesses that occur and remedy them in the best way it can afford putting in mind the known limitations of the economic conditions of the country.
Bayesian Modes in Analyzing Impact of Foreign Direct Investlnent on Macroeconomic in Yemen
(Neelain University, 2008) Esmail Ilasan Abdulatef Al Sabri
Abstract - ' » This thesis has paid attention to the importance of studying Bayesian approach so as to analyze the impact of foreign direct investment on macro-economy in the Yemen Republic. V A forecasting model has been constructed. The thesis has included studying the statistical theory of Bayesian Theory, then practical application has been followed through using economic data. This is what makes it a distinctive study other than others in this ﬁeld, as it included an applied and analytical study for the correlations ofmacro variables by using Bayesian approach. . Studying correlations between these variables enable us identify the nature of correlated relations and thus making forecasting; 'particularly there are so many methods to forecast and estimate parameters of linear regression like the method of OLS and Maximum Likelihood. All of them are concerned with reaching a model through which we can forecast the status of phenomenon under study in future. an The importance of this study appears in designing ‘effective and sustainable models so as to develop economic policies which can help attract foreign direct investments and also studying the efﬁciency of predictive models to obtain models that could assist decision-makers. The theoretical study of Bayesian approaches has been made in an applied manner from which we can benefit in analyzing economic data. A model of prediction has been elicited for the impact of foreign direct investment on the macro-economy. The predictive capacity of the model has been tested in comparison with the model which we have obtained through using the OLS method, concluding that the model estimated by Bayesian Approach is most efﬁcient than the model estimated by OLS mode, as the Theil's Inequality Coefﬁcient of estimation. » ' This is what conﬁrms the predictive capacity of the model being estimated by Bayesian Approach as a modern method in prediction against the model estimated by OLS mode. It has been concluded that the estimated» model has a high signiﬁcance and that independent variables in the model were signiﬁcant, as the value of (Fc?526.52). ln addition, the parameters of the model have been tested in a different way represented in creating the value of signiﬁcant probability to accept null hypothesis which assumes that the parameters of partial group of independent variables equals zero. The result was that the value of probability is [),(H,,/y)=6..9U7E_7, This value conﬁrmsthe signiﬁcance of the estimated model and it is reliable. The economic results related to the impact of foreign direct investment have been interpreted on macro economy andcoiicluding that the model is signiﬁcant. This is, independent variables (budget deﬁcit, the cost of foreign direct investment, volume of employment‘ in the mvestment sector, investment expenses allocated in the state’s budget and agricultural production) have signiﬁcant impact on dependent variable (the GDP) and has a high explanation capacity. In addition, foreign direct investment represented in investment cost of foreign direct investment has signiﬁcant impact on a group of productive ‘sectors and positive for all exports, imports, agriculture production, extraction industry, manufacturing industry, volume of employment in the investment sector, and it appeared minus and insigniﬁcant‘ with GDP rate only
Boundary Element Method For Porous Media Flow
(Al Neelain University, 2005-07) Azhari Ahmed Abdalla
The focus point of this study is to develop BEM formulation to overcome the difﬂculties caused by nonlinearity and heterogeneity in the solution of partial differential equations governing the porous media ﬂow .This dissertation consist of two major parts ,theory of BEM , and applications of BEM to two important ﬁelds of porous media ,water ﬂow in aquifers and oil ﬂow in reservoirs. The contribution done in the theory sections is mainly a mathematical derivation of the standard boundary element method for Lapiace's equation and the step by step formulation to the BEM , starting from its correspondence differential equation ,beside the developed form of BEM based on GEM and DRBEM that has presented. to handle both heterogeneous and nonlinearity. In the applications section a novel boundary integral solution was applied for determining : (1) Water table elevation in an unconﬁned homogeneous aquifer subjected to recharge and dewatering from a stream as well as ﬂuctuations induced by constant and continuous recharge in a two stream unconﬁned-aquifer system. (2) Changes in water table exposed to a transient boundary condition and space- dependent recharge. This technique was compared with the closed form solution obtained in [111] and excellent results were obtained. (3) Characteristics of the ﬂow through heterogeneous unsaturated porous aquifer . (4) Solution of reservoir engineering problems. This work adapted the most recent developments in boundary element methods to reservoir engineering problems. The transient pressure (diffusion) and convection- diffusion equations were solved in heterogeneous media using the Dual Reciprocity Boundary Element Method (DRBEM) and the Green Element Method (GEM). Numerical experiments showed that DRBEM is more accurate than a standard ﬁnite difference method. However like ﬁnite difference methods, DRBEM is subject to spurious oscillation at high Peclet numbers. DRBEM also requires the solution of a dense system of equations. GEM, which is a hybrid boundary elementlﬁnite element method, overcomes these disadvantages. The method was found to produce very accurate solutions to convection-diffusion problems and only shows small oscillations in the solution at very high Peclet numbers. A further important advantage is the sparse nature of the matrix system. GEM is also amenable to solving transient nonlinear problems, which makes it the basis for a new technique for multiphase ﬂow simulation. This work explores the advantages of a hybrid boundary element method known as the Green element method for modeling pressure transient tests. Boundary element methods are a natural choice for the problem because they are based on Green's functions, which are an established part of well test analysis. The classical boundary element method is limited to single phase ﬂow in homogeneous media. This works presents formulations which give computationally efﬂcient means to handle heterogeneity. Comparisons of the proposed Green element approach to standard ﬁnite difference simulation show that both methods are able to model the pressure change in the well over time. When pressure derivative is considered however the ﬁnite difference method produces very poor results which would give misleading interpretations. The Green element method in conjunction with singularity programming reproduces the derivative curve very accurately. Boundary element method was applied for solving Stokes ﬂow equations on multi particle system. Also, the method is modiﬁed for estimating flow parameters for a speciﬁed porous media. A new method for the so/ut/‘an of the unsteady incompressible Navier-Sta/res equations was presented
ciphring with elliptic curves
(Neelain University, 2011) Maha Touﬁg Fadle Elseid
ABSTRACT This research deals with different operations of encryption These are illustrated using elliptic curves where a program for this operation is used to embed a message in an elliptic curve and convert it to a point, so as to encrypt/decrypt the message. This is illustrated by ﬁnite ﬁeld of order p(where p is a prime number).The message is embed in an elliptic curve and transformed as a point and then, encrypt/decrypt it. A program is designed to do this operation using Java Programming and in particular Java Biglnteger to make it more difﬁcult
A CONTRIBUTION TO RISK AND DECISION ANALYSIS OF PETROLEUM EXPLORATION
(Neelain University, 2006) Hala Abbas Bedawi
Abstract In this study the problem specifications are as follows: 1) Assessment of the factors of risk in petroleum exploration. 2) Evaluation of the geological risk. 3) Estimating prospect reserves. 4) Utilization of the probability of geological risk and the results of estimating prospect reserves in the decision making for drilling. ln petroleum exploration the basic concept in assigning risk for the geologic factors is contraverse; therefore, the subjective probability is used to assess the factors which are independent thus; the multiplication rule of probability is used to evaluate the geological risk. The prospect reserves distribution being a lognormal distribution, is estimated by finding out first the mean and variance of all the reserve parameters in the prospect reserves. In our study two methods were explained for finding the mean and variance of the reserve parameters: 1) Swanson's 30-40-30 rule. 2) Three-point method Since the prospect drilling is too expensive, and to avoid the loss if a dry hole is resulted, one can use the decision tree initially to decide whether to drill or not. The calculation of prospect reserve will be illustrated by the use of worksheet from one of the Sudanese Petroleum Companies.
Convective Heat and Mass Transfer in Nano-fluid flow
(ALNEELAIN UNIVERSITY, 2022) Khalda Eltayeb Mohammed Elkhair Elsmani
الــمســـتخــلــص هذه الدراسة صممت للبحث فى مسألة النقل الحراري بالحمل فى الموائع النانوية وفى الواقع هذه الدراسة تحتوي على قسمين رئيسيين، حيث أننا فى القسم الأول تطرقنا للجزء النظري فى البابين الثاني والثالث. الباب الثاني بصورة عامة صمم من أجل إستنتاج المعادلات الحاكمة لحركة الموائع النانوية مثل معادلة الاستمرارية، كمية التحرك الخطية، الطاقة ومعادلة التركيز للموائع النانوية. فى الباب الثالث وضحـنا أسـاسيات طريقـة الطـيف العـددية بالاضافة الي التعـريف بمصفـوفة تشيبيشف التفـاضلية لتقـريب المشتقات عـدديا. كذلك إستنتجنا الصيغ التكـرارية لكـل من طــريقــة الطــيف للإســـترخـاء، الطــيف شــبيهـة الخـطــية والطــيف محــلية الخـطــية. القسم الثانى من هذة الدراسة عرض فى الأبواب الرابع، الخامس والسادس وهذا الجزء خصص لدراسة بعض الحالات الخاصة للجزء النظري فى القسم الاول كتطبيقات. الباب الرابع خصص لدراسة مسألة الحمل الحراري القسري فى مائع ماكسويلي نانوي يحتوي على خلايا حية دقيقة. النموذج الرياضي صمم لإظهار كيفية تأثير معدل القص على خصائص الانسياب فى زمن سابق. المعادلات التفاضلية الجزئية الحاكمة للنموذج حولت الي نظام معادلات تفاضلية عادية لاخطية بتحويلة متماثلة مناسبة. المعادلات التفاضلية العادية الناتجة حلت عدديا بإستخدام طريقة الطيف شبيهة الخطية. تأثيرات المعلمات الحاكمة مثل رقم ديبورا، رقم براندتل، معلمة الحركة البراونية، معلمة التهجير الحراري، رقم لويس، رقم لويس للحمل الحيوي، معلمة الانزلاق ورقم بيكلت للحمل الحيوي على خصائص النقل الحراري والمائع عرضت فى صورة رسومات. في الباب الخامس استخلصنا حل عددي لانسياب غير مستقر لمائع نانوي دوار فوق سطح أملس في وجود تفاعلات كيميائية متجانسة وغير متجانسة. لتصميم نموذج رياضي لهذه المسألة غمرنا حبيبات النحاس والفضة النانوية في ماء من اجل الحصول على مائع نانوي. المعادلات التفاضلية الجزئية الحاكمة حولت الى معادلات جزئية لابعديه باستخدام متغيرات لابعديه مناسبة. المعادلات المتحصل عليها حلت عدديا بواسطة تركيبة من طريقة الفروق المحدودة وطريقة الطيف للاسترخاء. النتائج المتحصل عليها عرضت في صورة رسومات. في الباب السادس درسنا مسألة الحمل الحراري المختلط في مائع نانوي موجود في طبقة أفقية فى وجود حقل كهرومغناطيسي. لقد استنتجنا صيغة تحليلة لرقم ريلية لبدية الحمل الحراري الثابت. لقد عرضنا النتائج فى هذا الباب فى صورة رسومات وهذة الدراسة شملت ايضا حالات خاصة لدراسات سابقة. Abstract This study is conducted in order to investigate the problem of convective heat transfer in nanoﬂuids. Actually, this study consists of two parts where the ﬁrst part is the theoretical which presented in chapter 2 and chapter 3. Chapter 2 was constructed mainly in order to derive the governing equations of nanoﬂuid ﬂow consisting of the continuity, momentum, energy and concentration of nanoﬂuids. In chapter 3 we stated fundamentals of spectral method as well as introducing the Chebyshev diﬀerentiation matrix in aim to approximate the derivatives numerically. Also we derived the iter- ative method behind the spectral relaxation method, the spectral quasilinearisation method and spectral local linearisation method. The second part of this study has been presented in chapter 3 - 6 to give some applications form the theoretical part. Chapter 4 is devoted to investigate the problem of forced convective heat transfer in a Maxwell Nano-ﬂuid ﬂow containing microorganism cells. The mathematical model is designed to show how the time history of shear rate reﬂect on the nanoﬂuid ﬂow. The highly nonlinear partial diﬀerential equations governing the model have been transformed into a system of nonlinear ordinary diﬀerential equations by using a sim- ilarity transformation. The resultant ODEs then integrated by using the spectral method based the quasi-linearisation method. Eﬀects of the governing parameters such as Deborah number, the Prandtal number, the Brownian motion parameter, the thermophoresis parameter, Lewis number, the bioconvection Lewis number, slip pa- rameter and the bioconvection P´eclet number on heat transfer characteristic as well as the ﬂuid properties were presented in graphical from. In chapter 5 we obtained numerical solutions for unsteady ﬂow of rotating nanoﬂu- ids over ﬂat surface in presence of homogeneous and heterogeneous chemical reac- tions. To design model of the problem, we suspended copper (Cu) and silver (Ag) nanoparticle into water based ﬂuid to generate the nanoﬂuids. Partial diﬀerential equations consisting of the continuity, momentum, energy and mass volume fraction are transformed into a non-dimensional partial diﬀerential equations using appropri- ate dimensionless variables. The resultant dimensionless PDEs then integrated by using the spectral relaxation method based ﬁnite diﬀerence. Eﬀects of governing pa- rameters such as Schimdt number, the measure of strength of the homogeneous and the ratio of the diﬀusion coeﬃcient on heat transfer characteristic as well as the ﬂuid properties were presented in graphical forms. In chapter 6 we investigated the problem of mixed convection in nanoﬂuid in a hor- izontal layer in presence of electromagnetic ﬁeld. The eﬀect of Darcy number, Lewis number, nanomagnetic number, thermophoresis parameter and the local Rayleigh number on the critical Rayleigh numbers is investigated. Analytical expressions of the critical Rayleigh numbers for the onset of stationary convection is derived. Our results have been presented in the graphical form, moreover in the limiting case some previously published results are recovered.
Convective heat transfer in Regular fluid and Nano-fluid Flows: Application of Spectral Method
(ALNEELAIN UNIVERSITY, 2022) Limia Elmnsour Omer Elmnsour
Abstract In this study we examined the problem of heat transfer in regular fluids and nanofluids numerically. We start our investigation by deriving the governing equations consisting of the continuity, momentum, energy and concentration equations for the case of regular fluids and then we generalized these equations to the case of nanofluids. The dimensional physical quantities have been used in defining the physical parameters such as Lewis, Reynolds, Prandtal numbers, buoyancy ratio, Brownian motion, Deborah number, vortex viscosity parameter, Schmidt number, Eckert number and thermophoresis parameter in which affects heat and mass transfer characteristics as well as fluid properties. The resulting dimensionless differential equations of the flow have been solved numerically by using both the spectral quasi-linearisation method and spectral local linearisation method. This study consists of three scientific papers two are published and the third one under reviewing. Paper 1. In this paper, the problem of two dimensional flow of Maxwell nanofluid in presence of the thermophoresis and Brownian motion impacts have been studied numerically. Basically the partial differential equations described the motion of the fluid were form-lated by means of Maxwell model of viscoelasticity by connecting spring with dash-pot in series. By using a suitable similarity transformations we mapped these partial differential equations into highly nonlinear ordinary differential equations, then solved numerically by using the spectral quasi-linearisation method. The impact of our governing parameters on velocity, temperature, mass volume fraction, fluid properties as well as heat and mass volume fraction transfer were examined and shown in graphical and tubular forms. Paper 2. This paper deals with the problem of convective heat and mass transfer along a vertical plate under the assumption that the fluid viscosity being temperature dependence and nanoparticles are not controllable at the plate surface but the nanoparticle flux is zero. The highly nonlinear partial differential equations in which governed the nano-fluid flow transformed into nonlinear ordinary differential equations by using a similarity transfor-mation, after that integrated by using spectral quasilinearisation method (SQLM). Effects of the governing parameters such as the buoyancy ratio, the Brownion motion parameter, the thermospheres parameter and Lewis number on heat and mass transfer characteristic as well as the fluid properties were presented in graphical forms. The inbuilt Matlab bup4c numerical routine has been used as a benchmark for testing the accuracy of the SQLM. Paper 3. The unsteady two-dimensional flow of an incompressible micropolar fluid is investigated. The highly non-linear governing partial differential equations are further formulated with a variable viscosity under the influence of thermophoresis and viscous dissipation effects. The resulting governing equations have been solved numerically using bivariate local linearization method. The effects of interest parameters governing the flow on heat and mass transfer, velocity, temperature, and concentration profiles in the boundary layers have been presented in graphical and tubular forms المستخلص في هذا البحث قدمنا دراسة عددية لمسائل الانتقال الحراري في الموائع العادية و النانوبة علي حد سواء، لقد قمنا بإستنتاج المعادلات التفاضلية الحاكمة لحركة الموائع العادية التي تتكون من معادلة الاستمرارية ، كمية التحرك الخطية ، الطاقة و التركيز و من ثم عممناها للموائع النانوية. هنا استفدنا من الكميات البعدية الفيزيائية في تعريف بعض المعلمات مثل رقم لويس، رقم رينولدس، رقم براندتل، الحركة البراونية، رقم ديبورا، رقم شميدت، رقم إكرت، و معلمة التهجير الحراري التي تؤثر علي النتقال الحراري و المادي و كذلك خصائص المائع. هنا المعادلات اللابعدية المتحصل عليها حلت عدديا بطريقة الطيف شبيهة الخطية بالاضافة الي طريقة الطيف محلية الخطية. هذة الدراسة حوت ثلاث أوراق علمية ، حيث تم نشر ورقتين الورقة الاولي: في هذة الورقة قمنا بدراسة مائع ماكسويل النانوي ثنائي الابعاد تحت تأثير التهجير الحراري و الحركة البراونية. المعادلات التفاضلية التي تحكم الحركة حولت الي معادلات تفاصلية عادية عالية اللاخطية والتي بدورها حلت عددياً بواسطة طريقة الطيف شبيهة الخطية. تأثيرات المعلمات الفيزيائية الحاكمة علي السرعة، الحرارة، الكتلة النانوية، خصائص المائع و ايضاً علي الانتقال الحراري بينت على شكل رسومات و جداول. الورقة الثانية : مسألة الانتقال الحراري و المادي بالحمل علي طول لوح راسي بافتراض أن لزوجة المائع تعتمد علي الحرارة بشكل اساسي و ابضا الذرات النانوية ليست قابلة للتحكم علي جدار اللوح حيث فقط فيض الكتلة النانوية هو الذي يتلاشي على جدار اللوح. المعادلات التفاضلية الجزئية اللاخطية التي تحكم انسياب المائع النانوي حولت الي معادلات تفاضلية لا خطية عادية بواسطة تحويلة متماثلة ومن ثم حلت عددياً باستخدام طريقة الطيف شبيهة الخطية. تأثيرات المعلمات الحاكمة مثل معامل الطفو، الحركة البراونية ، معلمة التهجير الحراري ورقم لويس علي مميزات الانتقال الحراري و المادي و كذلك علي خصائص المائع. لإختيار الدقة الجبرية لطريقة الطيف شبيهة الخطية عايرناها بطريقة عددية لمسائل القيم الحدية في الماتلاب. الورقة الثالثة: في هذة الورقة بحثنا في مسألة الانسياب المستقر لمائع فيه أجسام دقيقة. المعادلات التفاضلية الحاكمة صيغت علي اساس أن لزوجة المائع ليست مقدار ثابت تحت تأثير التهجير الحراري و التبدد بسبب اللزوجة. المعادلات اللابعدية الناتجة حلت عددياً باستخدام طريقة الطيف محلية الخطية الثنائية. تأثيرات المعلمات التي تحكم الانسياب علي معدل الانتقال الحراري و المادي، السرعة، الحرارة و التركيز داخل الطبقة الحدودية مثل رقم شميدت، رقم إكيرت، معلمة التهجير الحراري عرضت في صورة رسومات و جداول.
Effect of Age Group Length, Growth rate, & Degree of Development on the Aggregate & Disaggregate population forecasting Methods
(Neelain University, 2014) Raga Idreis Abdoon
Abstract This research investigates the performance of selected aggregate and disaggregate methods for population forecasts. The data used is that given by the United Nations Population Division- Department of Economic and Social Affairs and covers the period 1950-2010. Also, we used simulated data that were generated by Mathematical packages. The objective, with respect to the disaggregate methods, is to determine their performance under various age group length, degree of development, gender & growth rate. It is found that for all methods the precision of the forecast decreases with increase in age group length & growth rate and increase with the degree of development. Forecast of female population is in general more precise than of male population. The cohort component method proved to be the best among the disaggregate methods in forecasting population for individual age groups. The exponential smoothing method, which as far as the author knows, is used for the ﬁrst time as a disaggregate methods, provided the best forecast for the population total, followed by the cohort component method. As to the aggregate methods the cubic method showed the best performance. The sensitivity of the aggregate methods to the various factors is such that the precision of forecast decreases with increase in growth rate &increases with the degree of development. Looking at both aggregate & disaggregate methods the results conﬁrm that the exponential smoothing method, suggested by the author, provided the best performance for forecast is the population total.
The Formulation Of Equivalence Problems And Its Application
(Neelain University, 2014) Runda Abdalhafiz Abdelrhim . Bashir
Abstract In this research we considered Cartans equivalence problem . We defined the concept of equivalence and illustrated that by several cases . We introduced the equivalence problem for Coframs and then used Cartans equivalence method to determine whether two differential operators are equivalent , we also handle the classification problem of Lie algebras, ln particular we treated the case of semi-simple Lie algebras.
Generalization on LP - Contractivity of Semigroups Commutators and C 0-Semigroups of Resolvent Estimates
(Neelain University, 2008) Ria Hassan Mohamrned
We derive a pointwise estimate on the absolute difference between two corresponding diffusion kernels of two diffusion semigroups , as well as an L” —operator norm bound. We show that linear partial differential operators of order higher than two can not generate contraction semigroups on the Lebesgue space except for some fourth order operators in a restricted compact interval . We consider a comparison between two semigroups , a semigroup acting on scalar valued functions and a semigroup acting on vector valued functions . We give a sufficient condition for the criterion in the setting of square ﬁeld operator. We also consider the essential self a djointness of a perturbed semigroup . We discuss the existence and the continuity of the boundary values problem on the Lebesgue space of the resolvent of a self — adjoint operator of the conjugate operator method . we allow the conjugate operator to be the generator of a Co —semigroup and that ﬁrst commutator is not comparable to the self —adjoint operator . Strong application include the spectral theory of zero mass quantum ﬁeld models are considered .
The Geometric Structure 0f Group Invariant Solutions Of Diﬁerential Operators
(Neelain University, 2005) Abdelgadir Ahmed Hammdan Omer
Abstract Group invariant solutions have been used to a great effect in the description of the asymptotic behaviour of many general solution to systems of partial differential equations. The rigorous foundation of the general method for constructing group — invariant solution requires advanced formalism of differential geometry. From our point of view the Fibre bundle over a quotient manifold approach seems very promising in analyzing the mechanism of group-invariant solutions and classifying different types of behaviour of a system. In this research we shall explore the bundle over a quotient space approach. Our applications will are on some partial differential equations
The Geometric Structure 0f Group Invariant Solutions Of Diﬁerential Operators
(Neelain University, 2005) Abdelgadir Ahmed Hammdan Omer
Abstract Group invariant solutions have been used to a great effect in the description of the asymptotic behaviour of many general solution to systems of partial differential equations. The rigorous foundation of the general method for constructing group — invariant solution requires advanced formalism of differential geometry. From our point of view the Fibre bundle over a quotient manifold approach seems very promising in analyzing the mechanism of group-invariant solutions and classifying different types of behaviour of a system. In this research we shall explore the bundle over a quotient space approach. Our applications will are on some partial differential equations.
Geometrical Analysis of Differential Operator Theory on Complex Manifolds
(Neelain University, 2011) Riyad Mohammed Ibrahim
Abstract In this research we have used the theory of classiﬁcation of Fiber bundles and Atiyah-Singer index theorem to study the geometrical and topological properties of differential operator on complex manifolds. Of particular interest is Dirac equation and the generalized global form of Laplace equation. We have also treated the index of De Rham complex that generalizes the Gauss-Bonnet theorem. Our point of view in this treatment is that the De Rham complex represents only one possibility of other complexes that describe differential operators. These geometrical complexes include spin complex which give the moduli space of Dirac equation. All these concepts are related by the topological index of the operator. .
THE GEOMETRICAL QANTIZATION OF PHYSICAL FIELDS
(Alneelain University, 2007-10) Khalid Masoud Makin Mohamed Ali
ABSTRACT We considered the problem of geometric quantization. We ﬁrst started with the classical symplectic geometry and then'we used the complex line bundle to describe prequantization and quantization. Geometrically the Hilbert space of quantum states is constructed from the sections of the complex line bundle over the phase space. We then used the invariance group approach to the geometric quantization.
THE GEOMETRICAL QANTIZATION OF PHYSICAL FIELDS
(Neelain University, 2007) Khalid Masoud Makin Mohamed Ali
ABSTRACT We considered the problem of geometric quantization. We ﬁrst started with the classical symplectic geometry and then'we used the complex line bundle to describe prequantization and quantization. Geometrically the Hilbert space of quantum states is constructed from the sections of the complex line bundle over the phase space. We then used the invariance group approach to the geometric quantization.
THE GEOMETRICAL QUANTIZATION APPROACH TO MECHANICS & GRAVITY
(Neelain University, 2008) ASMA OSMAN OMER ALI
THE ABSTRACT The problem of quantizing gravity is a longstanding problem. Many approaches are accomplished to solve this problem. The Feynman path integral approach and Twistor program are just two trials. In our thesis we discussed both of them. However the geometrical quantization approach seems more promising. For this reason we built our construction of geometrical quantization of mechanics on any curved space, not necessarily Minkowskian. The geometric quantization passes through several steps that have been studied in our thesis.
Geometrical Reformulation of some Equations of Fluid Mechanics
(Neelain University, 2015) Mansour Hassan Mansour
Abstract The aim of this thesis is to explain some of the connections between fluid mechanics and differential geometry and to shed light on formulation of classical fluid mechanics in a differential geometric language. The thesis presents a reformulation of some of the most basic entities and equations of fluid mechanics, the continuity equation and the momentum equation of motion, in a modern differential geometric language using calculus of exterior differential forms on manifold (exterior calculus). Also, the study investigates the integrability of some fluid problems from geometrical perspective, with particular attention to the Eulefequations of motion.