الحارثي ، أمل علي

A carbon paste electrochemical sensor modified with TiO2 nanoparticles and 1- butyl-3- methylimidazolium Chloride [BMIM] CI ionic liquid and coated with a layer of poly (3,4- ethylene- dioxythiophene) (PEDOT) polymer was developed for sensitive and selective determination of diclofenac sodium (DCF). Electrochemistry of diclofenac sodium was studied at carbon paste electrode in the presence and absence of nanoparticles, ionic liquid, and polymer film. The presence of these materials plays a key role in enhancing the current signal obtained for the drug and thus the sensitivity of the method as a whole. Cyclic voltammetry (CV) differential pulse voltammetry(DPV) were utilized to verify the voltammetric behavior of diclofenac sodium in different media. The surface morphology and compositional properties of the modified electrode were characterized by electrochemical impedance spectroscopy,(EIS) transmission electron microscopy,(TEM) scanning electron microscopy,(SEM) Fourier transform infrared spectroscopy(FTIR) and X-ray diffraction (XRD). The modified electrode is selective for the determination of diclofenac sodium in presence of interfering molecules such as uric acid and ascorbic acid. The designed sensor showed good,reproducibility, high stability , sensitivity and anti-interference, ability, thus the sensor was further utilized to determine diclofenac sodium level in human urine as well as some of its drug formulations and satisfactory results are obtained with low detection limit

الغامدي، محمد فلاح حمود

The neutron diffusion equations are in general stiff nonlinear coupled partial differential equations. The solutions of this system describe the neutron flux and precursor concentration of delayed neutrons. The results of these solutions are of great importance for operation and safety of reactors. The safety of nuclear power reactors has become an urgent need for all world countries. These countries need an efficient and economic mathematical techniques to ensure the nuclear safety. So, the fast and accurate solutions for the time dependent neutron diffusion equations are important to improve the safety of nuclear power reactors. In this thesis, we developed an accurate numerical methods to solve the two energy groups space-time neutron diffusion equations with average one group of the precursor concentration of delayed neutrons. The proposed developed numerical methods are as expected to be accurate and fast compared with the conventional methods. The thesis is organized as follows: In the first part of this thesis, the mathematical form for two energy groups of three dimensional homogeneous reactors kinetics equations with average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called "two energy groups of the point kinetics equations", which is represented in the matrix form to suit our case. Generalization of the analytical exponential model (GAEM) is developed for solving the two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix, which obtained numerically using the Laguerre’s method for the roots of algebraic equation with real coefficients. Furthermore, the eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the conventional methods such as 3DKIN code and adaptive matrix formation (AMF) method. The result of comparison confirm the accuracy of the GAEM technique. In addition, the GAEM is faster than the AMF method. In the second part, the fundamental matrix method (FMM) is developed to solve the system of the two energy groups for the point kinetics equations for three dimensional homogeneous reactors. The FMM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix, where the inverse of the fundamental matrix is calculated analytically. The results of the FMM are compared with the conventional 2 methods such as 3DKIN, AMF and GAEM. The accuracy of the FMM are estimated at different types of reactivities. In addition to the agreement, the FMM is faster than the corresponding GAEM and AMF methods. In the third part, the generalization of the analytical exponential model and the fundamental matrix method are developed to solve the two energy groups of neutron diffusion equations for the two-dimensional heterogeneous nuclear reactor. The adopted methods are based on using five-point central finite difference approximation to the two energy groups of neutron diffusion equations at fixed time. In addition, the average values of the material parameters to change the heterogeneous reactor to homogeneous reactor are weighted over the volume. The results of the generalization of the analytical exponential model and the fundamental matrix method are compared with the numerical conventional methods such as TWIGL, AMF, Padé 11, LUMAC, MITKIN, SADI and TSM codes. The comparisons shows that the results of the developed GAEM and FMM methods for the heterogeneous nuclear reactor are in agreement with the results of the corresponding methods.

البقمي، نورة محمد حسين

Optimal control problems for parabolic partial differential equations appear in several branches of applied mathematics. These problems have dealt with the processes of hydro- and gas dynamics, heat physics, filtration, the physics of plasma and others. In the first chapter, we review briefly the basic concepts of some optimization algorithms and optimization problems governed by distributed parameter systems (DPS) and some applications. In second chapter, we consider an optimal control problem with respect to a parabolic equation with three controls in the right hand side of the equation, in the initial condition and in one of the boundary conditions. The well-posedness (existence and uniqueness of the solution) of the optimal control parabolic problem is proved. One of the approaches of building the gradient of the cost functional using the solving of the adjoint problem is investigated. Lipschitz continuity of the gradient cost functional is derived. In the third chapter, we solve numerically two special cases of the following optimal control problem governed by a parabolic partial differential equations (OPC) : Minimize                 l T f v u x T z x dx v t w t dt 0 2 2 0 2  ,   under the following conditions                                                  k u l t v t t T x u l t l x u t u x v x x l v x t x t x u x t x t x u x t T The two cases which solve numerically as follows: OCP1: In the first problem the control takes the form v (t)which appears in the second boundary condition. OCP2: In the second problem the control takes the form v (x) which appears in the initial condition of the parabolic equation. Remarks: 1) New results in chapter two included in a paper entitled: On An Optimal control Problem for Parabolic Equations, International Journal of Computational Engineering Research (IJCER), Vol. 3(5), 2250 -3005, 2015. 2) New results in chapter three included in a paper entitled: Computation of Optimal Controls for a Class of Distributed Parameter Systems, Journal of Computer and Mathematical Sciences, Vol.6(8),439-448, 2015.

الخثعمي ، عالية محمد سفير

الحارثي، نايف سعيد مرزوق

Let
be a ring (not necessary commutative) with identity 1 and  be a unitary right
-module. In this thesis we study the transfer of some algebraic properties between the base ring
and the generalized Mal’cev- Neumann series ring  =
((; , )). Also, we transfer some algebraic properties between the base module  and the generalized Mal’cev- Neumann series module  = (()) . Firstly, in Chapter (3), we show the following result: Let (, . ,≤) be a strictly totally ordered monoid which satisfies the condition that 1 ≤  for every  ∈  and  an -compatible module. If  is a PS-module, then  = (()) is a PS-module. Secondly, in Chapter (4), we prove the following result: Let  be an -compatible and -Armendariz module. Then  is a right zip
-module if and only if  = (()) is a right zip -module. Finally, in Chapter (5), we show the following result: Let (, . ,≤) be a strictly totally ordered monoid and
be an - compatible NI-ring with (
) nilpotent. If
satisfies the right weak Beachy-Blair condition, then  =
((; , )) satisfies the right weak Beachy-Blair condition. The results in Chapter (3) accepted for publication in Hacettepe Journal of Mathematics and Statistics. However the results in Chapter (4) and Chapter (5) have been submitted for publication in two papers with the same name of the associated chapter.

الحارثي، نايف سعيد مرزوق

Let
be a ring (not necessary commutative) with identity 1 and  be a unitary right
-module. In this thesis we study the transfer of some algebraic properties between the base ring
and the generalized Mal’cev- Neumann series ring  =
((; , )). Also, we transfer some algebraic properties between the base module  and the generalized Mal’cev- Neumann series module  = (()) . Firstly, in Chapter (3), we show the following result: Let (, . ,≤) be a strictly totally ordered monoid which satisfies the condition that 1 ≤  for every  ∈  and  an -compatible module. If  is a PS-module, then  = (()) is a PS-module. Secondly, in Chapter (4), we prove the following result: Let  be an -compatible and -Armendariz module. Then  is a right zip
-module if and only if  = (()) is a right zip -module. Finally, in Chapter (5), we show the following result: Let (, . ,≤) be a strictly totally ordered monoid and
be an - compatible NI-ring with (
) nilpotent. If
satisfies the right weak Beachy-Blair condition, then  =
((; , )) satisfies the right weak Beachy-Blair condition. The results in Chapter (3) accepted for publication in Hacettepe Journal of Mathematics and Statistics. However the results in Chapter (4) and Chapter (5) have been submitted for publication in two papers with the same name of the associated chapter.

البقمي ، زها رداد

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty such as probability theory, fuzzy set, rough set theory and vague set theory. This thesis aims to study soft α-open sets and soft 𝑏-open sets in soft topological spaces (𝑋, 𝜏, 𝐸) with soft ideal Ĩ and investigate some of their basic properties and relationships between them .This thesis contains three chapters, as follows: Chapter 1: In this chapter, we introduce most of the fundamental concepts, theories and results needed in this thesis about of soft set theory, soft topological spaces, soft ideals, supra soft topological spaces and some generalized soft open sets. Chapter 2: In this chapter, we continue to investigate further properties of soft α-open sets in soft topological spaces. First section, we define and discuss soft 𝛼-exterior, soft 𝛼-boundary, soft 𝛼-open neighborhood, soft 𝛼-open neighborhood systems, soft 𝛼-limit point, soft 𝛼-derived set, and soft 𝛼-subspace in soft topological spaces. Second section, we introduce soft α-local function in a soft topological space (𝑋, 𝜏, 𝐸) with soft ideal Ĩ and investigate some of their basic properties. New soft topology from the original one by using soft 𝛼∗-local function is deduced. Relations between soft topology and original one are obtained. Basic properties and characterization related these concepts are given. Third section, we introduce some types of soft ⍺-open sets with respect to soft ideal and weakly soft ⍺-open sets with respect to soft ideal in a soft topological space. We also investigate some of their fundamental properties. Let us mention here that the main results established in chapter (2) have been submitted for publication. Chapter 3: In this chapter we continue to investigate further properties of soft 𝑏-open sets in soft topological spaces. First section, we introduce and discuss soft 𝑏-kernel, soft 𝑏-kernel of soft sets, soft ⋀𝑏 -closed sets, soft ⋀𝑏 -open sets, soft 𝑏-border, soft 𝑏-open neighborhood systems, soft 𝑏-derived set and soft 𝑏-subspace in soft topological spaces. Second section, the concept of soft 𝑏-local function in a soft topological space (𝑋, 𝜏, 𝐸) with soft ideal Ĩ is introduced several of their properties are investigated. Soft topology from the original one by using soft 𝑏∗-local function is deduced .Some of relations between new soft topology and the original one are studied. Third section, some kinds of soft 𝑏-open sets with respect to soft ideal and weakly soft 𝑏-open sets with respect to soft ideal in a soft topological space are proposed with some of their fundamental characterization. Fourth section, we introduce the relations between soft 𝛼-open sets and soft 𝑏-open sets on soft topological spaces (𝑋, 𝜏, 𝐸) with respect to soft ideal Ĩ. Let us mention here that the main results established in chapter (3) have been submitted for publication.

عسيري ، فاطمة محمد

الجعيد ، جوهرة غويزي سالم

The integral equations has close contacts with many different areas of mathematics. Also integral equations arise in many scientific and engineering problems. A large class of initial and boundary value problems can be converted to Volterra or Fredholm integral equations. The potential theory contributed morethan any field to give rise to integral equations. Mathematical physics models, such as diffraction problems, scattering in quantum mechanics, conformal mapping, and water waves also contributed to the creation of integral equations. Integral equations often arise in electrostatic, low frequency electro magnetic problems, electro magnetic scattering problems and propagation of acoustical and elastical waves, see (Jerri [31], Kanwal [32], Krees[34], Green[27], Hochstadt[30], and Schiavone[45]) . These different problems have leed researchers to establish different methods for solving integral equations of different kinds analytically see (Linz[37],Kiselev & Makarenko [36], Kanwal [32]). At the same time the numerical methods takes an important place in solving the integral equation these methods depend on errors study resulting from these methods and properties of convergence and stability of these methods: Trapezoidal rule, Romberg integration method, Collocation method, Galerkin method, Block-by-block method, Rung- Kutta method, Nystrom method,Toeplitz matrix and simpson's rule, see( Atkinson [18 ], Delves and Walsh [23], Baker [19]) . This thesis consists of introduction, four chapters, (47 ) references, tables, figures, appendix, and Arabic summary. Chapter 1: Some Basic Concepts Chapter 1 consists of four sections. The first section is an introduction and in the second section, we present a review for some basic concepts, theorems, definitions and formulas which used during the work. Then , in section three we state the definition of the integral equation. Section four contains the type of the integral equations. Chapter 2 : Nonlinear Fredholm-Volterra Integral Equation and System of Nonlinear Fredholm Integral Equations . In this chapter, there are six sections. The first section is an introduction and in the second section, the existence and uniqueness of the solution of nonlinear Fredholm-Volterra integral equation of the second kind is considered. Then in section three, the system of nonlinear Fredholm integral equations. In the fourth section we use some numerical techniques for solving the system of nonlinear Fredholm integral equations by Trapezoidal rule, Simpson's rule and Romberg integration method. In section five, some examples are solved to explain these method. In the last section, the error in each method is discussed and calculated. From this chapter, the following paper has been submited: (Some numerical techniques for solve nonlinear Fredholm-Volterra integral equation). It was accepted for publication in Journal of Progressive Reseach in Mathematics . Chapter 3 : Nonlinear Fredholm-Volterra Integral Equation and System of Nonlinear Volterra Integral Equations . In this chapter, there are six sections. The first section is an introduction and in the second section, the existence and uniqueness of the solution of nonlinear Fredholm-Volterra integral equation of the second kind is considered. Then in section three, the system of nonlinear Volterra integral equations. In the fourth section we use a some numerical techniques for solving the system of nonlinear Volterra integral equations by Runge-Kutta method and Block-by Block method. In section five, some examples are solved to explain these method. In the last section, the error in each method is discussed and calculated. From this chapter, the following paper has been submited: (Runge-Kutta Method and Block by Block Method to Solve Nonliner Fredholm-Volterra Integral Equation with Continuous Kernel) is submitted for publication. Chapter 4 : Some Different Methods to Solve The Hammerstein- Volterra Integral Equation . In this chapter, there are six sections. The first section is an introduction and in the second section, the existence and uniqueness of the solution of Hammerstein-Volterra integral equation of the second kind are with discontinuity kernel considered. Then in section three, the system of Hammerstein integral equations. In the fourth section we use a some numerical techniques for solving the system of Hammerstein integral equations by the Toeplitz matrix method and the product Nystrom method. In section five, some examples are solved to explain these method. In the last section, the error in each method is discussed and calculated. From this chapter, the following paper has been submited: (Toeplitz matrix method and product Nystrom method to Solve Hammerstein-Volterra Integral Equation with Singular Kernel) was submitted for publication. For all numerical example are explained and the error in each cases is calculated. Programs are written in maple program version 18.

السبيعي، بيضاء محسن طامي

In this thesis, the analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode of radiation field in resonance case and off-resonance case is studies. The classical external field for the system is added and obtain the general solution by solving the Schrodinger equation. Therefor we study the influence of the classical external field on the present system. Some statistical aspects study for example the purity of the atomic state, which it is used to measure the degree of entanglement between the atom and the field. We can calculate the temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case. It have been show that maximum squeezing for the variance and entropy squeezing may be occurs when some values of the ratio between the amplifier coupling and the field frequency equals. Finally, we are looking for good results that have importance in the quantum information for certain values of the ratio between the interaction constant between the atom and the field to the energy of the free electromagnetic field so that the system can reaches the pure state

المطرفي، وردة مبروك مساعد

The present study was undertaken using O. spilurus (Tilapia) because of its wide availability and suitability as a model for toxicity testing as well as they had exhibited a time-honored place in the economical nutrition. Chlorpyrifos is a broad-spectrum organophosphate for agriculture. Therefore, the purpose of the present study was to evaluate the effect of sublethal toxicity of organophosphate insecticide CPF (Dursban 48) on some organs (liver, kidneys and muscles) of subadults O. spilurus L. This study aimed also to study the effect of CPF on some biomarker parameters as well as examine histopathological changes on liver, kidneys and muscles in tilapia O. spilurus. Moreover, the protective role of vit C supplementation against the different biochemical and histopathological effects of Dursban 48 pesticide was tested for a period of 14 days.

الحارثي، عايض مريسي سالم

Pattern Recognition is of great importance in many real life applications, for example face recognition, fingerprint verification, disease categorization, prediction of survival rates for patients of specific disease, chromosome shape discrimination, optical character recognition, speech recognition, texture discrimination, among others. The discovery of knowledge hidden in data depends on pattern and is a step for accurate recognition. Any raw image data has many degrees of freedom and it is not possible to handle all those dimensions, to achieve an identification system, it is required that it gives result within a stipulated time. Therefore, such systems are designed to work in the domain of low dimension so that some results can be obtained when they are required. If the number of features, i.e. the pattern dimension, is more than the classifier will take more time to measure the intra-class and interclass distances. For example the distance in 𝑅1 is simple than that of 𝑅3. Dimensionality reduction helps to save time, cost and effort in the process of decision making in general and especially in pattern recognition. The process of dimension reduction is done under the condition that the quality of information is preserved. Statistical analysis methods are used as a guided approach to almost all real live problems and consequently in pattern recognition. Regression approaches are used to reduce the object is in the problem. Consequently, we get more accurate and less expensive models in many fields for example biological, physical, and social sciences, as well as in business and engineering. Linear models are useful in both the planning stages of research and analysis of the resulting data. One of the important and recent tools of pattern recognition is rough sets theory. We aim in this thesis to spot light on directions of rough sets theory applications in pattern recognition problems, and to explore in detail this role using case studies and examples. In our presentations of these examples, we focused on three stages of applying rough set approaches in pattern recognition problems, which are classification, attribute reduction and decision rules extractions. From the above discussion it became clear that pattern recognition is important for almost all real life problems and statistical methods with rough sets technologies are good tools for this line of study. So, we chose the subject of our thesis: " Pattern Recognition and Rough Sets " This thesis consists of four chapters: Chapter 1: The purpose of this introductory chapter is to give an exploration for pattern recognition concepts, its importance and connections with rough set theory. Section 1.1 is devoted for the basics of pattern recognition. While section 1.2 aims to display applications and methods of pattern recognition. Also an account about rough sets applications in pattern recognition is given. Sections 1.3 is reserved for basic definitions and concepts used in this thesis. A brief account on information and entropy is given in section 1.4, while section 1.5 spots light on regression analysis. Sections 1.6 and 1.7 are concerned with thesis motivations and structure. Chapter 2: The main aim of this chapter is to give a comprehensive account on basic concepts of rough sets theory that play an important role in reduction of attributes, and extracting decision rules, which gives a generalized description of the knowledge contained in the data. Section 2.1 is an introduction, the target of section 2.2 is to give an account on basic concepts of rough sets theory, attributes reduction is discussed in section 2.3, the purpose of 2.4 is to compute some entropy measures of partitions in information systems, the goal of section 2.5 is to extract rules from an information system, finally section 2.6 concern about giving real life example for discover patterns (rules) in an information system for a biomedical experiment as typical. Chapter 3: The goal of this chapter is to explore some methods of reduction based on multivariate regression. Section 3.1 is an introduction, the purpose of section 3.2 is to give basic notions of comparison between regression methods. Finally section 3.3 is reserved for detail explanation for selecting best regression models and give examples. Chapter 4: This chapter proposes an approach based on similarity relation, which has the ability to deal with real-valued data whilst simultaneously retaining dataset semantics. More significantly, this chapter describes the underlying mechanism for this approach to utilize the information contained within the boundary region or region of uncertainty. The use of this information can result in the discovery of minimal feature subsets and improve classification accuracy. We give experimental evaluation which compares the suggested method with a number of existing feature selection techniques. Section 4.1 is an introduction, the target of section 4.2 is to give an account on reduction based on similarity, finally distance metric and mean lower approximation definitions are discussed in section 4.3, and all this supported by illustrative examples. Some results of chapter two have been presented in the scientific preparatory meeting for Fifth Scientific Conference in Riyadh.

الحارثي، عايض مريسي سالم

Pattern Recognition is of great importance in many real life applications, for example face recognition, fingerprint verification, disease categorization, prediction of survival rates for patients of specific disease, chromosome shape discrimination, optical character recognition, speech recognition, texture discrimination, among others. The discovery of knowledge hidden in data depends on pattern and is a step for accurate recognition. Any raw image data has many degrees of freedom and it is not possible to handle all those dimensions, to achieve an identification system, it is required that it gives result within a stipulated time. Therefore, such systems are designed to work in the domain of low dimension so that some results can be obtained when they are required. If the number of features, i.e. the pattern dimension, is more than the classifier will take more time to measure the intra-class and interclass distances. For example the distance in 𝑅1 is simple than that of 𝑅3. Dimensionality reduction helps to save time, cost and effort in the process of decision making in general and especially in pattern recognition. The process of dimension reduction is done under the condition that the quality of information is preserved. Statistical analysis methods are used as a guided approach to almost all real live problems and consequently in pattern recognition. Regression approaches are used to reduce the object is in the problem. Consequently, we get more accurate and less expensive models in many fields for example biological, physical, and social sciences, as well as in business and engineering. Linear models are useful in both the planning stages of research and analysis of the resulting data. One of the important and recent tools of pattern recognition is rough sets theory. We aim in this thesis to spot light on directions of rough sets theory applications in pattern recognition problems, and to explore in detail this role using case studies and examples. In our presentations of these examples, we focused on three stages of applying rough set approaches in pattern recognition problems, which are classification, attribute reduction and decision rules extractions. From the above discussion it became clear that pattern recognition is important for almost all real life problems and statistical methods with rough sets technologies are good tools for this line of study.

الزهراني ، نورة محمد كميخ

القرشي ، وعد عبيد الله

In this work, two series of ternary alloyed Cd1-xCoxS QDs were deposited onto TiO2 electrode using successive ionic layer adsorption and reaction (SILAR) technique. The energy band gaps of the prepared samples were tuned by alloying at a certain size and controlling the QDs size at a constant molar ratio. The first series contains five samples of ternary alloyed Cd1-xCoxS QDs were prepared with different Co molar ratio (x = 0, 0.1, 0.2, 0.3, and 0.4) at constant QDs size. While the second one involves 10 samples of ternary alloyed Cd0.8Co0.2S QDs at different SILAR cycles. The morphology of the bare TiO2 electrodes and prepared ternary alloyed Cd1-xCoxS QDs/TiO2 photoanodes were scanned using the scanning electron microscopy (SEM) and the transmittance electron microscopy (TEM). SEM and TEM measurements prove the successful synthesis of the ternary alloyed QDs. X-ray diffraction (XRD) patterns analysis proves the success of the alloying processes and confirms the formation of the hexagonal crystalline structure of the ternary alloyed Cd1-xCoxS QDs. The optical properties of the prepared samples were characterized using the photoacoustic spectroscopy and Uv.vis spectroscopy which exhibits similar results. For the first samples series, the energy band gaps decreased as the Co molar ratio increase which attributed to the alloying. The second samples series, the energy band gaps exhibit the same behavior as SILAR cycles increase due to the quantum confinement effect. Vegard's low was used to determine the bowing constant for ternary alloyed Cd1-xCoxS QDs that found to be 0.748 eV. The CdS QDs size has been calculated using the effective mass approximation (EMA) and it is equal to 4 nm. The photovoltaic performance of the fabricated Cd1-xCoxS QDs sensitized solar cells has been studied. Compared to pure CdS QDSSC, Cd1-xCoxS QDSSCs shows better photovoltaic performance. Cd0.9Co0.1S QDSSC has been exhibit the best balance between the increased absorption and energy alignment of the QDs.