Mathematics

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    An Analytic and Dynamic Programming Treatment for Solow and Ramsey Models
    (2014) Ahmad Yasir Amer Thabaineh; Dr. Mohammad Assa`d
    In this thesis, we studied two of the most important exogenous economic growth models; Solow and Ramsey models and their effects in microeconomics by using dynamic programming techniques. Dynamic programming (DP) is a general approach to solve economic growth problems. The main differences between Solow and Ramsey models are discussed in details. Bellman value function for the growth models is applied to the two models and an analytic formula are derived. Concerning the models under study, we then discussed the steady states for the model and derived a closed formula for the capital. This formula was checked by computer using Python codes where a new concave assumed value function is given; , to be compared with a value function given by other . These two initial functions have the same properties of being monotone and concave up. The comparison shows the excellence and advantages of our assumption. We reached the true value function faster.
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    Analytical and Numerical Aspects of Wavelets
    (2015) Noora Hazem Janem; Prof. Naji Qatanani
    Almost every physical phenomenon can be described via a waveform –a function of time, space or some other variables, in particular, sound waves. The Fourier transform gives us a unique and powerful way of viewing these waveforms. Nowadays, wavelet transformation is one of the most popular candidates of the time-frequency-transformations. There are three types of wavelet transforms, namely: continuous, discrete and fast wavelet transforms. In this work we will study Fourier transform together with its properties and present the connections between Fourier transform and wavelet transform. Moreover, we will show how the Wavelet-Galerkin method can be used to solve ordinary differential equations and partial differential equations. For the applications of wavelet transform we will consider two applications; first signal decomposition and reconstruction: in this section we use two filters to decompose a signal using the wavelet decomposition algorithm and then we use similar process to rebuild the original signal using the wavelet reconstruction algorithm. A second application is the audio fingerprint. Assume we have an audio. We read this audio and then convert it into signals. These signals are then divided into a number of frames. Next, we decompose each frame of this audio signal into five layer wavelets. Finally we use the wavelet coefficients to compute the variance, zero crossing, energy and centroid.
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    Analytical and Numerical Methods for Solving Linear Fuzzy Volterra Integral Equation of the Second Kind
    (2016) Jihan Tahsin Abdal-Rahim Hamaydi; prof. Naji Qatanani
    Integral equations, in general, play a very important role in Engineering and technology due to their wide range of applications. Fuzzy Volterra integral equations in particular have many applications such as fuzzy control, fuzzy finance and economic systems. After introducing some definitions in fuzzy mathematics, we focus our attention on the analytical and numerical methods for solving the fuzzy Volterra integral equation of the second kind. For the analytical solution of the fuzzy Volterra integral equation we have presented the following methods: The Fuzzy Laplace Transformation Method(FLTM), Fuzzy Homotopy Analysis Method(FHAM), Fuzzy Adomian Decomposition Method (FADM), Fuzzy Differential Transformation Method (FDTM), and the Fuzzy Successive Approximation Method (FSAM). For the numerical handling of the fuzzy Volterra Integral equation we have implemented various techniques, namely: Taylor expansion method, Trapezoidal method, and the variation iteration method. To investigate the efficiency of these numerical techniques we have solved some numerical examples. Numerical results have shown to be in a close agreement with the analytical ones. Moreover, the variation iteration method is one of the most powerful numerical techniques for solving Fuzzy Volterra integral equation of the second kind in comparison with other numerical techniques.
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    APPEALING THE JUDICIAL VERDICTS OF THE MILITARY COURTS IN PALESTINE
    (جامعة النجاح الوطنية, 2022-04-07) Shded, Abd Alrahman
    The trial procedures before the Security Forces Judiciary Commission in Palestine are of a special nature, specifically the methods of appealing the judgments issued by it. the Commission’s jurisdiction is over a specific segment of the Palestinian people, namely members of the Palestinian security forces, and any military crimes. The security forces judiciary is an entity that distinguishes from the regular and special courts in Palestine, as it combines the security institution and the judicial institution. This is why there is a need to know the nature this entity as well as what crimes fall within its jurisdiction of it. And on which category of the people its decisions apply on. At the end judges are human like us. They may be right or be wrong. So mechanisms and methods are put in place to challenge the rulings issued by it in order to preserve the right of everyone who’s not comfortable with ruling to file an appeal according to the methods of appealing these rulings. Before this judicial commission. Not all jurists and lawyers are aware of its procedures and methods of appealing its rulings , as they are aware of the procedures and laws of the regular judiciary body. Because this Security Forces Judiciary is of a special nature and governed by its own laws, and they also have specific methods of appealing them. The introductory part dealt with the nature of the security forces’ judiciary and its provisions. The first section address the legal nature of the security forces’ judiciary in terms of military crimes and what is the military issue and the individuals who are sued before this body based on the decisions of the Palestinian Court of Cassation, the laws governing the security forces’ judiciary and relevant Palestinian laws. In addition to addressing origin, jurisdiction and the nature of this body, whether it is an independent judicial body or a military institution. and its concentrated on the nature and types of judgments issued by it. As for the first chapter of this study, the researcher dealt with the normal methods of appealing the rulings issued by the Security Forces Judiciary commission. In the first section, the appeal by objection is addressed and the procedures for the objection and the effects of it, it’s also explained in the second section the procedure of appealing these rules and the effects of these appeals. As for the second chapter, its concentrated on unusual ways of appealing judgments issued by the Security Forces Judiciary Commission. In the first section, it’s dealt with the retrial of military judgments issued by this Commission, its procedures and effects. In the second section the ratification of military judgments and the powers of ratification.
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    Approximate Solutions of Systems of Integro-Differential Equations
    (جامعة النجاح الوطنية, 2019-02-27) جلال أحمد عيسى, أحمد
    في هذه الأطروحة ركزنا على الحل التقريبي لنظام معادلات فولتيرا التكاملية التفاضلية الخطية (system of linear Volterra integro-differential equations), وقمنا باستقصاء بعض الطرق العددية لحل نظام معادلات فولتيرا التكاملية التفاضلية الخطية. هذه الطرق العددية هي: إعادة بناء طريقة تكرار التباين (reconstruction of variational iteration method), طريقة التجميع السينك على أساس إقترانات السينك (sinc collocation method based on sinc function's), طريقة مويجات شيبيشيف (Chebyshev wavelet method). إن الأمثلة العددية التي تناولناها نفذت باستخدام هذه الطرق العددية لحل نظام معادلات فولتيرا التكاملية التفاضلية الخطية. تم وضع مقارنة بين هذه الطرق العددية حيث أظهرت لنا النتائج العددية أن طريقة مويجات شيبيشيف أكثر كفاءة وفاعلية بالمقارنة مع الطرق العددية الأخرى التي تم دراستها وذلك بناء على الأمثلة التي استخدمناها في الرسالة.
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    Approximate Solutions of Systems of Integro-Differential Equations
    (ِAn-Najah National University, 2019-02-27) Jalal, Ahmad
    في هذه الأطروحة ركزنا على الحل التقريبي لنظام معادلات فولتيرا التكاملية التفاضلية الخطية (system of linear Volterra integro-differential equations), وقمنا باستقصاء بعض الطرق العددية لحل نظام معادلات فولتيرا التكاملية التفاضلية الخطية. هذه الطرق العددية هي: إعادة بناء طريقة تكرار التباين (reconstruction of variational iteration method), طريقة التجميع السينك على أساس إقترانات السينك (sinc collocation method based on sinc function's), طريقة مويجات شيبيشيف (Chebyshev wavelet method). إن الأمثلة العددية التي تناولناها نفذت باستخدام هذه الطرق العددية لحل نظام معادلات فولتيرا التكاملية التفاضلية الخطية. تم وضع مقارنة بين هذه الطرق العددية حيث أظهرت لنا النتائج العددية أن طريقة مويجات شيبيشيف أكثر كفاءة وفاعلية بالمقارنة مع الطرق العددية الأخرى التي تم دراستها وذلك بناء على الأمثلة التي استخدمناها في الرسالة.
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    Approximation methods of Fractional Derivatives and Their Applications to Fractional Differential Equations
    (جامعة النجاح الوطنية, 2017-08-02) ظاهر, أصيل فازع حمد; المصري, معتصم
    Fractional calculus is a field of mathematics which concern on finding derivatives or integrals of non-integer order. The exact birthday of fractional calculus was in september 30, 1695. Over the years, many mathematicians contributed to this field, and bit by bit the importance of fractional calculus has appeared in many aspects of our life, such as physics, engineering, viscoelasticity, and many others. In this thesis, we start our work in chapter 1 by focusing on the definition of Riemann-Liouville fractional integral, and finding the fractional integral of any order p for many functions. In chapter 2, we study the two mostly used definitions of fractional differentiation namely; the Riemann-Liouville and the Caputo definitions, then we make comparison between the two definitions of fractional derivatives. In chapter 3, we focus on solving fractional initial value problems with Caputo operator or with Riemann-Liouville operator using the easiest method which is Laplace transform method. At the end of this thesis, we focus on some applications of fractional calculus in real life such as tautochrone problem.
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    Automatic Detection of Diabetic Retinopathy in Fundus Imagesby using Fuzzy C-means (FCM) Clustering
    (جامعة النجاح الوطنية, 2018-08-08) دويكات, تحرير
    اعتلال الشبكية بمرض السكري يعتبر من أكثر الأمراض خطورة على العين؛ التي تؤدي الى فقدان البصرالذي يصاب فيه مرضى السكري. تعتبر الافرازات من أولى العلامات الدالة على الاصابة بالمرض، لذلك من المهم اكتشافها واحصائها، من أجل العلاج والوقاية من تفاقم ¬¬المرض وفقدان البصر. في هذه الرسالة قمنا باقتراح طريقة تلقائية (اوتوماتيكية) للكشف عن الافرازات من صور شبكية العين لمرضى السكري، وذلك باستخدام خوارزمية متوسطات المراكز الضبابية بالاضافة الى مجموعة من تقنيات معالجة الصور باستخدام برنامج الماتلاب. لقد قمنا بعرض بعض المفاهيم الهامة عن أجزاء العين، مرض اعتلال الشبكية بالسكري، تقنيات وطرق معالجة الصور وكذلك الانظمة الضبابية، ونخص بالذكر خوارزمية متوسطات المراكز الضبابية. بعد ذلك قمنا بالتطبيق على صور شبكية العين لمرضى السكري، وكانت الخوارزمية تعتمد اولا على استخراج قرص العين والاوعية الدموية وذلك لتحسين عملية اكتشاف الافرازات، ثم قمنا بتعيين وتحديد الافرازات. في النهاية تم تقييم النتائج عن طريق حساب الحساسية، النوعية والدقة بمقارنتها بالصور التي تم رسمها عن طريق الاخصائيين والأطباء، وكانت متوسطات النتائج كما يلي: 86.29%, 98.42% و 98.35% على التوالي.
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    BEST APPROXIMATION AND BEST CO - APPROXIMATION IN CONE - NORMED SPACE
    (An-Najah National University, 2018-05-18)
    In this thesis, the concept of Best Approximation and Best Co-Approximation in cone – normed spaces are studied. We noticed similarities between Best Approximation and Best Co–Approximation in cone–normed spaces. We obtained new results among which, we proved that: 1. We can apply Best Approximation and Best Co-Approximation theorems in normed space to cone-normed space. 2. Best Co-Approximation in cone-normed space is a counter copy of Best Approximation in cone-normed space. The concept of Proximinal additivity and ᶲc-Summand in cone–normed space are introduced. Also we have answered some questions about them.
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    Best Approximation in General Normed Spaces
    (2001) Mu'tas Hasan Mahmoud Al-Sayed; Dr. Abdallah A. Hakawati
    Let X=(X,||.||) be a normed space and suppose that any given x in X is to be approximated by an element Y in Y, where Y is a fixed subspace of X. We let d denoted the distance from x to Y. By definition, d = d(x, Y) = infyєY ||x – y|| .Clearly, d depends on both x and Y, which we keep, fixed, so that the simple notation d is in order. If there exists a YoєY such that ||x - Yo|| =d. then Yo is called a best approximation of Y to x or a best approximant of x in Y. We see that a best approximation Yo is an element of minimum distance from the given x. Such a YoєY mayor may not exist; this raises the problem of existence. The problem of uniqueness is of practical interest, too, since for a given x and Y there may be more than one best approximation. My thesis consists of three chapters. In chapter one we summarize some of the essential and basic concepts which shall be needed in the following chapters, this chapter consists of two sections; in the first one we present metric, normed, Banach spaces, and the last one we present inner product, and Hilbert spaces. This chapter is absolutely fundamental. In chapter two, we define best approximations in section one. In section two we study some properties of the set of all best approximations P(x,Y). In section three we study some properties of the proximinaI set and show that compact subspace and finite-dimensional subspace are proximal. In section four we consider the problem of uniqueness of best approximation. In section five we review the properties of OrIicz spaces in which we introduce some of the basic theory of proximinality In chapter three, which is the main body of our thesis, we, in section one, study the main characterizations and properties of best approximations and some consequences of the characterization in arbitrary normed linear spaces. In sections two and three we gives some application in several spaces like L ¹(T,v), C(K) and CR(K).
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    Cantor Set in Measure Theory
    (2005) Alaa Jamal Moustafa Yaseen; Dr. Abdallah A. Hakwati - Supervisor; Dr. Jasser H. Sarsour - Co-Supervisor
    This thesis is a survey for the using of Cantor sets and in measure theory. It is proved that and are measurable and have zero measure. Following that it is shown that the measure of is positive and the measure of is zero. Also it is shown that there exists a subset of such that is non-measurable. At the end of this thesis it is shown that there is no subset such that is Bernstein in.
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    Clean Like Semiring Notions and Trivial Semiring Extension
    (جامعة النجاح الوطنية, 2020-10-25) Jamal, Sondos Osama Hussain
    Suppose that S is a commutative semiring with unity different than zero and M an S-semimodule. In this thesis, we study the algebraic and the ideal theoretic properties of SαM, where SαM denotes the trivial semiring extension (or the expectation of S), providing an analog results to the proved ones in the ring situation. In this thesis, different elements like units, zero divisors and other elements of SαM as well as the special ideals like subtractive ideals, prime ideals and other types of ideals of SαM will be identified. The generalization of some of the clean like notions into the semiring situation will be investigated; this thesis also examines some of their properties and the transfer of these notions in the trivial semiring extension. This thesis also provides an application of semirings in classification system which is considered an important technique in data mining which used to assign every element to specific groups based on the similarities between the referred to elements.
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    A Comparative Study in Cone Metric Spaces and Cone Normed Spaces
    (2016) Dua’a Abdullah Mohammad Al-Afghani; Dr. Abdallah A.Hakawati
    Cone metric spaces are, not yet proven to be generalization of metric spaces. In many occasions the answer was proved, not to be affirmative. In this thesis we made a comparison between) Cone Metric Spaces and Cone Normed Spaces) and ( Ordinary Metric Spaces and Normed Spaces) as a way to find an answer for our main contribution. We choose the most important branches of mathematics to make a comparison as in: convergence, topology and best approximation theory. We also tried to transplant the idea of cone metric spaces in Orlicz’s spaces. We obtained new results while we investigate some properties which were proven to be incorrect in cone metric spaces but hold in ordinary case like as Sandwich Theorem, which gives us a sense of generality here.
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    Composition operator on de Branges-Rovnyak spaces
    (An-Najah National University, 2017-08-29) ناصر, غادة فهمي نمر
    If α which is analytic and which maps the unit disc to itself. Then we describe the image of the de Branges-Rovnyak spaces H(b) under the composition operator Cα for algebraic functions b. In this thesis, we answered partially about what are the conditions on α such that Cα maps H(b) into itself, which are α’s such that Cα : H(b) −→ H(b), and which are α’s such that Cα maps H(b) to H(q).
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    Computational Techniques for Solving Linear Parabolic Partial Differential Equation
    (جامعة النجاح الوطنية, 2019-03-24) محمود مصلح, سمير
    كثيراً من الظواهر الفيزيائية والطبيعية تظهر على شكل نماذج رياضية وتحديدا تظهر كمعادلات تفاضلية جزئية تصف طبيعة هذه الظواهر. في هذه الرسالة استخدمنا المعادلة التفاضلية الجزئية الخطية المكافئة من الدرجة الثانية بحيث يتم التركيز على معادلة الحرارة كنموذج لوصف تلك الظواهر. في الواقع، فان معظم هذه المسائل يصعب حلها بطرق تحليلية. بدلا من ذلك، يمكن ان تحل عدديا باستخدام الاساليب الحسابية. في هذه الاطروحة، معادلة الحرارة المتجانسة مع انواع مختلفة من الشروط الحدية تم حلها عدديا باستخدام طريقة الفروق المحدودة وطريقة العناصر المحدودة لتقريب الحل لمعادلة التفاضلية الجزئية المكافئة. وبهذا يتم تحويل المعادلة الى شكل اخر للوصول الى نظام خطي من المعادلات يمكن حلها باستخدام طرق تكرارية، مثل: Jacobi, Gauss-Seidel, Successive Over Relaxation, Conjugate Gradient Methods وعمل مقارنة بينهم. وجدنا في هذا البحث من خلال ما بينته النتائج العددية ان طريقة الفروق المحدودة هي أكثر كفاءة من طريقة العناصر المحدودة للحصول على حل تقريبي للمعادلة وبأقل خطأ ممكن في حال كون المجال ذو اشكال هندسية منتظمة، وان طريقة العناصر المحدودة أكثر دقة للمجالات المعقدة والغير منتظمة. ايضا، نلاحظ ان الطريقة التكرارية Conjugate Gradient تعطي النتائج الاكثر دقة من بين الطرق التكرارية الاخرى.
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    Cone Metric Spaces
    (2016) Haitham Darweesh Abu Sarries; Dr. Abdallah A. Hakawati
    Cone metric spaces were introduced in [1] by means of partially ordering real Banach spaces by specified cones. In [4] and [8] , the nation of cone – normed spaces was introduced. cone- metric spaces, and hence, cone- normed spaces were shown to be first countable topological spaces. The reader may consult [5] for this development. In [6], it was shown that, in a sense, cone- metric spaces are not, really, generalizations of metric spaces. This was the motive to do further investigations. Now, we put things in order. 1. Definition:[1] Let (E ,‖∙‖) be a real Banach space and P a subset of E then P is called a cone if : (a) P is closed, convex, nonempty, and P ≠ {0}. (b) a,b ∈ ℝ ; a,b ≥ 0 ; x, y ∈ P ⇒ ax+by ∈ P. (c) x ∈ P and –x ∈ P ⇒ x = 0. 2. Example: [13] Let E= ℓ¹, the absolutely summable real sequences. Then the set P = {x ∈ E : xn ≥ 0 , n} is a cone in E. In our project, we will attempt to enforce the feeling that cone metric spaces are not real generalization of metric spaces by the necessary theory and examples. In the meantime, we will keep it conceivable to arrive at generalization aspects.
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    CONSTRUCTING NORMS OF SOME PHYSICAL FITNESS AND PHYSIOLOGICAL MEASURES AMONG PARTICIPANTS IN PHYSICAL FITNESS –HEALTH CENTERS AGED 20-30 YEARS
    (جامعة النجاح الوطنية, 2022-06-30) Qanees, Majd
    The study aimed at identifying the level of some physical and physiological measurements and the possibility of building standard levels for them for Participants in Physical Fitness –Health Centers Aged 20-30 Years , and determining the relationship between them. (72) male affiliates, representing a percentage of (60%) and (48) female affiliates, representing a percentage of (40%), of various ages between (20-30 years), and the study sample represents a percentage of (40%) of the original study population, and after collecting the data, it was statistically treated using the Statistical Package for Social Sciences (SPSS) program, using means, standard deviations, Pearson correlation coefficient and regression. The results of the study revealed that the means of: hand grip, legs muscular strength, arms muscular strength, arms strength endurance, and abdominal muscles’ strength endurance in males were respectively: (48.92 kg, 2.64 m, 6.47 m, 48.39 times, 53.94 times), while the mean for physiological measurements (anaerobic power, anaerobic capacity, maximum oxygen consumption, resting heart rate, resting metabolic rate, fats, lean body mass, cardiac index, lean body mass index, fat index) for males were, respectively: (43.93 kg.m/s, 37.51 kg.m/s, 47.41 milliliters/kg/min, 80.81 beats/min, 2100.86 calories per day, 12.89%, 62.87 kg, 2.24 liters. min/m², 21.44 kg/m², 3.47 kg/m². As for the means of physical measurements: (hand grip strength, legs muscular strength (long jump from stability), arms muscular strength (throwing the medicine ball), arms strength -endurance (push-up), abdominal strength endurance (Sit-up)) in females, they were Respectively: (25.09 kg, 1.82 m, 5.25 m, 23.92 times, 37.79 times).The means of physiological measures (maximum oxygen consumption, resting heart rate, resting metabolic rate, fat, lean body mass, cardiac index, lean body mass index, and fat index) for females were, respectively. : (25.54 kg.m/s, 21.01 kg.m/s, 23.37 ml/kg/min, 80.17 beats/min, 1506.40 calories per day, 25.83%, 45.03 kg, 2.60 liters. min/m², 17.65 kg/m², 5.95 kg/m2). Based on the results of the study, several recommendations were recommended, the most important of which are: Conducting similar studies on a broader scale for different age groups while addressing new variables. And circulating the study and its results to workers in health fitness centers to benefit from them.
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    Convexity, Fixed Point Theorems and Walrasian Equilibrium
    (2002) Abdul-Rahim Omar Amin Nur; Dr. Abdallah A. Hakawati; Dr. Rimon Abduh' Y. Jadoun
    In this thesis, I will deal with an application of fixed-point theorem of set valued map [Let X and Y be two subsets of Rⁿ: A set-valued map F from X to Y, is a map that associates with any x є X a subset F(x) of Y, A fixed point x for F exists if x є F(x) ], and convexity to prove the existence of Walrasian Equilibrium under sufficient conditions for both pure exchange economy and private ownership economy. Then I will show how to modify these theorems in more general cases under uncertainty and externalities.
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    CUBIC B-SPLINE FOR SOLUTIONS OF BOUNDARY VALUE PROBLEMS
    (2023-03-15) Doaa Shtayah
    Many of the mathematical models of engineering problems are expressed in terms of Boundary Value Problems (BVP). The Finite Difference Method (FDM) is the most modern method for solving (BVP). This is incredibly helpful in resolving challenging issues involving typical geometrical shapes or boundaries. Another numerical method, the B-spline method, has seen growing application in recent years in engineering research to solve mathematical models. The main objective of this study is to examine the effectiveness of cubic B-spline functions in addressing boundary value problems. The derivation of linear, quadratic, and cubic B-spline functions is covered at the start of the study. Subsequently, I use cubic Bspline functions to solve second-order linear boundary value problems with nonhomogeneous boundary conditions for ordinary differential equations, both in cases where coefficients are constant and where they are variable. Results from the examples show that the B-spline method leads to lower error rates compared to the Finite Difference Method. Keywords: Cubic spline, B-spline, differential equations, Boundary value problems, Finite difference methods
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    Decoding Turbo Codes with Linear Programming
    (2013) Hisham Hamed Abdel-Raouf Salahat; Dr. Mohammad Assa`d; Dr. Mohammad Omran
    In this thesis we investigate the application of Linear Programming LP relaxation to the problem of decoding an error-correcting code. LP relaxation is a standard technique in approximation algorithms and operation research, and it is used to find good suboptimal solution to very difficult optimization problems. The method of a posteriori probability and iterative decoding algorithm is used to decode product codes (a special type of turbo codes). We investigate a program using Matlab to make computations to our algorithm. The logistic distribution with variance one is used. We compare the results of our computations to those of other authors; we find that our results are the best all over the others. The LP method has its place in the generic turbo code, which is made up of asset of simpler" trellis-based" codes, we formulate the LP for a single trellis-based code as a min-cost flow problem, using the trellis as a directed flow. We extend this formulation to any turbo codes by applying constraints between the LP variables used in each component code. One of the most advantages for LP decoding is that whenever the decoder output a result it is guaranteed to be the optimal solution, the most likely (ML) information sent over the channel, we refer to this property as the ML certificate property.