Physical Sciences and Mathematics Commons^™

Efficient And Secure Digital Signature Algorithm (Dsa), Nissa Mehibel, M'Hamed Hamadouche

Emirates Journal for Engineering Research

The digital signature is used to ensure the integrity of messages as well as the authentication and non-repudiation of users. Today it has a very important role in information security. Digital signature is used in various fields such as e-commerce and e-voting, health, internet of things (IOT). Many digital signature schemes have been proposed, depending on the computational cost and security level. In this paper, we analyzed a recently proposed digital signature scheme based on the discrete logarithm problem (DLP). Our analysis shows that the scheme is not secure against the repeated random number attack to determine the secret keys …

Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

Theses

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …

The Reproducing Kernel Method For Solving Integro-Differential And Volterra Integral Equations, Khulood Gamal Qaid

Theses

Integro-differential equations are a class of mathematical equations that involve both derivatives and integrals. They have applications in a wide range of fields, including physics, engineering, finance, and biology such as the spread of diseases, population dynamics, and the behavior of financial markets. The study of these equations requires advanced mathematical techniques, including functional analysis, approximation methods, and numerical analysis. They are a rich area of research with many open questions and challenges.
In this thesis, we will develop and implement the reproducing kernel method to solve a class of integro-differential and Volterra integral equations. We discuss both cases when …

Valuation Of Asian Options In A High Volatility Market With Jumps, Zeeshan Khalid

Theses

The evaluation of financial derivatives represents a central part of financial risk management. There are many types of derivatives among other path-dependent options. In this study, we aim at valuing Asian options. They are path dependent and have several benefits. For instance, their values are habitually lower than European options. Also, an Asian option on a commodity drops the risk value close to maturity. Though, the disadvantage is that they are in general difficult to value since the distribution of the payoff is usually unknown. It is agreed in the literature that a stochastic process with a jumps model for …

A Support Theorem For A Wave Equation, Aysha Khaled Alshamsi

Theses

It is well known that the fundamental solution to the classical wave equation Δ𝑢 (𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0 is supported on the light cone {(𝑥, 𝑡) ∈ ℝ^𝑛× ℝ : ||𝑥|| = |𝑡|} if and only if the dimension 𝑛 is odd and ≥ 3. Because we are living in a 3-dimensional world we can hear each other clearly; One has a pure propagator without residual waves. In this thesis we consider the wave equation

2||𝑥||Δ_𝑘𝑢_𝑘(𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0, (𝑥, 𝑡) ∈ ℝ^𝑛 × ℝ …

Mathematical Models For Thalassemia, Hamda Mohammed Al Dhaheri

Theses

Thalassemia is a genetic blood disorder caused by gene mutation or deletion in a blood protein called hemoglobin. Treatment of thalassemia requires a life-long blood transfusion and removal of excessive iron in the blood stream, which usually causes a big pressure on health care systems. Various forms of thalassemia control measures have been used to reduce the prevalence of thalassemia major. This has resulted in a substantial reduction in the prevalence of thalassemia. However, the thalassemia carrier population remains high, which could lead to an increase in the thalassemia major population through carrier-to-carrier marriages. Thus, we developed two mathematical models …

On The Projections Of Commutative C*-Algebras, Alaa Ahmad Hamdan

Theses

Gelfand and Naimark proved that the Banach algebra of continuous complex-valued functions on a compact space Ω is the only example of commutative unital C*-algebras. We study the C*-algebra C(Ω) and its main elements, such as projections. Also, we discuss the mapping between projections, which preserves orthogonality (orthoisomorphism). A bijective θ between projections induces a bijective Θ between the Boolean algebra of clopen subsets of X. Then, we give main properties of such Θ. For a compact subset X of ℝ, we classify the projections of C(X) by introducing the similar relation on P(C(X)). We introduce an …

Valuation Of Options In A High Volatile Regime Switching Market, Tasnim Mazen Sharif Alhamad

Theses

Financial modeling by Stochastic Differential Equations-SDEs with regime-switching has been utilized to allow moving from one economic state to another. The aim of this thesis is to tackle the pricing of European options under a regime-switching model where the volatility is augmented. Regime-switching models are more realistic since they encompass the effect of an external event on the underlying asset prices. But they are challenging, considering in addition increased volatility in the model will for sure make the option pricing problem more complicated and its solution may not exist analytically. Numerical methods for finance could be very helpful in this …

Numerical Methods For Locating Zeros Of Polynomial Systems Using Resultant, Ayade Salah Abdelmalk

Theses

In this thesis, we modify two methods for locating zeros of polynomial systems which are one dimensional path following and Lanczos method. Both approaches are based on calculating the resultant matrix corresponding to each variable in the system. These methods are stable and preserving the spareness of these matrices. These methods are developed to avoid using the zeros of the multiresultant of each variable which are condition problems. Theoretical and numerical results will be given to show the efficiency of these methods. Finally, algorithms for the Mathematica codes are given.

Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model, Shymaa Mohammad Dadoa

Theses

The COVID-19 pandemic had shown the importance of the SEIR model in predicting the outcome of the disease spread and to find the best strategies to contain the pandemic. As this type of model has a limited number of compartments, many other models were derived from the SEIR model to cover, to the maximum, the complex dynamics of the disease spread. These extensions of the SEIR model bring natural validity questions: How can we validate these models? and how far/close are these extended models from giving us real insights into the pandemic?

This thesis investigates the SEIR epidemic model and …

Properties Of Certain Connected Graphs Related To Their Edge Metric Dimension, Sanabel Mahmoud Y. Bisharat

Theses

Metric dimension, resolving sets and edge metric dimension are very important invariants for the resolvability of graphs that have been studied and investigated intensively in the literature over the last decades. Their immense utilization in network topology, master mind games, robot navigation and representation of chemical compounds make their study very attractive. This thesis is concerned with the graph-theoretic properties of certain families of connected graphs related to their edge metric dimension. The main objective of this thesis is to study the comparison of metric dimension ver-sus edge metric dimension of certain families of graphs. The study investigates the relationship …

On The Generalized Hardy-Littlewood Maximal Operator, Namarig Hashim Hassan

Theses

No abstract provided.

Numerical And Theoretical Investigations Of Fractional Differential Equations, Sara Rafiq Al Fahel

Theses

Fractional calculus has been recently received huge attention from Mathematicians and engineers due to its importance in many real-life applications such as: fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present numerical algorithms for solving fractional IVPs and system of fractional IVPs where two types of fractional derivatives are used: Caputo-Fabrizio, and Atangana-Baleanu-Caputo derivatives. These algorithms are developed based on modified Adams-Bashforth method. In addition, we discuss the theoretical solution of special class of fractional IVPs. Several examples are discussed to illustrate the efficiency and accuracy of the present schemes.

Finitely Generated Modules Over A Principal Ideal Domain, Mariam Mutawa Meshaab Shemal Al-Dhaheri

Theses

This thesis covers the main theory of modules: modules, submodules, cosets, quotient modules, homomorphisms, ideals, direct sums, and some related topics. Using these notions, a theorem on the structure of finitely generated modules over domains of principal ideals is proved. As an application of this theorem, the theory of the structure of normal forms of matrices over various fields is presented.

Reproducing Kernel Method For Solving Fuzzy Initial Value Problems, Qamar Kamel Dallashi

Theses

In this thesis, numerical solution of the fuzzy initial value problem will be investigated based on the reproducing kernel method. Problems of this type are either difficult to solve or impossible, in some cases, since they will produce a complicated optimized problem. To overcome this challenge, reproducing kernel method will be modified to solve this type of problems. Theoretical and numerical results will be presented to show the efficiency of the proposed method.

Flow Of Quantum Genetic Lotka-Volterra Algebras On M2(ℂ), Sondos Muhammed Syam

Theses

In this thesis, a class of flow quantum Lotka-Volterra genetic algebras (FQLVG-A) is investigated and its structure is studied. Moreover, the necessary and sufficient conditions for the associativity and alternatively of FQGLV-A are derived. In addition, idempotent elements in FQGLV-A are found. Also, derivations of a class of FQLVG-A are described. Also, the automorphisms of a class of FQLVG-A and their positivity are examined.

Sum Of Squares With Q-Series, Gosper’S Q- Trigonometry, An New Identities Via An Extended Bailey Transform, Zina Al Houchan

Theses

This report is concerned about q-series and some of their applications. Firstly, Jacobi’s q-series proof for Legendre’s theorem on sums of four squares will be presented. By way of comparison, the classical approach of this result will be also discussed. Secondly, Gosper’s q-trigonometry will be introduced using Jacobi’s theta functions and the theory of elliptic functions shall be employed to confirm one of Gosper’s conjectures. As an application, a proof for Fermat’s theorem on the sums of squares will be provided. Thirdly, an extended version of Bailey’s transform will be established and as a consequence, a variety of new q-series …

The Q-Gauss Product, Q-Trigonometry Via Landen-Like Identities, And Positive Alternating Q-Series, Sarah Abo Touk

Theses

The object of this report is q-series and their relationship with certain special functions. Firstly, Jackson’s q-analogue of the Euler gamma function is introduced and a q-analogue for a famous formula of Gauss on products of the gamma function will be presented. Secondly, Jacobi’s theta functions will be discussed in details and new Landenlike half argument formulas will be established. As an application, q-trigonometric formulas shall be derived and a new proof for a well-known q-series relation of Jacobi will be given. Thirdly, an extended Bailey transform will be presented and a variety of new q-series will be deduced as …

Controllability And Observability Of Blood Glucose Levels And The Impact Of Covid-19 On Diabetic Patients, Mahra Salem Nasser Abdulla Alblooshi

Theses

Diabetes is a metabolic disorder that is characterized by high blood glucose concentrations resulting from insulin deficiency in case of type 1 or insulin inefficiency in case of type 2. While no cure for diabetes exists, the artificial pancreas is a possible way to manage diabetes, especially for type 1 diabetics. Where an artificial pancreas is a closed-loop control system with an integrated mathematical model. This control system imitates the function of a healthy pancreas. The first part of this thesis is concerned with the control system of an artificial pancreas that is based on Bergman’s minimal model of glucose-insulin …

Ovals And Niho Bent Functions In Small Dimensions, Rasha M. E. Shat

Theses

In this thesis hyperovals and ovals are considered in the projective plane PG(2,q), q = 2^m even. Traditionally these objects are studied algebraically via o-polynomials. In our work, a different approach is used by means of g-functions. These functions also provide a natural description of Niho bent functions. Using g-functions, all ovals and Niho bent functions are listed up to equivalency for dimensions m ≤ 6.

Stochastic Delay Differential Equations With Applications In Ecology And Epidemics, Hebatallah Jamil Alsakaji

Dissertations

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the …

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

Emirates Journal for Engineering Research

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response …

Universal Constraints Of Kleinian Groups And Hyperbolic Geometry, Hala Alaqad

Dissertations

Recent advances in geometry have shown the wide application of hyperbolic geometry not only in Mathematics but also in real-world applications. As in two dimensions, it is now clear that most three-dimensional objects (configuration spaces and manifolds) are modelled on hyperbolic geometry. This point of view explains a great many things from large-scale cosmological phenomena, such as the shape of the universe, right down to the symmetries of groups and geometric objects, and various physical theories. Kleinian groups are basically discrete groups of isometries associated with tessellations of hyperbolic space. They form the fundamental groups of hyperbolic manifolds. Over the …

Valuation Of Variance Swaps In Volatile Markets With Regime Switching, Mariam Zuwaid Salem Khamis Alshamsi

Mathematical Sciences Theses

Stochastic differential equations (SDEs) are extensively used to model various financial quantities. In the last decades, financial modeling by SDEs under regime-switching have been utilized to allow moving from an economic state to another. The aim of this research work is to tackle the pricing of variance swaps in a volatile market under regime switching model. SDEs under regime-switching models are more realistic but the solution is more complicated and may not exist analytically. Therefore, numerical methods for finance are explored. The study proposes a new SDE under regime-switching with high volatility model for the prices of the underlying financial …

Ground States And Gibbs Measures Of Λ-Model On Cayley Tree Of Order Two, Rauda Humaid Al Shamsi

Mathematical Sciences Theses

Abstract

Statistical mechanics deals with the average properties of a mechanical system. Some examples are; the water in a kettle, the atmosphere inside a room and the number of atoms in a magnet bar. These kinds of systems are made up of a large number of components, usually molecules. The observer has restricted power to consider all the components. All that can be done is to specify a few average quantities of the system such as its density, pressure or temperature. The main objective of statistical mechanics is to predict the relationship between the observable macroscopic properties of the system, …

Alexander Polynomials Of 3-Braid Knots, Marwa Emad Alrefai

Mathematical Sciences Theses

A knot is an embedding of a circle S¹ into the three-dimensional sphere S³. A component link is an embedding of n disjoint circles Ⅱᵢ^ⁿ =₁ S¹ into S³. The main objective of knot theory is to classify knots and links up to natural deformations called isotopies. While there is no simple algorithm that helps decide whether two given knots (or links) are equivalent, various topological invariants have been developed to help distinguish between non-equivalent knots and links. The Alexander polynomial ∆_L(t) is one of the oldest such tools. It …

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

Emirates Journal for Engineering Research

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.

Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, Raghad Kadhim Salih

Emirates Journal for Engineering Research

A proposed method is presented to solve n^th order linear retarded Volterra integro-differential equations (RVIDE's) numerically by using fourth-order block and Weddle methods. Comparison between numerical and exact results has been given in numerical examples for conciliated the accuracy of the results of the proposed scheme.

Shifted Third Kind Chebyshev Operational Matrix To Solve Bvps Over Infinite Interval, Bushra E. Khashem

Emirates Journal for Engineering Research

The main purpose of this research is to solve boundary value problems (BVPs) with an infinite number of boundary conditions. By reducing the infinite interval to finite interval that is large and approximating the variable using finite difference method, the resulting boundary value problem is reduced to linear system of algebraic equations with unknown shifted third kind chebychev coefficients. The applications are demonstrated via test examples.

Direct Iterative Algorithm For Solving Optimal Control Problems Using B-Spline Polynomials, Suha Shihab, Maha Delphi

Emirates Journal for Engineering Research

New technique for achieving an approximate solution to optimal control problems (OCPs) is considered in this paper. The algorithm is based upon B-spline polynomials (BSPs) approximation with state parameterization method. An important property concerning the B-spline functions is first presented then it is utilized to propose a modified restarted technique to reduce the number of unknown parameters with fast convergence. The method is applied through four illustrative examples and is compared with other results.