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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 …

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 …