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Capstone Projects
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Recent Submissions
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(Nazarbayev University School of Science and Technology, 2019-08-07)The Nonlinear Schrödinger equation (NLSE) is a prototypical example of nonlinear partial differential equation. It is commonly used to describe propagation of light in nonlinear optical fibers and is of great importance ...
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(Nazarbayev University School of Science and Technology, 2019-08-08)Rogue waves are fascinating destructive phenomena in nature that have not been fully explained so far [1-3]. Oceanographers commonly agree that linear theories cannot provide explanations for their existence[6,7]. Only ...
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(Nazarbayev University School of Science and Technology, 2019-08-07)We prove that the Cauchy problem for a transport equation with algebraic nonlinearity of degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that the analyticity of solutions persists ...
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(Nazarbayev University School of Science and Technology, 2019-08-08)The aim of this project is to analyze three different population models such as Gompertz, Logistic and Generalized Logistic based USA population data. Finding the appropriate model is essential in actuarial application. ...
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(Nazarbayev University School of Science and Technology, 2019-08-08)Credit risk modelling of a portfolio of exposures is essential part of activity of every financial institution. However this procedure is complicated since the joint behavior of chosen exposures must be known. In this paper ...
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(Nazarbayev University School of Science and Technology, 2019-08-07)When one studies certain rings, it is natural to classify them according to certain properties. This project focuses on the study of properties of commutative rings associated with algebraic sets. In particular, we consider ...
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(Nazarbayev University School of Science and Technology, 2018)The Financial Risk Management (FRM) aims to identify, measure and manage risks in different sectors. One of the core things during such operations is measuring different dependencies. Linear correlation is known as one of ...
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(Nazarbayev University School of Science and Technology, 2018)A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic solutions and non-periodic solutions in the pull-in analysis of a graphene-based MEMS lumped parameter ...
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(Nazarbayev University School of Science and Technology, 2018-05-10)In this Capstone Project, we analyze a second order nonlinear ordinary differential equation (NODE), y^" (x)=f(y^',y) that is impossible to solve analytically. First, using the Taylor Power Series method, we obtain a series ...
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(Nazarbayev University School of Science and Technology, 2018-05)Recurrent neural networks are very powerful sequence models which are used for language modeling as well. Under correct regularization such as naive dropout these models are able to achieve substantial improvement in their ...
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(Nazarbayev University School of Science and Technology, 2018-05)We apply singularity analysis in complex time to investigate the solutions of a dynamical system of one degree of freedom related to the oscillations of a Micro-Electro-Mechanical System (MEMS) of nonlinear elasticity. ...
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(Nazarbayev University School of Science and Technology, 2018-05-13)This paper presents the application of an iterative approach for prediction of uranium price by model identification, parameter estimation and diagnostic checking which are designed by Box and Jenkins. In particular, the ...
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(Nazarbayev University School of Science and Technology, 2018-05-10)This project presents a generalization of the classical logistic and the Gompertz model by using two parameter power law exponent. The suggested generalized with two parameters models was shown by numerical example to be ...
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(Nazarbayev University School of Science and Technology, 2015-04)In this thesis, I present different discretization techniques for boundary integral method for Stokes flow in case of an incompressible Newtonian fluid. Boundary integral method (BIM) is one of many techniques that are ...
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(Nazarbayev University School of Science and Technology, 2015)Separation of data into distinct groups is one of the most important tools of learning and means of obtaining valuable information from data. Cluster analysis studies the ways of distributing objects into groups with similar ...
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(Nazarbayev University School of Science and Technology, 2016-05)In this report we present an SEIS model for infectious diseases with latent period and no immune response for spatially heterogeneous environment. Spatial heterogeneity is designed by several metapopulations. It was shown ...
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(Nazarbayev University School of Science and Technology, 2015)The paper aims at developing new point compression algorithms which are useful in mobile communication systems where Elliptic Curve Cryptography is employed to achieve secure data storage and transmission. Compression ...
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(Nazarbayev University School of Science and Technology, 2016)In this Capstone Project, we worked with a class of closure systems called convex geometries, which are closure systems with a closure operator that satisfies the anti-exchange property. We first looked at the result of ...
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(Nazarbayev University School of Science and Technology, 2016-05)The goal of this project is to calculate the temperature distribu- tion of certain pressure-driven non-Newtonian ows inside a circular tube. The rheology under consideration is the type in which the shear stress is ...
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(Nazarbayev University School of Science and Technology, 2016)In this paper we study a stochastic two-particle system on Z where particles interact each other by pushing dynamics. We derive the explicit formulas of the transition probability and of the probability distributions of ...
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