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Mathematics: Recent submissions

  • (P,Q)-SUB-LAPLACIANS ON THE HEISENBERG GROUP 
    Abdikarim, Aidana; Suragan, Durvudkhan (Nazarbayev University School of Sciences and Humanities, 2020-08-01)
    The main purpose of this capstone project is to do some analysis related to (p,q)-sub-Laplacians on the Heisenberg group. In the first part of the project, Green’s identities for (p,q)-sub-Laplacians are given on the ...
  • Simulations of Implied Volatility and Option Pricing using Neural Networks and Finite Difference Methods for Heston Model 
    Arziyev, Sukhrat (Nazarbayev University School of Sciences and Humanities, 2020-04-30)
    The theory of option pricing made a dramatic step forward when Black and Scholes published a centennial paper with a solution for the prices of European call and put options. However, their solution only deals with the ...
  • Pricing Convertible Bonds by Finite Element Method 
    Kazbek, Rakhymzhan (Nazarbayev University School of Sciences and Humanities, 2020-05-07)
    In this thesis, the proposed problem is to solve the system of two-coupled Black-Scholes equations, which is the so called TF (Tsiveriotis and Fernandes) model [16], for pricing the convertible bonds by the finite element ...
  • A Finite Element Approach to Solving Leland Model for Options Pricing 
    Zhumakhanova, Gulzat (Nazarbayev University School of Sciences and Humanities, 2020-04-30)
    In this thesis work, the Leland model for pricing of European options is studied. Firstly, the derivation of the Leland model is introduced by using Ito’s lemma and synthesized replicate portfolio methodology. Then the ...
  • Some applications of potential theory for a degenerate type diffusion equation 
    Tengel, Kassymkhan (Nazarbayev University School of Sciences and Humanities, 2020-04-20)
    This thesis is aimed to study boundary conditions for heat potentials for degeneratetype diffusion equations with initial condition and conductivity coefficient given by a time variable. Equations can be one-dimensional ...
  • Experimental study of Manifold learning and tangent propagation 
    Aman, Ayazhan (Nazarbayev University School of Sciences and Humanities, 2020-05-12)
    In many data mining problems dealing with artificially high-dimensional data, can cause a lot of difficulties. This is due to the fact that interpreting a high-dimensional data can be very challenging. There are several ...
  • Analysis of Dead Core Phenomena in Reaction-Diffusion Problems 
    Sabit, Fariza (Nazarbayev University School of Sciences and Humanities, 2020-05-10)
    For some semilinear parabolic problems of reaction-diffusion, a dead core - a region of zero reactant concentration - may be formed in finite time. We study the large time behavior of the solution and give an estimate for ...
  • Calculation of manifold’s tangent space at a given point from noisy data 
    Toleubek, Moldir (Nazarbayev University School of Sciences and Humanities, 2020-05-04)
    Recently, several studies have been conducted in a field of machine learning to construct manifolds from data in a complex multidimensional space. Therefore manifold learning becomes remarkably attractable among researchers. ...
  • Robust Prediction with Risk Measures 
    Duisenbay, Yerlan (Nazarbayev University School of Sciences and Humanities, 2020-04-29)
    This thesis deals with coherent risk measures and its simulation with respect to different probability distributions. This study gives a numerical scheme to approximate any coherent risk measure via a sum of specific ...
  • Soliton surface associated with the WDVV equation for n = 3 case 
    Zhadyranova, A.A.; Myrzakul, Zhanbota (IOP Publishing, 2019-11-01)
    his paper describes the soliton surfaces approach to the Witten-Dijkgraaf-E.Verlinde-H. Verlinde (WDVV) equation. We constructed the surface associated with the WDVV equations using Sym-Tafel formula, which gives a connection ...
  • Classifying equivalence relations in the Ershov hierarchy 
    Mustafa, Manat; Bazhenov, Nikolay; Mauro, Luca San; Sorbi, Andrea; Yamaleev, Mars (Springer, 2020-02-13)
    Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽c. This gives rise to a rich degree structure. ...
  • Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids 
    Wei, Dongming; Al-Ashhab, Samer (Elsevier, 2019-04-20)
    The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, ...
  • Constructing Word Embeddings from the Random Hyperbolic Graph 
    Nurmukhamedov, Sultan (Nazarbayev University School of Sciences and Humanities, 2020-04-30)
    Recent studies have shown that the appropriate space for word embeddings is not the Euclidean space, but negatively curved, hyperbolic space. We randomly throw points in the hyperbolic disc and claim that these points are ...
  • Nonlinear Schrödinger-Airy Equation in Sobolev Spaces of Low Regularity 
    Sakayeva, Zhanna (Nazarbayev University School of Sciences and Humanities, 2020)
    The Nonlinear Schrödinger-Airy equation is one of the general examples of dispersive nonlinear partial differential equations. It is commonly used to characterize the nonlinear propagation of light pulses in optical ...
  • Finite Elements Solutions to the Black - Scholes Equation 
    Zhanatova, Nazym (Nazarbayev University School of Sciences and Humanities, 2020-05-01)
    Nowadays, for the financial industry it is important to implement mathematical tools of the advanced level. World’s well-known economists Fischer Black and Myron Scholes introduced the distinguished equation for option ...
  • Protein Family Classification using embedding methods 
    Saduakhas, Damilya (Nazarbayev University School of Sciences and Humanities, 2020-04-30)
    This capstone project examines the performance of existing embedding based alignment-free methods for protein family classification tasks. The distributed continuous representation of biological sequences such as DNA and ...
  • Semantics- and Syntax-related Subvectors in the Skip-gram Embeddings 
    Tezekbayev, Maxat (Nazarbayev University School of Sciences and HumanitiesNazarbayev University School of Sciences and Humanities, 2020)
    This project presents that using a modified version of Skip-gram with negative sampling with weight tying proposed by Assylbekov and Takhanov (2019) word embedding of each word can be decomposed into two subvectors: x ...
  • Analytical and numerical investigations of thecollapse of blood vessels with nonlinear wallmaterial embedded in nonlinear soft tissues 
    Ghazy, Mohammed; Elgindi, Mohamed B.; Wei, Dongming (Alexandria Engineering Journal, 2018-11-22)
    In this paper, shapes of nonlinear blood vessels, surrounded by nonlinear soft tissues,and buckled due to radial pressure are solved for analytically and numerically. The blood flow ratesthrough the bucked shapes are then ...
  • On the TASEP with Second Class Particles 
    Lee, Eunghyun (National Academy of Science of Ukraine, 2018-01-18)
    In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle ...
  • L-P-CAFFARELLI-KOHN-NIRENBERG TYPE INEQUALITIES ON HOMOGENEOUS GROUPS 
    Ozawa, Tohru; Ruzhansky, Michael; Suragan, Durvudkhan (OXFORD UNIV PRESS, 2019-03)
    We prove L-P-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already ...