Browsing Mathematics (Faculty of) by Title
Now showing items 1816-1835 of 2994
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An Npz Model With State-Dependent Delay Due To Size-Structure In Juvenile Zooplankton
(Society for Industrial and Applied Mathematics, 2016)The study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs. We study a closed nutrient-phytoplankton-zooplankton (NPZ) model that includes size structure in the juvenile ... -
The Number Field Sieve for Barreto-Naehrig Curves: Smoothness of Norms
(University of Waterloo, 2015-05-20)The security of pairing-based cryptography can be reduced to the difficulty of the discrete logarithm problem (DLP) in finite fields of medium characteristic. The number field sieve is the best known algorithm for this ... -
The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for , the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
Numerical analysis of divergence-free discontinuous Galerkin methods for incompressible flow problems
(University of Waterloo, 2022-04-29)In the first major contribution of this thesis, we present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact ... -
Numerical analysis of space-time hybridized discontinuous Galerkin methods for incompressible flows
(University of Waterloo, 2022-08-09)Many industrial problems require the solution of the incompressible Navier-Stokes equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact ... -
Numerical Methods for Continuous Time Mean Variance Type Asset Allocation
(University of Waterloo, 2010-04-19)Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in ... -
Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications
(University of Waterloo, 2019-08-26)Hamilton-Jacobi-Bellman (HJB) equations are nonlinear controlled partial differential equations (PDEs). In this thesis, we propose various numerical methods for HJB equations arising from three specific applications. First, ... -
Numerical Methods for Long-Term Impulse Control Problems in Finance
(University of Waterloo, 2008-05-16)Several of the more complex optimization problems in finance can be characterized as impulse control problems. Impulse control problems can be written as quasi-variational inequalities, which are then solved to determine ... -
Numerical Methods for Nonlinear Equations in Option Pricing
(University of Waterloo, 2003)This thesis explores numerical methods for solving nonlinear partial differential equations (PDEs) that arise in option pricing problems. The goal is to develop or identify robust and efficient techniques that ... -
Numerical Methods for Optimal Stochastic Control in Finance
(University of Waterloo, 2008-06-17)In this thesis, we develop partial differential equation (PDE) based numerical methods to solve certain optimal stochastic control problems in finance. The value of a stochastic control problem is normally identical to the ... -
Numerical Methods for Optimal Trade Execution
(University of Waterloo, 2012-09-19)Optimal trade execution aims at balancing price impact and timing risk. With respect to the mathematical formulation of the optimization problem, we primarily focus on Mean Variance (MV) optimization, in which the two ... -
Numerical Methods for Pricing a Guaranteed Minimum Withdrawal Benefit (GMWB) as a Singular Control Problem
(University of Waterloo, 2011-08-23)Guaranteed Minimum Withdrawal Benefits(GMWB) have become popular riders on variable annuities. The pricing of a GMWB contract was originally formulated as a singular stochastic control problem which results in a Hamilton ... -
Numerical Methods for Real Options in Telecommunications
(University of Waterloo, 2004)This thesis applies modern financial option valuation methods to the problem of telecommunication network capacity investment decision timing. In particular, given a cluster of base stations (wireless network with a ... -
Numerical Modelling of Wind Storms in the Lower Great Lakes
(University of Waterloo, 2019-01-07)Convective storms are incredible meteorological events; the impact of just one storm can be extreme and widespread. On July 21 1998, a convective storm formed west of Lake Michigan, moving quickly across the lower Great ... -
Numerical Simulation of Nonlinear and Dispersive Wave Equations using Adaptive Mesh Refinement (AMR)
(University of Waterloo, 2020-06-24)Numerical solution of time dependent Partial Differential Equations plays an important role in different fluid flow modelling problems. Sometimes a little portion of the computational domain needs high grid resolution in ... -
Numerical Simulation of Surface Waves using Meshfree Methods
(University of Waterloo, 2009-04-27)Smoothed Particle Hydrodynamics (SPH) is a Lagrangian-based numerical method used for simulating problems in fluid and solid mechanics. In this thesis, a basic introduction to particle and Smoothed Particle (SP) approximations ... -
Numerical simulations of convection and gravity currents near the temperature of maximum density
(University of Waterloo, 2022-08-09)Recently, the dynamics of flows in cold freshwater (temperatures around the temperature of maximum density, 3.98 oC) has garnered much interest in the environmental fluid dynamics community. From a dynamical perspective, ... -
Numerical Simulations of Internal Solitary and Solitary-Like Waves: Wave Interactions and Instabilities
(University of Waterloo, 2019-05-31)Internal solitary and solitary-like waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a ... -
Numerical Simulations of Shoaling Internal Solitary Waves of Elevation
(University of Waterloo, 2015-04-13)We present high-resolution, two- and three-dimensional direct numerical simulations of laboratory-scale, fully nonlinear internal solitary waves of elevation shoaling onto and over a small-amplitude shelf. The three-dimensional, ...