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Applied Mathematics

2012

All Theses

Articles 1 - 8 of 8

Full-Text Articles in Physical Sciences and Mathematics

Convex Hull Characterization Of Special Polytopes In N-Ary Variables, Ruobing Shen Dec 2012

Convex Hull Characterization Of Special Polytopes In N-Ary Variables, Ruobing Shen

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This paper characterizes the convex hull of the set of n-ary vectors that are lexicographically less than or equal to a given such vector. A polynomial number of facets is shown to be sufficient to describe the convex hull. These facets generalize the family of cover inequalities for the binary case. They allow for advances relative to both the modeling of integer variables using base-n expansions, and the solving of n-ary knapsack problems with weakly super-decreasing coefficients.

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Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao Aug 2012

Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao

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This paper concerns robust parameter estimation of the two-parameter Weibull distribution and the two-parameter Birnbaum-Saunders distribution. We use the proposed method to estimate the distribution parameters from (i) complete samples with and without contamination (ii) type-II censoring samples, in both distributions. Also, we consider the maximum likelihood estimation and graphical methods to compare the maximum likelihood estimation and graphical method with the proposed method based on quantile. We find the advantages and disadvantages for those three different methods.

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Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw Aug 2012

Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw

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In this paper, we examine various branch and bound algorithms for a minimum congestion origin-destination integer multi-commodity flow problem.
The problem consists of finding a routing such that the congestion of the most congested arc is minimum. For our implementation, we assume that all demands are known a priori.
We provide a mixed integer linear programming formulation of our problem and propose various new branching rules to solve the model. For each rule, we provide theoretical and experimental proof of their effectiveness.
In order to solve large instances, that more accurately portray real-world applications, we outline a path formulation model …

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A Set Of Tournaments With Many Hamiltonian Cycles, Hayato Ushijima-Mwesigwa Aug 2012

A Set Of Tournaments With Many Hamiltonian Cycles, Hayato Ushijima-Mwesigwa

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For a random tournament on $3^n$ vertices, the expected number of Hamiltonian cycles is known to be $(3^n -1)!/2^{3^n}$. Let $T_1$ denote a tournament of three vertices $ {v_1, v_2, v_3}$. Let the orientation be such that there are directed edges from $v_1 $to $v_2$ , from $v_2$ to $v_3$ and from $v_3$ to $ v_1$. Construct a tournament $T_i$ by making three copies of $T_{i-1}$, $T_{i-1}'$, $T_{i-1}''$ and $T_{i-1}'''$. Let each vertex in $T_{i-1}'$ have directed edges to all vertices in $T_{i-1}''$, similarly place directed edges from each vertex in $T_{i-1}''$ to all vertices in $T_{i-1}'''$ and from $T_{i-1}'''$ …

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Local Polynomial Regression With Application To Sea Surface Temperatures, Michael Finney Aug 2012

Local Polynomial Regression With Application To Sea Surface Temperatures, Michael Finney

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Our problem involves methods for determining the times of a maximum or minimum for a general mean function in time series data. The methods explored here involve polynomial smoothing. In theory, the methods calculate a general number of derivatives of the estimated polynomial. Using these techniques, we wish to find a balance between error, variance, and complexity and apply it to a time series of sea surface temperatures. We will first explore the theory behind the method and then find a way to optimally apply it to our data.

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Enhanced Physics Schemes For The 2d Ns-Alpha Models Of Incompressible Flow, Michael Dowling May 2012

Enhanced Physics Schemes For The 2d Ns-Alpha Models Of Incompressible Flow, Michael Dowling

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In this thesis, we study algorithms for the 2D NS-alpha model of incompressible flow. These schemes conserve both discrete energy and discrete enstrophy in the absence of viscous and external forces, and otherwise admit exact balances for them analogous to those of true fluid flow. This model belongs to a very small group that conserves both of these quantities in the continuous case, and in this work, we develop finite element algorithms for the vorticity-stream formulation of this model that will preserve numerical energy and enstrophy in the computed solutions.

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Numerical Study For A Viscoelastic Fluid-Structure Interaction Problem, Shuhan Xu May 2012

Numerical Study For A Viscoelastic Fluid-Structure Interaction Problem, Shuhan Xu

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In this thesis, we consider a viscoelastic flow in a moving domain, which has significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time descritization is carried by either the implicit Euler method or the Crank-Nicolson method. Numerical results are presented for a fluid in a moving domain, where the boundary movement is specified by a given function. Then, we extend our work to a fluid-structure interaction problem. This system consists of a two-dimensional viscoelastic …

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Champion Primes For Elliptic Curves, Jason Hedetniemi May 2012

Champion Primes For Elliptic Curves, Jason Hedetniemi

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Let Ea,b be the elliptic curve y2 = x3 + ax + b over Fp. A well known result of Hasse states that over Fp
(p+1) - 2p½ ≤ #Ea,b ≤ (p+1)+2p½
If #Ea,b = (p+1) + floor(2p½) over Fp and Ea,b is nonsingular, then we call p a champion prime for Ea,b. We will discuss methods for finding champion primes for elliptic curves. In addition, we will show that the set of elliptic curves which have a champion prime has density one.

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