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Full-Text Articles in Physical Sciences and Mathematics
Vertex-Relaxed Graceful Labelings Of Graphs And Congruences, Florin Aftene
Vertex-Relaxed Graceful Labelings Of Graphs And Congruences, Florin Aftene
Masters Theses & Specialist Projects
A labeling of a graph is an assignment of a natural number to each vertex
of a graph. Graceful labelings are very important types of labelings. The study of graceful labelings is very difficult and little has been shown about such labelings. Vertex-relaxed graceful labelings of graphs are a class of labelings that include graceful labelings, and their study gives an approach to the study of graceful labelings. In this thesis we generalize the congruence approach of Rosa to obtain new criteria for vertex-relaxed graceful labelings of graphs. To do this, we generalize Faulhaber’s Formula, which is a famous result …
Cayley Graphs Of Psl(2) Over Finite Commutative Rings, Kathleen Bell
Cayley Graphs Of Psl(2) Over Finite Commutative Rings, Kathleen Bell
Masters Theses & Specialist Projects
Hadwiger's conjecture is one of the deepest open questions in graph theory, and Cayley graphs are an applicable and useful subtopic of algebra.
Chapter 1 will introduce Hadwiger's conjecture and Cayley graphs, providing a summary of background information on those topics, and continuing by introducing our problem. Chapter 2 will provide necessary definitions. Chapter 3 will give a brief survey of background information and of the existing literature on Hadwiger's conjecture, Hamiltonicity, and the isoperimetric number; in this chapter we will explore what cases are already shown and what the most recent results are. Chapter 4 will give our decomposition …
Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen
Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen
Masters Theses & Specialist Projects
This thesis aims to investigate the controllability and observability of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally …
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Masters Theses & Specialist Projects
The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …
Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam
Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam
Masters Theses & Specialist Projects
Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …