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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Decompositions Of The Complete Mixed Graph By Mixed Stars, Chance Culver
Decompositions Of The Complete Mixed Graph By Mixed Stars, Chance Culver
Electronic Theses and Dissertations
In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions …
Calculating Infinite Series Using Parseval's Identity, James R. Poulin
Calculating Infinite Series Using Parseval's Identity, James R. Poulin
Electronic Theses and Dissertations
Parseval's identity is an equality from Fourier analysis that relates an infinite series over the integers to an integral over an interval, which can be used to evaluate the exact value of some classes of infinite series. We compute the exact value of the Riemann zeta function at the positive even integers using the identity, and then we use it to compute the exact value of an infinite series whose summand is a rational function summable over the integers.
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
Electronic Theses and Dissertations
What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this first passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a fixed n and also the posterior distribution of m when …
Gray Codes In Music Theory, Isaac L. Vaccaro
Gray Codes In Music Theory, Isaac L. Vaccaro
Electronic Theses and Dissertations
In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier …
Trees With Unique Italian Dominating Functions Of Minimum Weight, Alyssa England
Trees With Unique Italian Dominating Functions Of Minimum Weight, Alyssa England
Electronic Theses and Dissertations
An Italian dominating function, abbreviated IDF, of $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that for every vertex $v \in V(G)$ with $f(v)=0$, we have $\sum_{u \in N(v)} f(u) \ge 2$. That is, either $v$ is adjacent to at least one vertex $u$ with $f(u) = 2$, or to at least two vertices $x$ and $y$ with $f(x) = f(y) = 1$. The Italian domination number, denoted $\gamma_I$(G), is the minimum weight of an IDF in $G$. In this thesis, we use operations that join two trees with a single edge in order …
Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly
Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly
Electronic Theses and Dissertations
Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
Electronic Theses and Dissertations
In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …
Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur
Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur
Electronic Theses and Dissertations
Artificial Neural Network (ANN) models have recently become de facto models for deep learning with a wide range of applications spanning from scientific fields such as computer vision, physics, biology, medicine to social life (suggesting preferred movies, shopping lists, etc.). Due to advancements in computer technology and the increased practice of Artificial Intelligence (AI) in medicine and biological research, ANNs have been extensively applied not only to provide quick information about diseases, but also to make diagnostics accurate and cost-effective. We propose an ANN-based model to analyze a patient's electrocardiogram (ECG) data and produce accurate diagnostics regarding possible heart diseases …
Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam
Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam
Electronic Theses and Dissertations
The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …
Explicit Pseudo-Kähler Metrics On Flag Manifolds, Thomas A. Mason Iii
Explicit Pseudo-Kähler Metrics On Flag Manifolds, Thomas A. Mason Iii
Electronic Theses and Dissertations
The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) Kähler structure, famously used to realize the group's irreducible representations in holomorphic sections of certain line bundles (Borel-Weil theorem). Less well-known are the (indefinite) invariant pseudo-Kähler structures they also admit, which can be used to realize the same representations in higher cohomology of the sections (Bott), and whose analogues in a non-compact setting lead to new representations (Kostant-Langlands). The purpose of this thesis is to give an explicit description of these metrics in the case of the unitary group G=Un.