Graphs Of Classroom Networks,
2015
Georgia Southern University
Graphs Of Classroom Networks, Rebecca Holliday
College of Graduate Studies: Theses & Dissertations
In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …
Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications,
2015
Georgia Southern University
Labeled Trees And Spanning Trees: Computational Discrete Mathematics And Applications, Demet Yalman
College of Graduate Studies: Theses & Dissertations
In this thesis, we examine two topics. In the first part, we consider Leech tree which is a tree of order n with positive integer edge weights such that the weighted distances between pairs of vertices are exactly from 1 to n choose 2. Only five Leech trees are known and some non-existence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered in recent years. In this thesis, such Leech-type questions on distances between leaves are studied as well as some other labeling questions …
Decomposing The Blocks Of A Steiner Triple System Of Order 4v-3 Into Partial Parallel Classes Of Size V-1,
2015
Michigan Technological University
Decomposing The Blocks Of A Steiner Triple System Of Order 4v-3 Into Partial Parallel Classes Of Size V-1, Leah C. Tollefson
Dissertations, Master's Theses and Master's Reports
In this report we present a summary and our new results on finding partial parallel classes of uniform size of Steiner triple systems, STS(v). We show several results for STS(4v - 3), where v = 3 mod 12 and v = 9 mod 12. In Chapter 1 we provide background knowledge and introduce the problem. In Chapter 2 we discuss some important known results to the problem, introduce the needed ingredients, and explain the methodology of the construction. Finally, in Chapter 3, we conclude with a summary and discuss possibilities for future work.
Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products,
2015
Chapman University
Quaternionic Hardy Spaces In The Open Unit Ball And Half Space And Blaschke Products, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.
Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem,
2015
Chapman University
Self-Mappings Of The Quaternionic Unit Ball: Multiplier Properties, Schwarz-Pick Inequality, And Nevanlinna-Pick Interpolation Problem, Daniel Alpay, Vladimir Bolotnikov, Fabrizio Colombo, Irene Sabadini, Fabrizio Colombo
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study several aspects concerning slice regular functions mapping the quaternionic open unit ball B into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space H2(B). In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.
Infinite Product Representations For Kernels And Iteration Of Functions,
2015
Chapman University
Infinite Product Representations For Kernels And Iteration Of Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping R in one complex variable, and its iterations.
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters,
2015
Chapman University
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the system theory notion of state-space realization of matrix-valued rational functions, we describe the Ruelle operator associated with wavelet filters. The resulting realization of infinite products of rational functions have the following four features: 1) It is defined in an infinite-dimensional complex domain. 2) Starting with a realization of a single rational matrix-function M, we show that a resulting infinite product realization obtained from M takes the form of an (infinitedimensional) Toeplitz operator with the symbol that is a reflection of the initial realization for M. 3) Starting with a subclass of rational matrix functions, including scalar-valued ones corresponding …
Wiener-Chaos Approach To Optimal Prediction,
2015
Chapman University
Wiener-Chaos Approach To Optimal Prediction, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this work we combine Wiener chaos expansion approach to study the dynamics of a stochastic system with the classical problem of the prediction of a Gaussian process based on part of its sample path. This is done by considering special bases for the Gaussian space G generated by the process, which allows us to obtain an orthogonal basis for the Fock space of G such that each basis element is either measurable or independent with respect to the given samples. This allows us to easily derive the chaos expansion of a random variable conditioned on part of the sample …
Spectral Theory For Gaussian Processes: Reproducing Kernels, Random Functions, Boundaries, And L2-Wavelet Generators With Fractional Scales,
2015
Chapman University
Spectral Theory For Gaussian Processes: Reproducing Kernels, Random Functions, Boundaries, And L2-Wavelet Generators With Fractional Scales, Daniel Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by a host of applications, e.g., in mathematical physics, and in stochastic differential equations, and their use in financial models. In this paper, we show that, for three classes of cases in the correspondence, it is possible to obtain explicit formulas which are amenable to computations of the respective Gaussian stochastic processes. For achieving this, we first develop two functional analytic tools. They are: …
Combinatorial Game Theory: An Introduction To Tree Topplers,
2015
Georgia Southern University
Combinatorial Game Theory: An Introduction To Tree Topplers, John S. Ryals Jr.
College of Graduate Studies: Theses & Dissertations
The purpose of this thesis is to introduce a new game, Tree Topplers, into the field of Combinatorial Game Theory. Before covering the actual material, a brief background of Combinatorial Game Theory is presented, including how to assign advantage values to combinatorial games, as well as information on another, related game known as Domineering. Please note that this document contains color images so please keep that in mind when printing.
Extremal Theorems For Degree Sequence Packing And The Two-Color Discrete Tomography Problem,
2015
Saint Vincent College
Extremal Theorems For Degree Sequence Packing And The Two-Color Discrete Tomography Problem, Jennifer Diemunsch, Michael Ferrara, Sogol Jahanbekam, James Shook
Faculty Publications
No abstract provided.
Lucky Choice Number Of Planar Graphs With Given Girth,
2015
University of Colorado, Denver
Lucky Choice Number Of Planar Graphs With Given Girth, Axel Brandt, Jennifer Diemunsch, Sogol Jahanbekam
Faculty Publications
No abstract provided.
Domination Integrity Of Some Path Related Graphs,
2014
Saurashtra University
Domination Integrity Of Some Path Related Graphs, S. K. Vaidya, N. H. Shah
Applications and Applied Mathematics: An International Journal (AAM)
The stability of a communication network is one of the important parameters for network designers and users. A communication network can be considered to be highly vulnerable if the destruction of a few elements cause large damage and only few members are able to communicate. In a communication network several vulnerability measures like binding number, toughness, scattering number, integrity, tenacity, edge tenacity and rupture degree are used to determine the resistance of network to the disruption after the failure of certain nodes (vertices) or communication links (edges). Domination theory also provides a model to measure the vulnerability of a graph …
Private Out-Domination Number Of Generalized De Bruijn Digraphs,
2014
The Madura College
Private Out-Domination Number Of Generalized De Bruijn Digraphs, G. Marimuthu, B. Johnson
Applications and Applied Mathematics: An International Journal (AAM)
Dominating sets are widely applied in the design and efficient use of computer networks. They can be used to decide the placement of limited resources, so that every node has access to the resource through neighbouring node. The most efficient solution is one that avoids duplication of access to the resources. This more restricted version of minimum dominating set is called an private dominating set. A vertex v in a digraph D is called a private out-neighbor of the vertex u in S (subset of V(D)) if u is the only element in the intersection of in-neighborhood set of v …
Difference Cordial Labeling Of Graphs Obtained From Triangular Snakes,
2014
Sri Paramakalyani College
Difference Cordial Labeling Of Graphs Obtained From Triangular Snakes, R. Ponraj, S. S. Narayanan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we investigate the difference cordial labeling behavior of corona of triangular snake with the graphs of order one and order two and also corona of alternative triangular snake with the graphs of order one and order two.
A Study Of Graphical Permutations,
2014
University of Nevada, Las Vegas
A Study Of Graphical Permutations, Jessica Thune
UNLV Theses, Dissertations, Professional Papers, and Capstones
A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1
A Potential Foundation For Emergent Space-Time,
2014
University at Albany, State University of New York
A Potential Foundation For Emergent Space-Time, Kevin H. Knuth, Newshaw Bahreyni
Physics Faculty Scholarship
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an …
The Lp Relaxation Orthogonal Array Polytope And Its Permutation Symmetries,
2014
Air Force Institute of Technology
The Lp Relaxation Orthogonal Array Polytope And Its Permutation Symmetries, Andrew J. Geyer, Dursun A. Bulutoglu, Steven J. Rosenberg
Faculty Publications
Symmetry plays a fundamental role in design of experiments. In particular, symmetries of factorial designs that preserve their statistical properties are exploited to find designs with the best statistical properties. By using a result proved by Rosenberg [6], the concept of the LP relaxation orthogonal array polytope is developed and studied. A complete characterization of the permutation symmetry group of this polytope is made. Also, this characterization is verified computationally for many cases. Finally, a proof is provided.
Physics: Rethinking The Foundations,
2014
University at Albany, State University of New York
Physics: Rethinking The Foundations, Kevin H. Knuth
Physics Faculty Scholarship
Physics is traditionally conceived of as a set of laws that universally governs the behavior of physical systems. These laws, however they are decreed, are believed to govern the behavior of not only everything in the universe, but the form of the universe itself. However, this traditional concept of physics as a universal governance is at odds with our modern theories of quantum mechanics and relativity, which place the observer and information in a central role. In this talk, I aim to rethink the foundations and attempt to build physics from the bottom up based on a very simple foundational …
Fibonacci Number Of The Tadpole Graph,
2014
Kennesaw State University
Fibonacci Number Of The Tadpole Graph, Joe Demaio, John Jacobson
Faculty Articles
In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2) and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph …
