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Articles 1 - 9 of 9
Full-Text Articles in Other Mathematics
Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev
Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev
Masters Theses & Specialist Projects
The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we …
Roman Domination Cover Rubbling, Nicholas Carney
Roman Domination Cover Rubbling, Nicholas Carney
Electronic Theses and Dissertations
In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the …
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.
Electronic Theses, Projects, and Dissertations
Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
Journal Articles
The metric d(A,B)=trA+trB−2tr(A1∕2BA1∕2)1∕21∕2 on the manifold of n×n positive definite matrices arises in various optimisation problems, in quantum information and in the theory of optimal transport. It is also related to Riemannian geometry. In the first part of this paper we study this metric from the perspective of matrix analysis, simplifying and unifying various proofs. Then we develop a theory of a mean of two, and a barycentre of several, positive definite matrices with respect to this metric. We explain some recent work on a fixed point iteration for computing this Wasserstein barycentre. Our emphasis is on ideas natural to …
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Electronic Theses, Projects, and Dissertations
This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can be used to construct Leibniz's Harmonic Triangle and show how both triangles relate to combinatorics and arithmetic through the …
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Electronic Theses and Dissertations
There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Undergraduate Theses and Capstone Projects
This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …
Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we …
Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier
Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier
Electronic Theses and Dissertations
We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound …