Lower Bounds For The Total Distance $K$-Domination Number Of A Graph,
2025
Rice University
Lower Bounds For The Total Distance $K$-Domination Number Of A Graph, Randy R. Davila
Theory & Applications of Graphs
For $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total distance $k$-dominating set} of $G$ is a set of vertices $S \subseteq V(G)$ such that every vertex in $G$ is within distance $k$ to some vertex of $S$ other than itself. The \emph{total distance $k$-domination number} of $G$ is the minimum cardinality of a total $k$-dominating set in $G$ and is denoted by $\gamma_{k}^t(G)$. When $k=1$, the total $k$-domination number reduces to the \emph{total domination number}, written $\gamma_t(G)$; that is, $\gamma_t(G) = \gamma_{1}^t(G)$. This paper shows that several known lower bounds on the total domination number generalize …
The Integer-Antimagic Spectra Of A Weak Join Of Hamiltonian Graphs,
2025
Istanbul University-Cerrahpasa
The Integer-Antimagic Spectra Of A Weak Join Of Hamiltonian Graphs, Ugur Odabasi, Dan Roberts, Richard M. Low
Theory & Applications of Graphs
A simple graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is \emph{$\mathbb{Z}_{k}$-antimagic} if there exists a function $f: E(G) \to \mathbb{Z}_{k} \backslash \{0\}$ such that the induced function $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is injective. The \textit{integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}$. A \emph{weak join} of vertex-disjoint graphs is the collection of the graphs with additional simple edges (possibly none) between the original graphs. In this paper, we characterize IAM$(H)$ where $H$ is a weak join of Hamiltonian graphs.
Prime Labelings On A 3xn Grid Graph,
2025
University of Pittsburgh - Johnstown
Prime Labelings On A 3xn Grid Graph, Stephen J. Curran, Matt A. Ollis
Theory & Applications of Graphs
It is conjectured that the mxn grid graph has a prime labeling for all positive integers m and n. It is known that for any prime p and any integer n such that 1≤n≤p2, there exists a prime labeling on the pxn grid graph Pm x Pn. Also, it is known that the ladder P2 x Pn has a prime labeling for all positive integers n. We assume that Goldbach's Even Conjecture and a strengthened variant of Lemoine's Conjecture are true in order to show that the 3xn grid graph P …
Agent-Based Modeling: Introduction And Actuarial Applications,
2025
Bryant University
Agent-Based Modeling: Introduction And Actuarial Applications, Rick Gorvett
Mathematics and Economics Faculty Working Papers
Agent-based modeling (ABM) has become an important and valued approach to modeling complex systems. In this paper, I advocate for actuaries to recognize the complex systems-nature of socioeconomic and risk processes and for ABM models to become a regular resource in our actuarial toolkits. These models allow for the observation of potential macro-behavior emerging from the underlying agent-level micro-activity and characteristics. Therefore, ABM models can provide significant insight into the quantification of risk and the identification of optimal strategies. This paper is an introduction and guide to ABM models, and it includes several case studies to illustrate their utility.
A Selective Discontinuous Galerkin Implicit Particle-In-Cell Method For Plasma Simulation With Improved Interpolation,
2025
Missouri University of Science and Technology
A Selective Discontinuous Galerkin Implicit Particle-In-Cell Method For Plasma Simulation With Improved Interpolation, Siyu Wu, Yang Li, Hongtao Liu, Xiaoming He, Yong Cao
Mathematics and Statistics Faculty Research & Creative Works
This article dynamically incorporates multiple ideas into the existing direct implicit particle-in-cell (DIPIC) method for plasma simulation, in order to dramatically improve the DIPIC method for its local mesh refinement needs based on Cartesian meshes as well as its interpolation needs based on the locally refined meshes. One key tool is to utilize the selective discontinuous Galerkin method, which is based on the interior penalty discontinuous Galerkin formulation and the regular local finite element basis functions, as the electric field solver in the DIPIC simulation. This hybrid type finite element method combines the advantages of both continuous and discontinuous finite …
A Short Proof Of The Lemma Of The Logarithmic Derivative In Several Complex Variables,
2025
Texas A&M University-San Antonio
A Short Proof Of The Lemma Of The Logarithmic Derivative In Several Complex Variables, Qi Han, Jingbo Liu
All Faculty Scholarship (Archived)
In this work, we provide a concise proof of the logarithmic derivative lemma in Cn. We start by giving a complete proof of a critical result by Biancofiore and Stoll (Ann. of Math. Stud., No. 100, 29–45, 1981) via matrix theory, which is central to this area of study. Then, we follow Li (Trans. Amer. Math. Soc. 363, 6257–6267, 2011) and Ye (Math. Z. 222, 81–95, 1996) to present the shortest proof to date.
Math 115: College Algebra Instructor Guide,
2025
CUNY Queens College
Math 115: College Algebra Instructor Guide, Seth Lehman
Open Educational Resources
OER instructor guide for Math 115, College Algebra, Queens College
Conditional Quantization For Some Discrete Distributions,
2025
The University of Texas Rio Grande Valley
Conditional Quantization For Some Discrete Distributions, Edgar A. Gonzalez, Mrinal Kanti Roychowdhury, David A. Salinas, Vishal Veeramachaneni
School of Mathematical & Statistical Sciences Faculty Publications
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support {12𝑛:𝑛∈ℕ}. We have …
All Graphs Of Order N With Distinguishing Number N−1 Or N − 2,
2025
Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
All Graphs Of Order N With Distinguishing Number N−1 Or N − 2, Andi Pujo Rahadi, Edy Tri Baskoro, Suhadi Wido Saputro
Theory & Applications of Graphs
Let G be a simple connected graph. The distinguishing number of G, denoted by D(G), is the least integer d such that G has a vertex d-labeling preserved only by the trivial automorphism. In this paper, we characterize all graphs of order n with distinguishing number n − 1, or n − 2.
Similarity Metrics, Metrics, And Conditionally Negative Definite Functions,
2025
Chapman University
Similarity Metrics, Metrics, And Conditionally Negative Definite Functions, Daniel Alpay, Liora Mayats-Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give an example of a similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Global Attractivity Of Positive Solutions Of Higher Order Nonlinear Difference Equations And Its Applications,
2025
Mississippi State University
Global Attractivity Of Positive Solutions Of Higher Order Nonlinear Difference Equations And Its Applications, Abdulaziz Almaslokh
Theses and Dissertations
Difference equations play an effective role in many mathematical models that represent some phenomena in different fields such as physics, economics, engineering and biology. From this perspective, studying and analyzing such equations are interesting issues for the advancement of scientific research. In particular, studying the asymptotic behavior of positive solutions of some population models that are a system of difference equations has become a necessity. In this dissertation, we examine the global attractivity of positive solutions of certain higher order nonlinear difference equations and apply these results to some population models.
Entanglement Distribution Of Universal Quantum Cloners,
2025
Wofford College
Entanglement Distribution Of Universal Quantum Cloners, James B. Daughtry
Student Scholarship
Szab`o et al. [4] show that universal quantum cloning machines may be used to manipulate entanglement between bipartite states. Entanglement is measured with concurrence, C, and it is shown that as the fidelity of the cloner improves, more entanglement transfers from the reference to the cloned state. This thesis characterizes the nature of this entanglement transfer by analyzing the entanglement distribution of the cloner. In this analysis we will show that entanglement is generally destroyed after cloning except in cases where there is no cloning, two identical qubits are created, or there is complete qubit transfer. Along with …
On The Special Cases Of Carmichael’S Totient Conjecture,
2025
University of Nevada, Las Vegas
On The Special Cases Of Carmichael’S Totient Conjecture, Christopher Saito
UNLV Theses, Dissertations, Professional Papers, and Capstones
Euler’s totient function, φ(n), is the arithmetic function defined as the number of positive integers less than or equal to n that are relatively prime to n. In his 1922 paper [3], Professor R. D. Carmichael conjectured that for each positive integer n, there exists at least one positive integer m̸ = n such that φ(m) = φ(n).In this thesis, we consider some relevant literature and explore Carmichael’s totient conjecture for particular values of φ(n) = k. Our main consideration will be the set X_k = {n ∈ N : φ(n) = k}. In identifying X_k for k = 2^t, …
The Concept Of T-Basis And Vector-Valued Hardy Classes,
2025
Begin type...
The Concept Of T-Basis And Vector-Valued Hardy Classes, Bilal Bilalov, Sabina Rahib Sadigova
Turkish Journal of Mathematics
This paper introduces the concept of a t-basis generated by some bilinear mapping t(·;·). It is considered the vector-valued class Lp(X) := Lp(J; X), 1 ≤ p < +∞, where J = [−π, π] and X is a Banach space with the UMD property, and it is proven that the classical system of exponents {eint}n∈ℤ forms a t-basis for Lp(X), 1 < p < +∞. Using this fact, the Hardy vector classes nHp±(X), 1 < p < +∞, different from the classical ones, are defined, and an equivalent definition of these classes is given and some of their properties are studied. In addition, the concept of t-Riesz property of a system of exponentials is introduced in Lp(X), 1 < p < +∞, and it is proved that this system has the t-Riesz property. A new method is given for establishing the Plemelj–Sokhotski formulas for X-valued Cauchy type integrals when X has the UMD property. An abstract analogue of the “1/4-Kadets” theorem is obtained for …
Independent Vs. Signed Musicians: Does Thier Status Affect Their Success?,
2025
Bryant University
Independent Vs. Signed Musicians: Does Thier Status Affect Their Success?, Zachary Vincent
Honors Projects in Mathematics and Economics
As technology has advanced and become more widely available, and as the public learns more about the recording industry and its workings, more musicians are choosing not to sign with record labels, becoming independent musicians. This now raises the question: does a musician’s status of independent or signed determine their level of success? It has been previously found that independent musicians have a more difficult time competing with signed musicians due to the resources provided by record labels and the way labels negotiate with large streaming platforms, giving signed labels more opportunities to be seen in the public eye, but …
Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology,
2025
University of New Mexico
Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology, Mohammad Abirul Islam
Computer Science ETDs
We develop distributed robotics algorithms with analytical tools needed to define and analyze angle turned and distance traversed by robots executing geometric algorithms. We then use these analytical tools to obtain information, via sensor measurements, about an a priori unknown surface. Our contributions are threefold. First, we develop the Sketch Algorithm, which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance traversed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate that …
Analyticity, Superoscillations And Supershifts In Several Variables,
2025
Politecnico di Milano
Analyticity, Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing their highest Fourier component. A different way of thinking about superoscillations consists in realizing that it is possible to reproduce the exponential function far away from the origin by only knowing its value in a countable set of points near the origin. By using this perspective, one can extend the idea of superoscillations to functions that are not a sum of exponential functions, namely to the notion of supershift. The study …
Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions,
2025
Texas A&M International University
Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr
Theses and Dissertations
A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. …
Maximal Simple Regular Matroids,
2025
Syracuse University
Maximal Simple Regular Matroids, Elana Joy Israel
Dissertations - ALL
In 1980, Seymour completely classified regular matroids. In this thesis, we use this classification to provide a complete list of maximal simple regular matroids up through rank six. In each rank, exactly one of these is graphic. Additionally, there are one, two, and eight cographic, but not graphic, maximal simple regular matroids in ranks four, five, and six, respectively. In rank five, we also have the 10-element sporadic matroid, and in rank six we have a 12-element maximal simple regular matroid and 16-element maximal simple regular matroid, both of which are decomposable matroids that are not graphic, cographic, or sporadic. …
Asymptotics Of Fubini-Study Currents For Sequences Of Line Bundles,
2025
Syracuse University
Asymptotics Of Fubini-Study Currents For Sequences Of Line Bundles, Melody Ann Wolff
Dissertations - ALL
Let $(X,\omega)$ be a Kähler manifold, and $L_p$ be a sequence of line bundles on $X$ equipped with continuous hermitian metrics $h_p$. Let $\gamma_p$ be the Fubini-Study current and $h_p^{eq}$ the equilibrium metric corresponding to the metric $h_p$. Our goal is to generalize a theorem of Tian in Complex Geometry to a setting using arbitrary line bundles equipped with metrics with non-positive curvature. This amounts to finding sufficient conditions for $\gamma_p-c_1(L_p,h_p^{eq})$, when appropriately scaled, to converge to $0$ in the sense of currents. To achieve this goal, we imply methods of Demailly and the Oshawa-Takegoshi Extension Theorem to bound a …
