Other Mathematics Commons^™

Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard

Seaver College Research And Scholarly Achievement Symposium

We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.

Learning With Errors Parameter Analysis, Archana Parameswaran

Cybersecurity Undergraduate Research Showcase

We implement a systematic approach for generating, evaluating, and benchmarking Learning with Errors implementations in Sage Math by varying lattice dimensions, moduli, error standard deviations, and multiple error distributions to observe concrete security-efficiency tradeoffs. The security estimator maps parameter sets to concrete security levels and bits, while performance metrics measured computational efficiency and memory requirements. Results indicate that various distribution types do not significantly impact security, though binomial distributions require more computational overhead than discrete gaussian or uniform. Memory requirements increased when modulus q increased from 12289 to 65537. Larger dimensions have an exponentially growing requirement for memory, but this …

My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo

Journal of Stochastic Analysis

No abstract provided.

Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

The Importance Of Changing The High School Math Curriculum To Encourage More Students To Pursue A Degree In The Mathematics Field, Devin Cavicchi

Honors Projects in Mathematics and Economics

The mathematics field is a much larger field than many may think with mathematical analysis being involved in many jobs now, yet the need for more people to pursue mathematical careers and join the field is increasing daily. The focus of this thesis is to not only understand why some students are not inclined to pursue a degree in the mathematics field, but also to find methods to entice them to join the field. The literature researched demonstrated that experiences both in and out of the classroom have an impact on perception of the field, with the actual curriculum having …

Patterns Within The Collatz Conjecture, Kiel Harrison

SACAD: Scholarly Activities

The Collatz Conjecture, also known as 3n+1, one of the most famous unsolved problems in mathematics, has been forever out of reach of being truly solved. However, through the application of traces, there is now a new pathway forward to working out a potential solution. This study shows how this pathway was found, and what steps need to be taken to follow it.

Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

The Boltzmann-Enskog Equation With Brownian Forcing, Aurora Wallace

LSU Doctoral Dissertations

Interacting particle systems (IPS) are used to rigorously derive partial differential equations modeling macroscopic behavior given by systems of stochastic differential equa- tions in physics, biology, and other sciences. These systems model the time evolution of n interacting particles with desired dynamics. In the n-system studied here, only two parti- cles may interact at a time (binary collisions). The particles are exchangeable; that is, the ordering of the particles does not play a role, and the interaction between the ith particle and the jth particle models an elastic collision. In this thesis, we use the method of inter- acting particle …

An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih

Journal of Stochastic Analysis

No abstract provided.

American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah

Journal of Stochastic Analysis

No abstract provided.

About Fixed Points Of Quantum Channels, Raffaella Carbone

Journal of Stochastic Analysis

No abstract provided.

Subfitness In Distributive (Semi)Lattices, G. Bezhanishvili, J. Madden, M. A. Moshier, M. Tressl, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope.

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Hypergraph Association With Lie Algebra Of Upper Triangular Matrices And Its Application To Wireless Networks, Supriya S

Theses and Dissertations

A hypergraph is a generalized graph characterized by edges spanning more than one vertices describing multiple relationships among them. It provides a mathematical framework for comprehending and learning about a wide range of real-world challenges. On the other side, the theory of non-associative algebras, such as Jordan, Octonions, Malcev, and Lie, has found significant impetus in recent years. These structures proved intriguing from an algebraic standpoint; they generated novel concepts and approaches that aided in solving specific classic algebraic problems, also progressing towards application.

A preeminent observation that galvanizes this thesis is that hypergraph association is still unexplored in Lie …

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

Revisiting The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In previous work, we have explored some of the symmetries hidden in the multiplication tables of natural numbers and integers. In this article, we dive deeper into the hidden symmetries within the distribution of positive and negative integers. We also share various ideas to explore these symmetries in a classroom setting, encouraging active engagement and deeper understanding among students.

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.