Mathematics Commons^™

A Position Indicator With Applications In The Field Of Designing Forms With Artificial Intelligence, Ovidiu Ilie Șandru, Florentin Smarandache, Alexandra Șandru

Branch Mathematics and Statistics Faculty and Staff Publications

The indicators used so far within the Theory of Extension can be synthetically expressed by the notion of “position indicators”. More exactly, these indicators can be grouped in two main sub-categories: point-set position indicators and point-two sets position indicators. The secondary goal of this paper is to define these classifications, while the primary goal is that to extend the two notions to the most general notion of set-set position indicator.

Approches Neutrosophiques Et Plithogéniques En Science Des Données Et Analyse Multivariée : Contributions De La Ixe Réunion Ibéro-Américaine De Biométrie, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel-Basset

Branch Mathematics and Statistics Faculty and Staff Publications

Ce numéro spécial de "Neutrosophic Sets and Systems" rassemble une sélection de travaux remarquables présentés lors de la IXe Réunion Ibéro-américaine de Biométrie, qui a eu lieu les 8 et 9 juillet 2025 à Quito, en Équateur. Sous la direction d'une équipe éditoriale de prestige, ce volume explore l'application des approches neutrosophiques et plithogéniques dans divers domaines tels que la biométrie, la bioinformatique, la santé publique, l'éducation et l'économie. Les articles mettent en lumière la convergence entre les statistiques classiques et l'intelligence artificielle, illustrant comment les méthodes neutrosophiques offrent des outils puissants pour modéliser l'incertitude et la complexité des données …

Competition Super-Hypergraphs: Revealing Hierarchical Competition In Real-World Networks, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory provides a powerful language for modeling pairwise connections through vertices and edges [9, 20]. Hypergraphs generalize this idea by permitting hyperedges that join any number of vertices simultaneously [7], while super-hypergraphs iterate the Power-set operation to capture multi-level, hierarchical relationships among hyperedges [40, 22]. A competition hypergraph associates each prey species with a hyperedge containing all its predators, thereby encoding multi-way competition in ecological networks. In this work, we introduce the competition super-hypergraph, which lifts the competition concept to higher tiers of aggregation. We present its formal definition, explore theoretical properties, and illustrate its practical use in real-world …

Cvitlnn: A Hybrid Approach Based On Vision Transformer And Liquid Neural Network For Covid-19 Detection, Muhammad Waqaq, Florentin Smarandache, Muhammad Yasir, Farrukh Arslan, Anum Ali

Branch Mathematics and Statistics Faculty and Staff Publications

The COVID-19 pandemic has underscored the need for accurate and rapid diagnostic tools to assist clinical decision-making. Conventional deep learning models for COVID-19 detection in Chest X-Ray (CXR) images face challenges in poor generalization across imaging conditions and high computational demands. To address these issues, this study proposes CviTLNN, a novel hybrid model combining Vision Transformers (ViTs) and Liquid Neural Networks (LNNs) to improve feature extraction and classification. Specifically, CviTLNN employs a ViT with 24 transformer encoder blocks for efficient extraction of spatial features. The self-attention mechanism of ViTs effectively captures global and local dependencies in CXR images. Furthermore, …

Explicit Inverse Of Symmetric, Tridiagonal Near Toeplitz Matrices With Strictly Diagonally Dominant Toeplitz Part, Bakytzhan Kurmanbek, Yogi Erlangga, Yerlan Amanbek

All Works

Let T n = tridiag ( - 1 , b , - 1 ) , an n x n symmetric, strictly diagonally dominant tridiagonal matrix ( divided by b divided by > 2 ). This article investigates tridiagonal near-Toeplitz matrices T n & colone; [ t i , j ] , obtained by perturbing the ( 1 , 1 ) and ( n , n ) entry of T n . Let t 1 , 1 = t n , n = b not equal b . We derive exact inverses of T n . Furthermore, we demonstrate that these results …

Lipschitz Conditions On Operators And Matrices, Ryan Farrell

UNF Graduate Theses and Dissertations

Lipschitz functions on the real line find various applications across mathematics, including in differential equations, optimization, and machine learning. The goal of this thesis is to investigate functions which satisfy certain Lipschitz conditions when ap- plied to operators and matrices. Our study will review two classes of such functions, the class of Operator Lipschitz functions with respect to a given matrix norm, and the class consisting of functions which do not meet Lipschitz conditions in the traditional sense but satisfy inequalities which are Lipschitz in nature – we call such conditions ”Lipschitz-like”. The thesis concludes with a survey of these …

Geometric Properties Of Positive Definite Matrices: Means, Order, And Metrics, Blaine Dubois

UNF Graduate Theses and Dissertations

In this thesis, we study matrix means from a geometric point of view. In particular, we consider divergences of the form Tr[A + B − 2G(A, B)] for certain Geometric-Type matrix means G(A, B). We derive alternative formulations of this distance function through the application of one-sided inverses of G(A, B). When G(A, B) = A#B, we give a curve parametrization of the straight-line path between two points with respect to this semi-metric and present conditions under which this holds for other Geometric-Type means. For read- ability and self-containment, we introduce most of the preliminary concepts to build up to …

Fourier Transformation Of Non-Periodic Functions And Its Application In Computed Tomography, Sabrina Hossain

UNF Graduate Theses and Dissertations

Fourier analysis plays an important role in signal processing and imaging applications,

with computed tomography (CT) being a prominent example. CT imaging relies on recon-

structing cross-sectional images of objects from multiple projections, a process deeply rooted

in the mathematical framework of the Fourier series and its extensions. This thesis explores

the mathematical principle behind CT, demonstrating how periodic and non-periodic func-

tions can be decomposed into sinusoidal components to facilitate image reconstruction. We

begin by reviewing the Fourier series and its ability to represent periodic signals, and then

extend this concept to non-periodic functions through Fourier transforms. The connection …

Bifurcation And Index Theory With Applications To Nonlinear Differential Equations, Asrafi Yesmin

UNF Graduate Theses and Dissertations

This thesis presents a rigorous framework for the study of bifurcation phenomena in nonlinear differential equations. Semigroup theory and index theory are introduced to examine qualitative changes in the solution structures of the nonlinear dynamic system as the parameters vary. The theoretical framework is then applied to several nonlinear differential equations from biology and physics.

The Combinatorics Of Integer Partitions Enumerated By Some Exotic Weights, Hunter Waldron

Dissertations, Master's Theses and Master's Reports

Identities of integer partitions generally state that two dissimilar appearing families of partitions are in fact equinumerous when both are restricted to any fixed size. Euler's theorem is a classic example of such an identity, which equates the number of partitions with odd parts to the number of partitions with distinct parts. Lately, analogs of known partition identities involving weights other than size have begun to attract research interest. This dissertation is an investigation of two such weights. In Chapter 2, we study Schmidt weights, which count only parts with indices belonging to some given subset of the positive integers. …

Schaper Numbers, Palindrome Partitions, And Symmetric Functions, With Applications To Characters Of The Symmetric Group, Karlee J. Westrem

Dissertations, Master's Theses and Master's Reports

Finding the decomposition numbers for the symmetric group is a difficult problem and has led to many different research directions. For a given Specht module, the Schaper sum formula can be refined with knowledge of the Schaper number for the particular partition to give more precise information about the decomposition numbers. In Chapter 2, we give a combinatorial formula for the Schaper number when the partition has at most two columns. At the end, we provide a conjecture for the Schaper number for the partition of shaper (3^n).

Chapter 3 covers the joint work with my advisor, David Hemmer, and …

Partial Group Divisible 3-Designs, Apiwat Peereeyaphat

Chulalongkorn University Theses and Dissertations (Chula ETD)

We introduce a generalization of group divisible 3-designs, 3-GDDs, with two groups and two indices. A partial group divisible 3-design, 3-PGDD(gı + g2, k; A, (21, 112), is an ordered pair (GrU G2, B) where G, and G2 are disjoint finite sets called groups) of size g1 and 92, respectively; and B is a collection of k-subsets (called blocks) of G, UG, such that every 3-subset of G; occurs in exactly 1 blocks in B, and every i elements of G and j elements of G2 occur together in exactly Mig blocks in B for i. i € (1,2} and …

Construction Techniques For Linear Realizations Of Multisets With Small Support, M. A. Ollis

Emerson Authors, Researchers, & Creators

The Buratti-Horak Rosa Conjecture is a problem in graph theory asking when we can find a Hamiltonian path in the complete graph that has various properties to do with edge lengths. In this paper, we use constructive methods to show that the conjecture is true for various parameter sets where it was previously unknown.

Strategies For Playing Unshackle Games On Some Graphs, Thitiphut Leelathanakit

Chulalongkorn University Theses and Dissertations (Chula ETD)

Unshackle game is a combinatorial game for two players that starts with prisoners and shackles on a board such that each shackle has two ends, and each end is shackled to one prisoner. Two players alternately play a turn by destroying a shackle on the board until all shackles have been destroyed. A prisoner is free when all shackles that are shackled to him are destroyed, and the player who makes the most prisoners free wins and the other loses. Both players draw if neither of them can win. The prisoners and the shackles on the board can be considered …

Rings With Q-Torsionfree Canonical Modules, Naoki William Endo, Laura P. Ghezzi, Shiro S. Goto, Jooyoun Hong Phd, Shin-Ichiro Iai, Toshinori Kobayashi, Naoyuki Matsuoka, Ryo Takahashi

Publications and Research

Let A be a Noetherian local ring with canonical module K A . We characterize A when K A is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3 . If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module K A is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby’s result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein …

Random Graph Models For Dual Graphs, Anne Friedman

Scripps Senior Theses

This paper aims to better characterize dual graphs derived from state districting maps by developing random graph models that replicate their structural properties. Dual graphs provide a simplified way to represent districting maps, making it computationally feasible to analyze their structure. These representations enable researchers, legislators, and courts to assess district compactness, detect signs of gerrymandering, and generate alternative districting plans. A deeper understanding of the structural patterns of these dual graphs can help researchers choose or design more effective algorithms for redistricting analysis. The random graph models developed in this study serve as testbeds for evaluating algorithmic approaches to …

Empirical Analysis Of Political Districting Splitability Via Uniform Spanning Trees In Polynomial Time, Brooke C. Feinberg

Scripps Senior Theses

This work expands a recently proven conjecture that a polynomial fraction of all uniform spanning trees (USTs) are splittable into k balanced partitions on grid graphs to real-world political districting plans. We investigate whether similar structural properties hold for the planar dual graphs of U.S. counties (cnty) and tracts (t), using Wilson’s algorithm to generate uniform random spanning trees and Breadth- First Search (BFS) to check for splitability into balanced partitions. Our empirical findings suggest that real-world districting plans can be split into 2-balanced, connected partitions in a fraction of polynomial time. This result highlights the potential for scalable redistricting …

Students’ Concept Maps Profile On Environmental Pollution Material During The Covid-19 Pandemic, Sunarni Sunarni, Sri Widoretno, Puguh Karyanto, Bowo Sugiharto, Sri Dwiastuti, Chandra Adi Prabowo

Jurnal Pendidikan Sains

The study investigates the performance of students in constructing Concept Maps (CM) related to environmental pollution material during the COVID-19 pandemic. The data reveals that the overall achievement in CM construction was suboptimal, with no component reaching more than half of its maximum potential. The highest achievement was recorded in the valid relationship component, which attained 9.75% of its maximum possible score. This was followed by the hierarchy component, achieving 7.34%, and the branching component at 3.42%. The pattern component ranked fourth with 1.31%, closely followed by the example component at 1.30%. The lowest performance was observed in the crosslink …

Analysis Of Students’ Problem-Solving Skills In Newton’S Law With 5e Learning Cycle, Nidya Desyana, Sutopo Sutopo, Nandang Mufti

Jurnal Pendidikan Sains

The aim of this study is to identify students’ problem-solving skills in Newton’s laws through the implementation of the 5E learning cycle in the classroom. A pre-experimental design with a one-group pretest-posttest approach was employed. Data on problem-solving skills were collected from students’ pre-test and post-test responses to two essay questions. The indicator with the highest percentage of problem-solving skills was useful description (83% of students), while the indicator with the lowest percentage was specific application of physics (33% of students). Due to the non-normal distribution of the data, the Wilcoxon test was utilized. The results indicated a significant difference …

Development Of Conceptual Scaffolding-Assisted Formative Assessment For Enhancing Understanding Of Temperature And Heat, Ana Lailatul Fitriyah, Sentot Kusairi, Markus Diantoro

Jurnal Pendidikan Sains

This research aims to develop formative assessment media assisted by conceptual scaffolding to improve students’ understanding of temperature and heat, test its validity and practicality, and gauge student responses. Utilizing the ADDIE model, the research follows five stages: Analysis, Design, Development, Implementation, and Evaluation. In the Analysis stage, a literature review was conducted to identify critical components, including formative assessment, conceptual scaffolding, concept mastery, and previous research. The Design stage involved identifying users, defining competencies and indicators, creating a storyboard, integrating assessment components, and determining mastery levels. During the Development stage, the assessment media were developed into a functional product. …

Composite Volume Learning Media Based On Augmented Reality To Enhance Students’ Visual-Spatial Intelligence, Ria Kurniawati, Susiswo Susiswo, Syamsul Hadi

Jurnal Pendidikan Sains

Augmented Reality (AR) technology, a three-dimensional visual tool that integrates virtual objects or environments into real-world displays in real time (Azuma et al., 2001), is particularly useful for grasping complex concepts such as the composite volume of solids, which often confuses students when they need to decompose solids into their individual components. While previous research has predominantly focused on the introduction of solids, spatial nets, and the volume of singular shapes, this study aims to develop composite volume learning media based on AR to enhance students’ visual-spatial intelligence in a valid, practical, and effective manner, aligning with their concrete operational …

Design Of Motivational-Realistic-Pancasila Learning In Mathematics, Marup Marup, Suradi Tahmir, Ahmad Talib, Nurzatulshima Kamaruddin

Jurnal Pendidikan Sains

Learning mathematics in class greatly influences students' learning success both in terms of knowledge and attitudes. In carrying out learning, a learning design is needed that can foster student motivation so that they provide learning outcomes to the learning objectives. Motivational-Realistic-Pancasila learning design is considered to be an alternative solution. Morela is a design that combines motivational, realistic indicators and Pancasila values. The teaching of mathematics in the classroom significantly influences students' academic success, both in terms of knowledge and attitude. To effectively carry out the teaching process, a well-designed instructional approach is necessary to foster students' motivation to achieve …

A Novel Format For Math Circles: Circles With No Center, Frederick A. Peck, Ian P. Renga, Nick Grener, David R. Erickson, Matt B. Roscoe, Ke Wu

Journal of Math Circles

This paper shares a novel format for Math Circles, which we call “circles with no center.” Circles with no center do not have a traditional facilitator. The problem or activity is novel to everyone in the room. All members engage in mathematical inquiry, and everyone takes responsibility for running the gathering. The “no center” format has benefits for participants and organizers. For participants, the format offers more freedom and more responsibility. For organizers, the format is easier to organize, more fun, and involves less pressure. Our assessment of a 3-day retreat for teachers suggests participants may prefer a circle with …

Understanding Women, Infant And Children Feeding Decisions In Emergencies: The Case Of Covid-19 And The Formula Shortage, Davida Mensah, Edmund F. Agyemang, Constance Gewa

School of Mathematical & Statistical Sciences Faculty Publications

Background: The advantages of breastfeeding and its role in emergencies are undeniable. Studies show that many women in developed countries choose formula over breastmilk, even in emergencies. Nevertheless, no one knows if postpartum women under the Women, Infants and Children (WIC) program turned out to breastfeed or re-lactate their infants during these crises. This study aims to better understand WIC participants' perceptions about breastfeeding their babies in emergencies.

Methods: A chi-square test of independence was used to assess the association between breastfeeding choice and demographic characteristics and potential covariates of respondents. A post hoc analysis using Dunn's multiple comparisons test …

Effects Of Missing Data Imputation Methods On Univariate Blood Pressure Time Series Data Analysis And Forecasting With Arima And Lstm, Nicholas Niako, Jesus D. Melgarejo, Gladys E. Maestre, Kristina Vatcheva

School of Mathematical & Statistical Sciences Faculty Publications

Background: Missing observations within the univariate time series are common in real-life and cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in every incomplete univariate time series. Most of the existing studies focus on comparing the distributions of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series affect the forecasting performance of time series models. We evaluated the prediction performance of autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) network models on imputed time series data using ten different imputation techniques. …

Apex Graphs And Cographs, Jagdeep Singh, Vaidy Sivaraman, Thomas Zaslavsky

Theory & Applications of Graphs

A class G of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by G^{apex} the class of graphs G that contain a vertex v such that G − v is in G. Borowiecki, Drgas-Burchardt, and Sidorowicz proved that if a hereditary class G has finitely many forbidden induced subgraphs, then so does G^{apex}. We provide an elementary proof of this result.

The hereditary class of cographs consists of all graphs G that can be generated from K_1 using complementation and disjoint union. A graph is an apex cograph if it contains a …

Parallel Circles: A Math Club As A University Math Circle, Sarah C. Cobb, Marcos Lopez

Journal of Math Circles

This paper will discuss a monthly social event for the University Math Club. Over the past several years, the event has been shaped by the philosophy of a Student Math Circle. We will discuss the event's organization and the ways it has benefited from the influence of the Math Circle community.

On The Power Series Method For Solitons And Peakons Of Nonlinear Pde, Erika Olivares, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we discuss the power series method to obtain traveling wave solutions of nonlinear PDE in one space variable. The method, including a recursive procedure for the coefficients and error estimate for the partial sums, is presented for the Camassa-Holm equation. Numerical examples of approximate single soliton and single peakon solutions are included.

Existence And Uniqueness Of Solutions Of Fourth Order Iterative Boundary Value Problems, Zach Whaley

Theses and Dissertations

In this dissertation, we study the fourth-order iterative differential equation \begin{displaymath} x^{(4)}(t) = \f(t, x(t), x^{[2]}(t), \dots, x^{[m]}(t)) \end{displaymath} where $x^{[2]}(t) = x(x(t))$ and $x^{[j]}(t) = x(x^{[j - 1]}(t))$ for $j > 2$. We consider the above equation with multiple sets of boundary conditions, and we state results on the existence and uniqueness of solutions for each set of boundary conditions. In Chapter 2, the boundary conditions are conjugate boundary conditions, \begin{align*} &x(-a) = -a, \ x'(-a) = b, \ x''(-a) = c, \ x(a) = a \\ &x(-a) = -a, \ x(a) = a, \ x'(a) = b, \ x''(a) …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …