Mathematics Commons^™

Explicit Motion Planning In Digital Projective Product Spaces, Seher Fi̇şekci̇, İsmet Karaca

Turkish Journal of Mathematics

We introduce digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of digital projective product spaces. In addition, we obtain an upper bound for the digital topological complexity of these spaces through an explicit motion planning construction, which shows digital perspective validity of results given by S. Fişekci and L. Vandembroucq. We apply our outcomes on specific spaces in order to be more clear.

The Fourier Spectral Method For Determining A Heat Capacity Coefficient In A Parabolic Equation, Durdimurod Durdiev, Dilshod Durdiev

Turkish Journal of Mathematics

In this paper, the comparison of finite difference and Fourier spectral numerical methods for an inverse problem of simultaneously determining an unknown coefficient in a parabolic equation with the usual initial and boundary conditions is proposed. We represent the detailed description of the methods and their algorithms. The research work conducted in this paper shows that the Fourier spectral method is highly accurate.

$3d$-Flows Generated By The Curl Of A Vector Potential & Maurer-Cartan Equations, Oğul Esen, Partha Guha, Hasan Gümral

Turkish Journal of Mathematics

We examine $3D$ flows $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ admitting vector identity $M\mathbf{v} = \nabla \times \mathbf{A}$ for a multiplier $M$ and a potential field $\mathbf{A}$. It is established that, for those systems, one can complete the vector field $\mathbf{v}$ into a basis fitting an $\mathfrak{sl}(2)$-algebra. Accordingly, in terms of covariant quantities, the structure equations determine a set of equations in Maurer-Cartan form. This realization permits one to obtain the potential field as well as to investigate the (bi-)Hamiltonian character of the system. The latter occurs if the system has a time-independent first integral. In order to exhibit the theoretical results on some …

Translating Solitons Of Translation And Homothetical Types, Muhi̇tti̇n Evren Aydin, Rafael Lopez

Turkish Journal of Mathematics

We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate translating solitons that can be locally written as the product of two functions of one variable. We extend the results in Lorentz-Minkowski space.

From Ordered Semigroups To Ordered $\Gamma$-Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

In an attempt to show the way we pass from ordered semigroups to ordered $\Gamma$-hypersemigroups, we examine the results of Semigroup Forum (1992; 46: 341-346) for an ordered $\Gamma$-hypersemigroup. It has been shown that the concept of semisimple ordered $\Gamma$-hypersemigroup $S$ is identical with the concept "the ideals of $S$ are idempotent" and the ideals of $S$ are idempotent if and only if for all ideals $A, B$ of $S$, we have $A\cap B=(A\Gamma B]$. The main results of the paper are the following: The ideals of an ordered $\Gamma$-hypersemigroup $S$ are weakly prime if and only if they form …

Bessel Equation And Bessel Function On $\Mathbb{T}_{(Q,H)}$, Ahmet Yantir, Burcu Si̇li̇ndi̇r Yantir, Zehra Tuncer

Turkish Journal of Mathematics

This article is devoted to present nabla $(q, h)$-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla $(q, h)$-Bessel equation, we present nabla $(q, h)$-analysis regarding nabla generalized quantum binomial, nabla $(q,h)$-analogues of Taylor's formula, Gauss's binomial formula, Taylor series, analytic functions, analytic exponential function with its fundamental properties, analytic trigonometric and hyperbolic functions. We emphasize that nabla $(q, h)$-Bessel equation recovers classical, $h$- and $q$-discrete Bessel equations. In addition, we establish nabla $(q, h)$-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate …

The Interior-Boundary Strichartz Estimate For The Schrödinger Equation On The Half-Line Revisited, Bi̇lge Köksal, Türker Özsari

Turkish Journal of Mathematics

In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interior-boundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with …

2-Colored Rogers-Ramanujan Partition Identities, Mohammad Zadehdabbagh

Turkish Journal of Mathematics

In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some overpartition identities coincide with our findings. A correspondence between colored partitions and overpartitions is provided.

Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory

Turkish Journal of Mathematics

Denote by $\mathcal{G}(n,c,g,k)$ the set of all connected graphs of order $n$, having $c$ cycles, girth $g$, and $k$ pendant vertices. In this paper, we give a partial characterisation of the structure of those graphs in $\mathcal{G}(n,c,g,k)$ maximising the number of connected induced subgraphs. For the special case where $c=1$, we find a complete characterisation of all maximal unicyclic graphs. We also derive a precise formula for the corresponding maximum number given the following parameters: (1) order, girth, and number of pendant vertices; (2) order and girth; (3) order.

Investigation Of Neutrophil-Like Hl-60 Cell Migration In A 3d Collagen Matrix, Pouye Sedighian

CGU Theses & Dissertations

It is known that cell migration in innate and adaptive immune system plays a fundamental role in human health. Among the immune cells, neutrophils are one of the most essential cells in protecting the body against invading pathogens. In the presence of chemoattractants, these cells are the first responders that start a directed migration toward the injured area. As neutrophils approach the site of infection, they transmigrate to the tissue and follow the chemoattractant concentration gradient to locate and eliminate the invading pathogens. Understanding the patterns and mechanism of neutrophil migration in the presence of chemoattractants could possibly play an …

Mathematical Model For Giraffe Population Dynamics, Huntir Bass

Electronic Theses and Dissertations, 2020-2023

Since the 1980s the overall giraffe population has dropped at least 40% causing some researchers to label this rapid decline as the "Silent Extinction." Due to this plummet, understanding the behaviors of the giraffe population is absolutely necessary before they are on the brink of extinction. Through the usage of mathematical modeling methodologies, a general model is created to illustrate the relationship between juvenile and adult female giraffes through numerous interaction parameters. Variations on specific variables generate different simulations, which allows more biological accuracy. With each variation having an established coexistence equilibrium between the juvenile and adult female populations, the …

Various Dynamical Regimes, And Transitions From Homogeneous To Inhomogeneous Steady States In Nonlinear Systems With Delays And Diverse Couplings, Ryan Roopnarain

Electronic Theses and Dissertations, 2020-2023

This dissertation focuses on the effects of distributed delays modeled by 'weak generic kernels' on the collective behavior of coupled nonlinear systems. These distributed delays are introduced into several well-known periodic oscillators such as coupled Landau-Stuart and Van der Pol systems, as well as coupled chaotic Van der Pol-Rayleigh and Sprott systems, for a variety of couplings including diffusive, cyclic, or dynamic ones. The resulting system is then closed via the 'linear chain trick' and the linear stability analysis of the system and conditions for Hopf bifurcations that initiate oscillations are investigated. A variety of dynamical regimes and transitions between …

Combinatorial Optimization With Photonics-Inspired Clock Models, Mostafa Honari-Latifpour, Matthew S. Mills, Mohammad-Ali Miri

Publications and Research

NP-hard combinatorial optimization problems are in general hard problems that their computational complexity grows faster than polynomial scaling with the size of the problem. Thus, over the years there has been a great interest in developing unconventional methods and algorithms for solving such problems. Here, inspired by the nonlinear optical process of q-photon down-conversion, in which a photon is converted into q degenerate lower energy photons, we introduce a nonlinear dynamical model that builds on coupled single-variable phase oscillators and allows for efficiently approximating the ground state of the classical q-state planar Potts Hamiltonian. This reduces the exhaustive search in …

Actuarial Credibility Approach In Adjusting Initial Cost Estimates Of Transport Infrastructure Projects, Bartłomiej Rokicki, Krzysztof Ostaszewski

Faculty Publications – Mathematics

This paper presents a novel methodology based on the modified actuarial credibility approach. It allows for the adjustment of initial cost estimates of public infrastructure projects by accounting for the additional risk/uncertainty factor. Hence, it offers an interesting alternative to other existing forecasting methods. We test our approach by applying data for over 300 major infrastructure projects implemented in Poland between 2004 and 2020. We prove that, despite its simplicity, the actuarial credibility approach can deliver accurate cost estimates compared to more complex methods such as regression analysis (OLS) or machine learning (LASSO). In particular, we show that, although the …

The Role Of Interactive Features Within A Mathematics Storybook In Interpreting A Conflict And Conflict Resolution: The Case Of Three Fifth Graders, Mahtob Aqazade

Faculty Publications – Mathematics

Students often experience cognitive conflicts when trying to interpret negative numbers’ order and values because they do not correspond to their prior whole number knowledge. One way to trigger students’ cognitive conflicts and support their conflict resolution meaningfully is through stories. Thus, I used a temperature-related mathematics storybook—Temperature Turmoil—to highlight the cognitive conflict students often experience because of relying on the integers’ absolute value and introduce conflict resolution (i.e., integers have both absolute value and directed value). By incorporating interactive features, I used a multiple-case approach to describe three fifth graders’ cognitive conflict and conflict resolution experiences. Harry, Lola, and …

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …

Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein

CMC Senior Theses

The majority of seizures are self-limiting. Within a few minutes, the observed neuronal synchrony and deviant dynamics of a tonic-clonic or generalized seizure often terminate. However, a small epilesia partialis continua can occur for years. The mechanisms that regulate subcortical activity of neuronal firing and seizure control are poorly understood. Published studies, however, through PET scans, ketogenic treatments, and in vivo mouse experiments, observe hypermetabolism followed by metabolic suppression. These observations indicate that energy can play a key role in mediating seizure dynamics. In this research, I seek to explore this hypothesis and propose a mathematical framework to model how …

Mary Eleanor Spear's Importance To The History Of Statistical Visualization, Melanie Williams

CMC Senior Theses

This paper will demonstrate why Mary Eleanor Spear (1897-1986) is an important figure in the history of statistical visualization. She lead an impressive career working in the federal government as a data analyst before "data analyst" became a thing. She wrote and illustrated two comprehensive textbooks which furthered the art of statistical visualization. Her textbooks cover extensive graphing knowledge still valuable to statisticians and viewers today. Most notable of her works is her development of the box plot. In addition to Spear's career and contributions, this paper will also address the lack of female representation in science, technology, engineering, and …

Review Of Copula For Bivariate Distributions Of Zero-Inflated Count Time Series Data, Dimuthu Fernando, Mohammed Alqawba, Manar Samad, Norou Diawara

Mathematics & Statistics Faculty Publications

The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series.

However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used …

Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu

Mathematics & Statistics Faculty Publications

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and Q-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the Q-tensor theory in dynamic configurations.

Planning And Effects Of Equitable Teaching Practices In Emu Math 120 Class, Kyle Yapp

Senior Honors Theses and Projects

The purpose of this project is to evaluate the effects of implementing Equitable Teaching practices in Math 120 Calculus 1. We used the EQUIP instrument in order to measure the amount of participation from each student. We used the X-PIPS-M instrument in order to get the students' responses to the class as well as have Dr. Ross reflect as a teacher. We used the MCOPP+ in order for Dr. Ross to reflect as a teacher. We also used the Calculus 1 Concept Inventory assessment in order to evaluate students' content knowledge growth during the course. We found that students responded …

On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles

Graduate Theses/Dissertations

In this thesis we investigate the chromatic number of the Hasse diagram of a subgroup lattice. We combine results of Bollobás and Tůma to show that there exist infnite groups whose subgroup lattices have arbitarily high chromatic numbers. We show that fnite supersolvable groups have bipartite subgroup lattices but that CLT and non-solvable groups may not have bipartite subgroup lattices. Lastly, we give a preliminary argument suggesting that there are an infnite number of non-solvable groups whose subgroup lattices are bipartite.

Several Problems In Nonlinear Schrödinger Equations, Tim Van Hoose

Masters Theses

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.

The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood

Theses and Dissertations (Comprehensive)

The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …

2d N = (0, 1) Gauge Theories And Spin(7) Orientifolds, Sebastían Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu

Publications and Research

We initiate the geometric engineering of 2d N = (0, 1) gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity. We refer to such constructions as Spin(7) orientifolds. Spin(7) orientifolds explicitly realize the perspective on 2d N = (0, 1) theories as real slices of N = (0, 2) ones. Remarkably, this projection is geometrically realized as Joyce’s construction of Spin(7) manifolds via quotients of Calabi-Yau 4-folds by antiholomorphic …

Beyond Quenching Profile For Singular Semilinear Parabolic Partial Differential Equations With Mixed Boundary Conditions, Benjamin Thaitavorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Numerical Approximation To Ruin Probability Of Generalization Of Classical Risk Model, Kittiwat Woragate

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Random Forest Of Mixed Decision Trees And Minority Condensation Decision Trees For Class Imbalanced Problem, Suvaporn Homjandee

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

3d Building Internal Structural Component Segmentation From Point Cloud Data Using Dbscan And Modified Ransac With Normal Deviation Conditions, Thanapon Doougphummet

Chulalongkorn University Theses and Dissertations (Chula ETD)

Nowadays, the laser scanner plays an important role as a tool to capture building structure in a form of point cloud which can be used to draw a blueprint or a floor plan for reconstruction or renovation of an existing building. The point cloud data represent a shape or an object in three dimensions. This point cloud together with the utilization of Building Information Modeling (BIM) which is a workflow that provides information about the foundation and structure measurement of a building, make a planning and design to construction more convenient and efficient in several aspects than the traditional way. …

Connected Size Ramsey Numbers Of Matching And Some Graphs, Jirawat Mungtumklang

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.