Mathematics Commons^™

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

A Real World Example Of Solving A Quadratic Equation In Movie Cgi, Cynthia J. Huffman Ph.D.

Faculty Submissions

It is important to expose students to the beauty and usefulness of mathematics. Since computer graphics are familiar to most students due to video games and movies, they make a great source for motivating topics in mathematics. This activity shows students an application of solving quadratic equations to computing the line of sight to spherical objects in computer graphics.

Frobenius Objects In The Category Of Relations, Rajan Amit Mehta, Ruoqi Zhang

Mathematics Sciences: Faculty Publications

We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain cohomology classes in a compact oriented Riemannian manifold.

The Consent Of The Governed, Carter A. Hanson

Student Publications

The Consent of the Governed is a Kolbe Fellowship project investigating gerrymandering through the lens of mathematics, Supreme Court litigation, and the potential for redistricting reform. It was produced as a five-episode podcast during the summer of 2020; this paper is the transcription of the podcast script. The project begins with an analysis of the impact of gerrymandering on the composition of the current U.S. House of Representatives. It then investigates the arguments and stories of Supreme Court gerrymandering cases in the past twenty years within their political contexts, with a focus on the Court's reaction to different mathematical methods …

Pattern Of Health Behavior And Its Association With Self-Rated Health: Evidence From The 2018 Behavioral Risk Factor Surveillance System In The United States, Linh Nguyen, Mamunur Rashid, M. Mazharul Islam

Student Research

Aim: To improve public health services, we need to keep policymakers updated with health-related issues. This study (1) examines the recent pattern of physical activities, smoking, alcohol consumption, and SRH, and (2) investigates the association between the behaviors and SRH status among US citizens.

Method: We extracted data from the latest state-based survey of the 2018 Behavioral Risk Factor Surveillance System (BRFSS), which provides a nationally representative sample of 437,436 American adults. We analyzed the data, mainly employing chi-square tests and logistic regression models.

Results: Physical inactivity and smoking are more common among participants with lower education and household income. …

College Algebra Notes And Exercises (Gcsu), Rabia Shahbaz, Janice Alves

Mathematics Ancillary Materials

Developed as part of a Round 13 Mini-Grant, these updated supplementary materials for Stitz-Zeager Open Source Mathematics and the LibGuides Open Course for College Algebra at GCSU include notes and exercises on equations, inequalities, functions, polynomial and rational functions, and exponential and logarithmic functions are included in one .zip file.

Conjugacy Separability And Cyclic Conjugacy Separability Of Certain Hnn Extensions, Generalised Free Products And Tree Products, Hui Min Lim

Student Works (2020-2029)

In this thesis, we study two interrelated strong residually finite properties of groups, namely conjugacy separability and cyclic conjugacy separability. We extend them to certain HNN extensions, generalized free products and tree products where the associated subgroups and amalgamated subgroups are not necessarily cyclic. In the first part of the thesis, we consider HNN extensions. We begin by establishing two criteria, one for conjugacy separability and another for cyclic conjugacy separability. Using these two criteria we establish conditions for HNN extensions where the associated subgroups are central or they are a finite extension of a central subgroup or cyclic to …

Optical Soliton Perturbation With Quadratic-Cubic Nonlinearity, Asma Mir

Student Works (2020-2029)

Solitons can be defined as wave packets that can travel undistorted across long distances even transcontinental and transoceanic. They serve as modern telecommunication means through cables and optical fibers for fast Internet activities. To maintain high-fidelity and time sensitive transmission, optical pulses manage the efficient flow of data. From the last few years, Nonlinear Schrödinger Equation (NLSE) has been a great attraction of research activities across the globe. The governing model is the Nonlinear Schrödinger Equation (NLSE). From a mathematical standpoint, NLSE is a nonlinear partial differential equation (PDE) that has been studied in a variety of other areas of …

Structure Aware Runge–Kutta Time Stepping For Spacetime Tents, Jay Gopalakrishnan, Joachim Schöberl, Christoph Wintersteiger

Mathematics and Statistics Faculty Publications and Presentations

We introduce a new class of Runge–Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge–Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations.

Topics In Gravitational Wave Physics, Aaron David Johnson

Graduate Theses and Dissertations

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Plithogenic Cognitive Maps In Decision Making, Florentin Smarandache, Nivetha Martin

Branch Mathematics and Statistics Faculty and Staff Publications

Plithogenic sets introduced by Smarandache (2018) have disclosed new research vistas and this paper introduces the novel concept of plithogenic cognitive maps (PCM) and its applications in decision making. The new approach of defining instantaneous state neutrosophic vector with the confinement of indeterminacy to (0,1] is proposed to quantify the degree of indeterminacy. The resultant vector is obtained by applying instantaneous state vector through the connection matrix together with plithogenic operators comprising the contradiction degrees. The connection matrix is represented as fuzzy matrix and neutrosophic matrix and the resultant vector is determined by applying plithogenic fuzzy operators and plithogenic neutrosophic …

Homotopy Groups And Quantitative Sperner-Type Lemma, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

We consider a generalization of Sperner's lemma for triangulations of m-discs whose vertices are colored in at most m colors. A coloring on the boundary (m-1)-sphere defines an element in the corresponding homotopy group of the sphere. Depending on this invariant, a lower bound is obtained for the number of fully colored simplexes. In particular, if the Hopf invariant is nonzero on the boundary of 4-disk, then there are at least 9 fully colored tetrahedra and if the Hopf invariant is d, then the lower bound is 3d + 3.

Concrete Polytopes May Not Tile The Space, Alexey Garber, Igor Pak

School of Mathematical & Statistical Sciences Faculty Publications

Brandolini et al. conjectured in (Preprint, 2019) that all concrete lattice polytopes can multitile the space. We disprove this conjecture in a strong form, by constructing an infinite family of counterexamples in ℝ3 .

Numerical And Analytical Solutions Of The Integral Geometry Problem On The Families Of Parabola And Broken Lines, N.U Uteuliev, Gafur Djaykov, Seidullaev Abat

Karakalpak Scientific Journal

In this paper, the problem of reconstructing the function in the strip on the known integrals from it with a given weight function on the family of parabola and broken lines. Inversion formulas for the family of broken lines were obtained, on their basis the theorems of uniqueness and existence of the solution were proved. Estimations of stability of problem solving in Sobolev spaces are obtained, from which weak ill-posed of problems follows. For the problems of integral geometry on the parabola family we obtained a regularized solution. On the basis of these obtained results the numerical results of experiments …

Features Of Heart Activity Of Cattle In The Conditions Of Southern Aral Sea Region, Svetlana Mambetullaeva, Khayratdin Seytkamalov

Karakalpak Scientific Journal

In this article, the results of comparative analysis of electrocardiogram are shown for the cows of different breeds in the Aral Sea region. It is set that the high temperature of the environment and sunny insolation render a negative influence on the functional parameters of the cardiac vascular system of animals. There are facts about the cows of different breeds at the influence of different temperatures that have unidirectional functional changes in the operation of the heart. At the same time, we will mark that these changes are less expressed for the cows of the improved zebu visible cattle, what …

Photoelectric Injection Amplification Of Al–Al2o3–P-Cdte–Mo Structures At Low Bias Voltages, A K. Uteniyazov

Karakalpak Scientific Journal

The results of studies of photoelectric injection enhancement of the Al–Al₂O₃–p-CdTe –Mo structure upon application of low bias voltages. It has been shown that the studied Al-Al₂O₃–p-CdTe-Mo structure under can be represented as a n⁺-p-R_ом structure with a long base. Conducted researches show that Al-Al₂O₃–p-CdTe-Mo structure has unique properties. It has very high photocurrent and photosensitivity at both direct and reverse dias voltage under even small bias voltage (up to 500mV).

Synthesis Of Supramolecular Complex L– (-) – Menthol, Ziyada Djumanova Dr, Lolaxan Ettibaeva, Ugilay Abduraxmonova, Zulfiya Khalmuratova

Karakalpak Scientific Journal

In this article glycyrrhizic acid content with menthol in several various proportions (2:1; 4:1; 9:1), information was given on synthesis and physical and chemical properties of new supermolecular complexes. Received supramolecular complexes concerning 4:1 it was chemically defined and also studied the structure of supramolecular complexes by physical methods on the basis of interaction of organic molecules with electromagnetic radiation, in particular their range IR – of spectroscopy. Our work of the near future will be turned to check its recent supramolecular complexes on the basis of GA: Menthol for growth of a plant and biotic elasticity of tension …

Spectrophotometric Characterization Of The Complexation Of Gossypol Acetic Acid With Cobalt Ion, Ugilay Abdurahmanova, Habibjon Kushiev, Maral Askarova, Dilafruz Allanazarova

Karakalpak Scientific Journal

The authors of the article suggest simple and express method of spectrophotometric determination of cobalt with the help of derivatives of gossypol. Optimal conditions of determining cobalt are found. Under optimal conditions there was created a graded graph, which is more linear in the range for cobalt concentration of 10.0 – 50.0 microgram/25 ml, contents and constants of cobalt complex with gossypol vinegar acid.

An A Posteriori Error Analysis Of Stationary Incompressible Magnetohydrodynamics, Ari E. Rappaport

Mathematics & Statistics ETDs

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and …

A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens

Publications and Research

We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster’s small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster’s small MCM conjecture.

Discrete-Time Control With Non-Constant Discount Factor, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

This paper deals with discrete-time Markov decision processes (MDPs) with Borel state and action spaces, and total expected discounted cost optimality criterion. We assume that the discount factor is not constant: it may depend on the state and action; moreover, it can even take the extreme values zero or one. We propose sufficient conditions on the data of the model ensuring the existence of optimal control policies and allowing the characterization of the optimal value function as a solution to the dynamic programming equation. As a particular case of these MDPs with varying discount factor, we study MDPs with stopping, …

Superposed Ornstein-Uhlenbeck Processes, Julius Esunge, Auguste Muhau

Journal of Stochastic Analysis

No abstract provided.

Bipartite Dot Product Graphs, Sean Bailey, David E. Brown

Mathematics and Statistics Faculty Publications

Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝ^k and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot product representation exists for G is the bipartite dot product dimension of G, denoted bdp(G). We will show that such representations exist for all bipartite graphs as well as give an upper bound for the bipartite dot …

Studies On Polynomial Rings Through Locally Nilpotient Derivations., Nikhilesh Dasgupta Dr.

Doctoral Theses

No abstract provided.

What Is The Derivative Of Music?, Thad B. Welch, Cameron H. G. Wright, Michael G. Morrow

Electrical and Computer Engineering Faculty Publications and Presentations

In our continuing effort to prove to students that Signals & Systems is not just another mathematics course taught by the ECE Department, we ask the question, “What is the Derivative of Music?”

The first-order difference (or first-difference) is an incredibly simple algorithm that very accurately approximates the numeric derivative operator, especially for oversampled signals. Its inverse also accurately approximates the numeric integration operator, but not without numeric difficulty.

Given a real-time demonstration using winDSK8, we can now show students that these mathematical operators provide powerful signal processing filtering tools for real-world signals.

During this ASEE session, we will include …

Fuzzy Synergetic Control Nonlinear Dynamic Objects, Isomiddin Sidikov, Noilakhon Yakubova, Komil Usmanov, Saparbay Kazakhbayev

Karakalpak Scientific Journal

The article deals with the synthesis of effective algorithms for controlling a chemical reactor and developed a fuzzy synergistic controller for a class of indefinite nonlinear dynamic systems. A synergetic control scheme is proposed for solving the control problem for nonlinear systems. Non-linear systems with configurations and parameters that change over time require a completely non-linear model and adaptive control scheme for a practical operating environment. The synthesis of control laws is performed by the method of analytical design of aggregated controllers (ACAR). Fuzzy logic systems are used to evaluate the unknown nonlinear behavior of the system, and a new …

Using The Kellogg-Tsan Solution Decomposition In Numericalmethods For Singularly Perturbed Convection-Diffusion Problems, Relja Vulanović, Thái Ahn Nhan

Mathematics and Computer Science

The linear one-dimensional singularly perturbed convection-diffusion problem is solved numerically by a second-order method that is uniform in the perturbation parameter 𝜀. The method uses the Kellogg-Tsan decomposition of the continuous solution. This increases the accuracy of the numerical results and simplifies the proof of their 𝜀-uniformity

Von Neumann's Minimax Theorem For Continuous Quantum Games, Luigi Accardi, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

Colorado Mathematics Teacher

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.