Mathematics Commons^™

Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci

Mathematics Faculty Publications

Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N M reversal N M ⋅= ⋅ ( ) , our results are valid in a general numeration base b > 2 .

Modeling The Evolution Of Differences In Variability Between Sexes, Theodore P. Hill

Research Scholars in Residence

An elementary mathematical theory based on a “selectivity-variability” principle is proposed to address a question raised by Charles Darwin, namely, how one sex of a sexually dimorphic species might tend to evolve with greater variability than the other sex. Two mathematical models of the principle are presented: a discrete-time one-step probabilistic model of the short-term behavior of the subpopulations of a given sex, with an example using normally distributed perceived fitness values; and a continuous-time deterministic coupled ODE model for the long-term asymptotic behavior of the expected sizes of the subpopulations, with an example using exponentially distributed fitness levels.

Active Disturbance Rejection Control Of Torsional Plant With Unknown Frequency Harmonic Disturbance, Rafal Madonski, Momir Stanković, Sally Shao, Zhiqiang Gao, Jun Yang, Shihua Li

Mathematics and Statistics Faculty Publications

In this work, a new robust control algorithm is introduced for uncertain systems with harmonic disturbances of unknown frequencies. The proposed solution works under the active disturbance rejection control (ADRC) framework and utilizes a specialized observer for sinusoidal uncertainties, aided with an on-line harmonic disturbance frequency estimator. The entire governing structure is derived in a convenient error-based domain, easily deployable in various industrial control software. The idea behind the introduced approach is general, but is conveyed here using solely a three degrees-of-freedom torsional system, which is considered a benchmark for vibration phenomenon in many mechanical systems. The efficacy of the …

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. …

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 …

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.

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.

Families Of Homogeneous Licci Ideals, Jesse Keyton

Graduate Theses and Dissertations

This thesis is concered with the graded structure of homogeneous CI-liaison. Given two homogeneous ideals in the same linkage class, we want to understand the ways in which you can link from one ideal to the other. We also use homogeneous linkage to study the socles and Hilbert functions of Artinian monomial ideals.

First, we build off the work of C. Huneke and B. Ulrich on monomial liaison. They provided an algorithm to check the licci property of Artinian monomial ideals and we use their method to characterize when two Artinian monomial ideals can be linked by monomial regular sequences. …

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 …

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 …

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 …