Mathematics Commons^™

Estimation Of The Function Of Consentration For An Ordered Statistics, A. E. Madrahimov Candidate Of Physical And Mathematical Sciences, Associate Professor.

Scientific journal of the Fergana State University

This article examines the issue of estimating the concentration function for ordinal statistics and sample size.

Differential Games Of The Second Order, B. T. Samatov Doctor Of Physics-Mathematics, Professor, U. B. Soyibboev Master Student, U. A. Mirzamahmudov Master Student

Scientific journal of the Fergana State University

In this paper, we study the pursuit-evasion problem for the second order differential game when the initial positions of moving objects are linearly dependent and controls of the players have geometric constraints. The new sufficient solvability conditions are obtained for problems of the pursuit and evasion.

Repeat Length Of Patterns On Weaving Products, Zhuochen Liu

Mathematical Sciences Technical Reports (MSTR)

Interlacing strands have been used to create artistic weaving patterns. Repeated patterns form aesthetically pleasing products. This research is a mathematical modeling of weaving products in the real world by using Cellular Automata. The research is conducted by observing the evolution of the model to better understand products in the real world. Specifically, this research focuses on the repeat length of a weaving pattern given the rule of generating it and the configuration of the starting row. Previous studies have shown the range of the repeat length in specific situations. This paper will generalize the precise repeat length in one …

Nonlinear Reaction–Diffusion Process Models Improve Inference For Population Dynamics, Xinyi Lu, Perry J. Williams, Mevin B. Hooten, James A. Powell, Jamie N. Womble, Michael R. Bower

Mathematics and Statistics Faculty Publications

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long‐term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a …

Algebraic Frames And Ultrafilters, Papiya Bhattacharjee

Mathematics Colloquium Series

A frame, also known as pointfree topology, is a complete lattice that satisfies a strong distributive property, known as the 'frame law.' Originally, the study of frames began as studying topological spaces without points, hence the name pointfree topology. Due to this connection, different topological concepts can be generalized to frames, for example, compactness. In the first part of the talk, I will explain the basic notions of frames and their connection with topology. It turns out that we can find frame structure in other categories than topological spaces. For example, given a commutative ring R with identity, the lattice …

Be The Change: Re-Ignite Student’S Passion For Problem Solving & Mathematics, Joseph Bolz, Marti Shirley

Faculty Publications & Research

Outcomes!

• I will be able to facilitate an open ended and open middle problems in the classroom, complete with questioning techniques and student prompts.
• I will experience how to modify a textbook problem into a richer open task that encourages discussion and multiple approaches, with a focus on tailoring them to real world applications.
• I will leave with a list of questions, perfect for posing to students while engaged in the problem solving process, and also useful for any class period when students are lacking persistence

An Introduction To Shape Dynamics, Patrick R. Kerrigan

Physics

Shape Dynamics (SD) is a new fundamental framework of physics which seeks to remove any non-relational notions from its methodology. importantly it does away with a background space-time and replaces it with a conceptual framework meant to reflect direct observables and recognize how measurements are taken. It is a theory of pure relationalism, and is based on different first principles then General Relativity (GR). This paper investigates how SD assertions affect dynamics of the three body problem, then outlines the shape reduction framework in a general setting.

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

An Explicit Finite Volume Numerical Scheme For 2d Elastic Wave Propagation, Mihhail Berezovski, Arkadi Berezovski

Publications

The construction of the two-dimensional finite volume numerical scheme based on the representation of computational cells as thermodynamic systems is presented explicitly. The main advantage of the scheme is an accurate implementation of conditions at interfaces and boundaries. It is demonstrated that boundary conditions influence the wave motion even in the simple case of a homogeneous waveguide.

Reduced Bias For Respondent Driven Sampling: Accounting For Non-Uniform Edge Sampling Probabilities In People Who Inject Drugs In Mauritius, Miles Q. Ott, Krista J. Gile, Matthew T. Harrison, Lisa G. Johnston, Joseph W. Hogan

Statistical and Data Sciences: Faculty Publications

People who inject drugs are an important population to study in order to reduce transmission of blood-borne illnesses including HIV and Hepatitis. In this paper we estimate the HIV and Hepatitis C prevalence among people who inject drugs, as well as the proportion of people who inject drugs who are female in Mauritius. Respondent driven sampling (RDS), a widely adopted link-tracing sampling design used to collect samples from hard-to-reach human populations, was used to collect this sample. The random walk approximation underlying many common RDS estimators assumes that each social relation (edge) in the underlying social network has an equal …

A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin

Mathematics Faculty Publications

We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.

The Fock Space As A De Branges–Rovnyak Space, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show that de Branges–Rovnyak spaces include as special cases a number of spaces, such as the Hardy space, the Fock space, the Hardy–Sobolev space and the Dirichlet space. We present a general framework in which all these spaces can be obtained by specializing a sequence that appears in the construction. We show how to exploit this approach to solve interpolation problems in the Fock space.

Conceptual Models For Integer Addition And Subtraction, Nicole M. Wessman-Enzinger, Edward S. Mooney

Faculty Publications - College of Education

In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories – the conceptual models for integer addition and subtraction. These four conceptual models for thinking about and using integer addition and subtraction include Bookkeeping, Counterbalance, Relativity, and Translation, and are generated from the students’ posed stories. We also provide profiles of conceptual model use for two …

On The Equality Case Of The Ramanujan Conjecture For Hilbert Modular Forms, Liubomir Chiriac

Mathematics and Statistics Faculty Publications and Presentations

The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations π on GL(2) asserts that |av(π)| ≤ 2. We prove that this inequality is strict if π is generated by a CM Hilbert modular form of parallel weight two and v is a finite place of degree one. Equivalently, the Satake parameters of πv are necessarily distinct. We also give examples where the equality case does occur for primes of degree two.

Biorthogonal-Wavelet-Based Method For Numerical Solution Of Volterra Integral Equations, Mutaz Mohammad

All Works

© 2019 by the authors. Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is …

The Aluthge Transform Of Unilateral Weighted Shifts And The Square Root Problem For Finitely Atomic Measures, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we consider the following Square Root Problem for measures: Given a positive probability Borel measure μ (supported on an interval [a,b]⊆R+), does there exist a positive Borel measure ν such that μ=ν*ν holds? (Here * denotes the multiplicative convolution, properly defined on R+.) This problem is intimately connected to the subnormality of the Aluthge transform of a unilateral weighted shift. We develop a criterion to test whether a measure μ admits a square root, and we provide a concrete solution for the case of a finitely atomic measure having at most five atoms. In addition, we sharpen …

Experimental Demonstration Of Deterministic Chaos In A Waste Oil Biodiesel Semi-Industrial Furnace Combustion System, Shengyang Gao, Fashe Li, Qintai Xiao, Jianxin Xu, Huage Wang, Hua Wang

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the nonlinear dynamic characteristics of the oxygen-enriched combustion of waste oil biodiesel in semi-industrial furnaces were tested by the power spectrum, phase space reconstruction, the largest Lyapunov exponents, and the 0-1 test method. To express the influences of the system parameters, experiments were carried out under different oxygen content conditions (21%, 25%, 28%, 31%, and 33%). Higher oxygen enrichment degrees contribute to finer combustion sufficiency, which produces flames with high luminance. Flame luminance and temperature can be represented by different gray scale values of flame images. The chaotic characteristics of gray scale time series under different oxygen …

Diabetes And Its Effect On Abdominal Aortic Aneurysm Growth Rate In Hispanic Patients, Monica Betancourt-Garcia, Kristina Vatcheva, Amrit Thakur, Prateek Gupta, Eugene Postevka, Ricardo Martinez, R. Armour Forse

School of Mathematical & Statistical Sciences Faculty Publications

Background

The growth rate of abdominal aortic aneurysms (AAA) can vary depending on age, baseline diameter, blood pressure, race, and history of smoking. Paradoxically, previous studies show evidence of a protective effect of diabetes on the rate of AAA expansion despite its well-established role in the morbidity and mortality of cardiovascular disease. This study aims to investigate the impact diabetes plays on AAA growth within a Hispanic population.

Methods

Data were collected from patients who were predominantly Mexican-American at a single hospital site. Baseline and follow-up measures for AAA diameter were obtained from serial imaging studies. Demographics, medical history, the …

Student Perceptions Of Learning Introductory Mathematics In An Online Environment In Higher Education, Jamie Lynn Brooks

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the essence of student perception of learning introductory mathematics courses in an online environment at the college level. The central research question was, “What are the lived experiences of students who have completed introductory college mathematics courses in the online learning environment?” The phenomenon described was that of the beliefs and attitudes of the students who participated in introductory mathematics courses on the college level. The ideas explored were if students believe they learn effectively in this environment and how they believe they can best learn. Student beliefs and attitudes …

A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

Forecasting of real-time electricity load has been an important research topic over many years. Electricity load is driven by many factors, including economic conditions and weather. Furthermore, the demand for electricity varies with time, with different hours of the day and different days of the week having an effect on the load. This paper proposes a hybrid load-forecasting method that combines classical time series formulations with cubic splines to model electricity load. It is shown that this approach produces a model capable of making short-term forecasts with reasonable accuracy. In contrast to forecasting models that utilize a multitude of regressor …