Mathematics Commons^™

Merge Trees In Discrete Morse Theory, Benjamin Johnson

Mathematics Summer Fellows

The field of topological data analysis seeks to use techniques in topology to study large data sets. The hope is that rather than single quantities that summarize the data, such as mean or standard deviation, information about the data can be learned by studying the overall ``shape” of the data. One way to summarize this data is through a merge tree. Merge trees can be thought of as keeping track of certain clusters of data and determining when they merge together. In this paper, we will study merge trees induced by a discrete Morse function on a tree. Under a …

Properties Of A Class Of Mean Dependent On A Parameter, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Some properties of a new class of binary symmetric mean Mp(a,b) which depends on two positive numbers a and b, as well as a positive parameter p, are investigated. The logarithmic mean and arithmetic mean are two members of this class. It is shown that, for all values of the parameter p, the set of p-dependent means Mp(a,b) is bounded above by the mean M∞(a,b).

On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact.

An Analysis Of The Work Of Passengers Trains On Twozone Sections And Their Alert Automation, N. S. Tokhirov

Central Asian Problems of Modern Science and Education

Company "Uzbekistan railways" has made a great contribution to the safety of passenger traffic. It is expected that passenger trains will have a number of factors affecting the large passenger traffic in the coming days and will be in the future. That is why passenger trains require that the issuance of warnings from workers of the running facilities, electricity, signaling and communications, as well as station attendants at the station by dispatchers, be accurate and error free. This article describes the automation of issuing warnings for trains and trains at two zones

Development Of The Thickener Compositionwith Local Raw-Materials For Printing Blended Fabrics Cotton-Silk, F. N. Qurbonova, G. A. Ixtiyarova, X. Haydarova, N. Savriyeva

Central Asian Problems of Modern Science and Education

In the following article the developed new thickener are studied based on hydrolyzed acrylic emulsion (HAE), uzchitan and carbaxymethyl starch for printing mixed fabrics cotton-silk. Investigated coloristic prop- erty printed fabrics

Method For Determining Hydraulic Resistance During, K. Navruzov, Z. K. Shukurov, A. Sh. Begjanov

Central Asian Problems of Modern Science and Education

In the article, pulsating fluid flows in tubes with changing walls, which are of great importance in biological mechanics, in particular, in the flow of blood in the arterial vessel, are investigated. The solution of the problem obtained formulas for the distribution of pressure gradient, velocity and flow rate. Impedance method analyzed the increase in hydraulic resistance depending on the frequency of oscillation. It was found that with large values 2  of hydraulic resistance grow with growth 2  . For crowding out the same flow rates, for small and with large values of the vibrational number or frequency, …

Mathematical Models Of Multi-Coordinate Electromechatronic Systems Of Intellectual Robots, H. N. Nazarov, R. O. Temurbek

Central Asian Problems of Modern Science and Education

In the article mathematic description of mechatronic module in intelligent robots and robotic systems are observed. To display the structure of mechatronic modules, which consist of interrelated different electrical, magnetic and ELECTRONIC JOURNAL OF CENTRAL ASIAN PROBLEMS OF MODERN SCENCE AND EDUCATION. MARCH, 2019-I ISSN 2181-9750 81 mechatron components, mathematic models by the help of multiplication theory based on relations and visualising lines and points are designed. Analytical explanation of mechantronic modele in intelligent robots is provided

Development Of Linear Mathematical Models Of The Technological Process Of Crushing Seeds Crushing, F. Yusupov, T. Y. Kim, B. B. Nurmetova, J. M. Xojibayev

Central Asian Problems of Modern Science and Education

The simplified statistical linear model of the object under study is developed on the basis of experimental and statistical studies of the technological process of crushing the cottonseed of an oil extraction plant using the experimental design method. The analysis of the homogeneity of the dispersion, the significance of the coefficients of the linear model and the adequacy of the resulting model

Principles Of Automation Of Process Accounting And Control Devices Of Railway Automatics And Telemechanics, D. Kh. Baratov

Central Asian Problems of Modern Science and Education

The article deals with the issues of functional support of the automated system of accounting and control of railway automation and telemechanics devices: signaling, centralization and blocking; the components of the electronic Executive part of the system are presented; the conceptual model is proposed and the design features of the developed automated system are described.

Development Of The Thickener Compositionwith Local Raw-Materials For Printing Blended Fabrics Cotton-Silk, F. N. Qurbonova, G. A. Ixtiyarova, X. Haydarova, N. Savriyeva

Central Asian Problems of Modern Science and Education

In the following article the developed new thickener are studied based on hydrolyzed acrylic emulsion (HAE), uzchitan and carbaxymethyl starch for printing mixed fabrics cotton-silk. Investigated coloristic prop- erty printed fabrics

Principles Of Automation Of Process Accounting And Control Devices Of Railway Automatics And Telemechanics, D. Kh. Baratov

Central Asian Problems of Modern Science and Education

The article deals with the issues of functional support of the automated system of accounting and control of railway automation and telemechanics devices: signaling, centralization and blocking; the components of the electronic Executive part of the system are presented; the conceptual model is proposed and the design features of the developed automated system are described.

Method For Determining Hydraulic Resistance During, K. Navruzov, Z. K. Shukurov, A. Sh. Begjanov

Central Asian Problems of Modern Science and Education

In the article, pulsating fluid flows in tubes with changing walls, which are of great importance in biological mechanics, in particular, in the flow of blood in the arterial vessel, are investigated. The solution of the problem obtained formulas for the distribution of pressure gradient, velocity and flow rate. Impedance method analyzed the increase in hydraulic resistance depending on the frequency of oscillation. It was found that with large values 2  of hydraulic resistance grow with growth 2  . For crowding out the same flow rates, for small and with large values of the vibrational number or frequency, …

An Analysis Of The Work Of Passengers Trains On Twozone Sections And Their Alert Automation, N. S. Tokhirov

Central Asian Problems of Modern Science and Education

Company "Uzbekistan railways" has made a great contribution to the safety of passenger traffic. It is expected that passenger trains will have a number of factors affecting the large passenger traffic in the coming days and will be in the future. That is why passenger trains require that the issuance of warnings from workers of the running facilities, electricity, signaling and communications, as well as station attendants at the station by dispatchers, be accurate and error free. This article describes the automation of issuing warnings for trains and trains at two zones

Development Of Linear Mathematical Models Of The Technological Process Of Crushing Seeds Crushing, F. Yusupov, T. Y. Kim, B. B. Nurmetova, J. M. Xojibayev

Central Asian Problems of Modern Science and Education

The simplified statistical linear model of the object under study is developed on the basis of experimental and statistical studies of the technological process of crushing the cottonseed of an oil extraction plant using the experimental design method. The analysis of the homogeneity of the dispersion, the significance of the coefficients of the linear model and the adequacy of the resulting model

Mathematical Models Of Multi-Coordinate Electromechatronic Systems Of Intellectual Robots, H. N. Nazarov, R. O. Temurbek

Central Asian Problems of Modern Science and Education

In the article mathematic description of mechatronic module in intelligent robots and robotic systems are observed. To display the structure of mechatronic modules, which consist of interrelated different electrical, magnetic and ELECTRONIC JOURNAL OF CENTRAL ASIAN PROBLEMS OF MODERN SCENCE AND EDUCATION. MARCH, 2019-I ISSN 2181-9750 81 mechatron components, mathematic models by the help of multiplication theory based on relations and visualising lines and points are designed. Analytical explanation of mechantronic modele in intelligent robots is provided

Some Theoretical Links Between Shortest Path Filters And Minimum Spanning Tree Filters, Sravan Danda, Aditya Challa, B. S.Daya Sagar, Laurent Najman

Journal Articles

Edge-aware filtering is an important pre-processing step in many computer vision applications. In the literature, there exist several versions of collaborative edge-aware filters based on spanning trees and shortest path heuristics which work well in practice. For instance, tree filter (TF) which is recently proposed based on a minimum spanning tree (MST) heuristic yields promising results in many filtering applications. However, links between the tree-based filters and shortest path-based filters are faintly explored. In this article, we introduce an edge-aware generalization of the TF termed as UMST filter based on a subgraph generated by edges of all MSTs. The major …

Large And Small Data Blow-Up Solutions In The Trojan Y Chromosome Model, Rana D. Parshad, Matthew Beauregard, Eric M. Takyi, Thomas Griffin, Landrey Bobo

Faculty Publications

The Trojan Y Chromosome Strategy (TYC) is an extremely well investigated biological control method for controlling invasive populations with an XX-XY sex determinism. In [35, 36] various dynamical properties of the system are analyzed, including well posedness, boundedness of solutions, and conditions for extinction or recovery. These results are derived under the assumption of positive solutions. In the current manuscript, we show that if the introduction rate of trojan fish is zero, under certain large data assumptions, negative solutions are possible for the male population, which in turn can lead to finite time blow-up in the female and male populations. …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

Comparing Design Ground Snow Load Prediction In Utah And Idaho, Brennan L. Bean, Marc Maguire, Yan Sun

Mathematics and Statistics Faculty Publications

Snow loads in the western United States are largely undefined due to complex geography and climates, leaving the individual states to publish detailed studies for their region, usually through the local Structural Engineers Association (SEAs). These associations are typically made up of engineers not formally trained to develop or evaluate spatial statistical methods for their regions and there is little guidance from ASCE 7. Furthermore, little has been written to compare the independently developed design ground snow load prediction methods used by various western states. This paper addresses this topic by comparing the accuracy of a variety of spatial methods …

Are We At A Watershed Moment For The Quantitative Literacy Movement?: Review Of Shifting Context, Stable Core: Advancing Quantitative Literacy In Higher Education, By Luke Tunstall, Gizem Karaali, And Victor Piercey, Eds., Maura Mast

Numeracy

Luke Tunstall, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Concepts, Stable Core: Advancing Quantitative Literacy in Higher Education. Math Notes 88. (Mathematics Association of America, MAA Press). Print ISBN 978-0-88385-198-2. Electronic ISBN 978-1-61444-324-7.

The thematic approach of the edited MAA Notes volume Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education is that the “construct” of quantitative literacy is now fairly stable, but the contexts in which quantitative literacy is taught (and practiced) continue to change. Several chapters give the reader much to consider regarding what constitutes the foundation of this stable core and, relatedly, how quantitative …

Taking Multiple Regression Analysis To Task: A Review Of Mindware: Tools For Smart Thinking, By Richard Nisbett (2015), Jason Makansi

Numeracy

Richard Nisbett. 2015. Mindware: Tools for Smart Thinking.(New York, NY: Farrar, Strauss, and Giroux). 336 pp. ISBN: 9780374536244

Nisbett, a psychologist, may not achieve his stated goal of teaching readers to “effortlessly” extend their common sense when it comes to quantitative analysis applied to everyday issues, but his critique of multiple regression analysis (MRA) in the middle chapters of Mindware is worth attention from, and contemplation by, the QL/QR and Numeracy community. While in at least one other source, Nisbett’s critique has been called a “crusade” against MRA, what he really advocates is that it not be used as …

Quantitative Literacy And The Mathematical Association Of America In The 2000’S: Ql Subcommittee Of Cupm , Sigmaa Ql, And Maa Notes #70, Rick Gillman

Numeracy

This Roots and Seeds article is a partial history of the quantitative literacy movement in the Mathematical Association of America in the first decade of the 21st century. It focuses on the inclusion of QL in the MAA Committee on the Undergraduate Program in Mathematics’ CUPM Curriculum Guidelines (2004), the creation of the special interest group for MAA members (SIGMAA QL, 2004), and the work of that body in subsequent years, in particular, the MAA Notes #70, Current Practices in Quantitative Literacy (2006). I discuss some issues that were problematic in the QL movement in the MAA in those years …

The Ultimatum Game: An Introduction To Quantitative Literacy In A Social Justice Context, Robert G. Root

Numeracy

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

Roots And Seeds: Finding Our Place In The Social Practice Nexus That Is Quantitative Literacy, H. L. Vacher, Nathan D. Grawe

Numeracy

The purpose of our new Roots and Seeds feature is to provide an open-access space to archive first-hand accounts of QL activities that have preceded our journal (2008). The first two contributions in the collection appeared last issue: Linda Sons on the making of what has come to be known as the 1994 Sons Report (Mathematics Association of America), and Dorothy Wallace on her path to the Quantitative Literacy Design Team for Mathematics and Democracy (2001), and the questions that bedeviled them then – and us now. In this issue, we get Rick Gillman’s account of how the committee that …

Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This paper points students towards ideas they can use towards developing a convenient library for robot navigation, with examples based on Botball primitives, and points educators towards mathematics and programming exercises they can suggest to students, especially advanced high school students.

Quenching Estimates For A Non-Newtonian Filtration Equation With Singular Boundary Conditions, Matthew Beauregard, Burhan Selcuk

Faculty Publications

In this paper, the quenching behavior of the non-Newtonian filtration equation (φ(u))t = (|ux| r−2 ux)x with singular boundary conditions, ux (0, t) = u −p (0, t), ux (a, t) = (1 − u(a, t))−q is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when φ(u) = u and r = 2. Numerical experiments are provided to illustrate and provide additional validation of the theoretical estimates to the quenching rates and times.

Solution Of Fuzzy Fredholm Integral Equation Via Modified Homotopy Method, Raghad I. Sabri, Rasha Jalal Mitlif, Fatema Ahmed Sadeq

Emirates Journal for Engineering Research

In this paper, we proposed a modification to the Homotopy method by introducing accelerating parameters for solving fuzzy integral equations.The modified method is employed to find exact solutions for fuzzy Fredholm integral equations . The results imply that the modified method is very simple and effective.

Hierarchical Self-Assembly And Substitution Rules, Daniel Alejandro Cruz

USF Tampa Graduate Theses and Dissertations

A set of elementary building blocks undergoes self-assembly if local interactions govern how this set forms intricate structures. Self-assembly has been widely observed in nature, ranging from the field of crystallography to the study of viruses and multicellular organisms. A natural question is whether a model of self-assembly can capture the hierarchical growth seen in nature or in other fields of mathematics. In this work, we consider hierarchical growth in substitution rules; informally, a substitution rule describes the iterated process by which the polygons of a given set are individually enlarged and dissected. We develop the Polygonal Two-Handed Assembly Model …

Magnification Cross Sections For The Elliptic Umbilic Caustic Surface, Amir B. Aazami, Charles R. Keeton, Arlie O. Petters

Mathematics

In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as µ−2 for fold caustics and µ−2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as µ−2.5 in the two-image region and µ−2 in the …

L^{\Infty}-Estimates Of The Solution Of The Navier-Stokes Equations For Periodic Initial Data, Santosh Pathak

Mathematics & Statistics ETDs

In this doctoral dissertation, we consider the Cauchy problem for the 3D incompressible Navier-Stokes equations. Here, we are interested in a smooth periodic solution of the problem which happens to be a special case of a paper by Otto Kreiss and Jens Lorenz. More precisely, we will look into a special case of their paper by two approaches. In the first approach, we will try to follow the similar techniques as in the original paper for smooth periodic solution. Because of the involvement of the Fourier expansion in the process, we encounter with some intriguing factors in the periodic case …