Mathematics | Open Access Articles | Digital Commons Network™

Resilience Of Transportation Systems To Disasters, Nangga (Ga Nan) Oirat, Suman Balasubramanian Phd

Annual Student Research Poster Session

We used graph theory's centrality measures to process the resiliency of rail stations in India. Centrality measures are the principles of processing, while Python is the tool of processing.

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Big Cities: Air Pollution And Human Health, Natalie Michaels, Naima Shifa Phd

Annual Student Research Poster Session

Our project explores the growing issue of air pollution on urban environments throughout the United States. Through the use of the County Health Rankings data set, we investigated the connection amongst air pollution, health outcomes, and other socioeconomic and environmental risk factors.

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Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

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Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

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Awegnn: Auto-Parametrized Weighted Element-Specific Graph Neural Networks For Molecules., Timothy Szocinski, Duc Duy Nguyen, Guo-Wei Wei

Mathematics Faculty Publications

While automated feature extraction has had tremendous success in many deep learning algorithms for image analysis and natural language processing, it does not work well for data involving complex internal structures, such as molecules. Data representations via advanced mathematics, including algebraic topology, differential geometry, and graph theory, have demonstrated superiority in a variety of biomolecular applications, however, their performance is often dependent on manual parametrization. This work introduces the auto-parametrized weighted element-specific graph neural network, dubbed AweGNN, to overcome the obstacle of this tedious parametrization process while also being a suitable technique for automated feature extraction on these internally complex …

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Trimming Complexes, Keller Vandebogert

Theses and Dissertations

We produce a family of complexes called trimming complexes and explore applications. We first study ideals defining type 2 compressed rings with socle minimally generated in degrees s and 2s − 1 for s > 2. We prove that all such ideals arise as trimmings of grade 3 Gorenstein ideals and show that trimming complexes yield an explicit free resolution. In particular, we give bounds on parameters arising in the Tor-algebra classification and construct explicit ideals attaining all intermediate values for every s. This partially answers a question of realizability of Tor-algebra structures posed by Avramov. Next, we study how …

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Effects Of Virtual Math Mentorships On Elementary Student Math Scores, Tammy T. May

Doctoral Dissertations and Projects

The purpose of this quantitative, quasi-experimental study was to examine the relationship between college students’ virtual math mentorships and instruction on third grade students’ math academic success. College students in teacher preparation programs investigated deficiencies in third grade students’ competency of math concepts as specified by state standards, and they designed lessons to address these challenges through weekly virtual meetings. Third grade teachers wanted to provide additional math supports for their struggling students, and this partnership between the college students and the third graders was the foundation of this study at four Title 1 rural elementary schools. This research is …

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Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we derive the generalized log Burr XII (GLBXII) distribution [2] from the generalized Burr-Hatke differential equation. We characterize the GLBXII distribution via innovative techniques. We derive various reliability measures (series and parallel). We also authenticate the potentiality of the GLBXII model via economics applications. The applications of characterizations and reliability measures of the GLBXII distribution in different disciplines of science will be profitable for scientists.

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Computable Model Theory On Loops, Josiah Schmidt

All NMU Master's Theses

We give an introduction to the problem of computable algebras. Specifically, the algebras of loops and groups. We start by defining a loop and group, then give some of their properties. We then give an overview of comptability theory, and apply it to loops and groups. We conclude by showing that a finitely presented residually finite algebra has a solvable word problem.

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Enacting Systemic Change: The Evolving Landscape Of Computer Science Education In The State Of Wisconsin, Heather Bort

Dissertations (1934 -)

Over the last decade, the Systems Lab at Marquette University has undertaken a grand challenge to positively impact learners and educators in the state of Wisconsin with computer science education innovation. We have moved through a progression in maturity around recognizing the need for and implementing a propagation plan to achieve this desired outcome. This work showcases several novel innovations with increasing overall effectiveness in creating a more diverse community of computer science educators and learners in the state. We demonstrate a pattern of increased engagement, sustainable change, and measurable impact, that has resulted in a more accessible and inclusive …

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Sepsis Monitoring Using Contextually-Tailored Online Change Point Detection And Beyond, Nazmus Sakib

Dissertations (1934 -)

Considering morbidity, mortality, and annual treatment costs, the dramatic rise in the incidence of sepsis and septic shock among intensive care unit (ICU) admissions in US hospitals is an increasing concern. The recent excruciating statistics regarding sepsis mortality, the average length of hospital stay, and annual treatment costs made sepsis treatment and research a critical domain in medical informatics. The aims of this dissertation center around four research questions. First, we discuss how we can investigate the prevalence and underlying relation of the sepsis diagnosis criteria (qSOFA and SIRS) and its implications in Medical Informatics and predictive analytics. Second, we …

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Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …

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Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam

Electrical & Computer Engineering Theses & Dissertations

The problem statement for this dissertation is two-fold. The first problem considered is when does a Chen-Fliess series in an additive static feedback connection with a formal static map yield a closed-loop system with a Chen-Fliess series expansion? This work proves that such a closed-loop system always has a Chen-Fliess series representation. Furthermore, an algorithm based on the Hopf algebras for the shuffle group and the dynamic output feedback group is designed to compute the generating series of the closed-loop system. It is proved that the additive static feedback connection preserves local convergence and relative degree, but a counterexample shows …

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Latinx Students’ Mathematics Anxiety And Their Study Habits: Exploring Their Relationship At The Postsecondary Level, Luis M. Fernandez, Xiaohui Wang, Olga Ramirez, Cristina Villalobos

School of Mathematical & Statistical Sciences Faculty Publications

Increasing Latinx students’ success in college-level mathematics calls for exploration on their mathematics anxiety as it relates to study habits. Using a sample of Latinx students in a Hispanic Serving Institution and their levels of mathematics anxiety, pairwise analyses revealed significant differences among subgroups. Moreover, regression analyses showed Latinx students’ study habits being predictive of mathematics anxiety. As a result, recommendations are provided that could alleviate mathematics anxiety and its effects on Latinx college students.

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Modernization Of Scienttific Mathematics Formula In Technology, Iwasan D. Kejawa Ed.D, Prof. Iwasan D. Kejawa Ed.D

Department of Mathematics: Faculty Publications

Abstract
Is it true that we solve problem using techniques in form of formula? Mathematical formulas can be derived through thinking of a problem or situation. Research has shown that we can create formulas by applying theoretical, technical, and applied knowledge. The knowledge derives from brainstorming and actual experience can be represented by formulas. It is intended that this research article is geared by an audience of average knowledge level of solving mathematics and scientific intricacies. This work details an introductory level of simple, at times complex problems in a mathematical epidermis and computability and solvability in a Computer Science. …

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Polynomials, Primes And The Pte Problem, Joseph C. Foster

Theses and Dissertations

This dissertation considers three different topics. In the first part of the dissertation, we use Newton Polygons to show that for the arithmetic functions g(n) = n t , where t ≥ 1 is an integer, the polynomials defined with initial condition P g 0 (X) = 1 and recursion P g n (X) = X n Xn k=1 g(k)P g n−k (X) are X/ (n!) times an irreducible polynomial. In the second part of the dissertation, we show that, for 3 ≤ n ≤ 8, there are infinitely many 2-adic integer solutions to the Prouhet-Tarry-Escott (PTE) problem, that are …

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Simulation Of Pituitary Organogenesis In Two Dimensions, Chace E. Covington

Theses and Dissertations

The pituitary gland is a vital part of the endocrine system found in all vertebrates and is responsible for the production of hormones that influence many physiological processes in the organism’s body. Although much has been learned of pituitary organogenesis, studying the dynamics of the cells in the developing pituitary gland is difficult. Pituitary organogenesis has been studied through “snapshots” of a developing pituitary gland by removing and viewing the pituitary glands of different specimens. Thus, how the individual cells in the developing pituitary gland behave and interact with one another is not fully understood. To aid in understanding pituitary …

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Shutterplot: An R Package To Display All Summary Statistics Of A Simple Linear Regression Model, Siddhanta Phuyal, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

A shutterplot depicts all summary statistics in a simple linear regression model. Instead of reporting their numerical values, a shutterplot gives their visual representations. In this paper, we provide a step-by-step description of how the shutterplot package constructs a shutterplot and the options the user has in customizing it.

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Ivy Plot: Enhancing A Dot Plot By Representing Observations As Leaflets, Tri Ha Minh Nguyen '23, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

For a large data set, a dot plot poses a challenge—albeit unintended—in counting the dots. To overcome this shortcoming Sarkar and Rashid (2021) proposed an IVY plot, which represents tied data in batches of five by depicting an IVY leaf with five leaflets. These leaves are bottom-justified and stacked vertically, with the topmost leaf possibly having fewer than five leaflets, until the number of leaflets equals the frequency at each value

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Stability Of Peakons And Periodic Peakons For A Nonlinear Quartic Camassa-Holm Equation, Aiyong Chen, Tongjie Deng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the orbital stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation (QCHE).We first verify that the QCHE has global peakon and periodic peakon solutions. Then by the invariants of the equation and controlling the extrema of the solution, we prove that the shapes of the peakons and periodic peakons are stable under small perturbations in the energy space.

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Numerical Approaches Of Pricing European Options In The Cox-Ross-Rubenstein Models, Hai Phan, Seonguk Kim Phd

Annual Student Research Poster Session

The Cox-Ross-Rubinstein (CRR) market mode is used to price European and American Options without complex elements, including dividends, stocks, and stock indexes paying a continuous dividend yield, futures, and currency options. The model is an elegant, simple, but strong model to explain the general economic intuition behind option pricing and its principal techniques. In the paper, the CRR model's numerical elements and equations are indicated, and a practical event is examined to demonstrate the application of the model in the financial market. To make it easier to understand, figures, including tables and graphs, are also included to visualize and simplify …

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Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino

Faculty Publications

Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going …

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Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks

Graduate Theses and Dissertations

Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.

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Effect Of Excess Tellurium And Lead On Defor-Mation - Characteristics Of Polycrystalline Pbte Films, Yu.Yu. Vaitkus, Otajonov Salimjon

Scientific Bulletin. Physical and Mathematical Research

In this work, we studied the ef-fect of excess tellurium and lead on the defor-mation characteristics of polycrystalline PbTe films obtained on different substrates. It was found that the resistance of the films first increases and reach-es a maximum, and with a further increase in the level of deformation, it decreases and the sign of the tensile resistance begins to change, which are associated with the presence of internal stresses in the films. It was also shown that with an increase in the amount of lead in the composition of the PbTe film, the electrical conductivity increases in com-parison with …

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Structure And Electrophysical Properties Of A Solid Solution (Gaas1-Δbiδ)1-X-Y(Ge2)X(Znse)Y, S.Z. Zainabidinov, I.N. Karimov, Hotamjon Mansurov, Akramjon Boboev, Dilkhayotjon Pulatjon Ugli Abdurakhimov

Scientific Bulletin. Physical and Mathematical Research

This paper shows the possibility of growing a single-crystal solid solution of substitution (GaAs1-δBiδ)1-x-y(Ge2)x(ZnSe)y on GaAs substrates by liquid-phase epitaxy from a bismuthcontaining solution-melt. The grown films had a ptype of conductivity with a current carrier concentration of 1,86·1017 сm-3, a mobility of р = 300 cm2/V·s, and a resistivity of 0,13 Ohms·cm. Structural studies have shown that the epitaxial films have a sphalerite structure of the ZnS type and are monocrystalline with an orientation of (100). The crystal lattice parameter of the film was af = 0,56697 nm. Studies of current-voltage characteris-tics of n-GaAs – p-(GaAs1-δBiδ)1-x-y(Ge2)x(ZnSe)y heterostructures at different …

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Simulation Of Self-Heating Effect In Mosfet Based On 2d Mos2, Atabek E. Atamuratov, Xushnudbek Sh. Saparov, A Yusupov, Frank Schwierz

Scientific Bulletin. Physical and Mathematical Research

One of the main trends of today's electronics is the decreasing the sizes of MOSFET up to nanometer scale. In this connection there are two main views to the perspective of scaling. According to one of them limit of scaling is reached at sizes 10 nm order, however according to second view, still there are opportunity to decrease transistor to more lower sizes. In accordance with second approach it is suggested to continue the size scaling by modification the transistor structure or by using the new materials, particularly one or two dimensional materials. One of such suggestions is the designing …

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Method Of Characteristics For Solving The Problem Of Gas Outflow From An Elementary Sec-Tion Of A Gas Pipeline, Madaminjon K. Mahkamov, S.S. Akhmadjonov, I.K. Khujaev

Scientific Bulletin. Physical and Mathematical Research

Numerous problems based on equations of hyperbolic type are solved by the method of characteristics when boundary conditions of the first, second and third kinds are set on the boundary. These include, in particular, the problems of pipeline transportation of various media. The quasi-one-dimensional equations of conservation of mass and momentum are linearized and separate equations are drawn up for a specific indicator (flow rate, gas pressure) of the process. This approach is associated with the tradition of forming boundary conditions and solving problems only with respect to a specific indicator, in particu-lar, with respect to pressure, velocity, and flow …

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Electrophysical Properties Of Supercapacitor On The Basis Of New Gel Polymer Electrolyte, J.A. Shodmanov, Azamat Boymirzaev

Scientific Bulletin. Physical and Mathematical Research

The results showed a slight increase in internal resistance under the influence of bending and confirmed that the equivalent circuit model of electrons did not change under bending conditions as indicated in graphically illustrated the results by cyclic voltamperometry (TsV) at a scanning speed of 10 mV / s under the above bending angles of the SK prepared on the basis of PG 10 GPE. From ex-periments we found that the shapes are almost rec-tangular, with no redox peaks observed. We can see that the area of the TsV curves changes slightly as the bending angle increases, but this does …

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Influence Of A Strong Magnetic Field On Fermi Energy Oscillations In Two-Dimensional Semiconductor Materials, Gafur Gulyamov, Ulugbek Inayatillyevich Erkaboev, Rustam Gulomzhonovich Rakhimov, Nozimjon Sayidov Sayidov, Jasurbek Mirzaev

Scientific Bulletin. Physical and Mathematical Research

This article discusses the effect of a quantizing magnetic field and temperature on Fermi energy oscillations in nanoscale semiconductor materials. A generalized mathematical expression is obtained for calculating the dependence of the Fermi energy oscillations on the magnetic field, temperature, and thickness of the quantum well. It is shown that the Fermi energy in nanoscale semiconductor materials under a quantizing magnetic field is quantized. The proposed theory explains the experimental results in two-dimensional semiconductor structures with a parabolic dispersion law.

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Determination Of The Specific Thermo Emf Of Granulated Silicon Doped With Alkaline Metals., B.M. Abdurakhmanov, Zarnigor Sohibova, M.M. Adilov

Scientific Bulletin. Physical and Mathematical Research

The value of the specific thermo EMF is one of the most important thermoelectric parameters of a material and in practice is estimat-ed mainly by two well-known methods - integral and differential. To measure the thermo EMF of granular silicon, we used a differential method. In this work, the thermoelectric properties of granular silicon containing alkali metal atoms have been studied, the presence of which, for example, in single-crystal structures makes it possible to improve the characteristics of a number of devices, and in polycrystalline ones, the effect of grain boundaries on the electrical properties, in particular, to reduce the …

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Full-Text Articles in Mathematics

Resilience Of Transportation Systems To Disasters, Nangga (Ga Nan) Oirat, Suman Balasubramanian Phd

Annual Student Research Poster Session

Big Cities: Air Pollution And Human Health, Natalie Michaels, Naima Shifa Phd

Annual Student Research Poster Session

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

Awegnn: Auto-Parametrized Weighted Element-Specific Graph Neural Networks For Molecules., Timothy Szocinski, Duc Duy Nguyen, Guo-Wei Wei

Mathematics Faculty Publications

Trimming Complexes, Keller Vandebogert

Theses and Dissertations

Effects Of Virtual Math Mentorships On Elementary Student Math Scores, Tammy T. May

Doctoral Dissertations and Projects

Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

Computable Model Theory On Loops, Josiah Schmidt

All NMU Master's Theses

Enacting Systemic Change: The Evolving Landscape Of Computer Science Education In The State Of Wisconsin, Heather Bort

Dissertations (1934 -)

Sepsis Monitoring Using Contextually-Tailored Online Change Point Detection And Beyond, Nazmus Sakib

Dissertations (1934 -)

Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam

Electrical & Computer Engineering Theses & Dissertations

Latinx Students’ Mathematics Anxiety And Their Study Habits: Exploring Their Relationship At The Postsecondary Level, Luis M. Fernandez, Xiaohui Wang, Olga Ramirez, Cristina Villalobos

School of Mathematical & Statistical Sciences Faculty Publications

Modernization Of Scienttific Mathematics Formula In Technology, Iwasan D. Kejawa Ed.D, Prof. Iwasan D. Kejawa Ed.D

Department of Mathematics: Faculty Publications

Polynomials, Primes And The Pte Problem, Joseph C. Foster

Theses and Dissertations

Simulation Of Pituitary Organogenesis In Two Dimensions, Chace E. Covington

Theses and Dissertations

Shutterplot: An R Package To Display All Summary Statistics Of A Simple Linear Regression Model, Siddhanta Phuyal, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

Ivy Plot: Enhancing A Dot Plot By Representing Observations As Leaflets, Tri Ha Minh Nguyen '23, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

Stability Of Peakons And Periodic Peakons For A Nonlinear Quartic Camassa-Holm Equation, Aiyong Chen, Tongjie Deng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Numerical Approaches Of Pricing European Options In The Cox-Ross-Rubenstein Models, Hai Phan, Seonguk Kim Phd

Annual Student Research Poster Session

Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino

Faculty Publications

Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks

Graduate Theses and Dissertations

Effect Of Excess Tellurium And Lead On Defor-Mation - Characteristics Of Polycrystalline Pbte Films, Yu.Yu. Vaitkus, Otajonov Salimjon

Scientific Bulletin. Physical and Mathematical Research

Structure And Electrophysical Properties Of A Solid Solution (Gaas1-Δbiδ)1-X-Y(Ge2)X(Znse)Y, S.Z. Zainabidinov, I.N. Karimov, Hotamjon Mansurov, Akramjon Boboev, Dilkhayotjon Pulatjon Ugli Abdurakhimov

Scientific Bulletin. Physical and Mathematical Research

Simulation Of Self-Heating Effect In Mosfet Based On 2d Mos2, Atabek E. Atamuratov, Xushnudbek Sh. Saparov, A Yusupov, Frank Schwierz

Scientific Bulletin. Physical and Mathematical Research

Method Of Characteristics For Solving The Problem Of Gas Outflow From An Elementary Sec-Tion Of A Gas Pipeline, Madaminjon K. Mahkamov, S.S. Akhmadjonov, I.K. Khujaev

Scientific Bulletin. Physical and Mathematical Research

Electrophysical Properties Of Supercapacitor On The Basis Of New Gel Polymer Electrolyte, J.A. Shodmanov, Azamat Boymirzaev

Scientific Bulletin. Physical and Mathematical Research

Influence Of A Strong Magnetic Field On Fermi Energy Oscillations In Two-Dimensional Semiconductor Materials, Gafur Gulyamov, Ulugbek Inayatillyevich Erkaboev, Rustam Gulomzhonovich Rakhimov, Nozimjon Sayidov Sayidov, Jasurbek Mirzaev

Scientific Bulletin. Physical and Mathematical Research

Determination Of The Specific Thermo Emf Of Granulated Silicon Doped With Alkaline Metals., B.M. Abdurakhmanov, Zarnigor Sohibova, M.M. Adilov

Scientific Bulletin. Physical and Mathematical Research