Mathematics Commons^™

Arf Numerical Semigroups With Multiplicity $11$ And $13$, Hali̇l İbrahi̇m Karakaş, Sedat İlhan, Meral Süer

Turkish Journal of Mathematics

Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity $11$ and $13$, and combining these results with previous results about the number of Arf numerical semigroups with multiplicity $2, 3, 5, 7$, we share some observations about the set of Arf numerical semigroups with prime multiplicity.

A Multidimensional Diffusion Coefficient Determination Problem For The Time-Fractional Equation, Durdimurod Durdiev, Askar Rahmonov

Turkish Journal of Mathematics

In this paper, we consider a multidimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation the Schauder principle is applied. The local existence and uniqueness results are obtained.

Formulas For Special Numbers And Polynomials Derived From Functional Equations Of Their Generating Functions, Nesli̇han Kilar

Turkish Journal of Mathematics

The main purpose of this paper is to investigate various formulas, identities and relations involving Apostol type numbers and parametric type polynomials. By using generating functions and their functional equations, we give many relations among the certain family of combinatorial numbers, the Vieta polynomials, the two-parametric types of the Apostol-Euler polynomials, the Apostol-Bernoulli polynomials, the Apostol-Genocchi polynomials, the Fibonacci and Lucas numbers, the Chebyshev polynomials, and other special numbers and polynomials. Moreover, we give some formulas related to trigonometric functions, special numbers and special polynomials. Finally, some remarks and observations on the results of this paper are given.

Function Approximation Guarantees For A Shallow Neural Network Trained By Gradient Flow, Russell Gentile

Electronic Theses and Dissertations, 2020-2023

This work features an original result linking approximation and optimization theory for deep learning. Several examples from recent literature show that, given the same number of learnable parameters, deep neural networks can approximate richer classes of functions, with better accuracy than classical methods. The bulk of approximation theory results though, are only concerned with the infimum error for all possible parameterizations of a given network size. Their proofs often rely on hand-crafted networks, where the weights and biases are carefully selected. Optimization theory indicates that such models would be difficult or impossible to realize with standard gradient-based training methods. The …

Toward Permutation Bases In The Equivariant Cohomology Rings Of Regular Semisimple Hessenberg Varieties, Megumi Harada, Martha Precup, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Recent work of Shareshian and Wachs, Brosnan and Chow, and Guay-Paquet connects the wellknown Stanley–Stembridge conjecture in combinatorics to the dot action of the symmetric group S_n on the cohomology rings H∗ (Hess(S, h)) of regular semisimple Hessenberg varieties. In particular, in order to prove the Stanley–Stembridge conjecture, it suffices to construct (for any Hessenberg function h) a permutation basis of H∗ (Hess(S, h)) whose elements have stabilizers isomorphic to Young subgroups. In this manuscript we give several results which contribute toward this goal. Specifically, in some special cases, we give a new, purely combinatorial construction of classes …

New Lower Bounds On The Size-Ramsey Number Of A Path, Deepak Bal, Louis Debiasio

Department of Mathematics Faculty Scholarship and Creative Works

We prove that for all graphs with at most (3.75 − o(1))n edges there exists a 2-coloring of the edges such that every monochromatic path has order less than n. This was previously known to be true for graphs with at most 2.5n − 7.5 edges. We also improve on the best-known lower bounds in the r-color case.

Grade K-5 Teachers’ Perceptions Of Professional Development That Supports Mathematics Instruction, Shannon Annette Manley

Walden Dissertations and Doctoral Studies

Many Grade K-5 teachers in the United States do not receive the mathematics support they need from the professional development (PD) activities offered by their school districts. The purpose of this qualitative research was to explore the perceptions of Grade K-5 teachers on the PD activities they received from their school district to support mathematics instruction. The conceptual framework that supported this study was andragogy, an adult learning theory that takes the learner’s needs into account and values the connection to real-world situations. The research question addressed how Grade K-5 teachers perceive the PD that they were offered by their …

Investigaion Of The Gamma Hurdle Model For A Single Population Mean, Alissa Jacobs

Electronic Theses and Dissertations

A common issue in some statistical inference problems is dealing with a high frequency of zeroes in a sample of data. For many distributions such as the gamma, optimal inference procedures do not allow for zeroes to be present. In practice, however, it is natural to observe real data sets where nonnegative distributions would make sense to model but naturally zeroes will occur. One example of this is in the analysis of cost in insurance claim studies. One common approach to deal with the presence of zeroes is using a hurdle model. Most literary work on hurdle models will focus …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Global Existence And Blow-Up Phenomena For A Periodic Modified Camassa–Holm Equation (Moch), Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study global existence and blow-up for a periodic modified Camassa–Holm equation in nonhomogeneous Sobolev spaces. Also, we provide a key blow-up criteria to investigate norm inflation and ill-posedness problem for the equation in the critical Sobolev space.

Question 1: Ketchup Packets; Question 2: Dog Hair, Larry Weinstein

Physics Faculty Publications

Question 2: Dog hair How much dog hair is shed (and subsequently vacuumed) in the U.S. each year? How many ketchup packets are used in America every year?.

Solutions For Fermi Questions, May 2022, Larry Weinstein

Physics Faculty Publications

[Introduction] Question: If the James Webb Space Telescope could be turned to face the Earth, how small an object could it resolve? How does that compare to the Hubble Space Telescope?.

To answer this, we need to know the location of the JWST, its size, and the wavelengths it can image. (This is one of those Fermi questions where we're not really estimating, but we are calculating unusual order-of-magnitude answers.) The JWST is orbiting the Earth and Sun at the second Lagrange point, L2, which is located 1.5 × 10⁶ km beyond the Earth (so that the Sun, Earth and …

Solutions For Fermi Questions, March 2022, Larry Weinstein

Physics Faculty Publications

Answers the questions:

Question 1: Ketchup packets

How many ketchup packets are used in America every year?

Question 2: Dog hair

How much dog hair is shed (and subsequently vacuumed) in the U.S. each year?

Realtime Event Detection In Sports Sensor Data With Machine Learning, Mallory Cashman

Honors Theses and Capstones

Machine learning models can be trained to classify time series based sports motion data, without reliance on assumptions about the capabilities of the users or sensors. This can be applied to predict the count of occurrences of an event in a time period. The experiment for this research uses lacrosse data, collected in partnership with SPAITR - a UNH undergraduate startup developing motion tracking devices for lacrosse. Decision Tree and Support Vector Machine (SVM) models are trained and perform with high success rates. These models improve upon previous work in human motion event detection and can be used a reference …

Revisiting The Interval And Fuzzy Topsis Methods: Is Euclidean Distance A Suitable Tool To Measure The Differences Between Fuzzy Numbers?, Hosein Arman, Abdollah Hadi-Vencheh, Reza Kiani Mavi, Mehdi Khodadadipour, Ali Jamshidi

Research outputs 2022 to 2026

Euclidean distance (ED) calculates the distance between n-coordinate points that n equals the dimension of the space these points are located. Some studies extended its application to measure the difference between fuzzy numbers (FNs).This study shows that this extension is not logical because although an n-coordinate point and an FN are denoted the same, they are conceptually different. An FN is defined by n components; however, n is not equal to the dimension of the space where the FN is located. This study illustrates this misapplication and shows that the ED between FNs does not necessarily reflect their difference. We …

Corner’S Theorem On Modules With Anti-Isomorphic Endomorphism Algebras, Brendan Goldsmith, Noel White

Articles

We present a version of an unpublished result of A.L.S. Corner on p-adic modules with anti-isomorphic endomorphism algebras. The result gives a complete description of necessary conditions for two such modules to have anti-isomorphic endomorphism algebras and a sufficient condition is also given. A main difference in the current version is that extensive use is made of our ability to describe certain homomorphism groups.

Viscoelastic And Electromagnetic Materials With Nonlinear Memory, Claudio Giorgi, John Murrough Golden

Articles

A method is presented for generating free energies relating to nonlinear constitutive equations with memory from known free energies associated with hereditary linear theories. Some applications to viscoelastic solids and hereditary electrical conductors are presented. These new free energies are then used to obtain estimates for nonlinear integro-differential evolution problems describing the behavior of nonlinear plasmas with memory.

Rock Paintings, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Cloud Ripple Pattern, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Rock Paintings: Solutions For Fermi Questions, September 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Mathematics Learning, Teaching, And Equity In Policy And Programs: The Case Of Secondary Mathematics Teacher Education In The United States, Eryn M. Stehr Maher, Hyunyi Jung, Jill Newton

Mathematical Sciences: Faculty Publications

Professional organizations have provided recommendations for mathematics teaching and learning; however, few studies have investigated the practical integration of those recommendations into mathematics teacher education programs. In this study, we examine how the reported “big ideas” of courses in secondary mathematics teacher education programs emphasized the content and teaching practices necessary for future mathematics teachers, as recommended by policy documents. As part of a larger study, we conducted a series of interviews in secondary mathematics teacher education programs at four universities (names are descriptive pseudonyms): Great Lakes University (GLU), Midwestern Research University (MRU), Midwestern Urban University (MUU), and Southeastern Research …

Middle School Teacher Perceptions On Implementation Of The Math Workshop Model, Donna Mack

Walden Dissertations and Doctoral Studies

Mathematics achievement levels in the middle school grades have reportedly been below proficiency for students in the United States. The math workshop model has been identified as a possible approach to increase student achievement in mathematics. The purpose of this generic qualitative study, guided by Mezirow’s transformative learning theory, focused on understanding middle school teacher perceptions of the implementation of the math workshop model. The five research questions addressed middle school teacher perceptions of the implementation and influence of the math workshop and how it had transformed their understanding of teaching mathematics. Data were collected through semistructured interviews with nine …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Cryptography Through The Lens Of Group Theory, Dawson M. Shores

College of Graduate Studies: Theses & Dissertations

Cryptography has been around for many years, and mathematics has been around even longer. When the two subjects were combined, however, both the improvements and attacks on cryptography were prevalent. This paper introduces and performs a comparative analysis of two versions of the ElGamal cryptosystem, both of which use the specific field of mathematics known as group theory.

Solutions For Fermi Questions, April 2022, Larry Weinstein

Physics Faculty Publications

[Introduction] Answer: When an asteroid hits the Earth, it transfers thermal and kinetic energy to the ground. The kinetic energy moves rock and makes a crater. We'll start by estimating the kinetic energy needed to make a crater.

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …

Finite Index Right-Angled Mock Artin Groups In Right-Angled Mock Reflection Groups, Zachary Marcum

Murray State Theses and Dissertations

Associated to any graph Γ are several groups where their presentations are encoded by Γ. Two such groups are right-angled Coxeter groups and right-angled Artin groups. By introducing more structure to Γ, what we call "local involutions," the graph Γ becomes a right-angled mock reflection system and encodes the presentation of two more groups: right-angled mock reflection groups and right-angled mock Artin groups.

Here we show that every right-angled mock Artin group associated with an n-gon graph with local involutions is a finite index subgroup in some right-angled mock reflection group. We employ a strategy similar to the one Davis …

Maintenance Optimization In A Digital Twin For Industry 4.0, Abhijit Gosavi, Vy Khoi Le

Engineering Management and Systems Engineering Faculty Research & Creative Works

The advent of Internet of Things and artificial intelligence in the era of Industry 4.0 has transformed decision-making within production systems. In particular, many decisions that previously required significant human activity are now made automatically with minimal human intervention via so-called digital twins (DTs). In the context of maintenance and reliability modeling, this naturally calls for new paradigms that can be seamlessly integrated within DTs for decision-making. The input data for time to failure needed in reliability computations are directly collected from the work center in a digital setting and often do not satisfy a known distribution. A neural network …

Lasso: Listing All Subset Sums Obediently For Evaluating Unbounded Subset Sums, Christopher N. Burgoyne, Travis J. Wheeler

Graduate Student Theses, Dissertations, & Professional Papers

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum …

New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

This collective book presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.