Mathematics Commons^™

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.

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 …

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.

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 …

A Computationally Efficient Framework For Vector Representation Of Persistence Diagrams, Kit C. Chan, Umar Islambekov, Alexey Luchinsky, Rebecca Sanders

Mathematical and Statistical Science Faculty Research and Publications

In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in R² computed using tools of algebraic topology. However, this multi-set structure limits the utility of PDs in applications. Therefore, in recent years efforts have been directed towards extracting informative and efficient summaries from PDs to broaden the scope of their use for machine learning tasks. We propose a computationally efficient framework to convert a PD into a vector in Rⁿ, called a vectorized persistence block (VPB). We show that our representation …

Question 1: Dinosaur Killer Crater; Question 2: Graduation Speeches, Larry Weinstein

Physics Faculty Publications

The Fermi Questions: In 2003, the "Dinosaur Killer" asteroid crater was imaged for the first time (see National Geographic News, March 7, 2003). The crater is believed to be 100 km in radius and 1 km deep. What was the kinetic energy of the asteroid that made the crater? Express your answer in joules and in megatons (1 MT = 4 ·10 J).

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.

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 …

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.

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 …

The Infinity Conundrum: Understanding Topics In Set Theory And The Continuum Hypothesis, Sabrina Grace Helck

Senior Independent Study Theses

This project is concerned with articulating the necessary background in order to understand the famous result of the undecidability of the continuum hypothesis. The first chapter of this independent study discusses the foundations of set theory, stating fundamental definitions and theorems that will be used throughout the remainder of the project. The second chapter focuses on ordinal and cardinal numbers which will directly relate to the final chapter. First, there is a clear explanation of the notion of order and what it means for a set to be well-ordered. Then ordinal numbers are defined and some properties are listed and …

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …