The Development Of Notation In Mathematical Analysis,
2016
Loyola Marymount University
The Development Of Notation In Mathematical Analysis, Alyssa Venezia
Honors Thesis
The field of analysis is a newer subject in mathematics, as it only came into existence in the last 400 years. With a new field comes new notation, and in the era of universalism, analysis becomes key to understanding how centuries of mathematics were unified into a finite set of symbols, precise definitions, and rigorous proofs that would allow for the rapid development of modern mathematics. This paper traces the introduction of subjects and the development of new notations in mathematics from the seventeenth to the nineteenth century that allowed analysis to flourish. In following the development of analysis, we …
The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space,
2016
East Tennessee State Universtiy
The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal
Electronic Theses and Dissertations
A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show …
The Effect Of Tommy John (Ucl) Reconstructive Surgery On A Pitcher’S Arm And Career Progression,
2016
Bryant University
The Effect Of Tommy John (Ucl) Reconstructive Surgery On A Pitcher’S Arm And Career Progression, Jack Grant
Honors Projects in Mathematics
Injuries have plagued professional athletes since their sports have been in existence. The examination of how teams can diminish the side effects of the injuries en route to a speedy recovery remains an evolving process and a topic of concern for all. Injury preventative tactics have been implemented by coaching staffs and various training personnel. Major League Baseball (MLB) pitchers are noticing an increase in the number of surgeries performed each year. The tearing of the ulnar collateral ligament (UCL) in the elbow has become a predominant injury among pitchers in the MLB. Reconstructive surgery, also known as Tommy John …
Predictions Of Success In The Actuarial Major,
2016
Bryant University
Predictions Of Success In The Actuarial Major, Jessica Soojian
Honors Projects in Mathematics
This study finds predictive factors that have a significant effect on the ending Mathematics/Actuarial GPA of Actuarial majors at Bryant University. This was done to add clarity to incoming students for what it takes to do well in the actuarial major. There were 266 subjects consisting of Bryant students that graduated between the years 2009 and 2015. The data was received in the form of final transcripts upon graduation for these students. Through manipulation of these transcripts, GPAs were calculated for Mathematics/Actuarial, English/Literary Cultural Studies, History/Politics, Economics, Science, Social Sciences, Computer Information Systems, Finance, Accounting, Management, and Marketing. These GPAs …
What Is The True Cost To Stay In The Hospital?,
2016
Bryant University
What Is The True Cost To Stay In The Hospital?, Samantha Alicandro
Honors Projects in Mathematics
Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, …
Does Academic Performance Predict Workplace Productivity?,
2016
Bryant University
Does Academic Performance Predict Workplace Productivity?, Jodie-Gaye Hunter
Honors Projects in Economics
This research examines if college GPA affects productivity and compensation in the workplace. It uses data collected from a survey of approximately 23,000 Bryant University graduates in different stages of their career. About 10 percent of the alumni surveyed completed the survey. The econometric model used in this study allows estimating the effect of GPA on income after controlling for various demographic and socioeconomic variables, including education, major, occupation, gender, among others. The empirical work provides evidence that GPA has a positive and statistically significant impact on workplace productivity for females, but GPA seems to be a weaker predictor of …
Time-Dependent Neutral Stochastic Functional Differential Equations Driven By A Fractional Brownian Motion,
2016
Louisiana State University
Time-Dependent Neutral Stochastic Functional Differential Equations Driven By A Fractional Brownian Motion, B Boufoussi, S Hajji, E Lakhel
Communications on Stochastic Analysis
No abstract provided.
On The Second Fundamental Theorem Of Asset Pricing,
2016
Louisiana State University
On The Second Fundamental Theorem Of Asset Pricing, Rajeeva L Karandikar, B V Rao
Communications on Stochastic Analysis
No abstract provided.
A Stochastic Transport Theorem,
2016
Louisiana State University
A Stochastic Transport Theorem, Pedro Catuogno, Simão N Stelmastchuk
Communications on Stochastic Analysis
No abstract provided.
Solution Of The Dirichlet Problem For A Linear Second-Order Equation By The Monte Carlo Method,
2016
Louisiana State University
Solution Of The Dirichlet Problem For A Linear Second-Order Equation By The Monte Carlo Method, José Villa-Morales
Communications on Stochastic Analysis
No abstract provided.
Mean-Field Limit Versus Small-Noise Limit For Some Interacting Particle Systems,
2016
Louisiana State University
Mean-Field Limit Versus Small-Noise Limit For Some Interacting Particle Systems, Samuel Herrmann, Julian Tugaut
Communications on Stochastic Analysis
No abstract provided.
Moments Estimates For Local Times Of A Class Of Gaussian Processes,
2016
Louisiana State University
Moments Estimates For Local Times Of A Class Of Gaussian Processes, Olga Izyumtseva
Communications on Stochastic Analysis
No abstract provided.
Probability Distributions And Orthogonal Polynomials Associated With The One-Parameter Fibonacci Group,
2016
Louisiana State University
Probability Distributions And Orthogonal Polynomials Associated With The One-Parameter Fibonacci Group, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris
Communications on Stochastic Analysis
No abstract provided.
Stochastic Integral Representations Of F-Selfdecomposable And F-Semi-Selfdecomposable Distributions,
2016
Louisiana State University
Stochastic Integral Representations Of F-Selfdecomposable And F-Semi-Selfdecomposable Distributions, Nadjib Bouzar
Communications on Stochastic Analysis
No abstract provided.
Commutators In The Two-Weight Setting,
2016
Washington University in St. Louis
Commutators In The Two-Weight Setting, Irina Holmes, Michael T. Lacey, Brett D. Wick
Mathematics Faculty Research
Let R be the vector of Riesz transforms on Rn and let μ,λ∈Ap be two weights on Rn, 1p(μ)→Lp(λ)|| is shown to be equivalent to the function b being in a BMO space adapted to μ and λ. This is a common extension of a result of Coifman–Rochberg–Weiss in the case of both λ and μ being Lebesgue measure, and Bloom in the case of dimension one.
A Partition Function Connected With The Göllnitz-Gordon Identities,
2016
Georgia Southern University
A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
College of Graduate Studies: Theses & Dissertations
Nearly a century ago, the mathematicians Hardy and Ramanujan established their celebrated circle method to give a remarkable asymptotic expression for the unrestricted partition function. Following later improvements by Rademacher, the method was utilized by Niven, Lehner, Iseki, and others to develop rapidly convergent series representations of various restricted partition functions. Following in this tradition, we use the circle method to develop formulas for counting the restricted classes of partitions that arise in the Gollnitz-Gordon identities. We then show that our results are strongly supported by numerical tests. As a side note, we also derive and compare the asymptotic behavior …
Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces,
2016
CUNY Borough of Manhattan Community College
Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces, Lina Wu, Ye Li
Publications and Research
We obtain Liouville-type results for closed and p-pseudo-coclosed differential 1-forms ! with energy of lim inf r!1 1 r2 R B(x0;r) j!jqdv < 1 (that is, 2-finite growth), which extends finite q-energy ( R M j!jqdv < 1) in Lq spaces to infinite q-energy ( R M j!jqdv = 1) in non-Lq spaces. In particular, we recapture mathematicians' vanishing results of Liouville- type theorem for ! with finite q-energy in Lq spaces. Our method in this paper provides a successful way to work on Liouville-type problems for differential forms with a variety of energy conditions in broad spaces.
Homogenization Of Stokes Systems With Periodic Coefficients,
2016
University of Kentucky
Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu
Theses and Dissertations--Mathematics
In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
Best Approximations, Lethargy Theorems And Smoothness,
2016
Claremont McKenna College
Best Approximations, Lethargy Theorems And Smoothness, Caleb Case
CMC Senior Theses
In this paper we consider sequences of best approximation. We first examine the rho best approximation function and its applications, through an example in approximation theory and two new examples in calculating n-widths. We then further discuss approximation theory by examining a modern proof of Weierstrass's Theorem using Dirac sequences, and providing a new proof of Chebyshev's Equioscillation Theorem, inspired by the de La Vallee Poussin Theorem. Finally, we examine the limits of approximation theorem by looking at Bernstein Lethargy theorem, and a modern generalization to infinite-dimensional subspaces. We all note that smooth functions are bounded by Jackson's Inequalities, but …
Inverse Scattering For The Zero-Energy Novikov-Veselov Equation,
2016
University of Kentucky
Inverse Scattering For The Zero-Energy Novikov-Veselov Equation, Michael Music
Theses and Dissertations--Mathematics
For certain initial data, we solve the Novikov-Veselov equation by the inverse scat- tering method. This is a (2+1)-dimensional completely integrable system that gen- eralizes the (1+1)-dimensional Korteweg-de-Vries equation. The method used is the inverse scattering method. To study the direct and inverse scattering maps, we prove existence and uniqueness properties of exponentially growing solutions of the two- dimensional Schrodinger equation. For conductivity-type potentials, this was done by Nachman in his work on the inverse conductivity problem. Our work expands the set of potentials for which the analysis holds, completes the study of the inverse scattering map, and show that …
