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Articles 301 - 330 of 817
Full-Text Articles in Mathematics
An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers
An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers
Theses and Dissertations
This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms These modular forms can be represented in terms of Klein forms and the Dedekind eta function. The main focus of this thesis is to introduce the necessary theory to characterize these specific Ramanujan type congruences and prove their antichimerality.
An Investigation Into Optimal Descent Trajectories For Multipurpose Long Range Space Vehicles Under Advanced Conditions, John M. Levis
An Investigation Into Optimal Descent Trajectories For Multipurpose Long Range Space Vehicles Under Advanced Conditions, John M. Levis
Theses and Dissertations
In this work, we investigate the problem of fuel-optimal control of space vehicle descent trajectories. The main tool we use to establish optimality is Pontryagin’s Maximum Principle. We present a variety of scenarios with increasing complexities, including drag, wind, and moving landing platforms in the context of differing atmospheric and gravitational conditions. Throughout the paper, we use a balance of analytical and numerical techniques. Finally, observations and conclusions drawn from the investigation form the basis for suggestions into additional areas of analysis.
Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako
Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako
Theses and Dissertations
Missing data are common in real-life studies and missing observations within the univariate time series cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in the analysis of every incomplete univariate time series data. The reviewed literature has shown that the focus of existing studies is on comparing the distribution of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series data affect the fit and prediction performance of time series models. In this work, we evaluated the predictive performance of autoregressive integrated moving average …
The Development Of Sociomathematical Norms In The Transition To Tertiary Exam-Oriented Individualistic Mathematics Education In An East Asian Context, Woong Lim, Hyunkyoung Yoon, Younggon Bae, Oh Nam Kwon
The Development Of Sociomathematical Norms In The Transition To Tertiary Exam-Oriented Individualistic Mathematics Education In An East Asian Context, Woong Lim, Hyunkyoung Yoon, Younggon Bae, Oh Nam Kwon
School of Mathematical & Statistical Sciences Faculty Publications
This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students’ sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of academic social norms in a large-lecture course represented by the acquisition model of learning in college, detached from communal and collaborative disciplinary practices. Findings provide insights into the local educational context of an East Asian country as a case study when exam-oriented mathematics is institutionalized as normalcy.
Evaluation Of Black Holes In An Evolving Universe, John P. Naan
Evaluation Of Black Holes In An Evolving Universe, John P. Naan
Theses and Dissertations
There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …
Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo
Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo
Theses and Dissertations
In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code.
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n -means and the n th quantization errors for different …
Multiple Solutions Of P-Fractional Schrödinger-Choquard-Kirchhoff Equations With Hardy-Littlewood-Sobolev Critical Exponents, Xiaolu Lin, Shenzhou Zheng, Zhaosheng Feng
Multiple Solutions Of P-Fractional Schrödinger-Choquard-Kirchhoff Equations With Hardy-Littlewood-Sobolev Critical Exponents, Xiaolu Lin, Shenzhou Zheng, Zhaosheng Feng
School of Mathematical & Statistical Sciences Faculty Publications
In this article, we are concerned with multiple solutions of Schrödinger-Choquard-Kirchhoff equations involving the fractional p -Laplacian and Hardy-Littlewood-Sobolev critical exponents in R N . We classify the multiplicity of the solutions in accordance with the Kirchhoff term M ( ⋅ ) and different ranges of q shown in the nonlinearity f ( x , ⋅ ) by means of the variational methods and Krasnoselskii’s genus theory. As an immediate consequence, some recent related results have been improved and extended.
Cranks For Partitions With Bounded Largest Part, Dennis Eichhorn, Brandt Kronholm, Acadia Larsen
Cranks For Partitions With Bounded Largest Part, Dennis Eichhorn, Brandt Kronholm, Acadia Larsen
School of Mathematical & Statistical Sciences Faculty Publications
For 80 years, Dyson’s rank has been known as the partition statistic that witnesses the first two of Ramanujan’s celebrated congruences for the ordinary partition function. In this paper, we show that Dyson’s rank actually witnesses families of partition congruences modulo every prime . This comes from an in-depth study of when a “multiplicity-based statistic” is a crank witnessing congruences for the function p ` n, m˘ , which enumerates partitions of n with parts of size at most m. We also show that as the modulus increases, there is an ever-growing collection of distinct multiplicity-based cranks witnessing these same …
Generalized Spherical Aluthge Transforms And Binormality For Commuting Pairs Of Operators, Slaviša Djordjević, Jaewoong Kim, Jasang Yoon
Generalized Spherical Aluthge Transforms And Binormality For Commuting Pairs Of Operators, Slaviša Djordjević, Jaewoong Kim, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set …
Ramanujan–Sato Series For 1/Π, Timothy Huber, Daniel Schultz, Dongxi Ye
Ramanujan–Sato Series For 1/Π, Timothy Huber, Daniel Schultz, Dongxi Ye
School of Mathematical & Statistical Sciences Faculty Publications
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equations. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.
A Short Solution Of The Kissing Number Problem In Dimension Three, Alexey Glazyrin
A Short Solution Of The Kissing Number Problem In Dimension Three, Alexey Glazyrin
School of Mathematical & Statistical Sciences Faculty Publications
We give a short solution of the kissing number problem in dimension three.
P-Adic Cellular Neural Networks: Applications To Image Processing, B. A. Zambrano-Luna, Wilson A. Zuniga-Galindo
P-Adic Cellular Neural Networks: Applications To Image Processing, B. A. Zambrano-Luna, Wilson A. Zuniga-Galindo
School of Mathematical & Statistical Sciences Faculty Publications
The p-adic cellular neural networks (CNNs) are mathematical generalizations of the neural networks introduced by Chua and Yang in the 80s. In this work we present two new types of -adic CNNs that can perform computations with real data, and whose dynamics can be understood almost completely. The first type of networks are edge detectors for grayscale images. The stationary states of these networks are organized hierarchically in a lattice structure. The dynamics of any of these networks consists of transitions toward some minimal state in the lattice. The second type is a new class of reaction–diffusion networks. We investigate …
Continuous Semi-Supervised Nonnegative Matrix Factorization, Michael R. Lindstrom, Xiaofu Ding, Feng Liu, Anand Somayajula, Deanna Needell
Continuous Semi-Supervised Nonnegative Matrix Factorization, Michael R. Lindstrom, Xiaofu Ding, Feng Liu, Anand Somayajula, Deanna Needell
School of Mathematical & Statistical Sciences Faculty Publications
Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower rank. In certain applications it is desirable to extract topics and use them to predict quantitative outcomes. In this paper, we show Nonnegative Matrix Factorization can be combined with regression on a continuous response variable by minimizing a penalty function that adds a weighted regression error to a matrix factorization error. We show theoretically that as the weighting increases, the regression error in training …
Lacunary Eta Quotients With Identically Vanishing Coefficients, Timothy Huber, James Mclaughlin, Dongxi Ye
Lacunary Eta Quotients With Identically Vanishing Coefficients, Timothy Huber, James Mclaughlin, Dongxi Ye
School of Mathematical & Statistical Sciences Faculty Publications
For |q|<1 >, define fi=∏∞n=1(1−qin) , and let (A(q),B(q)) be any of the pairs (f41,f81f22), (f41,f101f23), (f61,f42f21), (f61,f141f42), (f101,f62f21), (f141,f53f1),(f141,f82f21). For any such pair (A(q),B(q)) , define the sequences {a(n)} and {b(n)} to be the coefficients of qn of A(q) and B(q) , respectively. Then for each pair it is shown that a(n) vanishes if and only if b(n) vanishes. In each case, a criterion is given which states precisely when a(n)=b(n)=0 . Moreover, for the pairs (f261,f93f1) , (f261,f162f61) it is shown that a(n)=b(n)=0 if 12n+13 satisfies a criteria of Serre for a(n)=0 .
Multi-Scale Hybridized Topic Modeling: A Pipeline For Analyzing Unstructured Text Datasets Via Topic Modeling, Keyi Cheng, Stefan Inzer, Adrian Leung, Xiaoxian Shen, Deanna Needell, Todd Presner, Michael Perlmutter, Michael R. Lindstrom, Joyce Chew
Multi-Scale Hybridized Topic Modeling: A Pipeline For Analyzing Unstructured Text Datasets Via Topic Modeling, Keyi Cheng, Stefan Inzer, Adrian Leung, Xiaoxian Shen, Deanna Needell, Todd Presner, Michael Perlmutter, Michael R. Lindstrom, Joyce Chew
School of Mathematical & Statistical Sciences Faculty Publications
We propose a multi-scale hybridized topic modeling method to find hidden topics from transcribed interviews more accurately and more efficiently than traditional topic modeling methods. Our multiscale hybridized topic modeling method (MSHTM) approaches data at different scales and performs topic modeling in a hierarchical way utilizing first a classical method, Nonnegative Matrix Factorization, and then a transformer-based method, BERTopic. It harnesses the strengths of both NMF and BERTopic. Our method can help researchers and the public better extract and interpret the interview information. Additionally, it provides insights for new indexing systems based on the topic level. We then deploy our …
On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev
On Characterization Of The Exponential Distribution Via Hypoexponential Distributions, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
The sum of independent, but not necessary identically distributed, exponential random variables follows a hypoexponential distribution. We focus on a particular case when all but one rate parameters of the exponential variables are identical. This is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.
Modeling And Computation For Unsteady Blood Flow And Solute Concentration In A Constricted Porous Artery, Daniel N. Riahi, Saulo Orizaga
Modeling And Computation For Unsteady Blood Flow And Solute Concentration In A Constricted Porous Artery, Daniel N. Riahi, Saulo Orizaga
School of Mathematical & Statistical Sciences Faculty Publications
We investigated a physical system for unsteady blood flow and solute transport in a section of a constricted porous artery. The aim of this study was to determine effects of hematocrit, stenosis, pulse oscillation, diffusion, convection and chemical reaction on the solute transport. The significance of this study was uncovering combined roles played by stenosis height, hematocrit, pulse oscillation period, reactive rate, blood speed, blood pressure force and radial and axial extent of the porous artery on the solute transported by the blood flow in the described porous artery. We used both analytical and computational methods to determine blood flow …
P-Adic Cellular Neural Networks, B. A. Zambrano-Luna, Wilson A. Zuniga-Galindo
P-Adic Cellular Neural Networks, B. A. Zambrano-Luna, Wilson A. Zuniga-Galindo
School of Mathematical & Statistical Sciences Faculty Publications
In this article we introduce the p-adic cellular neural networks which are mathematical generalizations of the classical cellular neural networks (CNNs) introduced by Chua and Yang. The new networks have infinitely many cells which are organized hierarchically in rooted trees, and also they have infinitely many hidden layers. Intuitively, the p-adic CNNs occur as limits of large hierarchical discrete CNNs. More precisely, the new networks can be very well approximated by hierarchical discrete CNNs. Mathematically speaking, each of the new networks is modeled by one integro-differential equation depending on several p-adic spatial variables and the time. We …
Hearing Healthcare Professionals’ Views About Over-The-Counter (Otc) Hearing Aids: Analysis Of Retrospective Survey Data, Vinaya Manchaiah, Anu Sharma, Hansapani Rodrigo, Abram Bailey, Karina C. De Sousa, De Wet Swanepoel
Hearing Healthcare Professionals’ Views About Over-The-Counter (Otc) Hearing Aids: Analysis Of Retrospective Survey Data, Vinaya Manchaiah, Anu Sharma, Hansapani Rodrigo, Abram Bailey, Karina C. De Sousa, De Wet Swanepoel
School of Mathematical & Statistical Sciences Faculty Publications
Over-the-counter hearing aids have been available to consumers in the US since 17 October 2022 following a ruling by the Food and Drug Administration. However, their reception by hearing healthcare professionals (HHP) has been mixed, and concerns have been expressed by many HHPs. The aim of this study was to examine the concerns that HHPs have towards over-the-counter (OTC) hearing aids. The study used a retrospective survey design. The survey data of HHPs (n = 730) was obtained from Hearing Tracker. A 22-item structured questionnaire was administered using a Question Scout platform. Descriptive analyses examined reported areas of concern and …
A Mathematical Investigation Of Landauer’S Principle, Paul Bracken
A Mathematical Investigation Of Landauer’S Principle, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
A minimal mathematical approach is used to state Landauer’s principle in a precise, general way. The results are obtained by means of a rigorous development which is based on the use of quantum statistical mechanics. A mathematical form of the principle results as an equality rather than an inequality. The equality version does imply the original statement of the principle as introduced by Landauer.
P-Adic Statistical Field Theory And Deep Belief Networks, Wilson A. Zuniga-Galindo
P-Adic Statistical Field Theory And Deep Belief Networks, Wilson A. Zuniga-Galindo
School of Mathematical & Statistical Sciences Faculty Publications
In this work we initiate the study of the correspondence between p-adic statistical field theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic spacetime can be formulated in a rigorous way. Nowadays these theories are considered just mathematical toy models for understanding the problems of the true theories. In this work we show these theories are deeply connected with the deep belief networks (DBNs). Hinton et al. constructed DBNs by stacking several restricted Boltzmann machines (RBMs). The purpose of this construction is to obtain a network with a hierarchical structure (a deep learning architecture). An …
Robust Explicit Estimation Of The Log-Logistic Distribution With Applications, Zhuanzhuan Ma, Min Wang, Chanseok Park
Robust Explicit Estimation Of The Log-Logistic Distribution With Applications, Zhuanzhuan Ma, Min Wang, Chanseok Park
School of Mathematical & Statistical Sciences Faculty Publications
The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In this paper, we consider several alternative estimators, which not only have closed-form expressions, but also are quite robust to a certain level of data contamination. We investigate the robustness property of each estimator in terms of the breakdown point. The finite sample performance and effectiveness of these estimators are evaluated through Monte Carlo simulations and a real-data application. Numerical results demonstrate that the proposed estimators perform favorably …
Current Scenario Of Solar Energy Applications In Bangladesh: Techno-Economic Perspective, Policy Implementation, And Possibility Of The Integration Of Artificial Intelligence, Monirul Islam Miskat, Protap Sarker, Hemal Chowdhury, Tamal Chowdhury, Md Salman Rahman, Nazia Hossain, Piyal Chowdhury, Sadiq M. Sait
Current Scenario Of Solar Energy Applications In Bangladesh: Techno-Economic Perspective, Policy Implementation, And Possibility Of The Integration Of Artificial Intelligence, Monirul Islam Miskat, Protap Sarker, Hemal Chowdhury, Tamal Chowdhury, Md Salman Rahman, Nazia Hossain, Piyal Chowdhury, Sadiq M. Sait
School of Mathematical & Statistical Sciences Faculty Publications
Bangladesh is blessed with abundant solar resources. Solar power is considered the most desirable energy source to mitigate the high energy demand of this densely populated country. Although various articles deal with solar energy applications in Bangladesh, no detailed review can be found in the literature. Therefore, in this study, we report on the current scenario of renewable energy in Bangladesh and the most significant potential of solar energy’s contribution among multiple renewable energy resources in mitigating energy demand. One main objective of this analysis was to outline the overall view of solar energy applications in Bangladesh to date, as …
Log-Optimal (D + 2)-Configurations In D–Dimensions, Peter D. Dragnev, Oleg R. Musin
Log-Optimal (D + 2)-Configurations In D–Dimensions, Peter D. Dragnev, Oleg R. Musin
School of Mathematical & Statistical Sciences Faculty Publications
We enumerate and classify all stationary logarithmic configurations of d + 2 points on the unit sphere in d–dimensions. In particular, we show that the logarithmic energy attains its local minima at configurations that consist of two orthogonal to each other regular simplexes of cardinality m and n. The global minimum occurs when m = n if d is even and m = n + 1 otherwise. This characterizes a new class of configurations that minimize the logarithmic energy on Sd−1 for all d. The other two classes known in the literature, the regular simplex (d + 1 points on …
Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White
Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White
School of Mathematical & Statistical Sciences Faculty Publications
We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the quasisymmetric function invariants associated to the combinatorial Hopf monoid. We show that the collection of all such coloring complexes forms a linearized combinatorial Hopf monoid, which is the terminal object in the category of combinatorial Hopf monoids with convex characters. We also study several examples of combinatorial Hopf monoids.
Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami
Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami
School of Mathematical & Statistical Sciences Faculty Publications
We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate …
On Viscoelastic Fiber Jet Formation By Forcespinning At High Rotation Rate, Daniel N. Riahi, Saulo Orizaga
On Viscoelastic Fiber Jet Formation By Forcespinning At High Rotation Rate, Daniel N. Riahi, Saulo Orizaga
School of Mathematical & Statistical Sciences Faculty Publications
We consider a nonlinear three-dimensional viscoelastic fiber jet that is generated during a forcespinning process. We provide a particular case for such a rotating jet at a high rotation rate. We use a viscoelastic constitutive model for the jet equations and then applying a new slender body approach, we continue with proper scaling and perturbation technique to develop a new model for such a jet system. We find that the profiles for jet quantities versus arc length are notably different from all those in related studies reported before for either high or low rotation rates. In particular, jet radius first …
The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken
The Effect Of Damping By An Environment On Emergence Of Classicality, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The role of dissipation with respect to a microscopic superposition of quantum states is investigated by means of master equations. This has implications for the study of the emergence of classicality from the quantum level. In particular, it illustrates why it is difficult to observe a macroscopic quantum state. The role of the environment is assumed by the measuring apparatus. A pure state is reduced to a mixture in the pointer basis of the system by means of the interaction with the apparatus. It is the intention that this type of analysis will have applications to experiments which are designed …
Spherical Aluthge Transform, Spherical P And Log-Hyponormality Of Commuting Pairs Of Operators Ii, Hyung Won Kim, Jaewoong Kim, Jasang Yoon
Spherical Aluthge Transform, Spherical P And Log-Hyponormality Of Commuting Pairs Of Operators Ii, Hyung Won Kim, Jaewoong Kim, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we consider the notions of spherical p, log, and w-hyponormality of commuting pairs of operators and study their properties and relations. We first show that spherically p-hyponormal 2-variable weighted shifts of hyponormal operators are invariant under powers and the generalized spherical Aluthge transformation. Second, we study the relation between spherical p-hyponormality and spherical w-hyponormality. Third, we study whether the spherical p-hyponormality with 0<p< 1 is invariant under the spherical Aluthge transformation. Finally, we briefly discuss the relation between log-hyponormality in single operators and spherically log-hyponormality in commuting pairs of operators.