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Articles 571 - 600 of 817
Full-Text Articles in Mathematics
Joint Spectra Of Spherical Aluthge Transforms Of Commuting N-Tuples Of Hilbert Space Operators, Chafiq Benhida, Raul E. Curto, Sang Hoon Lee, Jasang Yoon
Joint Spectra Of Spherical Aluthge Transforms Of Commuting N-Tuples Of Hilbert Space Operators, Chafiq Benhida, Raul E. Curto, Sang Hoon Lee, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
Let be a commuting n-tuple of operators on a Hilbert space , and let be its canonical joint polar decomposition (i.e. ⁎ ⁎ , a joint partial isometry, and ). The spherical Aluthge transform of T is the (necessarily commuting) n-tuple . We prove that , where denotes the Taylor spectrum. We do this in two stages: away from the origin, we use tools and techniques from criss-cross commutativity; at the origin, we show that the left invertibility of T or implies the invertibility of P. As a consequence, we can readily extend our main result to other spectral systems …
Fast Equilibration Dynamics Of Viscous Particle-Laden Flow In An Inclined Channel, Jeffrey Wong, Michael R. Lindstrom, Andrea L. Bertozzi
Fast Equilibration Dynamics Of Viscous Particle-Laden Flow In An Inclined Channel, Jeffrey Wong, Michael R. Lindstrom, Andrea L. Bertozzi
School of Mathematical & Statistical Sciences Faculty Publications
A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension either separates into two distinct fronts (settled) or forms a single, particle-laden front (ridged), depending on whether the initial concentration of particles exceeds a critical threshold. From past experiments, it is also clear that this equilibration time scale grows considerably near the critical concentration. This paper models …
Shape Equations For Two-Dimensional Manifolds Through A Moving Frame Variational Approach, Paul Bracken
Shape Equations For Two-Dimensional Manifolds Through A Moving Frame Variational Approach, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
A variational approach is given which can be applied to functionals of a general form to determine a corresponding Euler–Lagrange or shape equation. It is the intention to formulate the theory in detail based on a moving frame approach. It is then applied to a functional of a general form which depends on both the mean and Gaussian curvatures as well as the area and volume elements of the manifold. Only the case of a two-dimensional closed manifold is considered. The first variation of the functional is calculated in terms of the variations of the basic variables of the manifold. …
2-Hyponormality On Unilateral Weighted Shifts, Juan G. Benitez
2-Hyponormality On Unilateral Weighted Shifts, Juan G. Benitez
Theses and Dissertations
Given the concept of a normal operator, several weaker notions have been proposed in order to extend the properties of normal operators to a wider range of operators. One such notion is that of k-hyponormal operators. In this document, we focus our attention on the 2-hyponormality of weighted shift operators over a discrete Hilbert space. It will be shown that if a certain relation between the weights α = ( α0, α1,...) of a weighted shift Wα is satisfied, then the 2-hyponormality of Wα implies the hyponormality of Wαm for any m = 2, 3,....
Analysis Of The Cnn Algorithm In Target Recognition By Using The Mstar Database, Ligang Zou
Analysis Of The Cnn Algorithm In Target Recognition By Using The Mstar Database, Ligang Zou
Theses and Dissertations
With the rapid development of artificial intelligence technology and the emergence of a large number of innovative theories, the concept of deep learning is widely used in object detection, speech recognition, language translation and other fields. One of the important practices is target recognition in SAR images. Although it shows certain effectiveness in some researches, when using deep learning algorithm, there are still many problems that have not yet been solved. For example, people do not have a good understanding of how convolution works and the impact of convolution on the algorithm, although convolution works well in the CNN algorithm. …
Empirical Bayes Estimators And Borel-Tanner Distribution, Celestina Ruby Soltero
Empirical Bayes Estimators And Borel-Tanner Distribution, Celestina Ruby Soltero
Theses and Dissertations
The motivation for this paper stems from the role Borel-Tanner (BT) distribution has as the distribution of the total outbreak number in epidemics modeled by branching processes. We briefly review Borel-Tanner distribution and its applications. In Chapter II we outline the Bayes decision problem, a construction for an Empirical Bayes (EB) estimator proposed by Liang [9] and discuss risk analysis. In Chapter III, the importance of randomization addressed and a classical construction of a monotonized EB estimator proposed by Houwalingen [14] is outlined. Lastly in Chapter IV we use R software to perform a Monte Carlo simulation and conduct a …
Global Existence And Propagation Speed For A Generalized Camassa-Holm Model With Both Dissipation And Dispersion, Qiaoyi Hu, Zhijun Qiao
Global Existence And Propagation Speed For A Generalized Camassa-Holm Model With Both Dissipation And Dispersion, Qiaoyi Hu, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we study a generalized Camassa–Holm (gCH) model with both dissipation and dispersion, which has (N+1)-order nonlinearities and includes the following three integrable equations: the Camassa–Holm, the Degasperis–Procesi, and the Novikov equations, as its reductions. We first present the local well-posedness and a precise blow-up scenario of the Cauchy problem for the gCH equation. Then, we provide several sufficient conditions that guarantee the global existence of the strong solutions to the gCH equation. Finally, we investigate the propagation speed for the gCH equation when the initial data are compactly supported.
Properties Of A Class Of Mean Dependent On A Parameter, Paul Bracken
Properties Of A Class Of Mean Dependent On A Parameter, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
Some properties of a new class of binary symmetric mean Mp(a,b) which depends on two positive numbers a and b, as well as a positive parameter p, are investigated. The logarithmic mean and arithmetic mean are two members of this class. It is shown that, for all values of the parameter p, the set of p-dependent means Mp(a,b) is bounded above by the mean M∞(a,b).
Reduction Of The Kp Hierarchy, Adrian Eugenio Torres
Reduction Of The Kp Hierarchy, Adrian Eugenio Torres
Theses and Dissertations
This thesis will delve into the Kadomtsev-Petviashvili equation or KP equation and it's hierarchy. More specifically, the solition theory around it. To do so, we first explore the soliton theory for the Korteweg de-Vries equation or KdV equation by analysing it through the inverse scattering transform method and presenting it's soliton solutions. Second, we will introduce, Hirota's bilinear form, and understand its main idea. Third, introduce Sato Theory, and use it to formulate the KP hierarchy, via using pseudo-differential operators, presenting the lax operator, the dressing operator, Sato’s equation, and the zero curvature equation (Zakharov-Shabat Equation). Fourth, find the general …
Metric Geometry And The Determination Of The Bohmian Quantum Potential, Paul Bracken
Metric Geometry And The Determination Of The Bohmian Quantum Potential, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
A geometric approach to quantum mechanics which is formulated in terms of Finsler geometry is developed. It is shown that quantum mechanics can be formulated in terms of Finsler configuration space trajectories which obey Newton-like evolution but in the presence of an additional kind of potential. This additional quantum potential which was obtained first by Bohm has the consequence of contributing to the forces driving the system. This geometric picture accounts for many aspects of quantum dynamics and leads to a more natural interpretation. It is found for example that dynamics can be accounted for by incorporating quantum effects into …
Optimal Quantization For The Cantor Distribution Generated By Infinite Similutudes, Mrinal Kanti Roychowdhury
Optimal Quantization For The Cantor Distribution Generated By Infinite Similutudes, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
Let P be a Borel probability measure on ℝ generated by an infinite system of similarity mappings {Sj : j ∈ ℕ} such that P=Σ∞j=112jP∘S−1j, where for each j ∈ ℕ and x ∈ ℝ, Sj(x)=13jx+1−13j−1. Then, the support of P is the dyadic Cantor set C generated by the similarity mappings f1, f2 : ℝ → ℝ such that f1(x) = 1/3x and f2(x) = 1/3x+ 2/3 for all x ∈ ℝ. In this paper, using the infinite system of similarity mappings {Sj : j ∈ ℕ} associated with the probability vector (12,122,...), for all n ∈ ℕ, we …
Spherically Quasinormal Pairs Of Commuting Operators, Raul E. Curto, Jasang Yoon
Spherically Quasinormal Pairs Of Commuting Operators, Raul E. Curto, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
We first discuss the spherical Aluthge and spherical Duggal transforms for commuting pairs of operators on Hilbert space. Second, we study the fixed points of these transforms, which are the spherically quasinormal commuting pairs. In the case of commuting 2-variable weighted shifts, we prove that spherically quasinormal pairs are intimately related to spherically isometric pairs. We show that each spherically quasinormal 2-variable weighted shift is completely determined by a subnormal unilateral weighted shift (either the 0-th row or the 0-th column in the weight diagram). We then focus our attention on the case when this unilateral weighted shift is recursively …
Existence And Classification Of Solutions To Nonlinear Elliptic Equations, Haseeb E. Ansari
Existence And Classification Of Solutions To Nonlinear Elliptic Equations, Haseeb E. Ansari
Theses and Dissertations
The so-called Lane-Emden equation is a model in astrophysics, useful to problems in analysis and conformal geometry, and is closely related to the Yamabe Problem and the Uniformization Theorem. We discuss several important results for the equation, which include proving that the equation admits a distribution solution if and only if p is greater than the Serrin exponent, that classical solutions admit the form of a "bubble function" if p is equal to the Sobolev exponent, and no classical solutions exist for p less than the Sobolev exponent. A new proof of an extended result is also included.
Pm2.5 Data Reliability And Air Quality Improvement Trends In Beijing, Huimin Li
Pm2.5 Data Reliability And Air Quality Improvement Trends In Beijing, Huimin Li
Theses and Dissertations
PM2.5 has been a main environmental concern due to its adverse effects on human health and society. We used data from two sources: monitoring station of the U.S. Embassy in Beijing, and several nearby monitoring stations of the Chinese Ministry of Environmental Protection. This study includes investigating (1) PM2.5 historical data reliability, (2) PM2.5 real-time data reliability, and (3) air quality improvement trends in Beijing over the past decade. We used graphical methods, descriptive statistics, correlation analysis, and inferential analyses including paired samples t-test, ANOVA, and Kruskal-Wallis test. We reported effect sizes to aid study on practical significance. Inferential procedures' …
“Diabesity” Among Latinos: A Culturally Relevant Mathematics Activity By A Mathematics Teacher Candidate, Olga Ramirez, Cherie Mccollough
“Diabesity” Among Latinos: A Culturally Relevant Mathematics Activity By A Mathematics Teacher Candidate, Olga Ramirez, Cherie Mccollough
School of Mathematical & Statistical Sciences Faculty Publications
This paper summarizes a culturally relevant mathematics project conducted by a mentored secondary-level Latino teacher candidate (TC) as a requirement for an undergraduate mathematics project course at a south Texas university. The culturally relevant math project involved four secondary Latino students and their parents. The topic was “diabesity”; that is, diabetes and obesity among Latinos southern region in the United States of America with an emphasis on body mass index, proper diet, and exercise. Remarks by the faculty mentor and a faculty consultant about the TC work and reflections regarding this project are also included and provide perspectives on how …
The Generalized Weierstrass System In Three-Dimensional Euclidean Space, Paul Bracken
The Generalized Weierstrass System In Three-Dimensional Euclidean Space, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
In this chapter, some recent advances in the area of generalized Weierstrass representations will be given. This is an approach to the theory of surfaces in Euclidean three space. Weierstrass representations permit the explicit construction of surfaces in the designated space. The discussion proceeds in a novel and introductory manner. The inducing formulas for the coordinates of a surface are derived and important conservation laws are formulated. These lead to the inducing mechanism of a surface in terms of solutions to a system of two-dimensional Dirac equations. A set of fundamental forms as well as expressions for the mean and …
Attitudes Toward Using And Teaching Confidence Intervals: A Latent Profile Analysis On Elementary Statistics Instructors, Hyung Won Kim, Woo Jin Kim, Aaron T. Wilson, Ho Kyoung Ko
Attitudes Toward Using And Teaching Confidence Intervals: A Latent Profile Analysis On Elementary Statistics Instructors, Hyung Won Kim, Woo Jin Kim, Aaron T. Wilson, Ho Kyoung Ko
School of Mathematical & Statistical Sciences Faculty Publications
The use of confidence intervals (CIs) for making a statistical inference is gaining popularity in research communities. To evaluate college statistics instructors’ readiness to teach CIs, this study explores their attitudes toward teaching CIs in elementary statistics courses, and toward using CIs in inferential statistics. Data were collected with a survey that classifies instructors’ attitudes on the basis of three previously established pedagogical components: affective, cognitive, and behavioral. Based on the survey responses from 270 participants, we created three profiles (subgroups) via latent profile analysis, and identified each profile’s pattern of attitudes toward CIs and common characteristics of the instructors …
On The Regularity Radius Of Delone Sets In R3, Nikolay Dolbilin, Alexey Garber, Undine Leopold, Egon Schulte
On The Regularity Radius Of Delone Sets In R3, Nikolay Dolbilin, Alexey Garber, Undine Leopold, Egon Schulte
School of Mathematical & Statistical Sciences Faculty Publications
We complete the proof of the upper bound ρ^3≤10R for the regularity radius of Delone sets in three-dimensional Euclidean space. Namely, summing up the results obtained earlier, and adding the missing cases, we show that if all 10R-clusters of a Delone set X with parameters (r,R) are equivalent, then X is a regular system.
Blocks In The Category Of Finite-Dimensional Representations Of Principal W-Algebra For Q(2), Elena Poletaeva
Blocks In The Category Of Finite-Dimensional Representations Of Principal W-Algebra For Q(2), Elena Poletaeva
School of Mathematical & Statistical Sciences Faculty Publications
We describe the blocks in the category of finite-dimensional representations of the principal finite W-algebra for the Lie superalgebra Q(2).
The Near-Peer Mathematical Mentoring Cycle: Studying The Impact Of Outreach On High School Students’ Attitudes Toward Mathematics, Aaron T. Wilson, Sergey Grigorian
The Near-Peer Mathematical Mentoring Cycle: Studying The Impact Of Outreach On High School Students’ Attitudes Toward Mathematics, Aaron T. Wilson, Sergey Grigorian
School of Mathematical & Statistical Sciences Faculty Publications
College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts …
On A Class Of Parameter Dependent Series Generalizing Euler’S Constant, Paul Bracken
On A Class Of Parameter Dependent Series Generalizing Euler’S Constant, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
Series which depend on a parameter and generalize the constant discovered by Euler are introduced and studied. Convergence results are established. An infinite series expansion is obtained from these generalized formulas which can be used to evaluate the generalized constant. Euler’s constant can be obtained as a special case. Some asymptotic results are formulated and limits of some closely related sequences are given.
Connections Between Pre-Service Teachers’ Mathematical Dispositions And Self-Efficacy For Teaching Mathematics, Jasmine M. Cruz, Aaron T. Wilson, Xiaohui Wang
Connections Between Pre-Service Teachers’ Mathematical Dispositions And Self-Efficacy For Teaching Mathematics, Jasmine M. Cruz, Aaron T. Wilson, Xiaohui Wang
School of Mathematical & Statistical Sciences Faculty Publications
Mathematical dispositions (MD) and self-efficacy for teaching mathematics (SEFTM) are important elements of teachers‟ beliefs that significantly influence their behaviors and educational practices in the classroom. This study looked at relationships between pre-service teachers‟ (PSTs) MD and their SEFTM in connection with other descriptors related to their progress through the teacher education program and prior mathematical experiences. Survey data were collected from 238 PSTs at a midsized university in the US. Results include the finding that PSTs‟ intended grade-level and subject approximately mirror their MD and SEFTM: those planning to be elementary school (generalist) teachers were slightly behind both middle …
Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez
Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez
Theses and Dissertations
This thesis covers packings of spherical particles. The main object of this investigation is the contact number of a packing. New bounds for contact numbers of certain families of sphere packings in dimension 3 are obtained as the outcome of this research.
Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Theses and Dissertations
In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …
The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani
The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani
Theses and Dissertations
The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …
Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen
Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen
Theses and Dissertations
We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …
Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera
Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera
Theses and Dissertations
We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee
Theses and Dissertations
Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …
On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
School of Mathematical & Statistical Sciences Faculty Publications
The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. …
Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao
Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational …