Mathematics Commons^™

Strong Solution For A High Order Boundary Value Problem With Integral Condition, Ahcene Merad, Ahmed Lakhdar Marhoune

Turkish Journal of Mathematics

The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem.

On Integrability Of Golden Riemannian Structures, Aydin Gezer, Nejmi̇ Cengi̇z, Arif Salimov

Turkish Journal of Mathematics

The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. We discuss the problem of integrability for Golden Riemannian structures by using a \phi-operator which is applied to pure tensor fields. Also, the curvature properties for Golden Riemannian metrics and some properties of twin Golden Riemannian metrics are investigated. Finally, some examples are presented.

Extension Properties Of Pluricomplex Green Functions, Sidika Zeynep Ozal

Mathematics - Dissertations

In 1985, Klimek introduced an extremal plurisubharmonic function on bounded domains in Cn that generalizes the Green's function of one variable. This function is called the pluricomplex Green function of Ω with logarithmic pole at a and is denoted by g_Ω(.,a). The aim of this thesis was to investigate the extension properties of g_Ω(.,a). Let Ω0 be a bounded domain of Cn and E be a compact subset of Ω0 such that Ω : = Ω0 E is connected. In general, g_Ω(.,a) cannot be extended as a pluricomplex Green function to any subdomain of …

On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin

Department of Math & Statistics Faculty Publications

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.

In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …

Truncated Toeplitz Operators And Boundary Values In Nearly Invariant Subspaces, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

We consider truncated Toeplitz operator on nearly invariant subspaces of the Hardy space H². Of some importance in this context is the boundary behavior of the functions in these spaces which we will discuss in some detail.

Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H(b), mainly when b is a non-extreme point of the unit ball of H^∞.

Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda

Department of Math & Statistics Faculty Publications

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …

An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin

Department of Math & Statistics Faculty Publications

Suppose E is a subset of the unit circle T and H^∞C L^∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zⁿ H^∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

An Explicit Bijection Between Semistandard Tableaux And Non-Elliptic Sl3 Webs, Heather M. Russell

Department of Math & Statistics Faculty Publications

The sl₃ spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl₃). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and joins of webs. We build on Tymoczko’s bijection to give a simple and explicit algorithm for constructing all …

A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill

Department of Math & Statistics Faculty Publications

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter values, …

On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Holder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability, and bifurcation behavior, with the radius acting as a bifurcation parameter.

Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux

Mathematics, Statistics and Computer Science Faculty Research and Publications

Effective teaching assistants (TAs) are crucial for effective student learning. This is especially true in science, technology, engineering, and mathematics (STEM) programs, where TAs are enabling large programs to transition to more student-centered learning environments. To ensure that TAs are able to support these types of learning environments, their perspectives of training, their abilities, and other work related aspects must be understood. In this paper a survey that was created based on interviews conducted with eight TAs is discussed. The survey has four primary categories of content that are critical for understanding TAs' perspectives: (1) background, (2) motivation, (3) training, …

Genome-Wide Associations Of Signaling Pathways In Glioblastoma Multiforme, Serdar Bozdag, Stefan Wuchty, Alexei Vazquez, Peter O. Bauer

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: eQTL analysis is a powerful method that allows the identification of causal genomic alterations, providing an explanation of expression changes of single genes. However, genes mediate their biological roles in groups rather than in isolation, prompting us to extend the concept of eQTLs to whole gene pathways. Methods: We combined matched genomic alteration and gene expression data of glioblastoma patients and determined associations between the expression of signaling pathways and genomic copy number alterations with a non-linear machine learning approach. Results: Expectedly, over-expressed pathways were largely associated to tag-loci on chromosomes with signature alterations. Surprisingly, tag-loci that were associated …

A Proposal For A Problem-Driven Mathematics Curriculum Framework, Judith S. Zawojewski, Marta Magiera, Richard Lesh

Mathematics, Statistics and Computer Science Faculty Research and Publications

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework.

Rssi Based Indoor Localization For Smartphone Using Fixed And Mobile Wireless Node, Md O. Gani, Casey O'Brien, Sheikh Iqbal Ahamed, Roger O. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nowadays with the dispersion of wireless networks, smartphones and diverse related services, different localization techniques have been developed. Global Positioning System (GPS) has a high rate of accuracy for outdoor localization but the signal is not available inside of buildings. Also other existing methods for indoor localization have low accuracy. In addition, they use fixed infrastructure support. In this paper, we present a novel system for indoor localization, which also works well outside. We have developed a mathematical model for estimating location (distance and direction) of a mobile device using wireless technology. Our experimental results on Smartphones (Android and iOS) …

Recent Advances In Energy-Efficient Sensor Networks, Sheikh Iqbal Ahamed, Wei Wang, Jiman Hong

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Concept Of Sub-Independence, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distributions of the sums of independent random variables. The concept of sub-independence, which is weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is stronger than uncorrelatedness.

Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that for all f∈H², the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that for all f∈H². The first type of inequality above was explored with H² replaced by one of the model spaces (Θ H²)^⊥ by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss …

Characterizations Of Exponentiated Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the class of exponentiated distributions are presented. These characterizations are based on a simple relationship between two truncated moments and based on functions of the nth order statistic. The results are applied to certain well-known members of this class.

Robust Estimation Of The Correlation Matrix Of Longitudinal Data, Mehdi Maadooliat, Mohsen Pourahmadi, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ=DLL ^⊤ D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We …

The Zografos-Balakrishnan Log-Logistic Distribution: Properties And Applications, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Cross‐Campus Collaboration: A Scientometric And Network Case Study Of Publication Activity Across Two Campuses Of A Single Institution, Jeremy Birnholtz, Shion Guha, Y. Connie Yuan, Geri Gay, Caren Heller

Mathematics, Statistics and Computer Science Faculty Research and Publications

Team science and collaboration have become crucial to addressing key research questions confronting society. Institutions that are spread across multiple geographic locations face additional challenges. To better understand the nature of cross‐campus collaboration within a single institution and the effects of institutional efforts to spark collaboration, we conducted a case study of collaboration at Cornell University using scientometric and network analyses. Results suggest that cross‐campus collaboration is increasingly common, but is accounted for primarily by a relatively small number of departments and individual researchers. Specific researchers involved in many collaborative projects are identified, and their unique characteristics are described. Institutional …

Knight's Tours On 3 X N Chessboards With A Single Square Removed, Amanda M. Miller, David L. Farnsworth

Articles

The following theorem is proved: A knight’s tour exists on all 3 x n chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than the center square is removed, n = 5, n = 7 when any square other than square (2, 2) or (2, 6) is removed, n = 9 when square (1, 3), (3, 3), (1, 7), (3, 7), (2, 4), (2, 6), (2, 2), or (2, 8) is removed, or n = 11 when square (1, 3), (2, 4), …

The Weierstrass Approximation Theorem, Larita Barnwell Hipp

Theses and Dissertations

In this thesis we will consider the work began by Weierstrass in 1855 and several generalization of his approximation theorem since. Weierstrass began by proving the density of algebraic polynomials in the space of continuous real-valued functions on a finite interval in the uniform norm. His theorem has been generalized to an arbitrary compact Hausdorff space and the approximation with elements from more general algebras of continuous real-valued functions. We will consider proofs that use brute force and proofs based on convolutions and approximate identities, trudge through probability and the use of the Bernstein polynomials, and become intimately close to …

Shimura Images Of A Family Of Half-Integral Weight Modular Forms, Kenneth Allan Brown

Theses and Dissertations

In 1973, Shimura introduced a family of maps between modular forms of half-integral weight and modular forms of even integral weight. We will give explicit formulas for the images of two different classes of modular forms under these maps. In contrast to Shimura's difficult analytic construction, our formulas will fall out of relatively simple combinatorial derivations. Using the Shimura correspondence, we will prove congruences for the eigenvalues of a family of eigenforms introduced by Garvan. Using deep results of Eichler and Shimura, we state these congruences in terms of the number of points on associated elliptic curves, and we provide …

Analysis And Processing Of Irregularly Distributed Point Clouds, Kamala Hunt Diefenthaler

Theses and Dissertations

We address critical issues arising in the practical implementation of processing real point cloud data that exhibits irregularities. We develop an adaptive algorithm based on Learning Theory for processing point clouds from a stationary sensor that standard algorithms have difficulty approximating. Moreover, we build the theory of distribution-dependent subdivision schemes targeted at representing curves and surfaces with gaps in the data. The algorithms analyze aggregate quantities of the point cloud over subdomains and predict these quantities at the finer level from the ones at the coarser level.

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole

Theses and Dissertations

Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.

Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations, Rosalia Tatano

Theses and Dissertations

In this thesis we solve two-dimensional linear parabolic partial differential equations with pure Dirichelet boundary conditions, using the bilinear covolume-upwind finite volume method on rectangular grids to discretize the spatial variables and the Crank-Nicholson method for the time variable. These PDEs provide a model for problems from various fields of engineering and applied sciences, such as unsteady viscous flow problems, the simulation of oil extraction from underground reservoirs, transport of air and ground water pollutants and modeling of semiconductor devices. Finite volume method has the important advantage of allowing the conversion of integrations over the control volume to integrations over …

On Continuously Defective Elastic Crystals, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

We analyze mathematical underpinnings of Davini's theory of defective crystals when the defectiveness of a kinematic state may be material point dependent. We show how the underlying space can be identified with a suitably chosen homogeneous space and how the uniformly defective structure is just a special case.