Mathematics Commons^™

Quantitative Analysis Of Arterial Spin Labeling Fmri Data Using A General Linear Model, Luis Hernandez-Garcia, Hesamoddin Jahanian, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Arterial spin labeling techniques can yield quantitative measures of perfusion by fitting a kinetic model to difference images (tagged-control). Because of the noisy nature of the difference images investigators typically average a large number of tagged versus control difference measurements over long periods of time. This averaging requires that the perfusion signal be at a steady state and not at the transitions between active and baseline states in order to quantitatively estimate activation induced perfusion. This can be an impediment for functional magnetic resonance imaging task experiments. In this work, we introduce a general linear model (GLM) that specifies Blood …

A Methodology For Engineering Collaborative And Ad-Hoc Mobile Applications Using Syd Middleware, Praveen Madiraju, Srilaxmi Malladi, Janaka Balasooriya, Arthi Hariharan, Sushil K. Prasad, Anu Bourgeois

Mathematics, Statistics and Computer Science Faculty Research and Publications

Today’s web applications are more collaborative and utilize standard and ubiquitous Internet protocols. We have earlier developed System on Mobile Devices (SyD) middleware to rapidly develop and deploy collaborative applications over heterogeneous and possibly mobile devices hosting web objects. In this paper, we present the software engineering methodology for developing SyD-enabled web applications and illustrate it through a case study on two representative applications: (i) a calendar of meeting application, which is a collaborative application and (ii) a travel application which is an ad-hoc collaborative application. SyD-enabled web objects allow us to create a collaborative application rapidly with limited coding …

A Class Of Models For Uncorrelated Random Variables, Nader Ebrahimi, Gholamhossein Hamedani, Ehsan S. Soofi, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution …

Processing Induced Voxel Correlation In Sense Fmri Via The Ammust Framework, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Numerical Study On The Propagation And Interaction Of Strongly Nonlinear Solitary Waves, Qiyi Zhou

Dissertations

We study numerically a strongly nonlinear long wave model for surface gravity waves propagating in both one and two horizontal dimensions. This model often referred to as the Su-Gardner or Green-Naghdi equations can be derived from the Euler equations under the assumption that the ratio between the characteristic wavelength and water depth is small, but no assumption on the wave amplitude is required. We first generalize the model to describe large amplitude one-dimensional solitary waves in the presence of background shear of constant vorticity. After computing the solitary wave solution of the strongly nonlinear model, the interaction between two solitary …

Computational Methods For Two-Phase Flow With Soluble Surfactant, Kuan Xu

Dissertations

A mathematical model is formulated and solved for the two-phase flow of a viscous drop or inviscid bubble in an immiscible, viscous surrounding fluid in the zero Reynold's number or Stokes flow limit. A surfactant that is present on the interface is also soluble in the exterior fluid, and the drop is deformed by an imposed linear flow. The geometry is two-dimensional and Cartesian.

The dissolved surfactant is considered in the physically realistic limit of large bulk Péclet number. That is, it convects and diffuses as a passive scalar in the bulk flow where the ratio of its convection to …

Cannon-Thurston Maps And Relative Hyperbolicity., Abhijit Pal Dr.

Doctoral Theses

Let P : Y → T be a tree of strongly relatively hyperbolic spaces such that Y is also a strongly relatively hyperbolic space. Let X be a vertex space and i : X ֒→ Y denote the inclusion. The main aim of this thesis is to extend i to a continuous map i : X → Y , where X and Y are the Gromov compactifications of X and Y respectively. Such continuous extensions are called Cannon-Thurston maps. This is a generalization of [Mit98b] which proves the existence of Cannon-Thurston maps for X and Y hyperbolic. By generalizing a …

Single And Multiobjective Approaches To Clustering With Point Symmetry., Sriparna Saha Dr.

Doctoral Theses

In our every day life, we make decisions consciously or unconsciously. This decision can be very simple such as selecting the color of dress or deciding the menu for lunch, or may be as difficult as those involved in designing a missile or in selecting a career. The former decision is easy to take, while the latter one might take several years due to the level of complexity involved in it. The main goal of most kinds of decision-making is to optimize one or more criteria in order to achieve the desired result. In other words, problems related to optimization …

Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells

Articles

We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.

Hamilton Decompositions Of 6-Regular Abelian Cayley Graphs, Erik E. Westlund

Dissertations, Master's Theses and Master's Reports - Open

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made:

Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian.

The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture:

Alspach Conjecture: Every 2k-regular, connected Cayley graph on a …

Partial And Spectral-Viscosity Models For Geophysical Flows, Qingshan Chen, Max Gunzburger, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

Two models based on the hydrostatic primitive equations are proposed. the first model is the primitive equations with partial viscosity only and is oriented towards large-scale wave structures in the ocean and atmosphere. the second model is the viscous primitive equations with spectral eddy viscosity and is oriented towards turbulent geophysical flows. for both models, the existence and uniqueness of global strong solutions are established. for the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established. © 2010 Editorial Office of CAM (Fudan University) …

Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson

Mathematics and Statistics Faculty Research & Creative Works

Our sense of touch allows us to feel the forces in our limbs when we walk, swim, or hold our arms out the window of a moving car. We anticipate this sense is key in the locomotion of natural flyers. Inspired by the sense of touch, the overall goal of this research is to develop techniques for the estimation of aerodynamic loads from structural measurements for flight control applications. We submit a general algorithm for the direct estimation of distributed steady loads over bodies from embedded noisy deformation-based measurements. The estimation algorithm is applied to a linearly elastic membrane test …

Existence Of Energy-Minimal Diffeomorphisms Between Doubly Connected Domains, Tadeusz Iwaniec, Ngin-Tee Koh, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : omega -> omega* between bounded doubly connected domains such that Mod (omega) < Mod (omega*) there exists, unique up to conformal authomorphisms of omega, an energy-minimal diffeomorphism. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.

Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. the zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the …

Automated Theorem Prover Axiom Management, Ashley T. Holeman, Ewen Denney

STAR Program Research Presentations

Automated Theorem Provers (ATPs), are computer programs that use collections of axioms,which are logical statements assumed to be true, in order to prove conjectures. NASA uses these programs to verify safety and functional requirements in domains like Guidance, Navigation, and Control. There are about 30 axioms on each major topic including the theory of coordinate systems, elementary arithmetic and linear algebra. These axioms have been created over the duration of many projects and combined into a single file. One task is to manage the axioms by arranging them into logical sections, deleting unnecessary ones and rewriting some into a more …

Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Combinatorial Trigonometry With Chebyshev Polynomials, Arthur T. Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck

All HMC Faculty Publications and Research

We provide a combinatorial proof of the trigonometric identity cos(n_{θ) =} T_ncos(θ),
where T_n is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.

Discrete Groups And The Complex Contact Geometry Of Sl(2, C), Brendan Foreman

Mathematics and Computer Science

We investigate the vertical foliation of the standard complex contact structure on Γ \ Sl(2, C), where Γ is a discrete subgroup. We find that, if Γ is nonelementary, the vertical leaves on Γ \ Sl(2, C) are holomorphic but not regular. However, if Γ is Kleinian, then Γ \ Sl(2, C) contains an open, dense set on which the vertical leaves are regular, complete and biholomorphic to C ∗. If Γ is a uniform lattice, the foliation is nowhere regular, although there are both infinitely many compact and infinitely many nonclosed leaves.