Mathematics Commons^™

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.

Combinatorially Composing Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n ≥ 0, T_m(T_n(x)) = T_mn(x) and U_m-1 (T_n(x))U_n-1(x) = U_mn-1(x).

Anxiety In The Math Classroom, Jean Benner

Mathematics Graduate Theses

Math anxiety is a learned response that inhibits cognitive performance in the math classroom. It is widespread among students from elementary age through college. Students suffering from math anxiety have difficulty performing calculations and maintaining a positive outlook on mathematics. Math anxiety is the result of a cycle of math avoidance that begins with negative experiences regarding mathematics. Facts pertaining to math anxiety are discussed and strategies are suggested to assist teachers in helping students to overcome math anxiety or avoid the phenomenon altogether.

Manipulatives In The Secondary Mathematics Classroom Using A Traditional Algebra Text, Christina Mutnansky

Mathematics Graduate Theses

This paper is a review of the research available on manipulative use in the mathematics classroom. Mathematical manipulatives, objects that are used to aid a student in learning a mathematical concept, provide a way for students to learn abstract mathematical concepts in a non lecture situation through hands-on learning and discovery. It specifically focuses on the use of manipulatives in the secondary Algebra classroom and how they can be integrated into a traditional curriculum. It discusses the different types of manipulatives that are available as well as reasons why instructors do not use manipulatives. Guidelines are given for their proper …

Simultaneous Seismic Imaging And Inversion Using An Inverse Scattering Algorithm For One Dimensional Media, Ashley Ciesla

Theses, Dissertations and Culminating Projects

The goal of this thesis is to test the capability and efficiency of an inverse scattering algorithm for imaging seismic data. The algorithm we are investigating simultaneously images and inverts one-dimensional, one-parameter (velocity), acoustic reflection data. The algorithm does not require a velocity model or any other a priori information about the medium under investigation, the only input being a reference velocity (the speed of sound in water) and the data collected in the experiment. We assume that the data contains no source wavelet and all other events except primary reflections have been removed in preprocessing. We simulate two types …

A Formal Context Specific Trust Model (Ftm) For Multimedia And Ubiquitous Computing Environment, Sheikh Iqbal Ahamed, Munirul M. Haque, Nilothpal Talukder

Mathematics, Statistics and Computer Science Faculty Research and Publications

In order to ensure secure sharing of resources in an ad-hoc network of handheld devices in a multimedia and ubiquitous computing environment, mutual collaboration is essential. However, the limitations, such as poor storage and computational capability of these multimedia and ubiquitous devices stand as the bottleneck for effective sharing of resources. As a result of this drawback, the adversaries are obtaining access to the new doors for security breaches. Mutual Trust is the weapon used to combat security violations by restricting malicious devices from participating in any interaction in such an open and dynamic environment. In this paper, we present …

Noise Assumptions In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

Acm/Springer Mobile Networks And Applications (Monet) Special Issue On “Advanced Mobile Applications And Intelligent Multimedia Systems For Ubi-Com”, Jong Hyuk Park, Shu-Ching Chen, Mieso Denko, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.

Studies Of Meson Mass Spectra In The Context Of Quark-Antiquark Bound States, Mallika Dhar

Dissertations

This dissertation deals with the computation of meson mass spectra in the context of quarkantiquark (q ¯ q) bound-state. Traditionally the q ¯ q bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is necessary. It is well known that relativistic kinematics cannot be treated properly in position representation, but it can easily be handled in momentum representation. On the other hand, the linear potential and Coulomb-like potential have singularities in momentum-space and complicated subtraction procedure is necessary to treat the …

Trees In Connected Graphs, Ashish Gupta

Theses, Dissertations and Culminating Projects

The focus of the Master’s Thesis will be the investigation of current research involving trees that cover subsets of the vertex set of a connected graph. The primary goal is the extension of some recent results and a conjecture of Horak and McAvaney. Given certain conditions, we will reformulate their conjecture that states that if a graph can be spanned by a number of edge-disjoint trees, we can provide a bound on the maximum degree of this collection of edge-disjoint trees. We are able to show that this conjecture is true if the number of trees used to span the …

Supplementary Balance Laws And The Entropy Principle, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

In this work we study the mathematical aspects of the development in the continuum thermodynamics known as the “Entropy Principle”. It started with the pioneering works of B.Coleman, W.Noll and I. Muller in 60th of XX cent. and got its further development mostly in the works of G. Boillat, I-Shis Liu and T.Ruggeri. “Entropy Principle” combines in itself the structural requirement on the form of balance laws of the thermodynamical system (denote such system (C)) and on the entropy balance law with the convexity condition of the entropy density. First of these requirements has pure mathematical form defining so called …

Applications Of Linear Programming To Coding Theory, Nathan Axvig

Department of Mathematics: Dissertations, Theses, and Student Research

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem.

In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such …

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson

Mathematics Sciences: Faculty Publications

We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielli-Garofalo- Nhieu or Lu-Manfredi-Stroffolini) in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph.

Identification Of Parameters And The Distribution Of The Maximum And The Minimum, Lijuan Bi

Theses and Dissertations - UTB/UTPA

In problems of competing risks, where an individual may be subject to m causes of death and X(i) is the lifetime of an individual exposed to the ith cause, the X(i)s are not observable but only is their minimum, and inference is needed on the X(i) based on their minimum. The same is the case with a m-component system, where the components are connected in series, and we are interested in inference on the lifetimes of the individual components. These examples motivate problems on parameter identification by the distribution of the minimum. Similarly, the example of a m-component system where …