Nightmares,
2013
Butler University
Nightmares, Jeremiah Farrell, Karen Farrell
Scholarship and Professional Work - LAS
Jeremiah's puzzle "Nightmare", which was exchanged at the 2013 Washington, DC International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle was a special puzzle gift that was given to IPP32 exchangers by its designer, Jerry Farrell, in memory of longtime IPP member, Tom Rodgers, Jr.
Flying Saucer,
2013
Butler University
Flying Saucer, Jeremiah Farrell, Karen Farrell
Scholarship and Professional Work - LAS
Jeremiah's puzzle "Flying Saucer", which was exchanged at the 2013 International Puzzle Party in Washington, DC. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle is also manufactured by Walter Hoppe as "Flying Saucer".
On A Paley-Wiener Theorem For The Zs-Akns Scattering Transform,
2013
University of Kentucky
On A Paley-Wiener Theorem For The Zs-Akns Scattering Transform, Ryan D. Walker
Theses and Dissertations--Mathematics
In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on a set of real potentials. We also demonstrate one application of our techniques to the study of an inverse spectral problem for a half-line Miura potential Schroedinger equation.
Young Children Investigating Advanced Mathematical Concepts With Haptic Technologies: Future Design Perspectives,
2013
University of Montana
Young Children Investigating Advanced Mathematical Concepts With Haptic Technologies: Future Design Perspectives, Stephen Hegedus
The Mathematics Enthusiast
In this chapter, we focus on how new technologies can be used with young children to investigate mathematical ideas and concepts that would normally be introduced at a later age. In particular, we focus on haptic technologies that allow learners to touch and feel objects through force feedback in addition to visual images on a screen. The main purpose of this paper is to describe how these technologies can be used to enable young learners to construct meaning about geometric shapes and surfaces as well as attributes of particular mathematical constructions in multiple dimensions (particularly 2D and 3D for purposes …
Smooth Quantile Processes For Right Censored Data,
2013
University of Texas at Arlington
Smooth Quantile Processes For Right Censored Data, Katsuhiro Uechi
Mathematics Dissertations - Archive
The development of an estimator of a quantile function Q(p) is discussed. The smooth nonparametric estimator Qn(p) of a quantile function Q(p) is defined as the solution to Fn(Qn(p)) = p, where Fn is a smooth Kaplan-Meier estimator of an unknown continuous distribution function F(x). The asymptotic properties of the smooth quantile process, n(Qn(p) - Q(p)) , based on right censored lifetimes are studied. The asymptotic properties of the bootstrap quantile process, n(Q n(p) - Q(p)) are also investigated and shown to have the same limiting distribution as the smooth quantile process. The bootstrap method to approximate the sampling distribution …
The Generalized Two-Component Hunter-Saxton System,
2013
University of Texas at Arlington
The Generalized Two-Component Hunter-Saxton System, Byungsoo Moon
Mathematics Dissertations - Archive
This thesis is concerned with the generalized two-component Hunter-Saxton system. In the periodic setting, we study the wave-breaking phenomenon and global existence for the generalized two-component Hunter-Saxton system. We obtain a brief derivation of the model. We also briefly sketch a standard local well-posednessresult using Kato's semigroup approach. We establish a wave-breaking criterion for solutions and some interesting results of wave-breaking solutions with certain initial profiles. We demonstrate the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions.
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities,
2013
University of Texas at Arlington
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities, Charles K. Garrett
Mathematics Dissertations - Archive
A matrix Riccati differential equation (MRDE) is a quadratic ODE of the form X' = A₂₁ + A₂₂X - XA₁₁ - XA₁₂X ; where X is a function of t with X : R Rnxm and the Aij's are constant or functions of t with matrix sizes to respect the size of X. It is well known that MRDEs may have singularities in their solution even if all the Aij are constant. In this dissertation, several di erent ideas for the meaning of the solution of an MRDE past a solution singularity are analyzed and it is shown how all …
Strongly Gorenstein Flat And Gorenstein Fp-Injective Modules,
2013
TÜBİTAK
Strongly Gorenstein Flat And Gorenstein Fp-Injective Modules, Chunhua Yang
Turkish Journal of Mathematics
In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfd_RM=Gpd_RM, and hence SGfd_RM< \infty if and only if Gfd_RM
Existence And Multiplicity Of Positive Solutions For A Class Of Nonlinear Elliptic Problems,
2013
TÜBİTAK
Existence And Multiplicity Of Positive Solutions For A Class Of Nonlinear Elliptic Problems, Asadollah Aghajani, Jamile Shamshiri, Frajollah Mohammadi Yaghoobi
Turkish Journal of Mathematics
We study the existence and multiplicity of nonnegative solutions for the nonlinear elliptic problem, -\Delta u+v(x)u=a(x)u^p+\lambda f(x,u) for x\in\Omega and u=0 on \partial\Omega, where \Omega is a bounded region in R^N, N>2, 1
Finitistic Dimension Conjectures For Representations Of Quivers,
2013
TÜBİTAK
Finitistic Dimension Conjectures For Representations Of Quivers, Sergio Estrada, Salahatti̇n Özdemi̇r
Turkish Journal of Mathematics
Let R be a ring and Q be a quiver. We prove the first Finitistic Dimension Conjecture to be true for RQ, the path ring of Q over R, provided that R satisfies the conjecture. In fact, we prove that if the little and the big finitistic dimensions of R coincide and equal n
Valuation Of Over-The-Counter (Otc) Derivatives With Collateralization,
2013
University of Central Florida
Valuation Of Over-The-Counter (Otc) Derivatives With Collateralization, Leon Guerrero
Electronic Theses and Dissertations
Collateralization in over-the-counter (OTC) derivatives markets has grown rapidly over the past decade, and even faster in the past few years, due to the impact of the recent financial crisis and the particularly important attention to the counterparty credit risk in derivatives contracts. The addition of collateralization to such contracts significantly reduces the counterparty credit risk and allows to offset liabilities in case of default. We study the problem of valuation of OTC derivatives with payoff in a single currency and with single underlying asset for the cases of zero, partial, and perfect collateralization. We assume the derivative is traded …
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations,
2013
Scripps College
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden
Scripps Senior Theses
This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.
Deducing Vertex Weights From Empirical Occupation Times,
2013
University of South Carolina
Deducing Vertex Weights From Empirical Occupation Times, David Collins
Theses and Dissertations
We consider the following problem arising from the study of human problem solving: Let $G$ be a vertex-weighted digraph with marked "start" and "end" vertices. Suppose that a random walker begins at the start vertex, steps to neighbors of vertices with probability proportional to their weights, and stops upon reaching the end vertex. Could one deduce the weights from the paths that many such walkers take? We analyze an iterative numerical solution to this reconstruction problem, in particular, given the empirical mean occupation times of the walkers. We then consider the existence of a choice of weights for a given …
Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation,
2013
Eastern Kentucky University
Applications Of Leggett Williams Type Fixed Point Theorems To A Second Order Difference Equation, Charley Lockhart Seelbach
Online Theses and Dissertations
Using extensions of the Leggett-Williams fixed-point theorem, we prove the existence of solutions for a class of second-order difference equations with Dirichlet boundary conditions. We present these fixed point theorems and then show what conditions have to be met in order to satisfy the theorem. Finally, we provide specific examples to show the hypotheses of the theorems do not contradict one another.
Effective Methods Of Formative Assessment,
2013
Eastern Kentucky University
Effective Methods Of Formative Assessment, Chelse Rae Bugg
Online Theses and Dissertations
The purpose of this research is to explore the implementation of formative assessment in the mathematics classroom. Formative assessment is considered to be any data-driven activity that an educator uses to help guide and improve instruction. While there is an abundance of research that concludes that formative assessment does indeed improve student achievement, practical methods of implementation are not thoroughly discussed. To partially determine which methods of formative assessment most positively impact student achievement, a study was conducted at Lafayette High School. The researcher compared two popular methods of formative assessment: daily exit slips and unit probing (pre-, middle-, and …
Increasing Automaticity,
2013
Eastern Kentucky University
Increasing Automaticity, Sara Burns
Online Theses and Dissertations
Automaticity is defined as the process of developing fluency in mathematics and the ability to answer a basic math problem routinely. Automaticity is one of the most important skills that a student can possess in mathematics. While there are many ways that an educator can implement strategies to increase automaticity in the classroom, the purpose of this study was to determine which of these methods of implementation is more effective: requiring students to practice automaticity three times per week or requiring students to practice automaticity five times per week.
Gaussian Amicable Pairs,
2013
Eastern Kentucky University
Gaussian Amicable Pairs, Ranthony Ashley Clark
Online Theses and Dissertations
Amicable pairs are two integers where the sum of the proper divisors of one is the other and vice versa. Since the Gaussian integers have many of the properties of the regular integers, we sought to discover whether there exist any pairs of Gaussian integers with the same property. It turns out that they do exist. In fact, some of the normal amicable pairs carry over as Gaussian amicable pairs. Also discovered are pairs that have a complex part.
Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem,
2013
Eastern Kentucky University
Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem, Sarah Schulz King`
Online Theses and Dissertations
The existence of smallest positive eigenvalues is established for the linear differential equations $u^{(4)}+\lambda_{1} q(t)u=0$ and $u^{(4)}+\lambda_{2} r(t)u=0$, $0\leq t \leq 1$, with each satisfying the boundary conditions $u(0)=u'(p)=u''(1)=u'''(1)=0$ where $1-\frac{\sqrt{3}}{3}\le p < 1$. A comparison theorem for smallest positive eigenvalues is then obtained. Using the same theorems, we will extend the problem to the fifth order via the Green's Function and again via Substitution. Applying the comparison theorems and the properties of $u_0$-positive operators to determine the existence of smallest eigenvalues. The existence of these smallest eigenvalues is then applied to characterize extremal points of the differential equation $u^{(4)} + q(t)u = 0$ satisfying boundary conditions $u(0) = u'(p) = u''(b) = u'''(b)= 0$ where $1-\frac{
Barred Preferential Arrangements,
2013
Harvey Mudd College
Barred Preferential Arrangements, Connor Thomas Ahlbach '13, Jeremy Usatine '14, Nicholas Pippenger
All HMC Faculty Publications and Research
A preferential arrangement of a set is a total ordering of the elements of that set with ties allowed. A barred preferential arrangement is one in which the tied blocks of elements are ordered not only amongst themselves but also with respect to one or more bars. We present various combinatorial identities for r_m‚_ℓ, the number of barred preferential arrangements of ℓ elements with m bars, using both algebraic and combinatorial arguments. Our main result is an expression for r_m,_ℓ as a linear combination of the r_k (= r_0,_ …
Nonlocal Aggregation Models: A Primer Of Swarm Equilibria,
2013
Harvey Mudd College
Nonlocal Aggregation Models: A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz
All HMC Faculty Publications and Research
Biological aggregations such as fish schools, bird flocks, bacterial colonies, and insect swarms have characteristic morphologies governed by the group members' intrinsic social interactions with each other and by their interactions with the external environment. Starting from a simple discrete model treating individual organisms as point particles, we derive a nonlocal partial differential equation describing the evolving population density of a continuum aggregation. To study equilibria and their stability, we use tools from the calculus of variations. In one spatial dimension, and for several choices of social forces, external forces, and domains, we find exact analytical expressions for the equilibria. …
