Mathematics Commons^™

With One Breath, Jessica Solfest

Honors Theses, 1963-2015

Biologists know that the cardiovascular and respiratory systems interact and coordinate via the baroreflex and other pathways, but there is still much to discover regarding the dynamical aspects of their communication. Synchronization patterns between the respiratory and cardiovascular systems evince their interaction. This thesis focuses on the synchronization of cardiovascular and respiratory activity. I analyze the frequency of this synchrony to determine patterns and characterize the systems’ adaptability to changes in the environment. I applied time series analysis and Markov processes to dynamical systems in an attempt to unearth meaning behind cardiorespiratory communicative mysteries. Through this research, I found that …

Ioana's Superrigidity Theorem And Orbit Equivalence Relations, Samuel Coskey

Mathematics Faculty Publications and Presentations

We give a survey of Adrian Ioana’s cocycle superrigidity theoremfor profinite actions of Property (T) groups and its applications to ergodic theory and set theory in this expository paper. In addition to a statement and proof of Ioana’s theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence) and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas’s theorem that the classification of torsion-free abelian groups of …

Navigating The Seas Of Mathematics Education: New Waves In Research To Improve Student Learning, Jinfa Cai, Sasha Wang

Mathematics Faculty Publications and Presentations

This issue focuses on research in the domain of mathematics education. Although mathematics has been a subject of study for many centuries, mathematics education is a relatively new field of scholarly inquiry, having been established as an independent field of research only in the early twentieth century. The most significant milestone was the establishment of the International Commission on Mathematical Instruction (ICMI) in 1908. Since 1969, ICMI has organized the International Congress on Mathematical Education, a quadrennial international meeting whose aim is to present the current states and trends in mathematics education research and in the practice of mathematics teaching …

The Archimedean - January 2013, Department Of Mathematics, Syracuse University

Newsletters from the Department of Mathematics - The Archimedean

No abstract provided.

New Bounds And Computations On Prime-Indexed Primes, Jonathan Bayless, Dominic Klyve, Tomas Oliveira E Silva

Mathematics Faculty Scholarship

In a 2009 article, Barnett and Broughan considered the set of prime-index primes. If the prime numbers are listed in increasing order (2, 3, 5, 7, 11, 13, 17, . . .), then the prime-index primes are those which occur in a prime-numbered position in the list (3, 5, 11, 17, . . .). Barnett and Broughan established a prime-indexed prime number theorem analogous to the standard prime number theorem and gave an asymptotic for the size of the n-th prime-indexed prime.

We give explicit upper and lower bounds for π²(x), the number of prime-indexed primes up to …

Methods In Visual Mathematics: Reductionism In Researching Mathematical Principles In Art, Lauren N. Colie

AUCTUS: The Journal of Undergraduate Research and Creative Scholarship

People traditionally rely on visual arts as an effective communication tool and medium of self-expression for when words fail to convey abstract concepts. Thera Mjaaland, anthropologist and professional photographer, writes, “Art is capable of negotiating conceptual gaps caused by a dichotomized epistemology” (393). In essence, Mjaaland asserts that art helps relate different modes of thinking by illustrating the abstract and difficult to grasp—privileging the communicative value of an image over that of text. Within this method of communication is a collection of works acknowledged by public consensus to be of an elevated status or value. The art world is deeply …

A New Recursion For Three-Column Combinatorial Macdonald Polynomials, Elizabeth Niese

Mathematics Faculty Research

The Hilbert series of the Garsia–Haiman module M_μ can be described combinatorially as the generating function of certain fillings of the Ferrers diagram of μ where μ is an integer partition of n . Since there are n ! fillings that generate , it is desirable to find recursions to reduce the number of fillings that need to be considered when computing combinatorially. In this paper, we present a combinatorial recursion for the case where μ is an n by 3 rectangle. This allows us to reduce the number of fillings under consideration from (3n)! to (3n)!/(3!ⁿn!).

Chasing Squares [Pamphlet], Jeremiah Farrell

Scholarship and Professional Work - LAS

Pamphlet accompanying Jeremiah Farrell's mass-produced "Chasing Squares" puzzle.

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.

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, 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, 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, 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, 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 …

Creating An Interdisciplinary Research Course In Mathematical Ecology, Glenn Ledder, Brigitte Tenhumberg

School of Biological Sciences: Faculty Publications

An integrated interdisciplinary research course in biology and mathematics is useful for recruiting students to interdisciplinary research careers, but there are difficulties involved in creating and implementing it. We describe the genesis, objectives, design policies, and structure of the Research Skills in Theoretical Ecology course at the University of Nebraska–Lincoln and discuss the difficulties that can arise in designing and implementing interdisciplinary courses.

An Interdisciplinary Research Course In Theoretical Ecology For Young Undergraduates, Glenn Ledder, Brigitte Tenhumberg, G. Travis Adams

School of Biological Sciences: Faculty Publications

As part of an interdepartmental effort to attract promising young students to research at the interface between mathematics and biology, we created a course in which groups of recent high school graduates and first-year college students conducted a research project in insect population dynamics. The students set up experiments, collected data, used the data to develop mathematical models, tested their models against further experiments, and prepared their results for dissemination. The course was self-contained in that the lecture portion developed the mathematical, statistical, and biological background needed for the research. A special writing component helped students learn the principles of …

Number Representation And Calculation: An Overview Of Chapter 4 Of Thinking Mathematically, Emily Pawlicki

A with Honors Projects

A presentation providing an overview of numeration systems and using different bases in calculations.

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, 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, 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