Mathematics Commons^™

Polynomial Extension Operators. Part Iii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary ∂K coincides with w. Furthermore, the extension operator is …

On The Singular Weyl-Titchmarsh Function Of Perturbed Spherical Schrödinger Operators, Aleksey Kostenko, Gerald Teschl

Articles

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L1(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular mfunction belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows …

Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev

Articles

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan’s classification and having additional reductions.

Polynomial Bundles And Generalised Fourier Transforms For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander V. Mikhailov, Tihomir Valchev

Articles

A certain class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions is analysed via the Inverse Scattering Method (ISM). The class contains systems of nonlinear evolution equations (NLEEs) associated with a Lax operator (for the time-evolution) polynomial in the spectral parameter. Using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the `squared solutions' (generalised exponentials) are derived. Next, expansions of Q and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform …

A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford

All Graduate Theses, Dissertations, and Other Capstone Projects

We present here a method for computing the homology of a substitution tiling space. There is a well established cohomology theory that uses simple matrix computations to determine if two tiling spaces are dierent. We will show how to compute Putnam's homology groups for these spaces using simple linear algebra. We construct a Markov Partition based on the substitution rules, and exploit the properties of this partition as a shift of finite type to construct algebraic invariants for the tiling space. These invariants form a chain complex, of which we can compute the homology. In our examples we will demonstrate …

A Characterization Of Connected (1,2)-Domination Graphs Of Tournaments, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom_1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is …

Multi-Dimensional Weiss Operators, Sergey Bori̇senok, Mehmet Hakan Erkut, Yaşar Polatoğlu, Rüştü Murat Demi̇rer

Turkish Journal of Mathematics

We present a solution of the Weiss operator family generalized for the case of R^d and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.

A Class Of Generalized Shannon-Mcmillan Theorems For Arbitrary Discrete Information Source, Kangkang Wang

Turkish Journal of Mathematics

In this study, a class of strong limit theorems for the relative entropy densities of random sum of arbitrary information source are discussed by constructing the joint distribution and nonnegative super martingales. As corollaries, some Shannon-McMillan theorems for arbitrary information source, mth-order Markov information source and non-memory information source are obtained and some results for the discrete information source which have been obtained by authors are extended.

The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle

Mathematics Faculty Publications

We will give a positive answer for the unimodality of the Hilbert functions in the smallest open case, that of Artinian level monomial algebras of type three in three variables.

An Investigation Of The Conceptual Understanding Of Continuity And Derivatives In Calculus Of Emerging Scholars Versus Non-Emerging Scholars Program Students, Susan Lai Chan

Mathematics Theses - Archive

The Emerging Scholars Program (ESP) has been adapted at colleges and universities across the nation in efforts to increase student access to Science, Technology, Engineering and Mathematics (STEM) disciplines. This study uses a written assessment to gain insight regarding conceptual knowledge on continuity and derivatives for ESP students versus non-ESP students in the same lecture course in first semester calculus at large urban university in the southwest. We analyze the assessment results of 22 ESP and 48 non-ESP students and discuss findings, particularly, those that indicate statistically significant differences regarding continuity over an interval.

A Snapshot Of Advanced High School Students' Understanding Of Continuity, Melissa Jo Vela

Mathematics Theses - Archive

We report on a study of sixteen high school calculus and seven precalculus students' concept image and concept definition of continuity after one-trimester of instruction at a large suburban high school in the southwestern United States. The researchers developed a questionnaire based upon the work of Tall and Vinner (1981) to determine if calculus students had developed a more sophisticated concept image and concept definition of continuity than students in pre-calculus after a typical treatment in both courses. Using data from the written assessment it was not evident that calculus students demonstrated a more sophisticated concept image and concept definition …

Predictive Model For Bigheaded Carps In Mississippi River, Jitendra K. Shrestha

Mathematics Theses - Archive

Bigheaded carps refer to two species of fish called Silver carp and Bigheaded carp which have invaded the Upper Mississippi River System and are causing nuisance to the native fish like catfish, paddlefish and gizzard Shad by encroaching their habitat. The exponential growth of their population due to their overwhelming reproduction capability and adaptation features calls for a careful study of their population dynamics. In this study, we offer a mathematical model with artificial excessive fishing effort to reduce the population of Bigheaded carps. We numerically observe the correlation among growth rate, fishing rate and the future population of the …

Plasma Myeloperoxidase Predicts Incident Cardiovascular Risks In Stable Patients Undergoing Medical Management For Coronary Artery Disease, W.H. Wilson Tang, Yuping Wu, Stephen J. Nicholls, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

BACKGROUND: Myeloperoxidase (MPO) concentrations predict adverse clinical outcomes in the setting of acute coronary syndromes and heart failure, but the prognostic role of MPO in stable patients with known atherosclerotic burden is unclear. METHODS: We examined plasma MPO concentrations and their relationship with prevalent significant coronary artery disease (defined as >50% stenosis in any coronary vessel) and incident major adverse cardiovascular events (MACEs), including death, myocardial infarction, and stroke, in a 3-year prospective follow-up study of 1895 patients undergoing elective coronary angiography. RESULTS: The median plasma MPO concentration was 101 pmol/L (interquartile range 68–187 pmol/L). Patients with plasma MPO concentrations …

Diminished Antioxidant Activity Of High-Density Lipoprotein–Associated Proteins In Systolic Heart Failure, W.H. Wilson Tang, Yuping Wu, Shirley Mann, Michael Pepoy, Kevin Shrestha, Allen G. Borowski, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background— Diminished serum arylesterase activity, catalyzed by the high-density lipoprotein–associated paraoxonase-1, is associated with heightened systemic oxidative stress and atherosclerosis risk. In the present study, we sought to determine the prognostic role of serum arylesterase activity in subjects with systolic heart failure, particularly in relation to established cardiac biomarkers. Methods and Results— We measured serum arylesterase activity in 760 subjects with impaired left ventricular systolic function (left ventricular ejection fraction <50%), and prospectively followed major adverse cardiac events (including death, nonfatal myocardial infarction, and stroke) for 3 years. In our study cohort (mean age, 64±11 years; 74% men; median left ventricular ejection fraction, 35%; median creatinine clearance, 96 mg/dL), mean serum arylesterase activity (98±25 μmol/L/min/mL) was lower compared with that in healthy control subjects (mean, 115±26 μmol/L/min/mL, P<0.01) but higher compared with advanced decompensated heart failure subjects (mean, 69±22 μmol/L/min/mL, P<0.01). Within our cohort, there was modest correlation between serum arylesterase activity and high-density lipoprotein cholesterol (r=0.33, P<0.01) as well as B-type natriuretic peptide (r=−0.23, P<0.01). Lower serum arylesterase activity was a strong predictor of poorer outcomes (hazard ratio, 2.94; 95% confidence interval, 1.54, 5.62; P<0.001). After adjusting for traditional risk factors, medication use, B-type natriuretic peptide, and creatinine clearance, lower serum arylesterase still conferred an increased risk of major adverse cardiac events at 3 years (hazard ratio, 2.69; 95% confidence interval, 1.37 to 5.28; P=0.004). Conclusions— In patients with systolic heart failure, decreased serum arylesterase activity, a measure of diminished antioxidant properties of high-density lipoprotein, predicts higher risk of incident long-term adverse cardiac event independent of established clinical and biochemical risk factors.

Discrete-Time Recurrent Neural Network And Its Application To Compression Of Infra-Red Spectrum, Leong-Kwan Li, Sally S. L. Shao

Mathematics and Statistics Faculty Publications

We study the discrete-time recurrent neural network that derived from the Leaky-integrator model and its application to compression of infra-red spec- trum. Our results show that the discrete-time Leaky-integrator recurrent neural network (RNN) model can be used to approximate the continuous-time model and inherit its dynamical characters if a proper step size is chosen. Moreover, the discrete-time Leaky-integrator RNN model is absolutely stable. By developing the double discrete integral method and employing the state space search algorithm for the discrete-time recurrent neural network model, we demonstrate with quality spectra regenerated from the compressed data how to compress the infra-red spectrum …

On Socle-Regularity And Some Notions Of Transitivity For Abelian P-Groups, Brendan Goldsmith, Peter Danchev

Articles

In the present work the interconnections between various notions of transitivity for Abelian p-groups and the recently introduced concepts of socle-regular and strongly socle-regular groups are studied.

Bayesian Inference For Exponential Random Graph Models, Alberto Caimo, Nial Friel

Articles

Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can be carried out in a Bayesian framework using a MCMC algorithm, which circumvents the need to calculate the normalising constants. We use a population MCMC approach which accelerates convergence and improves mixing of the Markov chain. This approach improves performance with respect to the Monte Carlo maximum likelihood method of Geyer and Thompson (1992).

On Graded Prime And Primary Submodules, Kürşat Hakan Oral, Ünsal Teki̇r, Ahmet Göksel Ağargün

Turkish Journal of Mathematics

Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.

A Note On Weighted A_P(G)-Modules, Serap Öztop

Turkish Journal of Mathematics

Let G be a locally compact abelian group and w be a weight function on G. In this paper, we show that the space A_{p,w}(G) is a Banach module over the Figà-Talamanca Herz algebra A_p(G) and study the multiplier space from A_p(G) to A_{p,w}(G).

On Almost Complex Structures In The Cotangent Bundle, Ari̇f Sali̇mov, Aydin Gezer, Seher Aslanci

Turkish Journal of Mathematics

E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold M_n to its cotangent bundle T^{\ast} (M_n). Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold M_n to T^{\ast} (M_n) and proved that when \varphi defines an integrable almost complex structure on M_n, its complete lift ^C \varphi is a complex structure. The main result of the present paper is the following theorem: Let \varphi be an almost complex structure on a Riemannian manifold M_n. Then the complete lift ^C …

Rotational Embeddings In E^4 With Pointwise 1-Type Gauss Map, Kadri̇ Arslan, Bengü Kiliç Bayram, Betül Bulca, Young Ho Ki̇m, Cengi̇zhan Murathan, Günay Öztürk

Turkish Journal of Mathematics

In the present article we study the rotational embedded surfaces in E^4. The rotational embedded surface was first studied by G. Ganchev and V. Milousheva as a surface in E^4. The Otsuki (non-round) sphere in E^4 is one of the special examples of this surface. Finally, we give necessary and sufficient conditions for the flat Ganchev-Milousheva rotational surface to have pointwise 1-type Gauss map.

The Wright Message, 2011-2012, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Around Wright Hall
-- New College
-- Programs Revision
-- Math ≠ 800
-- Baumler Mathematics Education Scholarship
-- Two Retire
-- Putnam Exam
-- Math Ed Lab - Then and now
-- 2011 - 2012 Tenure-Stream Faculty
-- Making an Impact
-- The Question
-- Spotlight on Undergraduates
-- Projects and Grants
-- P.S.M. Program in Industrial Mathematics
-- Actuarial Science Alumni
-- Department of Mathematics Contribution Form
-- Department of Mathematics Funds

Prospective Teachers’ Conceptions About Teaching Mathematically Talented Students: Comparative Examples From Canada And Israel, Mark Applebaum, Viktor Freiman, Roza Leikin

The Mathematics Enthusiast

In this paper we analyze prospective mathematics teachers' conceptions about teaching mathematically talented students. Forty-two Israeli participants learning at mathematics education courses for getting their teaching certificates, and fifty-four Canadian pre-service (K-8) teachers participating in mathematics didactics course were asked to solve a challenging mathematical task. We performed comparative analysis of problem-solving strategies, solution results and participants' success. Based on the discussion with 25 Israeli participants we composed an attitude questionnaire, in which prospective teachers were asked to express their degree of agreement with statements expressing different beliefs about education of mathematically talented students. The questionnaire was presented to 56 …

Mathematical And Didactical Enrichment For Pre-Service Teachers: Mentoring Online Problem Solving In The Casmi Project, Manon Leblanc, Viktor Freiman

The Mathematics Enthusiast

In order to teach successfully, future teachers should not only be educated about students’ conceptions, but also about different forms of knowledge and classroom culture. In our research, we examined whether the participation in the Internet-based challenging problem solving community CASMI contributes to the development of the aforementioned awareness and understanding in order to meet the needs of all students including the gifted ones. The results obtained enabled us to note that the pre-service teachers’ perceptions of the project as a source of enrichment are mainly positive. However, analyzing schoolchildren’s strategies, the participants preferred to use pre-determined criteria instead of …

Disrupting Gifted Teenager’S Mathematical Identity With Epistemological Messiness, Paul Betts, Laura Mcmaster

The Mathematics Enthusiast

Mathematics is widely perceived as a universal and uncontested discipline, contrary to the philosophy of mathematics literature. Other researchers have considered the potential role of philosophy in school, but there is little work with gifted students engaged with issues concerning the nature of mathematics. We developed a philosophy of mathematics unit intended to enlarge gifted students’ perceptions of the nature of mathematics by exposing the uncritical and tidy rendering of mathematics within school math. Using a narrative methodology, we attended to gifted student’s students’ stories of relationship with mathematics, based on the premise that a person’s relationship with mathematics is …

Gifted Students And Advanced Mathematics, Edward J. Barbeau

The Mathematics Enthusiast

The extension to a wide population of secondary education in many countries seems to have led to a weakening of the mathematics curriculum. In response, many students have been classified as “gifted” so that they can access a stronger program. Apart from the difficulties that might arise in actually determining which students are gifted (is it always clear what the term means?), there are dangers inherent in programs that might be devised even for those that are truly talented.

Sometimes students are moved ahead to more advanced mathematics. Elementary students might be taught algebra or even subjects like trigonometry and …

The Promise Of Interconnecting Problems For Enriching Students’ Experiences In Mathematics, Margo Kondratieva

The Mathematics Enthusiast

The interconnecting problem approach suggests that often one and the same mathematical problem can be used to teach various mathematical topics at different grade levels. How is this approach useful for the development of mathematical ability and the enrichment of mathematical experiences of all students including the gifted ones? What are the benefits for teachers’ and what would teachers need to implement this approach? What directions would further research on these issues take? The paper discusses these and closely related questions.

I propose that a long-term study of a progression of mathematical ideas revolved around one interconnecting problem is useful …

Creativity Assessment In School Settings Through Problem Posing Tasks, Ildikó Pelczer, Fernando Gamboa Rodríguez

The Mathematics Enthusiast

Research in math education on mathematical creativity relies on the idea that creativity is potentially within all students and it can be fostered by properly structured activities. The tasks most commonly used for its assessment are problem solving and problem posing. In our approach we use problem posing tasks to get insight into students’ creativity. Based on a qualitative analysis of the participants’ answers to the questionnaire that followed the task, we define algorithmic, combined and innovative creativity as constructs that can be put in correspondence with the types and level of knowledge involved in the problem posing task. We …

Forthcoming Tmme Vol8,No3 [August 2011: Special Section On The North Calotte Conference In Mathematics Education : Tromsø-2010], Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.