Mathematics Commons^™

Strong Bounded Solutions For Nonlinear Parabolic Systems, Nsoki Mavinga, M. N. Nkashama

Mathematics & Statistics Faculty Works

In this article we study the existence of strong bounded solutions for nonlinear parabolic systems on a domain which is bounded in space and unbounded in time (namely the entire real line). We use nonlinear iteration arguments combined with some a priori estimates to derive the existence results. We also provide conditions under which we have a positive solution. Some examples are given to illustrate the results.

Using Topology To Explore Mathematics Education Reform, Carling Sugarman

HMC Senior Theses

Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, …

There And Back Again: Elliptic Curves, Modular Forms, And L-Functions, Allison F. Arnold-Roksandich

HMC Senior Theses

L-functions form a connection between elliptic curves and modular forms. The goals of this thesis will be to discuss this connection, and to see similar connections for arithmetic functions.

Zp-Modules With Partial Decomposition Bases In L Δ ∞Ω, Carol Jacoby, Peter Loth

Mathematics Faculty Publications

We consider the class of mixed Zp-modules with partial decomposition bases. This class includes those modules classified by Ulm and Warfield and is closed under L∞ω-equivalence. In the context of L∞ω- equivalence, Jacoby defined invariants for this class and proved a classification theorem. Here we examine this class relative to Lδ∞ω, those formulas of quantifier rank ≤ some ordinal δ, defining invariants and proving a classification theorem. This generalizes a result of Barwise and Eklof.

Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza

MPP Published Research

We follow two of the many paths leading from Newton’s to Euler’s scientific productions, and give an account of Euler’s role in the reception of some of Newton’s ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton’s conceptions within a new conceptual frame also influenced by Descartes’s views sand Leibniz’s formalism.

Applications Of Cubical Arrays In The Study Of Finite Semifields, Kelly Casimir Aman

Mathematics Dissertations - Archive

It is well known that any finite semifield, S, can be viewed as an n-dimensional vector space over a finite field or prime order, Fp, and that the multiplication in S defines and can be defined by an n x n x n cubical array of scalars, A. For any element a E S, the matrix, La, corresponding to left multiplication by a can be determined from A. In this paper we show that there exists a unique monic polynomial of minimal degree, f E Fp[x], such that f(a) = 0, and which divides the minimal polynomial of La. Furthermore, …

Brain Control Of Functional Reach In Healthy Adults And Stroke Survivors, Janis J. Daly, Ken Hrovat, John Holcomb, Svetlana Pundik

Mathematics and Statistics Faculty Publications

Purpose: Recovery of the most basic shoulder-flexion/elbow-extension components of functional reach is critical for effective arm function following stroke. In order to understand the mechanisms of motor recovery, it is important to characterize the pattern of brain activation during the reach task. Methods: We evaluated 11 controls and 23 moderately to severely impaired chronic stroke survivors (>6 months), with impaired shoulder flexion and elbow extension. Measures were acquired for Arm Motor Ability Test (AMAT) and functional Magnetic Resonance Imaging (fMRI) during the basic shoulder/elbow reach. Results: First, in controls, lateralization of fMRI signal during the reach task was less …

Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli

Articles

We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.

Some Notes On Nil-Semicommutative Rings, Yinchun Qu, Junchao Wei

Turkish Journal of Mathematics

A ring R is defined to be nil-semicommutative if ab \in N(R) implies arb \in N(R) for a, b, r \in R, where N(R) stands for the set of nilpotents of R. Nil-semicommutative rings are generalization of NI rings. It is proved that (1) R is strongly regular if and only if R is von Neumann regular and nil-semicommutative; (2) Exchange nil-semicommutative rings are clean and have stable range 1; (3) If R is a nil-semicommutative right MC2 ring whose simple singular right modules are YJ-injective, then R is a reduced weakly regular ring; (4) Let R be a nil-semicommutative …

On Minimal Poincaré 4-Complexes, Alberto Cavicchioli, Friedrich Hegenbarth, Dusan Repovs

Turkish Journal of Mathematics

We consider 2 types of minimal Poincaré 4-complexes. One is defined with respect to the degree 1-map order. This idea was already present in our previous papers, and more systematically studied later by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.

Covers And Preenvelopes By V-Gorenstein Flat Modules, Xiaoyan Yang

Turkish Journal of Mathematics

In this paper, we introduce and study V-Gorenstein flat modules and show the stability of the category of V-Gorenstein flat modules. We investigate the existence of V-Gorenstein flat covers and V-Gorenstein flat preenvelopes for any left R-module. Also we prove that (V-GF,V-GF^\bot) is a perfect hereditary cotorsion pair in B^l(R), where V-GF stands the class of V-Gorenstein flat left R-modules and B^l(R) is the left Bass class. Some applications are given.

Coverings And Crossed Modules Of Topological Groups With Operations, Osman Mucuk, Tunçar Şahan

Turkish Journal of Mathematics

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent. This equivalence enables us to introduce the cover of crossed modules within topological groups with operations. Finally, we draw relations between the coverings …

On The K-Ring Of The Classifying Space Of The Generalized Quaternion Group, Mehmet Kirdar, Sevi̇lay Özdemi̇r

Turkish Journal of Mathematics

We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.

An Alternative Approach To The Adem Relations In The Mod 2 Steenrod Algebra, Neşet Deni̇z Turgay

Turkish Journal of Mathematics

The Leibniz--Hopf algebra F is the free associative algebra over Z on one generator S^n in each degree n>0, with coproduct given by \Delta(S^n) = \sum_{i+j=n} S^i \otimes S^j. We introduce a new perspective on the Adem relations in the mod 2 Steenrod algebra A_2 by studying the map \pi^\ast dual to the Hopf algebra epimorphism \pi: F \otimes Z/2 \to A_2. We also express Milnor's Hopf algebra conjugation formula in A_2^\ast in a different form and give a new approach for the conjugation invariant problem in A_2^\ast.

Notes On The Tangent Bundle With Deformed Complete Lift Metric, Aydin Gezer, Mustafa Özkan

Turkish Journal of Mathematics

In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.

Pseudosymmetric Lightlike Hypersurfaces, Sema Kazan, Bayram Şahi̇n

Turkish Journal of Mathematics

We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.

Functionals Of Gasser--Muller Estimators, Petre Babilua, Elizbar Nadaraya, Grigol Sokhadze

Turkish Journal of Mathematics

The asymptotic properties of a general functional of the Gasser--Muller estimator are investigated in the Sobolev space. The convergence rate, consistency, and central limit theorem are established.

Robust Calibration Of Cameras With Telephoto Lens Using Regularized Least Squares, Mingpei Liang, Xinyu Huang, Chung-Hao Chen, Gaolin Zheng, Alade Tokuta

Electrical & Computer Engineering Faculty Publications

Cameras with telephoto lens are usually used to recover details of an object that is either small or located far away from the cameras. However, the calibration of this kind of cameras is not as accurate as the one of cameras with short focal lengths that are commonly used in many vision applications. This paper has two contributions. First, we present a first-order error analysis that shows the relation between focal length and estimation uncertainties of camera parameters. To our knowledge, this error analysis with respect to focal length has not been studied in the area of camera calibration. Second, …

Sensor Selection And Integration To Improve Video Segmentation In Complex Environments, Adam R. Reckley, Wei-Wen Hsu, Chung-Hao Chen, Gangfeng Ma, E-Wen Huang

Electrical & Computer Engineering Faculty Publications

Background subtraction is often considered to be a required stage of any video surveillance system being used to detect objects in a single frame and/or track objects across multiple frames in a video sequence. Most current state-of-the-art techniques for object detection and tracking utilize some form of background subtraction that involves developing a model of the background at a pixel, region, or frame level and designating any elements that deviate from the background model as foreground. However, most existing approaches are capable of segmenting a number of distinct components but unable to distinguish between the desired object of interest and …

The Wright Message, 2014-2015, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Around Wright Hall
-- Tenure Stream Faculty 2014 - 2015
-- The 2014 Hari Shankar Lecture
-- New Faculty: Heather Gallivan
-- Faculty Spotlight: Russell Campbell
-- UNI on the March
-- Farewell Tour
-- The Center for Teaching and Learning Mathematics
-- Student Organizations
-- Donor Spotlight: Robert Minch & Mary Bothwick
-- An Interview with Dr. Theron Hitchman
-- Alumni Spotlight: Allysen Lovstuen, Jodi Osthus, & Benjamin Wadsley
-- Addresses by Mathematics Faculty
-- Student Spotlight: Caryn Knight & Emily Stumpff
-- Contributions to an Account - Recognition …