Mathematics Commons^™

Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫^t₀C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various L^p properties are studied under suitable conditions on the functions involved with this equation.

Leadership Founded In Habits Of Inquiry And Reflection (Abstract), Robert C. Bolz Jr.

Kenneth C. Schraut Memorial Lectures

Leadership in the Science, Technology, Engineering, and Mathematics (STEM) disciplines has been the foundation of leadership in the world for over 600 years.

Ninth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Envy-Free Cake Divisions Cannot Be Found By Finite Protocols, Walter Stromquist

Mathematics & Statistics Faculty Works

We show that no finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece.

Hermit Points On A Box, R. Hess, Charles M. Grinstead, M. Grinstead, Deborah J. Bergstrand

Mathematics & Statistics Faculty Works

No abstract provided.

The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza

MPP Published Research

Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …

A Probabilistic Analysis Of The Trading The Line Strategy, V. Abramov, M. K. Khan, Rasul A. Khan

Mathematics and Statistics Faculty Publications

We provide analytic models for which the appropriate statistics of the trading the line strategy, N h , can be derived in closed form. In particular, we provide closed-form expressions concerning the average duration of the open position, E(N h ), the variance of the open duration, Var(N h ), the average of the stopped log price, E(S N h ), the variance of the stopped log price, Var(S N h ), the correlation, Corr(N h , S N h ), and the Laplace transform, E(e−s N h ). These results are obtained, in discrete time settings, for binomial and …

Higher Derivatives Of Spectral Functions Associated With One-Dimensional Schrodinger Operators, Daphne Gilbert, B.J. Harris, S.M. Riehl

Articles

We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory.

The Wright Message, 2008, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- New Faces in the Department
-- New Mathematics Education Center
-- Math Murder Mystery
-- Student Competitions
-- PSM
-- Mathematics After Hours
-- Faculty Notes
-- Integration Bee
-- Alliance Program
-- SOAR (Student Online Achievement Resources)
-- DoDEA
-- Hawaii Department of Education (Professional Development Facilitator Training)
-- Focus on Two Endowment Funds

Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen

Department of Math & Statistics Faculty Publications

In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H²ƟBH², where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H²ƟBH² is the compression of a Toeplitz operator. This result complements a related result of Sarason [6].

Proceedings Of The Second Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 2nd Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents
• Letter from President

Virtual Vs. Concrete Manipulatives In Mathematics Teacher Education: A Call For Research, Annita W. Hunt

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Are virtual manipulatives as effective as concrete (hands-on) manipulatives to build conceptual understanding of number concepts and relationships in pre-service middle grades teachers? In the past, the use of concrete manipulatives in mathematics courses for Clayton State University’s preservice middle grades teachers has proven to be a very effective way to build conceptual understanding of a variety of mathematical topics. This paper presents an argument for the need for research into the usefulness of virtual manipulatives for enhancing mathematics teacher education and their potential to supplement (or replace?) concrete manipulatives.

Inverse Limits Of Permutation Maps, Robbie A. Beane

Doctoral Dissertations

"In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to …

Origin Of Conductive Surface Layer In Annealed Zno, David C. Look, B. Claflin, Helen Smith

Mathematics and Statistics Faculty Publications

The highly conductive surface layers found in nearly all as-grown or annealed bulk ZnO wafers are studied by temperature-dependent Hall-effect and secondary-ion mass spectroscopy (SIMS) measurements. In this work, we have used annealing in N₂ at 900 degrees C, and forming gas (5% H₂ in N₂) at 600 degrees C, to cause a large enough surface conduction that SIMS measurements can be reliably employed. The increased near-surface donor density, as determined from two-layer Hall-effect modeling, is consistent with an increased near-surface concentration of Al, Ga, and In atoms, resulting from diffusion. There is no evidence for …

G-Perfect Nonlinear Functions, James A. Davis, Laurent Poinsot

Department of Math & Statistics Faculty Publications

Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both Z₂ -valued and Z^{a …}

Molecular Targets Of 2,3,7,8-Tetrachlorodibenzo-P-Dioxin (Tcdd) Within The Zebrafish Ovary: Insights Into Tcdd-Induced Endocrine Disruption And Reproductive Toxicity, Tisha C. King Heiden, Craig Struble, Matthew L. Rise, Martin J. Hessner, Reinhold J. Hutz, Michael J. Carvan Iii

Mathematics, Statistics and Computer Science Faculty Research and Publications

TCDD is a reproductive toxicant and endocrine disruptor, yet the mechanisms by which it causes these reproductive alterations are not fully understood. In order to provide additional insight into the molecular mechanisms that underlie TCDD's reproductive toxicity, we assessed TCDD-induced transcriptional changes in the ovary as they relate to previously described impacts on serum estradiol concentrations and altered follicular development in zebrafish. In silico computational approaches were used to correlate candidate regulatory motifs with observed changes in gene expression. Our data suggest that TCDD inhibits follicle maturation via attenuated gonadotropin responsiveness and/or depressed estradiol biosynthesis, and that interference of estrogen-regulated …

Delta Function For An Affine Subspace, Jeremy Becnel

Faculty Publications

The Kubo–Yokoi and Donsker delta functions are well known generalized functions in infinite dimensional distribution theory. In this paper we develop the delta function for an affine subspace and show that it is a generalization of the Kubo–Yokoi and Donsker delta functions. The Wiener– Itˆo expansion of the delta function for an affine subspace is also given.

Writing Representations Over Proper Division Subrings, Stephen P. Glasby

All Faculty Scholarship for the College of the Sciences

Let �� be a division ring, and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of ��. Let �� = ��^G be the division subring of elements of �� fixed by G. Given a representation p : �� →��^d×d of an �� -algebra ��, we give necessary and sufficient conditions for p to be writable over ��. (Here ��^d×d denotes the algebra of d×d matrices over ��, and a matrix A writes p over �� if A⁻¹p(��)A ⊆ F^d×d.) We give an algorithm for constructing an …

Radical Anti-Invariant Lightlike Submanifolds Of Semi-Riemannian Product Manifolds, Erol Kiliç, Bayram Şahi̇n

Turkish Journal of Mathematics

We introduce radical anti-invariant lightlike submanifolds of a semi Riemannian product manifold and give examples. After we obtain the conditions of integrability of distributions which are involved in the definition of radical anti-invariant lightlike submanifolds, we investigate the geometry of leaves of distributions. We also obtain the induced connection is a metric connection and a radical anti-invariant lightlike submanifold is a product manifold under certain conditions. Finally, we study totally umbilical radical anti-invariant lightlike submanifolds and observe that they are totally geodesic under a condition.

Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or …

Lipschitz Continuity Of The Best Approximation Operator In Vector-Valued Chebyshev Approximation, Martin Bartelt, John Swetits

Mathematics & Statistics Faculty Publications

When G is a finite dimensional Haar subspace of C(X, R^k), the vector-valued continuous functions (including complex-valued functions when k is 2) from a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C(X, R^k) the best approximation operator satisfies the strong unicity condition of order 2 and a Lipschitz (H˝older) condition of order 1/2. This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1.

Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb

Dartmouth Scholarship

Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …

Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi

Mathematics, Statistics and Data Science Faculty Works

We show that, given any n and α, every embedding of any sufficiently large complete graph in R³ contains an oriented link with components Q₁, ..., Q_n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a₂(Qi)|≥α, where a₂(Q_i) denotes the second coefficient of the Conway polynomial of Q_i.

Weight Systems For Milnor Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We use Polyak's skein relation to give a new proof that Milnor's string link homotopy invariants are finite type invariants, and to develop a recursive relation for their associated weight systems. We show that the obstruction to the triviality of these weight systems is the presence of a certain kind of spanning tree in the intersection graph of a chord diagram.

Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra

Mathematics, Statistics and Data Science Faculty Works

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Value Monoids Of Zero-Dimensional Valuations Of Rank 1, Edward Mosteig

Mathematics, Statistics and Data Science Faculty Works

Classically, Grobner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas by providing a class of valuations on k(x, y) that are suitable for this framework. For these valuations, we compute ν(k[x, y] ∗ ) and use this to perform computations concerning ideals in the polynomial ring k[x, y]. Interestingly, for these valuations, some ideals have a finite Grobner basis with respect to the valuation that is not …

Cohomology Of Categorical Self-Distributivity, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito

Mathematics, Statistics and Data Science Faculty Works

We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Yang–Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All …

Optimal Packings Of Up To 6 Equal Circles On A Triangular Flat Torus, Anna Castelaz, William Dickinson, Daniel Guillot, Sandi Xhumari

Student Summer Scholars Manuscripts

How do you optimally pack equal circles into the standard triangular torus? In this paper, we proved the optimal packings of 1 through 6 equal circles. In order to do this we used techniques from graph theory and also mathematical softwares like Maple and LaTeX. I only worked on proving the optimal packing of 6 equal circles on this special container called the standard triangular torus. In addition, I also contributed in improving the previous proofs for 5 or less equal circles. The purpose of my research was to prove the best packing of 6 equal circles into this at …

Matrix Model Superpotentials And Ade Singularities, Carina Curto

Department of Mathematics: Faculty Publications

We use F. Ferrari’s methods relating matrix models to Calabi–Yau spaces in order to explain much of Intriligator and Wecht’s ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. We find that ADE superpotentials in the Intriligator–Wecht classification exactly match matrix model superpotentials obtained from Calabi–Yau with corresponding ADE singularities. Moreover, in the additional Ô, Â, Dˆ and Ê cases we find new singular geometries. These “hat” geometries are closely related to their ADE counterparts, but feature non-isolated singularities. As a byproduct, we give simple descriptions for …

Towards Universal Cover Decoding, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker

Department of Mathematics: Faculty Publications

Low complexity decoding of low-density paritycheck (LDPC) codes may be obtained from the application of iterative message-passing decoding algorithms to the bipartite Tanner graph of the code. Arguably, the two most important decoding algorithms for LDPC codes are the sum-product decoder and the min-sum (MS) decoder. On a bipartite graph without cycles (a tree), the sum-product decoder minimizes the probability of bit error, while the min-sum decoder minimizes the probability of word error [9]. While the behavior of sum-product and min-sum is easily understood when operating on trees, their behavior becomes much more difficult to characterize when the Tanner graph …