Mathematics Commons^™

New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo

Turkish Journal of Mathematics

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota

Turkish Journal of Mathematics

In this paper we study the multiplicative, tensor, Sobolev and convolution inequalities in certain Banach spaces, the so-called Bilateral Grand Lebesque Spaces. We also give examples to show the sharpness of these inequalities when possible.

Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza

MPP Published Research

"Both historians and philosophers of mathematics frequently speak of mathematical objects. Are they speaking of the same or of similar things? Better: are they appealing to the same notion or to similar notions?"

Packing Rates Of Measures And A Conjecture For The Packing Density Of 2413, C. B. Presutti, Walter Stromquist

Mathematics & Statistics Faculty Works

We give a new lower bound of 0.10472422757673209041 for the packing density of 2413, justify it by a construction, and conjecture that this value is actually equal to the packing density. Along the way we define the packing rate of a permutation with respect to a measure, and show that maximizing the packing rate of a pattern over all measures gives the packing density of the pattern.

Whitehead Products In Function Spaces: Quillen Model Formulae, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f : X→Y, in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f. These results follow from a purely algebraic development in the setting of chain complexes of derivations of differential graded Lie algebras, which is of interest in its own right. We apply the results to study the Whitehead length of function space components.

Heat Transfer Through The Boundary Layer On A Moving Cylindrical Fibre, Brendan Redmond, David Mcdonnell

Articles

This paper applies boundary layer theory to the process of manufacturing polymer fibres known as the melt spinning process. The rate of heat loss of the fibre during this process, characterised by the local Nusselt number, is evaluated by means of a Pohlhausen integral method.

Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang

Turkish Journal of Mathematics

For Schrödinger systems on metric graphs with \delta'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

Some Properties Of C-Fusion Frames, Mohammad Hasan Faroughi, Reza Ahmadi

Turkish Journal of Mathematics

In [10], we generalized the concept of fusion frames, namely, c-fusion frames, which is a continuous version of the fusion frames. In this article we give some important properties about the generalization, namely erasures of subspaces, the bound of c-erasure reconstruction error for Parseval c-fusion frames, perturbation of c-fusion frames and the frame operator for fusion pair.

The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen

Turkish Journal of Mathematics

The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.

The Wright Message, 2010, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2010 - 2011 Tenure-Stream Faculty
-- Spotlight on Undergraduates
-- Projects and Grants
-- Secondary Mathematics Education Programs
-- UNI I-Teach
-- Crane Scholarship
-- Actuarial Science and the Actuarial Science Fund
-- Alliance Project
-- Mathematics Contribution Form
-- Additional Mathematics Funds
-- Around Wright Hall
-- In Memoriam
-- Dr. Ridenhour Retires

Gender And Mathematics Education In Pakistan: A Situation Analysis, Anjum Halai

The Mathematics Enthusiast

This paper reports from a situation analysis of gender issues in mathematics education in Pakistan. It was undertaken at the initiation of a large scale project which aimed to understand how curriculum change in mathematics and science education may be implemented in ways that contribute to poverty alleviation and promote gender equity in disadvantaged rural settings. The paper posits that issues of access, achievement and quality of mathematics education are integrally linked with questions of equity, in this case gender equity. It identifies several questions and arenas for further research and makes recommendations for policy and practice in mathematics education.

High School Teachers Use Of Dynamic Software To Generate Serendipitous Mathematical Relations, Manuel Santos-Trigo, Hugo Espinosa-Pérez

The Mathematics Enthusiast

In this study, we document and analyse problem-solving approaches that high school teachers exhibited as a result of using dynamic software (Cabri-Geometry) to construct and examine geometric configurations. What type of questions do teachers pose and pursue while representing and exploring mathematical tasks or objects dynamically? To what extent their initial problem solving strategies are enhanced with the use of the tools? Results indicate that the use of the tool offered the participants the opportunity of constructing geometric configuration (formed by simple mathematical objects) that led them to identify and explore key mathematical relations.

“What Was Really Accomplished Today?” Mathematics Content Specialists Observe A Class For Prospective K–8 Teachers, Andrew M. Tyminksi, Sarah Ledford, Dennis Hembree

The Mathematics Enthusiast

One of the important activities mathematics teacher educators engage in is the development of teachers at both the in-service and pre-service levels. Also of importance is the professional development of these professional developers. In the summer of 2004, a summer institute was held that allowed mathematics teacher educators watch the teaching of a mathematics content course for prospective K–8 teachers. This paper examines the manner in which a specific group of mathematics content specialists experienced this professional development.

Randomness: Developing An Understanding Of Mathematical Order, Steve Humble

The Mathematics Enthusiast

Is randomness merely the human inability to recognise a pattern that may in fact exist?

The three activities described show how order can be found in seemly random activities. The author has found that by using these activities on randomness, his students have developed a greater understanding of mathematical pattern and sequence. The teaching mathematical concepts in this way, engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can sometimes occur in the classroom. By taking the maths beyond the classroom, …

The Constructs Of Phd Students About Infinity: An Application Of Repertory Grids, Serdar Aztekin, Ahmet Arikan, Bharath Sriraman

The Mathematics Enthusiast

Infinity has been one of the more difficult concepts for humanity to grasp. A major component of the research on mathematics education related to infinity has been the study of student’s conceptions and reasoning about calculus subjects, particularly limits and series. Some related studies are about Cantor’s ordinal and cardinal infinity. However since most students at the high school and college level are unfamiliar with symbolic representations and terminology, such as a set theoretic approach, a context (generally geometric) is used for investigating notions of infinity indirectly. In this paper we report on a study on the constructs of PhD …

When Is .999... Less Than 1?, Karin Usadi Katz, Mikhail G. Katz

The Mathematics Enthusiast

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999... be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.

Review: Pythagoras’ Revenge: A Mathematical Mystery; The Housekeeper And The Professor, Susan Jane Colley

Faculty & Staff Scholarship

No abstract provided.

Bringing Toric Codes To The Next Dimension, Ivan Soprunov, Jenya Soprunova

Mathematics and Statistics Faculty Publications

This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes in $\mathbb{R}^n$. We show that the minimum distance is multiplicative with respect to taking the product of polytopes, and behaves in a simple way when one builds a k-dilate of a pyramid over a polytope. This allows us to construct a large class of examples of higher dimensional toric codes where we can compute the minimum distance explicitly.

Alternative Technical Efficiency Measures: Skew, Bias, And Scale, William Clinton Horrace, Qu Feng

Center for Policy Research

In the fixed-effects stochastic frontier model an efficiency measure relative to the best firm in the sample is universally employed. This paper considers a new measure relative to the worst firm in the sample. We find that estimates of this measure have smaller bias than those of the traditional measure when the sample consists of many firms near the efficient frontier. Moreover, a two-sided measure relative to both the best and the worst firms is proposed. Simulations suggest that the new measures may be preferred depending on the skewness of the inefficiency distribution and the scale of efficiency differences.

[Introduction To] Ordinary And Particial Differential Equations: An Introduction To Dynamical Systems, John W. Cain, Angela M. Reynolds

Bookshelf

Differential equations arise in a variety of contexts, some purely theoretical and some of practical interest. As you read this textbook, you will find that the qualitative and quantitative study of differential equations incorporates an elegant blend of linear algebra and advanced calculus. This book is intended for an advanced undergraduate course in differential equations. The reader should have already completed courses in linear algebra, multivariable calculus, and introductory differential equations.