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2006

Mathematics

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Articles 1 - 26 of 26

Full-Text Articles in Physical Sciences and Mathematics

Spectrally Arbitrary Tree Sign Pattern Matrices, Krishna Kaphle Dec 2006

Spectrally Arbitrary Tree Sign Pattern Matrices, Krishna Kaphle

Mathematics Theses

A sign pattern (matrix) is a matrix whose entries are from the set {+,–, 0}. A sign pattern matrix A is a spectrally arbitrary pattern if for every monic real polynomial p(x) of degree n there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). All 3 × 3 SAP's, as well as tree sign patterns with star graphs that are SAP's, have already been characterized. We investigate tridiagonal sign patterns of order 4. All irreducible tridiagonal SAP's are identified. Necessary and sufficient conditions for an irreducible tridiagonal …

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Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr. Dec 2006

Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

There are always a lot of questions that need to be answered at the beginning of a course. When are office hours? What are the grading policies? How many exams will there be? Will late homework be accepted? We have all seen the answers to these sorts of questions form the bulk of a standard course syllabus, and most of us feel an obligation (and rightly so) to provide such information.

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On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth Nov 2006

On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …

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Multiattribute Acceptance Sampling Plans., Anup Majumdar Dr. Sep 2006

Multiattribute Acceptance Sampling Plans., Anup Majumdar Dr.

Doctoral Theses

Irrespective of the type of product, evaluation of conformity to specified requirements of its quality characteristics is an integral part of quality assurance. Although they form a set of necessary verification activities almost at all stages of production, these activities, known as inspection do not add value to the product on their own and are to be kept at their minimum. The sampling inspection where a portion of a collection of product units is inspected on a set of characteristics with a view to making decision about acceptance or otherwise becomes relevant in this context.The number of elements of the …

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Essays On Individual And Collective Powers In A Voting Body., Sonali Roy Dr. Aug 2006

Essays On Individual And Collective Powers In A Voting Body., Sonali Roy Dr.

Doctoral Theses

MotivationThe issue of measurement of voting power is a very important topic of discussion in social science these days. The concept of voting power concerns any collective decision making body (or, equivalently, a collectivity) which makes ‘yes’ or ‘no’ decisions on any issue, by the process of voting. Examples of such bodies abound in today’s world. The United Nations Security Council, The Council of Ministers in the European Union, the Parliament of the republic of India, the board room of any corporate house etc., are all examples of such decision making bodies.The voting process of each of these bodies is …

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Teaching Time Savers: Style Points, Michael E. Orrison Jr. Aug 2006

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I began as an assistant professor, I had a pretty good sense of how much time it would take for me to prepare for each class. After a few conversations with my new colleagues, I even had a good sense of how much time I should devote to tasks like office hours and committee work. Somewhere in the middle of grading my first exam, though, it became painfully clear that I had underestimated the amount of time I would need to grade exams!

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Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr. Jul 2006

Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr.

Doctoral Theses

No abstract provided.

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On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell Jul 2006

On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell

Theses and Dissertations

In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.

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Hole Dynamics In Polymer Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Lu Zou Jun 2006

Hole Dynamics In Polymer Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Lu Zou

All HMC Faculty Publications and Research

This article develops a model for the closing of a gaseous hole in a liquid domain within a two-dimensional fluid layer coupled to a Stokesian subfluid substrate, and compares this model to experiments following hole dynamics in a polymer Langmuir monolayer. Closure of such a hole in a fluid layer is driven by the line tension at the hole boundary and the difference in surface pressure within the hole and far outside it. The observed rate of hole closing is close to that predicted by our model using estimates of the line tension obtained by other means, assuming that the …

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Σary, Minnesota State University Moorhead, Mathematics Department May 2006

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

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Teaching Time Savers: A Recommendation For Recommendations, Michael E. Orrison Jr. May 2006

Teaching Time Savers: A Recommendation For Recommendations, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

I admit it — I enjoy writing recommendation letters for my students. I like
learning about their hopes and dreams, where they have been and where they want to go. A recommendation letter is an opportunity to remind myself how much my students can grow while they are in college, and how much I have grown as an instructor, advisor, and mentor.

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How Have Teachers Affected The Disinterest Towards Mathematics?, Amy Brown May 2006

How Have Teachers Affected The Disinterest Towards Mathematics?, Amy Brown

Senior Honors Projects

In our school system today there is a collective disinterest and lack of enthusiasm towards mathematics as a whole. This apathy is prevalent as early as elementary school and continues through higher education. It is disheartening that so many students avoid mathematics because of their misconception that it is too difficult and has little value in their future. How well prepared are our teachers to deal with this? I began my research by looking at the past perceptions of mathematics and how the reform movement has changed this perspective. I also looked at the changing standards and how the Principles …

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Abstracts Of Papers, 84th Annual Meeting Of The Virginia Academy Of Science Apr 2006

Abstracts Of Papers, 84th Annual Meeting Of The Virginia Academy Of Science

Virginia Journal of Science

Full abstracts of papers for the 84th Annual Meeting of the Virginia Academy of Science, May 25-26, 2006, Virginia Polytechnic Institute and State University, Blacksburg, VA

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Gender And Educational And Occupational Choices, Jacquelynne Sue Eccles Mar 2006

Gender And Educational And Occupational Choices, Jacquelynne Sue Eccles

STEM for Success Resources

Why Do Women and Men Make Such Different Choices for Their Lives? In most cultures, women and men are concentrated in quite different occupations and roles. Why? This presentation goal is to provide one perspective on this quite complex question – a perspective grounded in Expectancy –Value Models of Achievement-related Choices

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A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts Mar 2006

A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts

Faculty Publications

No abstract provided.

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Studies On Pairing-Based And Constant Round Dynamic Group Key Agreement., Ratna Dutta Dr. Feb 2006

Studies On Pairing-Based And Constant Round Dynamic Group Key Agreement., Ratna Dutta Dr.

Doctoral Theses

This thesis describes research that I conducted during the course of my Ph.D. study at Indian Statistical Institute (ISI), Kolkata. I hope that this work is of use and will be carried on.I would like to begin by thanking my supervisor, Prof. Rana Barua for his support and endless patience. He has provided me background in Cryptography, Combinatorics and Theory of Automata during the period 2000-2002 of my course work of M.Tech in Computer Science at Indian Statistical Institute. I really appreciate his extraordinary patience in reading my numerous inferior drafts, for listening and analyzing all my ideas, forcing me …

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Quantum Stochastic Dilation Of A Class Of Quantum Dynamical Semigroups And Quantum Random Walks., Lingaraj Sahu Dr. Feb 2006

Quantum Stochastic Dilation Of A Class Of Quantum Dynamical Semigroups And Quantum Random Walks., Lingaraj Sahu Dr.

Doctoral Theses

No abstract provided.

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Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz Feb 2006

Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz

Dartmouth Scholarship

Let X be an H-space of the homotopy type of a connected, finite CW-complex, f : X→X any map and pk : X→X the kth power map. Duan proved that pkf : X → X has a fixed point if k ≥ 2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map …

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Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa Jan 2006

Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa

Faculty Publications

We discuss when a subspace of ωω is paracompact in some forcing extension.

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An Application Of Quadratic Functions To Australian Government Policy On Funding Schools, R. Nillsen Jan 2006

An Application Of Quadratic Functions To Australian Government Policy On Funding Schools, R. Nillsen

Faculty of Informatics - Papers (Archive)

In the Sydney Morning Herald newspaper of 23rd March 2005 the economics writer Ross Gittins argued that the funding arrangements for private schools in Australia positively encourage parents to move their children from the state system to the private system. The Federal minister, Dr Brendan Nelson, responded by saying that the policy of subsidising pupils who go to a private school results in taxpayer savings of $4 billion. However, the minister's response did not address the extent to which more funds could possibly be saved by having a different subsidy from the one currently offered by the government. Now, there …

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History Of The Department Of Mathematical Sciences At The University Of Montana: A Collection Of Interviews, Varoujan Bedros, Daniel F. Finch, Charles Myers, Merry Rampy, Johnny W. Lott (Editor) Jan 2006

History Of The Department Of Mathematical Sciences At The University Of Montana: A Collection Of Interviews, Varoujan Bedros, Daniel F. Finch, Charles Myers, Merry Rampy, Johnny W. Lott (Editor)

History of the Department of Mathematical Sciences at UM: A Collection of Interviews

A collection of transcribed oral history interviews conducted in 1999 with current and recently retired faculty members of the Department of Mathematics.

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The Sonic Representation Of Mathematical Data, Charlie Cullen Jan 2006

The Sonic Representation Of Mathematical Data, Charlie Cullen

Doctoral

Conveying data and information using non-speech audio is an ever growing field of research. Existing work has been performed investigating sonfication and its applications, and this research seeks to build upon these ideas while also suggesting new areas of potential. In this research, initial work focused on the sonification of DNA and RNA nucleotide base sequences for analysis. A case study was undertaken into the potential of rhythmic parsing of such data sequences, with test results indicating that a more effective method of representing data in a sonification was required. Sonification of complex data such as DNA and RNA was …

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Discourse On The Interface Of Matheatics And Physics: A Panel Discussion Sponsored By Dit And The Ria., Brendan Goldsmith Jan 2006

Discourse On The Interface Of Matheatics And Physics: A Panel Discussion Sponsored By Dit And The Ria., Brendan Goldsmith

Articles

No abstract available

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Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison Jan 2006

Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison

Branch Mathematics and Statistics Faculty and Staff Publications

The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed …

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Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao Jan 2006

Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao

Faculty Publications

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi–Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, …

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The Kronecker Product, Bobbi Jo Broxson Jan 2006

The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

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