Mathematics Commons^™

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

Faculty Publications

No abstract provided.

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

Doctoral Theses

No abstract provided.

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 …

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 p_k : X→X the k^th power map. Duan proved that p_kf : 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 …

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.

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 …

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

Articles

No abstract available

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, …

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 …

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 …

Wallpaper Groups, Cassondra Fett

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

A Survey On Intrusion Detection Approaches, A Murali M. Rao

International Conference on Information and Communication Technologies

Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Usages of computer network services are tremendously increasing day by day and at the same time intruders are also playing a major role to deny network services, compromising the crucial services for Email, FTP and Web. Realizing the importance of the problem due to intrusions, many researchers have taken up research in this area and have proposed several solutions. It has come to a stage to take a stock of the research results and project a comprehensive view so …

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Hand-Held Calculators And Mathematics Achievement: What The 1996 National Assessment Of Educational Progress Eighth-Grade Mathematics Exam Scores Tell Us, Kenneth L. Wareham

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to analyze the 1996 National Assessment of Educational Progress data to identify the relationship between calculator use and student performance on the National Assessment of Educational Progress Mathematics Assessment. This general purpose includes several sub issues. In addition to being interested in the overall relationship between use and National Assessment of Educational Progress achievement (including the effort to control for spurious factors), this study examined the contextual factors that moderate the impact of calculator use. Similarly, it analyzed the relationship between calculator use and student performance on calculator-allowed and calculator-restricted items, as well as …

Some Nonparametric And Semiparametric Methods For Discriminant Analysis., Anil Kumar Ghosh Dr.

Doctoral Theses

Discriminant analysis (see e.g., Devijver and Kittler, 1982; Duda, Hart and Stork, 2000; Hastle, Tibahirani and Friedman, 2001) deals with the separation of different groups of obaervationa and allocation of a new oboervation to one of the previously delined grouga. In a J-class discriminant analysis problem, we usually hae a training sample of the form {(xk, ck) : k = 1,2,...,N}, where xk = (Ik1,Ik2,...J) is a d-dimensional measarement vector, and ca € {1,2,...,J} is its class label. On the basis of thia training sample, one aims to form a decision rule d(x) : Rd + (1,2,...,J} for clasifying the …

A Look At The Astrolabe, Emily Storrar

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors program.

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.

Doctoral Theses

In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …

On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.

Doctoral Theses

In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified …

Continued Radicals, Jamie Johnson

Masters Theses & Specialist Projects

If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the …

Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) Growing up as a child in southern England, my early memories of snow include trudging home from school with my father, gazing at the seemingly enormous snowdrifts that smoothed the hedgerows, fields and bushes, while listening to the soft “scrunch” of the snow under my Wellington boots. In the country, snow stretching as far as I could see was not a particularly uncommon sight. The quietness of the land under a foot of snow seemed eerie. I cannot remember the first time I looked at snowflakes per se; my interests as a small child were primarily in their …

Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner

Pitzer Faculty Publications and Research

Sir Isaac Newton revolutionized physics and astronomy in his Principia. How did he do it? Would his method work on any area of inquiry, not only in science, but also about society and religion? We look at how some Newtonians, most notably Colin Maclaurin, combined sophisticated mathematical modeling and empirical data in what has come to be called the "Newtonian Style." We argue that this style was responsible not only for Maclaurin’s scientific success but for his ability to solve problems ranging from taxation to insurance to theology. We show how Maclaurin’s work strengthened the prestige of Newtonianism and …

Outerplanar Crossing Numbers, The Circular Arrangement Problem And Isoperimetric Functions, Eva Czabarka, Ondrej Sykora, Laszlo A. Szekely, Imrich Vrt'o

Faculty Publications

We extend the lower bound in [15] for the outerplanar crossing number (in other terminologies also called convex, circular and one-page book crossing number) to a more general setting. In this setting we can show a better lower bound for the outerplanar crossing number of hypercubes than the best lower bound for the planar crossing number. We exhibit further sequences of graphs, whose outerplanar crossing number exceeds by a factor of log n the planar crossing number of the graph. We study the circular arrangement problem, as a lower bound for the linear arrangement problem, in a general fashion. We …

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Some Statistical Contributions To The Analysis Of Human Genome Diversity And Evolution., Analabha Basu Dr.

Doctoral Theses

The work embodied in this thesis pertains to human population genetics. In particular, the overarching goals of this thesis are to contribute to the understanding of genomic diversity of human populations and to the development of statistical methods for making inferences in genome diversity studies. With these two goals in mind, we have carried out a detailed statistical analysis of genomic data on a large number of ethnic populations of India, generated in the laboratory of the Anthropology & Human Genetics Unit, Indian Statistical Institute, Kolkata. Additionally, wherever relevant, we have compared our data with those collated from the published …