Physical Sciences and Mathematics Commons^™

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 …

Contributions To Emerging Techniques In Survey Sampling., Sanghamitra Pal Dr.

Doctoral Theses

This dissertation contains seven Chapters. The contents in the respective Chapters may be briefly recounted as follows.A topic of classical interest in survey sampling is how to ensure the existence of a uniformly non-negative (UNN) unbiased estimator for the mean square error (MSE) of a homogeneous linear estimator (HLE) for a finite survey population total. Hájek (1958), Vijayan (1975), Rao and Vijayan (1977) and Rao (1979) developed a number of results which boil down to the folowing as narrated in the monograph by Chaudhuri and Stenger (1992).If there exist non-zero constants w, and the unknown values y, of the variable …

Some Studies On Uncertainty Management In Dynamical System Using Fuzzy Techniques With Applications., Kausik Majumdar Dr.

Doctoral Theses

Unceriain information processing by fuzzy if-then rules has received a lot of attention. Here we have taken a different path to model a system. about which we do not have precise information namely. modelling the system by fuzy valued functions without resorting to fuzzy if-then rules. As a result. the phase (state) space of the system becomes a full set and the underlying fuzzy mapping becomes a fuzzy attainability vet mappine. A fuzzy phase space is a collection of special class of furry subsets (fuzsy points) of R&for some positive integral n. Let the collection of all fuzr, real numbers …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Intersection Properties Of Balls In Banach Spaces And Related Topics., Sudipta Dutta Dr.

Doctoral Theses

In the first part of this chapter, we explain in general terms the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. In the second part, we introduce some notations and preliminaries that will be used in the subsequent chapters.As a prototype of the properties we will study in this thesis, let us call a closed linear subspace Y of a Banach space X a (P)-subspace of X if Y has a certain property P as a subspace of X. If a Banach space X, in its canonical embedding, is a (P)-subspace …

Can The Love Of Learning Be Taught?, R. Nillsen

Faculty of Informatics - Papers (Archive)

This paper is an expanded version of a talk given at a Generic Skills Workshop at the University of Wollongong, and was originally intended for academic staff from any discipline and general staff with an interest in teaching. The issues considered in the paper include the capacity of all to learn, the distinction between learning as understanding and learning as information, the interaction between the communication and the content of ideas, the tension between perception and content in communication between persons, and the human functions of a love of learning. In teaching, the creation of a fear-free environment is emphasised, …

Mathematical Magic, Arthur T. Benjamin

All HMC Faculty Publications and Research

In this paper, we present simple strategies for performing mathematical calculations that appear magical to most audiences. Specifically, we explain how to square large numbers, memorize pi to 100 places and determine the day of the week of any given date.

The Use Of Filters In Topology, Abdellatif Dasser

Electronic Theses and Dissertations

Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).

Technology And Mathematics Standards: An Integrated Approach, Chris Merrill, Mark Comerford

Publications

The article focuses on the use of standards-based teaching and learning that has been gaining significant attention in the education world. State and national associations now base their specific subject area or discipline solely on standards, i.e., International Technology Education Association (ITEA), National Council of Teachers of Mathematics (NCTM), National Science Education Association (NSEA). Moreover, at the public school level, state boards of education are holding school districts accountable for teaching standards-based curricula. It is with the latter definition in mind that the authors created a standards-based, integrated technology and mathematics lesson using the design and construction of stair systems.

Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.

Objectivity, Information, And Maxwell's Demon, Steven Weinstein

Dartmouth Scholarship

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Combinatorial Techniques For Digital Image Charecterization And Retrieval:Algorithms,Architectures,And Applications., Arijit Bishnu Dr.

Doctoral Theses

Interest in digital images stems mostly from its application to various areas of computer vision [33, 57] and pattern recognition [145). Problems include robotic vision and con- trol, geographic and topographic map matching, target recognition, space applications, character recognition, scene analysis, fingerprint and face recognition, etc. Lately, with the advent of content-based image retrieval (CBIR) and proliferation of the Internet, digital imaging applications are in vogue now than ever before. In almost all the cases, the data size is enormously large, and at the same time, fast on-line as well as real- time computation is needed. For example, in fingerprint …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Discovering Properties Of Complex Numbers By Starting With Known Properties Of Real Numbers, Esther D. Hatch

Honors College

No abstract provided.

Essays In Financial Intermediation., Bappaditya Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

On The Approximability Of Linear Ordering And Related Np-Optimization Problems., Sounaka Mishra Dr.

Doctoral Theses

We investigate approximability of both maximum and minimum linear ordering problems (MAX-LOP and MIN-LOP) and several related problems such as the well known feedback set problems, acyclie subdigraph problem and several others and their variants.We show that both MAX-LOP and MIN-LOP are strongly NP-complete, and MIN- LOP, MIN-QAP(S) (a special case of minimum quadratic assignment problem) and MIN-W-FAS are equivalent with respect to strict-reduction. The strict-equivalence is also established among these problems as well as MIN-W-FVS, with weights on arcs/vertices bounded by a polynomial, and the unweighted versions of the feedback set. problems. We also show that MAX-LOP is strict-equivalent …

Deformation Theory Of Dialgebras., Anita Majumdar Dr.

Doctoral Theses

The main objective of this thesis is to develop an algebraic deformation theury for associative dialgebras, which are binary quadratic algebras discovered by J.-L. Loday in (16). (17), and subisequently, to derive a G-algebra siructure ou the dialgebra colhomology with cocfticients in itself.Deformation theory dates back at Ieast to Riemann's 1837 memoir on alelian fianetions in which he studied IHanifolds of complex dimension one and calculated the mumber of parameters (called moduli) upon which a deformation depends. The modern theory of deformations of structures on manifolds was developed extensively ly Frolicher-Kodaira-Nijenhnis-Nirenberg-Spencer (13], [14], [15). [25|, [26).The study of deformations of …

Spectral Triples And Metric Aspects Of Geometry On Some Noncommutative Spaces., Partha Sarathi Chakraborty Dr.

Doctoral Theses

Quantization of mathematical theories is now more than half a century old idea in mathe- matics. It goes back to Gelfand-Naimarks seminal paper [37] in 1943. As the name suggests noncommutative geometry is the quantization" of differential geometry. It is the study of noncommutative algebras as if they were algebras of functions on spaces like the commuta- tive algebras associated to affine algebraic varieties, smooth manifolds, topological spaces. One can trace its roots in the Gelfand-Naimark theorems (1943, 37]). In modern terminol- ogy their theorem says there is an antiequivalence between the category of (locally) compact Hausdorff spaces and (proper, …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …

Resources Related To Mathematics, Art And Nature, Vicki Beitler

Sabbaticals

The purpose of my sabbatical work was to learn about resources related to mathematics and art, nature, music and architecture. These subjects appeal to a wide audience, yet their mathematical connections are often on the periphery of a mathematics student's studies. In this way I planned to increase my knowledge of mathematics but at the same time broaden my understanding of cross-disciplinary subjects.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Wavelet-Based Simulation Of Geological Variables, T. T. Tran

Theses: Doctorates and Masters

This thesis introduces a number of conditional simulation algorithms using wavelet bases. These make use of two orthogonal wavelet bases, the Haar and the Db2 bases. Firstly, two single-level algorithms are introduced, HSIM: with the Haar basis and DB2SIM with the Db2 basis. HSIM reproduces the histogram and semivariogram model of isotropic samples but not the semivariogrnm model of anisotropic samples. DB2SIM reproduces the histogram and semivariogram model in both the isotropic and anisotropic cases but, because of the conditioning method employed, is not as computationally efficient as we would wish. Because of the limitations of HSIM and Db2SIM two …

Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti

Dartmouth Scholarship

No abstract provided.

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

An Extension Of Elton's L(1)(N) Theorem To Complex Banach Spaces, S J. Dilworth, Joseph P. Patterson

Faculty Publications

No abstract provided.