Physical Sciences and Mathematics Commons^™

Mathematics At Chartres Cathedral, Richard Stout

ACMS Conference Proceedings 1997

Having had several opportunities to travel to France, often with groups of students, our trips have usually included a visit to Chartres, especially to visit the magnificent Gothic cathedral that dominates the town. On a recent visit I was again struck by the beauty, majesty and awe that the cathedral inspires. The building not only does a remarkable job of telling Biblical stories and of enclosing a space conducive to worship, it directs one's eyes and one's spirits upward. This is achieved not only by the beautiful stained glass windows and the striking sculptures, but also by the overall design …

An Investigation Of The Behavior Of Calculus Students Working Collaboratively In An Interactive Software Environment, Angela Hare

ACMS Conference Proceedings 1997

Recent work in the area of cognitive research in mathematics education focuses on detailed examinations of the learning process of students and how this process is affected by current innovations in the classroom, including collaborative learning and the use of computers and interactive software. Much of this work is supported by the learning framework of constructivism, a school of thought which is based on the work and writings of Jean Piaget. Piaget, a French psychologist in the mid-twentieth century, observed the learning behavior of children and concluded that individuals construct their own knowledge by creating mental structures which explain their …

A Tale Of Two Transitions, David Klanderman, Sharon Robbert, Robert Wheeler

ACMS Conference Proceedings 1997

In this paper, we examine transitions to proof courses at two institutions. Bob Wheeler has taught the course at Northern Illinois University. Both Sharon Robbert and Dave Klanderman have taught a related course at Trinity Christian College. We analyze various features of these courses and offer suggestions for other colleges and universities.

Using Java And Html For Linear Algebra Instruction, Jonathan R. Senning

ACMS Conference Proceedings 1997

This paper addresses some of the issues involved with using the HTML, JavaScript and Java to develop and serve a sequence of laboratory modules for use in teaching linear algebra. Attention is paid to the rationale for this approach as opposed to the more traditional approach of laboratory exercises executed using MATLAB or some similar computational tool. Several methods to display mathematics with HTML are described. Some implementation detail and a brief description of the HTML and Java based Linear Algebra Visualization Assistant (LAVA) is presented.

Fractal Geometry And Chaos Theory: From Old Problems To New Models And Methods, Terence H. Perciante

ACMS Conference Proceedings 1997

Fractal geometry and chaos theory are deeply rooted in significant problems in the history of mathematics and science. While mathematicians have geometrical descriptions of space with its properties, scientists have attempted to characterize the physical properties of fundamental entities present in space and time. The separate investigations frequently influenced each other and led to profound theories, answers, and models. However, at the same time new problems repeatedly arose internal to mathematics and externally in the applications to which mathematics was applied. Fractal geometry issues from these antecedents in response to features and processes in nature not easily represented by historical …

Introduction (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Schedule (1997), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1997

Eleventh ACMS Conference on Mathematics from a Christian Perspective

Oscillation Properties Of First Order Neutral Delay Differential Equations, Roderick B. Holmes

Theses (Pre-2016)

N/A

Celluloid Blackness : Race, Modernity, And The Conflicted Roots Of American Cinema (1915-1939), Lincoln Farr

Honors Theses

Introduction: "The Problem of the Twentieth Century" In a full page interview in the New York Times on May 29, 1912, the Swiss psychiatrist Dr. Carl G. Jung told the American people, "It seems to me that you are about to discover yourselves. You have discovered everything else-all the land of this continent; all the resources, all the hidden things of nature."Jung used the interview to address the American people, at a moment which he somehow recognized as crucial in the development of human civilization. America, the "tragic" country which he struggled to comprehend, would soon become the harbinger of …

On Some New Constructions Of Difference Sets, Sarah Agnes Spence

Honors Theses

Difference sets are mathematical structures which arise in algebra and combinatorics, with applications in coding theory. The fundamental question is when and how one can construct difference sets. This largely expository paper looks at standard construction methods and describes recent findings that resulted in new families of difference sets. This paper provides explicit examples of difference sets that arise from the recent constructions. By gaining a thorough understanding of these new techniques, it may be possible to generalize the results to find additional new families of difference sets. The paper also introduces partial and relative difference sets and discusses how …

Putting The Pieces Together: Understanding Robinson’S Nonperiodic Tilings, Aimee S. A. Johnson, K. M. Madden

Mathematics & Statistics Faculty Works

A discussion of Robinson's nonperiodic tilings and nonperiodic tilings with nonsquare tiles (Penrose and pinwheel).

The Link Between Scrambling Numbers And Derangements, Barry Balof, Eric Farmer, Jamie Kawabata

Mathematical Sciences Technical Reports (MSTR)

The group equation abcdef = dabecf can be reduced to the equation xcde = dxec. In general, we are interested in how many variables are needed to represent group equations in which the right side is a permutation of the variables on the left side. Scrambling numbers capture this information about a permutation. In this paper we present several facts about scrambling numbers, and expose a striking relationship between permutations that cannot be reduced and derangements.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner

Pitzer Faculty Publications and Research

We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics. The Newtonian tradition in calculus did not come to an end in Maclaurin's Britain. Instead, Maclaurin's Treatise served to transmit Newtonian ideas in calculus, improved and expanded, to the Continent. We will look at what these ideas were, what Maclaurin did with them, and what happened to this work afterwards. Then, we will ask what by then should be an interesting question: why has Maclaurin's role been so consistently underrated? Thse questions will involve general matters of …

Geometric Aspects Of Second-Order Scalar Hyperbolic Partial Differential Equations In The Plane, Martin Jurás

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this dissertation is to address various geometric aspects of second-order scalar hyperbolic partial differential equations in two independent variables and one dependent variable

F(x, y, u, u_x, u_y, u_xx, u_xy, u_yy) = 0

We find a characterization of hyperbolic Darboux integrable equations at level k (1) in terms of the vanishing of the generalized Laplace invariants and provide an invariant characterization of various cases in the Goursat general classification of hyperbolic Darboux integrable equations (1). In particular we give a contact invariant characterization of equations integrable by …

On The Automatic Generation Of Network Protocol Simulators, Andrew Chen

Honors Theses

Computers communicate with each other over various communication networks via a language known as a protocol. The design of the protocol can have a significant impact on the efficiency (and effectiveness) of the network. Because building an actual network to test the performance (and reliability) of a new protocol is rather expensive and time consuming, there is an interest in simulating network protocols in order to determine how efficient the communication network is. We are therefore interested in automatically generating simulators that could measure the performance of the new protocols. There are two main parts to this project. The first …

Parallel Programming, Peter Dailey

Honors Theses

The speed of technology is always increasing, especially in the field of computing. Unfortunately, the size of the problems needing to be solved are also growing in many areas. In order to keep up with this, parallel computing has become an important research area. The term parallel computing essentially refers to using multiple processors cooperating to solve a problem. For certain problems this can speed up the solution by a factor ofN, the number of processors being used. There are algorithms, for which there is no speed increase due to certain dependencies.

Temporal Flocking And Cacophony Simulating Agent Communication In A Noisy Environment, Jessica R. Crawford

Honors Theses

Realistic communication is one of the most difficult aspects of simulating group behavior because the patterns produced by group communication are complex and not easily definable. In this paper, we present a model, developed using artificial life methodology, for creating simulations of group communication. Our model employs autonomous, artificial agents to produce emergent group behavior that resembles the communication patterns of a group, specifically, a flock of birds. Each agent collects information about its environment and its neighbors and follows a set of rules designed to meet both group goals and individual agent goals. Because we seek to establish emergent …

Ua66/10/2 Alumni Newsletter, Wku Mathematics

WKU Administration Documents

Alumni newsletter created by and about the WKU Mathematics department.

Short-Lived Intermediates In Aspartate Aminotransferase Systems, George Czerlinski, Richard Levin, Tjalling Ypma

Mathematics Faculty Publications

The kinetics of the reaction of aspartate aminotransferase with erythro-beta-hydroxy-aspartate, in which rapid mixing is followed (upon reaching a suitable stationary state) by a very fast temperature jump, is numerically simulated. Values for rate constants are used to the extent known, otherwise estimated. It is shown that reaction steps not resolvable by rapid mixing can be resolved by subsequent chemical relaxation. Since several absorption spectra of enzyme complexes overlap, use of a pH-indicator is investigated. When the pH-indicator is coupled to the protonic dissociation of free enzyme, the fast steps are easily detected in the chemical relaxation portion of the …

On Some Problems Related To Hermite And Laguerre Expansions., P. K. Ratnakumar Dr.

Doctoral Theses

The first three chapters of this thesis are concerned with the spherical means associated to the Hermite and Laguerre expansions. The study of spherical means has a very long history. The classic work of F. John deals with various applications of the spherical means to the theory of partial differential equations. They entered Fourier analysis with the celebrated theorem of E. Stein on spherical analogue of the Lebesgue differentiation theorem. Ever since they have appcared again and again in several areas of analysis like integral geometry, inversion of Fourier transforms and related arcas.

The Fixed Point Index As A Local Lefschetz Number., Neeta Pandey Dr.

Doctoral Theses

In this thesis we defitne a class of self maps of connected compact polyhodza - those which prmserve erpanding directions - and define the fixed point indices of such maps at an isolated set of fixed points of the map as a local Lefschets rumber. Our definition uses simplicial approximations of the given map in the spirit of O Nell (I19| and Fournier (71) and is intrinsic so that it is computable.Let X be a connected compact polyhedron and f:X→ X be a map an X. The Lefscheta number L() of / is then defined to be ([13]),L) -E(-1)jTrace {, …

On Cvt Minimization In Single Machine Scheduling., D. K. Manna Dr.

Doctoral Theses

Scheduling problens are quite common in real life. They arise whenever there is a need to plan execution of various tasks over time and therefore they play very important roles in commercial set-ups concerning manufacturing or service in the optimal use of resources and/or customers satisfaction. The theory of scheduling deals with the construction of suitable models and their analyses. Researchersattention was drawn to the study of scheduling problems using mathematical modeling, probably for the first time when Johnson (1954] published his famous work on flowshop problem. Since then, the study of scheduling problem and its context has gradually attracted …

Fourier Transforms Of Very Rapidly Decreasing Functions On Certain Lie Groups., M. Sundari Dr.

Doctoral Theses

Recall that for a function f ϵ L1(Rn ), its Fourier transform fÌ‚ is definedby: fÌ‚ (ƹ) = ʃ Rnf(x)ei(ƹ,x)dx ( 0.1.1)where (.,.) denotes the standard inner product on Rn and dr the Lebesgue measure on Rn. A celebrated theorem of L. Schwartz asserts that a function f on Rn is rapidly decreasing (or in the Schwartz class ) if and only if its Fourier transform is rapidly decreasing . In sharp contrast to Schwartz s theorem, is a result due to Hardy ([18) which says that ʃ and fÌ‚ cannot both be very rapidly decreasing . More precisely, if …

Recurrence And Transience Of Reflecting Diffusions., S. Balaji Dr.

Doctoral Theses

An attempt to obtain conditions for certain stability properties of reflecting diffusions in unbounded domains with boundary has been made in this thesis. For diffusions in R', such stability properties like recurrence, transience and positive recurrence have been studied extensively; see Bhattacharya (1978), Kliemann (1987), Pinsky (1987). One might see Pinsky (1995) for an up-to-date review of kuown methods and results in this all case. (For corresponding recurrence classification results on Markov chains using martin- gale ideas based on stoxchastic analogues of Lyapunov functions, see Meyn and Tweedie (1993a), (1993b) and the references given therein). The main concern in this …

Peak-To-Mean Power Control And Error Correction For Ofdm Transmission Using Golay Sequences And Reed-Muller Codes, James A. Davis, J Jedwab

Department of Math & Statistics Faculty Publications

A coding scheme for OFDM transmission is proposed, exploiting a previously unrecognised connection between pairs of Golay complementary sequences and second-order Reed-Muller codes. The scheme solves the notorious problem of power control in OFDM systems by maintaining a peak-to-mean envelope power ratio of at most 3dB while allowing simple encoding and decoding at high code rates for binary, quaternary or higher-phase signalling together with good error correction.

Absorption Processes: Models For Q-Identities, Don Rawlings

Mathematics

Several extensions of Blomqvist's absorption process are presented. Inherent in some of the associated distributions is a method for establishingq-identities ranging from properties of Gaussian polynomials to product expansions of basic hypergeometric series to extensions of results on Mahonian statistics. One process links the comajor index to Russian roulette. Also given are examples involving the Rogers–Ramanujan identities that demonstrate howq-expressions may be modeled with absorption processes.

Generalized Conjugacy Classes, Pramod N. Achar

Mathematical Sciences Technical Reports (MSTR)

Generalized conjugation is the action of a group on its underlying set given by (g,x) -> p(g)xg^-1, where p is some fixed endomorphism of G. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if p has nontrivial kernel, or if it is an inner automorphism, and we give a construction that allows a partial analysis in the general case.

On A Proximal Point Method For Optimization In Banach Spaces, Alfredo N. Iusem, Dan Butnariu

Mathematics Technical Papers

We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of …