Mathematics Commons^™

Tessellations, Zan Jabara

Humanistic Mathematics Network Journal

No abstract provided.

The Smarandache Semantic Paradox, Anthony Begay

Humanistic Mathematics Network Journal

No abstract provided.

Mr. Trapezoid's Walk, Michael Pillar

Humanistic Mathematics Network Journal

No abstract provided.

Fun With Algebra!, Janelle Kulik

Humanistic Mathematics Network Journal

No abstract provided.

Poem, Natalie Kashhefi

Humanistic Mathematics Network Journal

No abstract provided.

Death, Trial And Life, Prem N. Bajaj

Humanistic Mathematics Network Journal

No abstract provided.

Robert Davis: In Memoriam, Carolyn A. Maher, Robert Speiser

Humanistic Mathematics Network Journal

No abstract provided.

Geometry In Nature, Rachel Finkelstein

Humanistic Mathematics Network Journal

No abstract provided.

Real Data, Real Math, All Classes, No Kidding, Martin Vern Bonsangue

Humanistic Mathematics Network Journal

No abstract provided.

A Comparison Of Deterministic And Stochastic Population Models, Clarissa Smith

Masters Theses & Specialist Projects

In this thesis, the author considers the exponential and the predator-prey population models. A comparison of the deterministic and stochastic versions of each is made. The author shows that on average a stochastic model is precisely its corresponding deterministic model. The first model considered is the exponential model. A solution is provided for both the deterministic and the stochastic versions. A predator-prey model is also analyzed. A solution of the stochastic predator-prey model is shown to be intractable. Analysis of this model is performed through numerical simulation.

Math Poem, Beth Corridori

Humanistic Mathematics Network Journal

No abstract provided.

The Poem Of Math, Michelle Wang

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: The Courage To Teach By Parker Palmer, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

I Love To Add, Kyle Cotler

Humanistic Mathematics Network Journal

No abstract provided.

Math Rules, Blake Mayer

Humanistic Mathematics Network Journal

No abstract provided.

Geometric Shapes, Sam Dudley

Humanistic Mathematics Network Journal

No abstract provided.

On Different Integrable Systems Sharing The Same Nondynamical R-Matrix, Zhijun Qiao, Walter Strampp

School of Mathematical & Statistical Sciences Faculty Publications

In a recent paper @Zhijun Qiao and Ruguang Zhou, Phys. Lett. A 235, 35 ~1997!#, the amazing fact was reported that a discrete and a continuous integrable system share the same r-matrix with the interesting property of being nondynamical. Now, we present three further pairs of different continuous integrable systems sharing the same r-matrix again being nondynamical. The first pair is the finite-dimensional constrained system ~FDCS! of the famous AKNS hierarchy and the Dirac hierarchy; the second pair is the FDCS of the well-known geodesic flows on the ellipsoid and the Heisenberg spin chain hierarchy; and the third pair is …

Statistical Characterization Of Fluvial-Deltaic Reservoirs With Archetypes, Laura L. Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Optimizing the extraction of oil and other hydrocarbon products from existing sites is important. One source of hydrocarbon products is reservoirs found within sedimentary rock formations. Understanding fluid behavior within such formations can be quite useful in optimizing oil production. Fluid behavior within sedimentary formations is influenced by the bedform structure and permeabilities within the formation. Thus, we are concerned with developing a physically and statistically valid method of characterizing sedimentary rock formations. The use of archetypal analysis to generate synthetic bedforms, as well as the use of Kriging to assign permeabilities within a bedform, was explored. With these tools, …

Problems In Harmonic Function Theory, Ronald A. Walker

Honors Theses

Harmonic Function Theory is a field of differential mathematics that has both many theoretical constructs and physical connections, as well as its store of classical problems.

One such problem is the Dirichlet Problem. While the proof of the existence of a solution is well-founded on basic theory, and general methods for polynomial solutions have been well studied, much ground is still yet to be overturned. In this paper we focus on the examination, properties and computation methods and limitations, of solutions for rational boundary functions.

Another area that we shall study is the properties and generalizations of the zero sets …

Classification Of Hereditary Matrices, Jim Agler, J. W. Helton, Mark Stankus

Mathematics

A classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices T such that p(T) = 0. We consider matrices and operators which satisfy a different type of polynomial constraint. Let H be a complex Hilbert space, T be a bounded linear transformation of H, T* be the adjoint of T, and C[x, y] be the algebra of polynomials in x and y with complex coefficients. For a polynomial p E C[x, y] in …

Counting Structures In The Möbius Ladder, John P. Mcsorley

Articles and Preprints

The Möbius ladder, M_n, is a simple cubic graph on 2n vertices. We present a technique which enables us to count exactly many different structures of M_n, and somewhat unifies counting in M_n. We also provide new combinatorial interpretations of some sequences, and ask some questions concerning extremal properties of cubic graphs.

Ua66/10/2 Alumni Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

Sparse Equation-Eigen Solvers For Symmetric/Unsymmetric Positive-Negative-Indefinite Matrices With Finite Element And Linear Programming Applications, Hakakizumwami Birali Runesha

Civil & Environmental Engineering Theses & Dissertations

Vectorized sparse solvers for direct solutions of positive-negative-indefinite symmetric systems of linear equations and eigen-equations are developed. Sparse storage schemes, re-ordering, symbolic factorization and numerical factorization algorithms are discussed. Loop unrolling techniques are also incorporated in the coding to enhance the vector speed. In the indefinite solver, which employs various pivoting strategies, a simple rotation matrix is introduced to simplify the computer implementation. Efficient usage of the incore memory is accomplished by the proposed "restart memory management" schemes. A sparse version of the Interior Point Method, IPM, has also been implemented that incorporates the developed indefinite sparse solver for linear …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Neuro Fuzzy Reasoning For Pattern Classification And Object Recognition., Jayati Ghosh Dr.

Doctoral Theses

In real world, pattern classification and object recognition problems are faced with fuzzi- ness that is connected with diverse facets of cognitive activity of the human being. An origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification and /or recognition procedures. Though a lot of scientific efforts have already been dedicated to pattern recognition problems, especially to classification procedures, still pattern recognition is confronted with a continuous challenge coming from a human being who can perform lot of ex- tremely complex classification tasks by …

Nonlinear Modes Of Liquid Drops As Solitary Waves, Andrei Ludu, J. P. Draayer

Publications

The nonlinear dynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg–de Vries (KdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such “rotons” were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to droplike systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.

The Stable Manifold Theorem For Sde's (Probability Seminar, University Of California, Irvine), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

In this talk, we formulate a local stable manifold theorem for stochastic differential equations in Euclidean space, driven by multi-dimensional Brownian motion. We introduce the concept of hyperbolicity for stationary trajectories of a SDE. This is done using the Oseledec muliplicative ergodic theorem on the linearized SDE along the stationary solution. Using methods of (non-linear ergodic theory), we construct a stationary family of stable and unstable manifolds in a stationary neighborhood around the hyperbolic stationary trajectory of the non-linear SDE. The stable/unstable manifolds are dynamically characterized using anticipative stochastic calculus.

Computer Simplification Of Formulas In Linear Systems Theory, J. W. Helton, Mark Stankus, John J. Wavrik

Mathematics

Currently, the three most popular commercial computer algebra systems are Mathematica, Maple, and MACSYMA. These systems provide a wide variety of symbolic computation facilities for commutative algebra and contain implementations of powerful algorithms in that domain. The Gröbner Basis Algorithm, for example, is an important tool used in computation with commutative algebras and in solving systems of polynomial equations.

On the other hand, most of the computation involved in linear control theory is performed on matrices, and these do not commute. A typical issue of IEEE TRANSACTIONS ON AUTOMATIC CONTROL is full of linear systems and computations with their coefficient …

Games To Teach Mathematical Modelling, James A. Powell, Jim S. Cangelosi, Ann M. Harris

Mathematics and Statistics Faculty Publications

We discuss the use of in-class games to create realistic situations for mathematical modelling. Two games are presented which are appropriate for use in post-calculus settings. The first game reproduces predator-prey oscillations and the second game simulates disease propagation in a mixing population. When used creatively these games encourage students to model realistic data and apply mathematical concepts to understanding the data.