Applied Mathematics Commons^™

Mathematics At Chartres Cathedral, Richard Stout

ACMS Journal 2004

Chartres Cathedral is highly regarded as a magnificent Gothic structure including beautiful stained glass windows and striking sculptures. Mathematics, especially geometry, played a central role in the design of this cathedral. This paper explores that mathematics and how it contributes to the overall effectiveness of the design.

Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch

ACMS Journal 2004

The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …

Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker

Department of Mathematics: Faculty Publications

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite field since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the Nordstrom–Robinson code is the image under the Gray mapping of an algebraic geometric code over Z = 4Z.

Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the positive solutions to the semilinear equation:

-Δu(x) = λf(u(x)) for x ∈ Ω

u(x) = 0 for x ∈ ∂Ω

where Ω denotes a smooth bounded region in R^N (N > 1) and λ > 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) < 0 (semipositone). Assuming that f'(∞) ≡ lim t→∞ f'(t) > 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)'. When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how …

On The Level Crossing Of Multi-Dimensional Delayed Renewal Processes, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the crossing level and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier …

The Effect Of Three-Dimensional Freestream Disturbances On The Supersonic Flow Past A Wedge, Peter W. Duck, D. Glenn Lasseigne, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al. [P W. Duck, D. G. Lasseigne, and M. Y. Hussaini, ''On the interaction between the shock wave attached to a wedge and freestream disturbances,'' Theor. Comput. Fluid Dyn. 7, 119 (1995) (also ICASE Report No. 93-61)] through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of …

Scattering From Stellar Acoustic-Gravity Potentials: Ii. Phase Shifts Via The First Born Approximation, J. A. Adam, I. Mckaig

Mathematics & Statistics Faculty Publications

Using the first Born approximation, properties of the scattering phase shift are investigated for waves that are scattered by a schematic representation of a large-scale “stellar potential,” i.e., one for which the star itself is viewed as the potential inducing a phase shift in an incoming wave. In particular, the phase shift properties are examined as functions of the relative wavenumber (α) and the azimuthal wavenumber (l), high l-values being of interest in helioseismology.

The Hadamard Matroid And An Anomaly In Its Single Element Extensions, C. H. Cooke

Mathematics & Statistics Faculty Publications

A nonstandard vector space is formulated, whose bases afford a representation of what is called a Hadamard matroid, M_p. For prime p, existence of M_p is equivalent to the existence of both a classical Hadamard matrix H(p,p) and a certain affine resolvable, balanced incomplete block design AR(p). An anomaly in the representable single element extension of a Hadamard matroid is discussed.

The Duals Of Warfield Groups, Peter Loth

Mathematics Faculty Publications

A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.

Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …

Algebraic Fiberings Of Grassmann Varieties, R. J. D. Ferdinands, R. E. Schultz

University Faculty Publications and Creative Works

No abstract provided.

Time-Optimal Tree Computations On Sparse Meshes, D. Bhagavathi, V. Bokka, H. Gurla, S. Olariu, J. L. Schwing

Computer Science Faculty Publications

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite …

Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.