Digital Commons Network^™

Gnarled Defined, Rudy Rucker

SWITCH

The article is a reflection of the author’s conception of the term ‘gnarly’, extending the term’s meaning from its origins in California surfer slang. 'Gnarly' is often used in a colloquial context, however, the author believes that the term is able to be used in an academic field as it pertains to outcomes and results of equations. Discussions towards the application of the term 'gnarly' showcase how it can be used in a scientific, mathematical, and artistic context through seemingly random patterns. In order to be gnarly, things must lie and exist between the realm of orderly and chaotic often …

The Exponential Stability Of A Coupled Hyperbolic/Parabolic System Arising In Structural Acoustics, George Avalos

Department of Mathematics: Faculty Publications

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE’s which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domain Ω, coupled to a “parabolic–like” beam equation holding on ∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic …

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

Imsa Math Journal: A Resource Notebook For High School Mathematics, Illinois Mathematics And Science Academy

IMSA Math Journal

We are proud to present the fourth issue of the IMSA Math Journal. In this edition we have included work by IMSA faculty, support staff, students, and alumni as well as articles by a faculty member of a sister school, The North Carolina School of Science and Mathematics and a colleague at Eastern Illinois University.

Excerpt: Letter from the Editors

Determinants Of The Tournaments, Clifford A. Mccarthy '94, Arthur T. Benjamin

All HMC Faculty Publications and Research

No abstract provided in this article.

Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam

Mathematics and Statistics Faculty Publications

Let G be a finite group and let pi(G) denote the proportion of (x, y) ∈ G2 for which the set {x2,xy,yx,y2} has cardinality i. We show that either 0 < pi(G) + p2(G) ≤ 1/2 or pi(G) + p2(G) = 1, and that either p4(G) = 0 or 5/32 ≤ p4(G) ≤ 1. Each of the preceding inequalities are the best possible.

Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny

Physics Faculty Publications

Unusual microstructures of YBa₂Cu₃O_x (123) crystals have been observed. These structures have been shown to pass very high transport currents. A model of the solidification of 123 from a melt with Y₂BaCuO₅ (211) inclusions indicates that the stability of the 123 interface can depend on the sizes of the 211 inclusions. The observed formations are interpreted in the light of this instability.

An Efficient Spectral Method For Ordinary Differential Equations With Rational Function Coefficients, Evangelos A. Coutsias, Thomas Hagstrom, David Torres

Branch Mathematics and Statistics Faculty and Staff Publications

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple 3-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e., matrix representations of multiplication by a function) are banded for …

Exact Solutions For Orthogonal And Non-Orthogonal Magnetohydrodynamic Stagnation-Point Flow, Shahrooz Moosavizadeh

Mathematics & Statistics Theses & Dissertations

The viscous plane flow of an electrically conducting fluid towards an infinite wall is solved in the presence of a magnetic field which is aligned with the flow far from the wall. The problem has two dimensionless parameters-- ε, the magnetic Prandtl number, and β, the square of the ratio of Alfven velocity to fluid velocity far from the wall. The problem has a similarity solution which reduces the governing equations to a system of coupled ordinary differential equations which can be solved numerically. For extreme values of ε, both large and small, singular perturbation techniques are used to derive …

Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.

Doctoral Theses

No abstract provided.

Function Approximation Using A Sinc Neural Network, Wael R. Elwasif, Laurene V. Fausett

Mathematics and System Engineering Faculty Publications

Neural networks for function approximation are the basis of many applications. Such networks often use a sigmoidal activation function (e.g. tanh) or a radial basis function (e.g. gaussian). Networks have also been developed using wavelets. In this paper, we present a neural network approximation of functions of a single variable, using sinc functions for the activation functions on the hidden units. Performance of the sinc network is compared with that of a tanh network with the same number of hidden units. The sinc network generally learns the desired input-output mapping in significantly fewer epochs, and achieves a much lower total …

Oncogenic Ret Receptors Display Different Autophosphorylation Sites And Substrate Binding Specificities, Xin Liu, Quinn Vega, Ruth A. Decker, Akhilesh Pandey, Carolyn A. Worby, Jack E. Dixon

Department of Mathematics Faculty Scholarship and Creative Works

The c-ret proto-oncogene encodes a receptor tyrosine kinase which plays an important role in neural crest as well as kidney development. Genetic studies have demonstrated that germ line mutations in the ret oncogene are the direct cause of multiple endocrine neoplasia (MEN) 2A and 2B, familial medullary thyroid carcinoma (FMTC), and Hirschsprung's disease. However, despite the large body of genetic and biological evidence suggesting the importance of RET in development and neoplastic processes, the signal transduction mechanisms of RET remain unknown. To begin to understand the molecular mechanisms of the disease states caused by mutations in RET, the patterns of …

Divergence Diagrams: More Than Cantor Dust Lies At The Edge Of Feigenbaum Diagrams, John H. Rickert, Aaron Klebanoff

Mathematical Sciences Technical Reports (MSTR)

The dynamical system analysis of the logistic map f(x)=ax(1-x) is studied for values of a greater than 4.

Combinatorics Of Open Covers (I): Ramsey Theory, Marion Scheepers

Mathematics Faculty Publications and Presentations

We study several schemas for generating from one sort of open cover of a topological space a second sort of open cover. Some of these schemas come from classical literature, others are borrowed from the theory of ultrafilters on the set of positive integers. We show that the fact that such a schema actually succeeds in producing a cover imposes strong combinatorial structure on the family of open covers of a certain sort. In particular, we show that certain analogues of Ramsey’s theorem characterize some of these circumstances.

New Mathematical Properties Of The Least Square Value, Irinel Dragan

Mathematics Technical Papers - Archive

The Least Square Values for cooperative TU games (briefly, LS-values) represent a family of solutions of the following family of optimization problems associated with a cooperative TU game: minimize the sum of weighted squares of deviations of the excesses from their average, on the preimputation set; the weights were positive numbers associated to the coalitions, depending only on their size. For each system of weights a LS-value is obtained by the Lagrange multipliers method; the Shapley value belongs to the family for specified weights. L. Ruiz, F. Valenciano and J. Zarzuelo who introduced this class of values (see[9]), gave two …

Effective Characteristic Polynomials And Two-Point Pade Approximants As Summation Techniques For The Strongly Divergent Perturbation Expansions Of The Ground State Energies Of Anharmonic Oscillators, Jiri Cizek, Ernst Joachim Weniger, Paul Bracken, Vladimir Spirko

School of Mathematical & Statistical Sciences Faculty Publications

Pade approximants are able to sum effectively the Rayleigh-Schrodinger perturbation series for the ground state energy of the quartic anharmonic oscillator, as well as the corresponding renormalized perturbation expansion [E.J. Weniger, J. Cizek, and F. Vinette, J. Math. Phys. 34, 571 (1993)]. In the sextic case, Pade approximants are still able to sum these perturbation series, but convergence is so slow that they are computationally useless. In the octic case, Pade approximants are not powerful enough and fail. On the other hand, the inclusion of only a few additional data from the strong coupling domain [E.J. Weniger, Ann. Phys. (N.Y.) …

Employement Fluctuations In Rural India:A Statistical Analysis With Special Reference To Maharsatra., Kaushik Bhattacharya Dr.

Doctoral Theses

This dissertation attempts to find out the nature and the extent of employment fluctuation in rural India. The dissertation is partly theoretical and partly empirical in nature. On the methodological side, it builds up a consistent analytical frame- work. Employment fluctuation is measured in terms of a new mobility measure proposed in this dissertation. The empirical work is basod on the data collected by the National Sample Survey Organisation (NSSO), Government of India, in their 38-th round survey operation. I, therefore, thank NSSO for allowing me to work with the data. The views expressod in this dissertation or the errors …

A Novel Cytoplasmic Dual Specificity Protein Tyrosine Phosphatase Implicated In Muscle And Neuronal Differentiation, Robert J. Mourey, Quinn Vega, Jean S. Campbell, Mary Pat Wenderoth, Stephen D. Hauschka, Edwin G. Krebs, Jack E. Dixon

Department of Mathematics Faculty Scholarship and Creative Works

Dual specificity protein tyrosine phosphatases (dsPTPs) are a subfamily of protein tyrosine phosphatases implicated in the regulation of mitogen- activated protein kinase (MAPK). In addition to hydrolyzing phosphotyrosine, dsPTPs can hydrolyze phosphoserine/threonine-containing substrates and have been shown to dephosphorylate activated MAPK. We have identified a novel dsPTP, rVH6, from rat hippocampus. rVH6 contains the conserved dsPTP active site sequence, VXVHCX2GX2RSX5AY(L/I)M, and exhibits phosphatase activity against activated MAPK. In PC12 cells, rVH6 mRNA is induced during nerve growth factor-mediated differentiation but not during insulin or epidermal growth factor mitogenic stimulation. In MM14 muscle cells, rVH6 mRNA is highly expressed in proliferating …

Evolutionary Semigroups And Dichotomy Of Linear Skew-Product Flows On Locally Compact Spaces With Banach Fibers, Y. Latushkin, S. Montgomery-Smith, Timothy W. Randolph

Mathematics and Statistics Faculty Research & Creative Works

We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from non-autonomous abstract Cauchy problems and C0-semigroups, and linear skew-product flows. The spectral mapping theorem for these semigroups is proved. The hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew-product flow. To this end a Banach algebra of weighted composition operators is studied. The results are applied in the study of: "roughness" of the dichotomy, dichotomy and solutions of nonhomogeneous equations, Green's function for a linear skew-product …

An Existence Result For Linear Partial Differential Equations With C∞ Coefficients In An Algebra Of Generalized Functions, Todor D. Todorov

Mathematics

We prove the existence of solutions for essentially all linear partial differential equations with C^∞-coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy’s equation has solutions whenever its right-hand side is a classical C^∞-function.

Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we show that, for each λ>0, the set of radially symmetric solutions to the boundary value problem

-Δu(x) = λu(x) + u(x)|u(x)|, x ε B := {x ε R⁶:|x|<1},

u(x) = 0, x ε ∂B

is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

Building Home Plate: Field Of Dreams Or Reality?, Michael J. Bradley

Mathematics Faculty Publications

No abstract provided.

A Note On Generators Of Least Degree In Gorenstein Ideals, Matthew Miller, Rafael H. Villarreal

Faculty Publications

No abstract provided.

Continuous Deformation Of A Developable Surface, Chili Ping Hsu

Mathematics Technical Papers - Archive

A developable surface can be developed from a piece of planar region, or vice versa. Several methods are known to construct an isometric mapping between the developable and the planar region. A simple and efficient algorithm based on the differential geometry and differential equations is presented to construct such an isometric mapping. This algorithm contains a deformation parameter ^, where ^ varies between 0 and 1, that can trace the development of the surface in a fashion that ^ = 0 corresponds to the planar region and ^ = 1 recovers the developable. An error estimation shows the error, in …

On The Inner Automorphisms Of Finite Transformation Semigroups., Inessa Levi

Faculty Bibliography

No abstract provided.

Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough

Mathematics and Statistics Faculty Research & Creative Works

The upside-down normal loss function (UDNLF) is a weighted loss function that has accurately modeled losses in a product engineering context. The function''s scale parameter can be adjusted to account for the actual percentage of material failing to work at specification limits. Use of the function along with process history allows the prediction of expected loss-the average loss one would expect over a long period of stable process operation. Theory has been developed for the multivariate loss function (MUDNLF), which can be applied to optimize a process with many parameters-a situation in which engineering intuition is often ineffective. Computational formulae …

Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

In this article, we derive explicit asymptotic formulas for the solutions of Oseen's equations in space dimension two in a channel at large Reynolds number (small viscosity ε). These formulas exhibit typical boundary layers behaviors. Suitable correctors are defined to resolve the boundary obstacle and obtain convergence results valid up to the boundary. We study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infinity in which case the boundary layer tends to pervade the whole domain.

Application Of The Residue Method To A Mixed Problem, Y. A. Mamedov, M. Can

Turkish Journal of Mathematics

In this paper, the residue method of separation of variables is applied to a mixed problem which includes the flow of a stratified compresslble fluid and inner gravitational waves of a stratified incompressible fluid for special values of the coefficients of the equation. To apply this method one defines two auxiliary problems. The first one is a spectral problem and the second is a Cauchy problem. Using the solutions of auxiliary problems, an existence and uniqueness theorem is proved for the given mixed problem.

Products And Quotients Of (P,\Sigma)-Absolutely Continuous Operator Ideals^*, Enrique A. Sanchez Perez

Turkish Journal of Mathematics

We obtain a generalization of the ideal {\cal M}_{(q,p)} of (q,p)-mixing operators-in the sense of Pietsch- as a consequence of the study of the quotients of (p, \sigma)-absolutely continuous operator ideals {\cal P}_{p, \sigma} -in the sense of Jarchow and Matter-. Inclusions {\cal P}_{p, \sigma} (E,F) \subset {\cal M}_{(q,s)} (E,F) are also investigated, specially for the cases E={\cal C}(K) and E=L_1.

On Surjectivity Of The Arens Homomorphism, S. Alpay, B. Turan

Turkish Journal of Mathematics

We define approximate separation and extension properties of a Banach lattice and study the relation between these and topological fullness of the ideal centre. Banach lattices with topologically full ideal centre are characterized as those for which the Arens homomorphism m: Z(E)''\rightarrow Z(E') is surjective. Among the positive operators T:E\rightarrow F between Banach lattices E,F we distinguish nearly Z(E) and Z(F) extremal ones and study their properties.