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Articles 6451 - 6480 of 7997

Full-Text Articles in Physical Sciences and Mathematics

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn Jan 2007

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Mathematics Faculty Publications

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

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On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li Jan 2007

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

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On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li Jan 2007

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

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A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis Jan 2007

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

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Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty Jan 2007

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

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Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman Jan 2007

Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to provide an introduction to how technology can be used in the mathematical classroom to enhance students' learning of mathematics, while at the same time leading students to a richer and deeper understanding of those mathematical concepts. The topics were selected based on their relevance to the Utah State Core Curriculum for middle and secondary mathematics courses. It was intended that each lesson plan would challenge a preservice mathematics educator to build relationships between different areas of mathematics and/or to create deeper understandings of specific mathematical concepts. At the same time many of the …

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Cauchy Integrals And Möbius Geometry Of Curves, David E. Barrett, Michael Bolt Jan 2007

Cauchy Integrals And Möbius Geometry Of Curves, David E. Barrett, Michael Bolt

University Faculty Publications and Creative Works

No abstract provided.

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Geometry Of Sub-Finsler Engel Manifolds, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens Jan 2007

Geometry Of Sub-Finsler Engel Manifolds, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens

University Faculty Publications and Creative Works

We analyze the geometry of sub-Finsler Engel manifolds, computing a complete set of local invariants for a large class of these manifolds. We derive geodesic equations for regular geodesics and show that in the symmetric case, the rigid curves are local minimizers. We end by illustrating our results with an example.

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Characterizations Of Pseudo-Codewords Of Ldpc Codes, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker Jan 2007

Characterizations Of Pseudo-Codewords Of Ldpc Codes, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker

Department of Mathematics: Faculty Publications

An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of …

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Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan Jan 2007

Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan

LSU Doctoral Dissertations

In this dissertation we show that the solution of the pure initial-value problems for the KP and regularize KP equations are the same, to within the order of accuracy attributable to either, on the time scale from zero to epsilon to negative three halves power, during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.

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Sign Ambiguities Of Gaussian Sums, Heon Kim Jan 2007

Sign Ambiguities Of Gaussian Sums, Heon Kim

LSU Doctoral Dissertations

In 1934, two kinds of multiplicative relations, extit{norm and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample disproving the conjecture when Gaussian sums are considered as numbers. This counterexample was a new type of multiplicative relation, called a {it sign ambiguity} (see Definition ef{defi:of_sign_ambi}), involving a $pm$ sign not connected to elementary properties of Gauss sums. In Chapter $5$, we provide an explicit product formula giving an infinite class …

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Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu Jan 2007

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu

Scholarship

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

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A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache Jan 2007

A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …

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Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen Jan 2007

Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider Turing patterns for reaction-diffusion systems on the surface of a growing sphere. In particular, we are interested in the effect of dynamic growth on the pattern formation. We consider exponential isotropic growth of the sphere and perform a linear stability analysis and compare the results with numerical simulations.

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S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker Jan 2007

S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker

Department of Mathematics: Faculty Publications

Binary self-dual codes and additive self-dual codes over F4 have in common interesting properties, for example, Type I, Type II, shadows, etc. Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F4, give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths and (shadow) weight …

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Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang Jan 2007

Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang

Mathematics and Statistics Faculty Publications and Presentations

The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …

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Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal Jan 2007

Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal

Publications

Phototransduction is the process by which light is converted into an electrical response in retinal photoreceptors. Rod photoreceptors contain a stack of (about 1000) disc membranes packed with photopigment rhodopsin molecules, which absorb the photons. We present computational experiments which show the profound effect on the response of the distances (how many discs apart) photons happen to be absorbed at. This photon-distribution effect alone can account for much of the observed variability in response.

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Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang Jan 2007

Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang

Faculty Articles

The authors consider the higher order boundary-value problem u (n)(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i-1)(0) = u (n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n -2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

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Estimates Of Positive Solutions To A Boundary Value Problem For The Beam Equation, Bo Yang Jan 2007

Estimates Of Positive Solutions To A Boundary Value Problem For The Beam Equation, Bo Yang

Faculty Articles

We consider a two-point boundary value problem for the fourth order beam equation. New upper and lower estimates of positive solutions of the problem are obtained.

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Dynamics Of Starvation In Humans, Baojun Song, Diana M. Thomas Jan 2007

Dynamics Of Starvation In Humans, Baojun Song, Diana M. Thomas

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A differential equation model describing the dynamics of stored energy in the form of fat mass, lean body mass and ketone body mass during prolonged starvation is developed. The parameters of the model are estimated using available data for 7 days into starvation. A simulation of energy stores for a normal individual with body mass index between 19 and 24 and an obese individual with body mass index over 30 are calculated. The length of time the obese subject can survive during prolonged starvation is estimated using the model.

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Elementary Fuzzy Matrix Theory And Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2007

Elementary Fuzzy Matrix Theory And Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out …

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Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang Jan 2007

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang

Scholarship

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

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Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert Jan 2007

Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …

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Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov Jan 2007

Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance. While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves …

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Water Waves And Integrability, Rossen Ivanov Jan 2007

Water Waves And Integrability, Rossen Ivanov

Articles

The Euler’s equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler’s equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.

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Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov Jan 2007

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion …

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Fundamental Frequency Of Clamped Plates With Circularly Periodic Boundaries, Huseyin Yuce, Chang Y. Wang Jan 2007

Fundamental Frequency Of Clamped Plates With Circularly Periodic Boundaries, Huseyin Yuce, Chang Y. Wang

Publications and Research

A boundary perturbation method is developed to determine the fundamental frequency of vibrating plates. The method is then applied to wavy, star shape and polygonal plates with clamped boundary conditions. Approximate analytical solutions of the fundamental frequency are obtained with an accuracy of O(e^4), where e is the deviation from the unit circle.

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The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter Shiue, Leetsch Hsu Jan 2007

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter Shiue, Leetsch Hsu

Scholarship

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.

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Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He Jan 2007

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He

Scholarship

No abstract provided.

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Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge Jan 2007

Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge

Articles

This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based …

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