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Articles 6871 - 6900 of 7953

Full-Text Articles in Applied Mathematics

Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek Jan 2003

Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek

Articles and Preprints

We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analyzing, step by step, the action of homogeneous transformations on the homogeneous part of the same degree of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and a dual canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms (resp., their dual canonical forms) coincide. We give an explicit construction of transformations bringing …

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A Christian Perspective On Mathematics – History Of Mathematics And Study Guides, Johan Deklerk Jan 2003

A Christian Perspective On Mathematics – History Of Mathematics And Study Guides, Johan Deklerk

ACMS Journal 2004

This paper addresses two questions: (1) Will a study of the history of the subject serve any purpose in promoting a Christian perspective on mathematics? (2) Can the "science in context" approach be of further help in promoting such a perspective? The author answers both positively and provides specific examples of how he has done this in his own classes.

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Creationism – A Viable Philosophy Of Mathematics, Jonathan Zderad Jan 2003

Creationism – A Viable Philosophy Of Mathematics, Jonathan Zderad

ACMS Journal 2004

In this paper, the author addresses two classical questions of the philosophy of mathematics: What, if any, of mathematics exists in the objective sense? How do humans know that our knowledge of mathematics is correct? He argues that the Christian doctrine of God as creator provides a basis for answering these questions. He also provides a critique of eight widely discussed philosophies of mathematics.

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On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue Jan 2003

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

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Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang Jan 2003

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

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Mathematics And The Love Of God: An Introduction To The Thought Of Simone Weil, Scott Taylor Jan 2003

Mathematics And The Love Of God: An Introduction To The Thought Of Simone Weil, Scott Taylor

ACMS Journal 2004

Simone Weil was the sister of Andre Weil, one of the twentieth century's foremost mathematicians. She is a widely read and creative writer on spiritual themes. She addressed mathematics extensively in her writings. This paper discusses her views of mathematics and beauty, her critiques of modern science, her views on truth, and her concept that mathematical ideas can serve as symbols of spiritual ideas.

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Homogeneous Weights And Exponential Sums, José Felipe Voloch, Judy L. Walker Jan 2003

Homogeneous Weights And Exponential Sums, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

In this paper, we give a formula as an exponential sum for a homogeneous weight defined by Constantinescu and Heise [3] in the case of Galois rings (or equivalently, rings of Witt vectors) and use this formula to estimate the weight of codes obtained from algebraic geometric codes over rings.

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Thesis Digest: Mathematical Interpretation Of Political Power And The Arkansas State Government, Andrew King Jan 2003

Thesis Digest: Mathematical Interpretation Of Political Power And The Arkansas State Government, Andrew King

Inquiry: The University of Arkansas Undergraduate Research Journal

On the whole, political power can he very difficult to quantify. A person may be powerful due to his or her personal charm, wealth, fame, credibility, or influential connections. Political bodies do not account for these qualities when creating voting procedures; they only assign voting rules to specific positions. For example, most would say that in the United States government that a Senator is more powerful than a Representative, but less powerful than the President, without knowing any way to quantify or verify those differences. Since the 1950's, mathematicians and political scientists have attempted to create mathematical models that partially …

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Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan Jan 2003

Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.

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The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp Jan 2003

The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We consider the Dirichlet problem Δu + λu + |u|2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in RN, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

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An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty Jan 2003

An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

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Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal Jan 2003

Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We present new random fixed point theorems in spaces with two metrics. Our results extend recent results of Tan and Yuan [10] and Xu [11].

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Simulation Of Dynamic Electrochemical Processes, John Cassidy Jan 2003

Simulation Of Dynamic Electrochemical Processes, John Cassidy

Articles

This work is designed to introduce electrochemists in a tutorial manner to the basics of modeling of electrochemical systems based primarily on diffusion equations. There is an introduction to analytical and numerical methods with examples taken from typical electrochemical experiments. The Laplace transform is used to derive the Cottrell equation and chronopotentiometry. The response of an electrode to a Gaussian concentration profile is detailed. Laplace’s equation is solved for a simple cell to determine the potential distribution. Discrete methods are employed to calculate the current time behavior following a potential step using the explicit finite difference method. Cyclic voltammetry is …

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Finite Subsets Of The Plane Are 18-Reconstructible, L. Pebody, A. J. Radcliffe, A. D. Scott Jan 2003

Finite Subsets Of The Plane Are 18-Reconstructible, L. Pebody, A. J. Radcliffe, A. D. Scott

Department of Mathematics: Faculty Publications

We prove that every finite subset of the plane is reconstructible from the multiset of its subsets of at most 18 points, each given up to rigid motion. We also give some results concerning the reconstructibility of infinite subsets of the plane.

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A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu Jan 2003

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!

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A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan Jan 2003

A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the ux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different, in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to …

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Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand Jan 2003

Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand

LSU Master's Theses

This work presents Gauss' justification of the method of least squares, following the treatment given by Gauss himself in "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," where the main idea is to show that the least squares estimate is the unbiased linear estimate of minimum variance. (Actually, we present Gauss' argument both in his terminology and translated into matrix terminology.) We show how this contrasts with Gauss' earlier justfication in "Theoria Motus Corporum Coelestium" which was based on the assumption of a normal distribution of errors, and yielded the estimate of maximum likelihood. We present as a background the development from …

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Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory Jan 2003

Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory

LSU Master's Theses

The mathematical study of stock price modeling using Brownian motion and stochastic calculus is a relatively new field. The randomness of financial markets, geometric brownian motions, martingale theory, Ito's lemma, enlarged filtrations, and Girsanov's theorem provided the motivation for a simple characterization of the concepts of stock price modeling. This work presents the theory of stochastic calculus and its use in the financial market. The problems on which we focus are the models of an investor's portfolio of stocks with and without the possibility of insider trading, opportunities for fair pricing of an option, enlarged filtrations, consumptions, and admissibility. This …

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On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb Jan 2003

On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb

LSU Doctoral Dissertations

The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact …

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A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu Jan 2003

A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu

LSU Master's Theses

Hamilton-Jacobi (HJ)-theory is an extension of Lagrangian mechanics and concerns itself with a directed search for a coordinate transformation in which the equations of motion can be easily integrated. The equations of motion of a given mechanical system can often be simplified considerably by a suitable transformation of variables such that all the new position and momemtum coordinates are constants. A particular type of transformation is chosen in such a way that the new equations of motion retain the same form as in the former coordinates; such a transformation is called canonical or contact and can greatly simplify the solution …

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The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris Jan 2003

The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris

LSU Doctoral Dissertations

In this work, we study the structure of the Kauffman bracket skein module of the quaternionic manifold over the field of rational functions. We begin with a brief survey of manifolds whose Kauffman bracket skein modules are known, and proceed in Chapter 2 by recalling the facts from Temperley-Lieb recoupling theory that we use in the proofs. In Chapter 3, using recoupling theory and with Mathematica's assistance, we index an infinite presentation of the skein module, and conjecture that it is five-dimensional. In Chapter 4, using a new set of relations, we prove that the skein module is indeed spanned …

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A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch Jan 2003

A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch

LSU Master's Theses

We present how blackjack is related to a discrete-time control problem, rather than a zero-sum game. Using the compiler Visual C++, we write a program for a strategy for blackjack, but instead of maximizing the expected value, we use a risk-averse approach. We briefly describe how this risk-averse strategy is solved by using a special type of dynamic programming called fractional dynamic programming.

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Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno Jan 2003

Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno

LSU Doctoral Dissertations

Let g be a class of graphs and ≤ be a graph containment relation. A splitter theorem for g under ≤ is a result that claims the existence of a set O of graph operations such that if G and H are in g and H≤G with G≠H, then there is a decreasing sequence of graphs from G to H, say G=G0≥G1≥G2...Gt=H, all intermediate graphs are in g, and each Gi can be obtained from Gi-1 by applying a single …

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Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang Jan 2003

Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang

LSU Doctoral Dissertations

Suppose $S$ is a parametrized surface in complex projective 3-space $mathbf{P}^3$ given as the image of $phi: mathbf{P}^1 imes mathbf{P}^1 o mathbf{P}^3$. The implicitization problem is to compute an implicit equation $F=0$ of $S$ using the parametrization $phi$. An algorithm using syzygies exists for computing $F$ if $phi$ has no base points, i.e. $phi$ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple base points of total multiplicity k. We accomplish this in three chapters. In Chapter 2, we develop the concept and properties of Castelnuovo-Mumford regularity in biprojective spaces. …

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Book Embeddings Of Graphs, Robin Leigh Blankenship Jan 2003

Book Embeddings Of Graphs, Robin Leigh Blankenship

LSU Doctoral Dissertations

We use a structural theorem of Robertson and Seymour to show that for every minor-closed class of graphs, other than the class of all graphs, there is a number k such that every member of the class can be embedded in a book with k pages. Book embeddings of graphs with relation to surfaces, vertex extensions, clique-sums and r-rings are combined into a single book embedding of a graph in the minor-closed class. The effects of subdividing a complete graph and a complete bipartite graph with respect to book thickness are studied. We prove that if n ≥ 3, …

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Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao Jan 2003

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Mathematics and Statistics Faculty Publications

No abstract provided.

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Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo Jan 2003

Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo

Mathematics Faculty Publications

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

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Integral Transforms Of Functionals In L2(C0[0, T]), Byoung Soo Kim, David Skough Jan 2003

Integral Transforms Of Functionals In L2(C0[0, T]), Byoung Soo Kim, David Skough

Department of Mathematics: Faculty Publications

In this paper we give a necessary and sufficient condition that a functional F(x) in L2(C0[0, T]) has an integral transform Fα,βF(x) which also belongs to L2(C0[0, T]).

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A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat Jan 2003

A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat

Mathematics and Statistics Faculty Publications and Presentations

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.

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Advances In The Use Of Neurophysiologycally-Based Fusion For Visualization And Pattern Recognition Of Medical Imagery, Mario Aguilar, Joshua New, Erion Hasanbelliu Jan 2003

Advances In The Use Of Neurophysiologycally-Based Fusion For Visualization And Pattern Recognition Of Medical Imagery, Mario Aguilar, Joshua New, Erion Hasanbelliu

Research, Publications & Creative Work

The ever increasing number of image modalities available to doctors for diagnosis purposes has established an important need to develop techniques that support work-load reduction and information maximization. To this end, we have improved on an image fusion architecture first developed for night vision applications. This technique, presented at Fusion 2002, utilizes 3D operators to combine volumetric image sets while maximizing information content. In our approach, we have combined the use of image fusion and userdefined pattern recognition within a 3D human-computer interface. Here, we present our latest advances towards enhancing information visualization and supporting pattern recognition. We also report …

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