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Articles 2281 - 2310 of 2877

Full-Text Articles in Mathematics

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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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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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 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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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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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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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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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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Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek Dec 2002

Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We study the feedback group action on two-inputs non-linear control systems. We follow an approach proposed by Kang and Krener which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes that obtained in the single-input case. We also give homogeneous m-invariants of the action of the group of homogeneous transformations on the homogeneous systems of the same degree. We illustrate our results by analyzing the normal form and invariants of homogeneous systems of degree two.

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Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden Oct 2002

Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden

Mathematical Sciences Technical Reports (MSTR)

We explore some questions related to one of Brizolis: does every prime p have a pair (g, h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not only fixed points but also two-cycles. Campbell and Pomerance have not only answered the fixed point question for sufficiently large p but have also rigorously estimated the number of such pairs given certain conditions on g and h. We attempt to give heuristics for similar estimates given other conditions on g and h and also in the case …

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Pattern Recognition For Electric Power System Protection, Yong Sheng Oct 2002

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

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Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah Sep 2002

Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of locating and describing an internal point defect in a one­ dimensional rod W by controlling the heat inputs and measuring the subsequent temperatures at the boundary of W. We use a variation of the forward heat equation to model heat flow through W, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.

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The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt Sep 2002

The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt

All HMC Faculty Publications and Research

We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.

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Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty Sep 2002

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty

Mathematics and Statistics Faculty Publications

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

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Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman Sep 2002

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

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A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga Sep 2002

A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga

Mathematics Research Reports

Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.

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Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang Aug 2002

Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang

Mathematics Research Reports

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

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Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang Jul 2002

Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern Jul 2002

Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern

Mathematics and Statistics Faculty Publications

Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of …

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On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li May 2002

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=N\ω is an exterior domain in N, ω⊂N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈Cαloc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

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Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli Mar 2002

Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli

CMC Faculty Publications and Research

A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.

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A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga Feb 2002

A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga

Mathematics Research Reports

A new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergence at element edge centers for the regular pattern.

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On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang Jan 2002

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C1,1 solution to the uniformly elliptic equation F(D2u) = 0 must belong to C2,α, if the equation has the Liouville property.

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