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2003

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Articles 181 - 210 of 269

Full-Text Articles in Mathematics

Coloring Graphs With Crossings, Wei Zhao Jan 2003

Coloring Graphs With Crossings, Wei Zhao

Honors Capstones

No abstract provided.

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

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

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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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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Fuzzy Cognitive Maps And Neutrosophic Cognitive Maps, W. B. Vasantha Kandasamy, Florentin Smarandache Jan 2003

Fuzzy Cognitive Maps And Neutrosophic Cognitive Maps, W. B. Vasantha Kandasamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As extension of Fuzzy Cognitive Maps are now introduced the Neutrosophic Cognitive Maps

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Irreducible Polynomials Over Gf(2) With Three Prescribed Coefficients, Robert W. Fitzgerald, Joseph L. Yucas Jan 2003

Irreducible Polynomials Over Gf(2) With Three Prescribed Coefficients, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

For an odd positive integer n, we determine formulas for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of xn-1, xn-2 and xn-3 are specified in advance. Formulas for the number of elements in GF(2n) with the first three traces specified are also given.

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Multiple Positive Solutions For A Class Of Quasilinear Elliptic Boundary-Value Problems, Kanishka Perera Jan 2003

Multiple Positive Solutions For A Class Of Quasilinear Elliptic Boundary-Value Problems, Kanishka Perera

Mathematics and System Engineering Faculty Publications

Using variational arguments we prove some nonexistence and multiplicity results for positive solutions of a class of elliptic boundary-value problems involving the p-Laplacian and a parameter.

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Common Fixed Point Theorems For A Pair Of Countably Condensing Mappings In Ordered Banach Spaces, Bapurao C. Dhage, Donal O'Regan, Ravi P. Agarwal Jan 2003

Common Fixed Point Theorems For A Pair Of Countably Condensing Mappings In Ordered Banach Spaces, Bapurao C. Dhage, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.

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A Monopole Homology For Integral Homology 3-Spheres, Weiping Li Jan 2003

A Monopole Homology For Integral Homology 3-Spheres, Weiping Li

Turkish Journal of Mathematics

To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow I_{\eta}(\Theta; \eta_0), where \Theta is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and \eta_0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) is invariant among Riemannian metrics with same I_{\eta}(\Theta; \eta_0). This provides a chamber-like structure for …

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Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski Jan 2003

Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski

Turkish Journal of Mathematics

A stronger form of the adjunction inequality is proved for immersed real surfaces in non simply-connected Stein surfaces. The result is applied to the geometry of Stein domains and analytic continuation on complex surfaces.

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On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç Jan 2003

On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç

Turkish Journal of Mathematics

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.

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Galois Symmetry On Floer Cohomology, Kenji Fukaya Jan 2003

Galois Symmetry On Floer Cohomology, Kenji Fukaya

Turkish Journal of Mathematics

In this article, we define an action of \hat{\Bbb Z} on the A_{\infty} category whose objects are rational Lagrangian submanifolds together with some other data. The group \hat{\Bbb Z} is a Galois group of the (universal) Novikov ring (field) over Laurent polynomial field. By mirror symmetry it will corresponds to the algebraic fundamental group of a punctured disk which parametrize the maximal degenerate family of the mirror complex manifold.

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Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun Jan 2003

Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun

Turkish Journal of Mathematics

The converse of [7, Theorem 3.3] is provided. For an Artinian \Gamma-ring, a few results are investigated.

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Open Problems From The Linz2000 Closing Session, Lawrence Stout Jan 2003

Open Problems From The Linz2000 Closing Session, Lawrence Stout

Scholarship

No abstract provided.

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Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris Jan 2003

Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris

Mathematics Faculty Publications

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

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Finding Common Ground: Collaboration Across The Disciplines In The Scholarship Of Teaching, Elaine K. Yakura, Curtis D. Bennett Jan 2003

Finding Common Ground: Collaboration Across The Disciplines In The Scholarship Of Teaching, Elaine K. Yakura, Curtis D. Bennett

Mathematics, Statistics and Data Science Faculty Works

Many recent writings on the scholarship of teaching discuss the need to locate this scholarship within the disciplines. The authors argue that while scholarship within the disciplines is important, it should not come at the expense of work across the disciplines. They demonstrate the usefulness of cross-disciplinary collaboration for the scholarship of teaching and learning through the specific example of how collaboration contributed to their understanding of the role of such scholarship in the teaching of mathematics and negotiations courses. The authors also outline some of the pitfalls of cross-disciplinary collaboration, and they offer suggestions for beginning collaborative initiatives.

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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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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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Planar Minimally Rigid Graphs And Pseudo-Triangulations, Ruth Haas, David Orden, Günter Rote, Francisco Santos, Herman Servatius, Diane Souvaine, Ileana Streinu, Walter Whiteley Jan 2003

Planar Minimally Rigid Graphs And Pseudo-Triangulations, Ruth Haas, David Orden, Günter Rote, Francisco Santos, Herman Servatius, Diane Souvaine, Ileana Streinu, Walter Whiteley

Mathematics Sciences: Faculty Publications

Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial constraints. The proofs yield efficient embedding algorithms. They also provide - to the best of our knowledge - the first algorithmically effective result on graph embeddings with oriented matroid constraints other than convexity of faces. These constraints are described by combinatorial pseudo-triangulations, first defined and studied in this paper. Also …

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A Dynamical System For Plant Pattern Formation: A Rigorous Analysis, Pau Atela, Christophe Golé, S. Hotton Jan 2003

A Dynamical System For Plant Pattern Formation: A Rigorous Analysis, Pau Atela, Christophe Golé, S. Hotton

Mathematics Sciences: Faculty Publications

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system, as well as by the structure of their bifurcation diagram. We provide a detailed study of this diagram.

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Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang Jan 2003

Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang

Mathematics Sciences: Faculty Publications

The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t-3/2. While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.

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Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen Jan 2003

Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen

Mathematics & Statistics Faculty Publications

We report our results in classifying protein matrix-assisted laser desorption/ionizationtime of flight mass spectra obtained from serum samples into diseased and healthy groups. We discuss in detail five of the steps in preprocessing the mass spectral data for biomarker discovery, as well as our criterion for choosing a small set of peaks for classifying the samples. Cross-validation studies with four selected proteins yielded misclassification rates in the 10-15% range for all the classification methods. Three of these proteins or protein fragments are down-regulated and one up-regulated in lung cancer, the disease under consideration in this data set. When cross-validation studies …

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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 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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Multi-Variable Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin Jan 2003

Multi-Variable Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin

Mathematics Faculty Publications

Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and for this reason polynomial solutions are of interest in that they can supply the fundamental units in infinite families of such fields. In this paper an algorithm is described which allows one to construct, for each positive integer n, a finite collection, {Fi}, of multi-variable polynomials (with integral coefficients), each satisfying a multi-variable polynomial Pell’s equation C 2 i − FiH 2 i = (−1)n−1 , where Ci and Hi are multi-variable polynomials with integral coefficients. Each positive integer whose square-root has a regular continued …

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On The Divergence In The General Sense Of Q-Continued Fractions On The Unit Circle, Douglas Bowman, James Mclaughlin Jan 2003

On The Divergence In The General Sense Of Q-Continued Fractions On The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

We show, for each q-continued fraction G(q) in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which G(q) diverges in the general sense. This class includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fraction. We discuss the implications of our theorems for the general convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle.

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Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin Jan 2003

Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin

Mathematics Faculty Publications

Finding polynomial solutions to Pell’s equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic fields. In this paper, for each triple of positive integers (c, h, f) satisfying c 2 − f h2 = 1, where (c, h) are the smallest pair of integers satisfying this equation, several sets of polynomials (c(t), h(t), f(t)) which satisfy c(t) 2 − f(t) h(t) 2 = 1 and (c(0), h(0), f(0)) = (c, h, f) are derived. Moreover, it is shown that the pair (c(t), h(t)) constitute the fundamental polynomial …

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Crowded And Selective Ultrafilters Under The Covering Property Axiom, Krzysztof Ciesielski Jan 2003

Crowded And Selective Ultrafilters Under The Covering Property Axiom, Krzysztof Ciesielski

Faculty & Staff Scholarship

In the paper we formulate an axiom CPA_{prism}^{game}, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to \omega1, while \continuum=\omega2: the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number u. We will also show that CPA_{prism}^{game} implies the existence of crowded and selective ultrafilters as well as nonselective P-points. In addition we prove that under CPA_{prism}^{game} every …

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The Euler Line In Non-Euclidean Geometry, Elena Strzheletska Jan 2003

The Euler Line In Non-Euclidean Geometry, Elena Strzheletska

Theses Digitization Project

The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ

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Necessary And Sufficient Condition That The Limit Of Stieltjes Transforms Is A Stieltjes Transform, Jeffrey S. Geronimo, Theodore P. Hill Jan 2003

Necessary And Sufficient Condition That The Limit Of Stieltjes Transforms Is A Stieltjes Transform, Jeffrey S. Geronimo, Theodore P. Hill

Research Scholars in Residence

The pointwise limit S of a sequence of Stieltjes transforms (Sn) of real Borel probability measures (Pn) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) →−1as y →∞, in which case Pn converges to P in distribution. Applications are given to several problems in mathematical physics.

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A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng Jan 2003

A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng

Mathematics Faculty Publications

In this paper we continue to explore cross-symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales. Dynamic equations under delta and nabla differentiations are considered. It is proven that, by introducing a proper companion problem, the solution of a dynamic equation is cross-symmetric to the solution of the companion problem. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.

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