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Articles 91 - 115 of 115
Full-Text Articles in Physical Sciences and Mathematics
Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal
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].
Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang
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.
Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao
Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao
Mathematics and Statistics Faculty Publications
No abstract provided.
An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty
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.
Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek
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 …
The Mathematics Of Object Recognition In Machine And Human Vision, Sunyoung Kim
The Mathematics Of Object Recognition In Machine And Human Vision, Sunyoung Kim
Theses Digitization Project
The purpose of this project was to see why projective geometry is related to the sort of sensors that machines and humans use for vision.
Advances In The Use Of Neurophysiologycally-Based Fusion For Visualization And Pattern Recognition Of Medical Imagery, Mario Aguilar, Joshua New, Erion Hasanbelliu
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 …
Homogeneous Weights And Exponential Sums, José Felipe Voloch, Judy L. Walker
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.
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
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.
Finite Subsets Of The Plane Are 18-Reconstructible, L. Pebody, A. J. Radcliffe, A. D. Scott
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.
A Risk-Averse Strategy For Blackjack Using Fractional Dynamic Programming, Ryan A. Dutsch
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.
The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris
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 …
A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat
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.
On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb
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 …
A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu
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!
Gauss' Method Of Least Squares: An Historically-Based Introduction, Belinda B. Brand
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 …
Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno
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 …
Book Embeddings Of Graphs, Robin Leigh Blankenship
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, …
Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang
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. …
A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu
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 …
Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory
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 …
A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan
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 …
On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue
On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue
Tian-Xiao He
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.
A Comparison Of Semi-Analytical And Numerical Solutions For The Microwave Heating Of A Lossy Material In A Three-Dimensional Waveguide, Prof. Tim Marchant
A Comparison Of Semi-Analytical And Numerical Solutions For The Microwave Heating Of A Lossy Material In A Three-Dimensional Waveguide, Prof. Tim Marchant
Tim Marchant
The microwave heating of a three-dimensional block in an infinitely long rectangular waveguide propagating the TE10 mode is considered. The electrical conductivity (the dielectric loss) is assumed to be a function of temperature, and modelled by the Arrhenius law. A coupled set of equations is obtained that describes the electromagnetic fields and the temperature distribution in the block. The numerical solutions of this problem are obtained by two methods, the well known FD-TD scheme and a frequency domain method which makes the further assumption that a single TE10 mode exists in the waveguide and material. The results show that an …
Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He
Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He
Tian-Xiao He
In this paper, we apply a boundary-type quadrature technique to derive a type of boundary element scheme, which is used to solve the boundary-value problems of partial differential equations.Numerical examples for solving the exterior boundary-value problem of Helmholtz equation by using the spline approximation and the spline wavelet approximation are given.