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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
The Operator (Sgn X) D²/Dx² Is Similar To A Selfadjoint Operator In L² (R), Branko Ćurgus, Branko Najman
The Operator (Sgn X) D²/Dx² Is Similar To A Selfadjoint Operator In L² (R), Branko Ćurgus, Branko Najman
Mathematics Faculty Publications
Krein space operator-theoretic methods are used to prove that the operator (sgn x) d²/dx² is similar to a selfadjoint operator in the Hilbert space L²(R).
Lazutkin Coordinates And Invariant Curves For Outer Billiards, Edoh Y. Amiran
Lazutkin Coordinates And Invariant Curves For Outer Billiards, Edoh Y. Amiran
Mathematics Faculty Publications
The outer billiard ball map (OBM) is defined from and to the exterior of a domain, Ω, in the plane as taking a point, q, to another point, q 1, when the line segment with endpoints q and q 1 is tangent to the boundary, ∂Ω (with a chosen orientation), and the point of tangency with the boundary divides the segment in half. Let C be an invariant circle for the OBM on Ω, with ∂Ω smooth with positive curvature. After computing the loss of derivatives between ∂Ω and C, it is shown via KAM theory that …
Historical Development Of The Newton-Raphson Method, Tjalling Ypma
Historical Development Of The Newton-Raphson Method, Tjalling Ypma
Mathematics Faculty Publications
This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.
Positive Solutions For Higher Order Ordinary Differential Equations, Paul W. Eloe, Johnny Henderson
Positive Solutions For Higher Order Ordinary Differential Equations, Paul W. Eloe, Johnny Henderson
Mathematics Faculty Publications
Solutions that are positive with respect to a cone are obtained for the boundary value problem, u(n) + a(t)f(u) = 0, u(i)(0) = u(n−2)(1) = 0, 0 _ i _ n − 2, in the cases that f is either superlinear or sublinear. The methods involve application of a _xed point theorem for operators on a cone.
Multipoint Boundary Value Problems For Functional Differential Equations, Paul W. Eloe, Johnny Henderson, Denise Taunton
Multipoint Boundary Value Problems For Functional Differential Equations, Paul W. Eloe, Johnny Henderson, Denise Taunton
Mathematics Faculty Publications
No abstract provided.
Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe
Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe
Mathematics Faculty Publications
Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.
Singular Boundary Value Problems For Quasi-Differential Equations, Paul W. Eloe, Johnny Henderson
Singular Boundary Value Problems For Quasi-Differential Equations, Paul W. Eloe, Johnny Henderson
Mathematics Faculty Publications
Solutions are obtained of boundary value problems for Lny+f(x,L0y,…,Ln−2y), satisfying L2y(0)=Ln−1y(1)=0, 0≤i≤n−2, where Li, denotes the ith quasiderivative, and where f(x,y1,…,yn−1) has singularities at yi=0, 1≤i≤n−1.
A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn
A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn
Mathematics Faculty Publications
The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rn into R that was strictly increasing with respect to the new order imposed on Rn. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …
Galois Module Structure Of Ideals In Wildly Ramified Cyclic Extensions Of Degree P2, Gove Griffith Elder
Galois Module Structure Of Ideals In Wildly Ramified Cyclic Extensions Of Degree P2, Gove Griffith Elder
Mathematics Faculty Publications
For L/K, any totally ramified cyclic extension of degree p2 of local fields which are finite extensions of the field of p-adic numbers, we describe the Zp[Gal(L/K)]-module structure of each fractional ideal of L explicitly in terms of the 4p+1 indecomposable Zp[Gal(L/K)]-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.
Spectral Properties Of Operators Having Dense Orbits, Valentin Matache
Spectral Properties Of Operators Having Dense Orbits, Valentin Matache
Mathematics Faculty Publications
In the following H will denote a separable, infinite-dimensional, complex Hilbert space. The term operator will always mean linear, bounded operator on H. By invariant subspace we mean closed, invariant linear manifold. For a given operator T, the set of all invariant subspaces of T will be denoted LatT, since obviously it is a lattice. The set of all operators commuting with T is denoted {T}'. A subspace will be called hyperinvariant for T if it is invariant under any operator in {T}'.