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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
On Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader
On Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader
Mathematics Faculty Publications
No abstract provided.
A Density Property Of The Tori And Duality, Peter Loth
A Density Property Of The Tori And Duality, Peter Loth
Mathematics Faculty Publications
In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.
The Brunn-Minkowski Inequality, Richard J. Gardner
The Brunn-Minkowski Inequality, Richard J. Gardner
Mathematics Faculty Publications
In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of Rn, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, and some applications.
Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding
Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding
Mathematics Faculty Publications
Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first n - 1 derivatives.
Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova
Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova
Mathematics Faculty Publications
The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.
The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao
The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao
Mathematics Faculty Publications
The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.
Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe
Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe
Mathematics Faculty Publications
The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.
Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin
Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin
Mathematics Faculty Publications
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher degree for both numerator and denominator polynomials, with particular attention given to cases in which the degrees are equal. We extend work of Ramanujan on continued fractions with rational limits and also consider cases where the limits are irrational.