Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 5 of 5
Full-Text Articles in Entire DC Network
A Stronger Triangle Inequality, Herb Bailey
A Stronger Triangle Inequality, Herb Bailey
Mathematical Sciences Technical Reports (MSTR)
The triangle inequality is basic for many results in real and complex analysis. The geometric form states that the sum of any two sides of a triangle is greater than the third. This was included as Proposition XX in the first book of Euclid's Elements. Many geometric triangle inequalities involving sides, angles, altitudes, inscribed circles and circumscribed circles have been found. Hundreds of these inequalities are summarized in [l] and [2]. A nice geometric proof of the triangle inequality is given in [3].
Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt M. Bryan, Lester F. Caudill
Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt M. Bryan, Lester F. Caudill
Mathematical Sciences Technical Reports (MSTR)
An inverse problem for a parabolic initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in Rn from measurements of Dirichlet data on a known portion of the boundary. It is shown that under reasonable hypotheses uniqueness results hold.
Cwatsets: Weights, Cardinalities, And Generalizations, Richard Mohr
Cwatsets: Weights, Cardinalities, And Generalizations, Richard Mohr
Mathematical Sciences Technical Reports (MSTR)
This report provides an upper bound on the average weight of an element in a cwatset and discusses the ratio of the cardinality of a cwatset to the cardinality of the group containing the cwatset. The concept of a generalized cwatset is also introduced.
Divergence Diagrams: More Than Cantor Dust Lies At The Edge Of Feigenbaum Diagrams, John H. Rickert, Aaron Klebanoff
Divergence Diagrams: More Than Cantor Dust Lies At The Edge Of Feigenbaum Diagrams, John H. Rickert, Aaron Klebanoff
Mathematical Sciences Technical Reports (MSTR)
The dynamical system analysis of the logistic map f(x)=ax(1-x) is studied for values of a greater than 4.
Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius
Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius
Mathematical Sciences Technical Reports (MSTR)
We study the effective behaviour of a periodic array of microscopic cracks inside a homogeneous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular, due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. The results have implications for our earlier work on impedance imaging.