Department of Mathematics
http://hdl.handle.net/1957/13737
2014-09-01T23:36:26ZSkew Disperson and Continuity of Local Time
http://hdl.handle.net/1957/51760
Skew Disperson and Continuity of Local Time
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain a characterization of large scale
parameters and behavior by an analysis at the fine scale of stochastic particle motions.
In particular, considering particle concentration modeled by a diffusion equation with
piecewise constant diffusion coefficient, it is shown that the continuity of a natural
modification of local time is the individual (stochastic) particle scale equivalent to continuity
of flux at the scale of the (macroscopic) particle concentrations. Consequences
of this involve the determination of a skewness transmission probability in the presence
of an interface, as well as corollaries concerning interfacial effects on occupation time
of the associated stochastic particles.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/10955.
2014-07-01T00:00:00Z3D cone beam reconstruction formulas for the transverse-ray transform with source points on a curve
http://hdl.handle.net/1957/51754
3D cone beam reconstruction formulas for the transverse-ray transform with source points on a curve
Wongsason, Patcharee
3D vector tomography has been explored and results have been achieved in the last few decades. Among these was a reconstruction formula for the solenoidal part of a vector field from its Doppler transform with sources on a curve. The Doppler transform of a vector field is the line integral of the component parallel to the line. In this work, we shall study the transverse ray transform of a vector field, which instead integrates over lines the component of the vector field perpendicular to the line. We provide a reconstruction procedure for the transverse ray transform of a vector field with sources on a curve fulfilling Tuy’s condition of order 3. We shall recover both the potential and solenoidal parts. We present two steps for the reconstruction. The first one is to reconstruct the solenoidal part and the techniques we use are inspired by work of Katsevich and Schuster. A procedure for recovering the potential part will be the second step. The main ingredient is the difference between the measured data and the reprojection of the solenoidal part. We also provide a variation of the Radon inversion formula for the vector part of a quaternionic-valued function (or vector field) and an inversion formula in cone-beam setting with sources on the sphere.
Graduation date: 2015
2014-07-23T00:00:00ZSome analytical properties of bivectors
http://hdl.handle.net/1957/51740
Some analytical properties of bivectors
Luehr, Charles Poling
Graduation date: 1956
1955-11-28T00:00:00ZError bounds for iterative solutions of Fredholm integral equations
http://hdl.handle.net/1957/51736
Error bounds for iterative solutions of Fredholm integral equations
Rall, Louis B.
Graduation date: 1954
1954-04-29T00:00:00Z