# Homepage of William C. Troy

## Recent Research Papers:

##

"New Singular Standing Wave Solutions Of The Nonlinear Schrodinger Equation,"
Feb. (2019),
##

##

##

##

##

##

##

(I) Errors
in low temperature predictions of Einstein's theory of a solid are
identified and corrected.

##

(II) Errors
in low temperature predictions of the Fermi-Firac, Boltzman, and Bose-Einstein models
are identified and corrected.

(III) Modeling growth and regression of tumors with a Gompertzian delay-differential equation system.

## Publications:

## Research Projects:

# Movies showing the formation of N-bump solutions, rotating waves
and target pattern
for a 2-dimensional integral equation (joint work with Carlo Laing).
For a copy of the N-bump paper (use a color printer if possible) click on gzipped-ps
or pdf

### First row: Click on 1st figure to see the formation of a
stationary 12-bump solution. Click on 2nd picture to see the rotating 3-bump movie.
Second row: Click on the 1st picture and 2nd pictures to see rotating spiral
movies. Click on the 3rd picture to see the target pattern movie.

- Movie No.6
The level curve version for the 12-bump formation.
- Movie No. 7
shows the formation of the 7-bump solution.
- Movie No.8 The level curve version of 7-bump formation.

Latex
Commands

## Contact Information:

Mathematics Department

University of Pittsburgh

Pittsburgh, Pa. 15260

USA

Phone: 412-624-8325

Fax: 412-372-2802

E-mail: troy@math.pitt.edu