- I have relocated to the National Institute
of Standards and Technology (NIST)
where I recently won a National Research
Council Research Postdoctoral Associateship.
I am working in the Applied and Computational Mathematics Division in the Information
Technology Laboratory with the group who developed the Digital Library
of Mathematical Functions and published the NIST
Handbook of Mathematical Functions. Prior to that,
I graduated from the Department of Mathematics at the University of Auckland with a
Doctor of Philosophy working with
Tom ter Elst
in analysis and Rod Gover in differential
geometry. The title of my thesis was
"Fourier and Gegenbauer expansions for fundamental solutions
of the Laplacian and powers in
**R**^{d}and**H**^{d}."

- Over the past year my research has focused on computing closed form expressions for
fundamental solutions (Green's functions) for integer powers (k) of some important linear
partial differential operators. I obtain fundamental solutions for integer powers of
these operators by recursively determining an appropriate sequence of functions which when
operated k-times by the operator yields the n-dimensional Dirac delta distribution. Initially
my focus was on the fundamental solution for integer powers of the Laplacian operator in
R
^{n}. It is well-known that the functional behaviour of the fundamental solution of the Laplacian is given by a function of the Euclidean distance depending on the dimension (n) of the space. The derivation has been completed and it is noted that the behaviour of these functions are different depending on whether the dimension of the space is even or odd. The derivation was followed-up by completely determining Fourier series expansions for the fundamental solutions (for integer powers of the Laplacian in a set of rotationally invariant coordinate systems in R^{n}). I then proceeded to compute fundamental solutions for integer powers of the Helmholtz operator (Laplacian plus a constant) in R^{n}. In both even and odd dimensions (R^{n}), I then computed closed form expressions for the fundamental solution of the Helmholtz operator, and for integer powers of the Helmholtz operator in terms of Hankel functions of the first kind.

- As a very interesting experience, I am co-chairing the New Zealand Mathematics and Statistics Postgraduate Conference 2008 which is going to be held from November 18-21 in Whitianga in the Coromandel peninsula.

- After completing my postdoc at the University of Exeter in the UK, I decided
to chase my long-time dream of studying mathematics at a more dedicated level. I applied
for a position in a PhD program in Mathematics at a variety of Universities in the southern
hemisphere. Ultimately I was offered a position in the Department of Mathematics at the
University of Auckland and I've been here in Auckland since March, 2006. I am focusing on
matters of Mathematical interest in the area of linear partial differential equations and
for fundamental solutions (Green's functions) for certain linear partial differential equations.
I am working with Rod Gover and Tom ter Elst.

- It has now just begun summer in New Zealand and I am going to be attending three conferences; one in Queenstown (in the southen alps on the south island) which I am departing for tomorrow -- New Zealand Mathematics and Statistics Post-Graduate's Conference, Thursday 22nd - Friday 23rd November, 2007; one in Wellington (at the bottom of the north island) in December -- Joint Meeting of the AMS - NZMS 2007 incorporating the New Zealand Mathematics Colloquium 2007 Victoria University of Wellington, New Zealand Wednesday 12th - Saturday 15th December, 2007, and another in Nelson (at the top of south island) in January -- New Zealand Mathematics Research Institute, Summer Workshop on Conformal geometry and geometric approaches to PDE, Nelson, Sunday 6th - Saturday 12th January, 2008.

- I am working on lecturer Matthew Bate's smooth particle
hydrodynamics (SPH) code in the school of physics at the University of Exeter in the county
of Devon in the United Kingdom (England). I am attempting to put
radiation transport into his code so that we can do cluster star
formation with the addition of adding in radiation from newly formed stars
in his SPH simulations.

- I recently attended a conference in Kiev, Ukraine, "Symmetry
in Nonlinear Mathematical Physics" and presented a talk there entitled,
"The Proper Treatement of Linear Inhomogeneity in 3-Space and 1-Time."

- After presenting in Kiev, I went to Warsaw, Poland to meet with
Prof. Antoni Sym and his graduate student Robert Prus who have recently
found an R-separable coordinate system for the 3-variable Helmholtz
equation. This coordinate geometry is cylcidic in nature, but it is
not rotationally invariant.

- I am now in the process of settling in the stellar astrophysics group in the School of Physics at the University of Exeter, United Kingdom.

- I am relocating to the University of Exeter in the
United Kingdom (England). I am going to be working with their
astrophysics group in the School of Physics at the University
of Exeter. The School of Physics just started the small three
professor team in 2000! Now, I get to go to this brand new group
and help them get some good physics in their coding efforts.
I am looking forward to this trip, in the mean time, I am going
to be traveling around the country. I am headed towards Baton
Rouge, Louisiana to do some work with my collaborators over there.
Then I will spend the holidays with my fam. I then take off for
a meeting with the Domina Eberle Spencer who works at the Department
of Mathematics at the University of Connecticut, Storrs. Then,
I am headed to the University of Chicago, and finally to the
University of Minnesota. I will be able to contact people through
e-mail basically because so many people have e-mail these days.
Plus I should have access to a computer when I am at academic
institutions. My web site has continued to evolve, check out my
site at Howie's site.
If you feel like responding, feel free and e-mail me at
hcohl@sdf.org.

- Check out my most recent publication, "Portent
of Heine's Reciprocal Square Root Identity," Cohl, H.S. (2002)
which was presented in the proceedings of the 1st 3D Stellar Evolution
Workshop, in Livermore, California, 2002.

- Joel E. Tohline has recently written an annual reviews article
on the topic of binary star formation. If you are interested in this
hot topic in theoretical astrophysics, you should check it out!
Annual Review in Astronomy and Astrophysics 2002 40:349-85.

- Two new additions to my web site! Online CHAT and online FORUM. Join me in a global conversation with the people of this our planet earth. Welcome!

- I am now working on postdoctoral research for the djehuty project at the Lawrence Livermore National Laboratory. The goal of this research is aimed at numerically simulating three-dimensional stellar interior structure. My current focus is on algorithmicly enhancing the solution by improving key physics packages. H. S. Cohl and Doug Peters are producing a nonaxisymmetric Newtonian boundary solver combined and code to solve Poisson's eqation for the Newtonian potential throughout the interior of the star. Gravitational potential Dirchlet boundary solutions for Poisson's equation are obtained by convolving the mass density with the Green's function for generalized equation of axisymmetric potential theory over the dual mesh. The elliptic PDE solve is using djehuty's preexisting radiation solve code. The solution of the matrix problem is obtained using HYPRE preconditioners (multigrid) followed by an iterative conjugate gradient solve.

- We are proud to inaugurate our new site and new look located at http://hcohl.sdf.org. Our new provider,http://www.shell42.com, is an awesome UNIX shell access provider, with excellent rates for high-quality access to the UNIX world!

- We have published our PRA PAPER. It has been published in
Physical Review A: Atomic and Molecular
Structure and Dynamics
*"Useful alternative to the multipole expansion of 1/r potentials."*It is in the November 1st, 2001 PRA issue, vol 64, Issue 5, 052509.

- OK. Getting back in full order. Here is the original CCGF paper:
ApJ 1999 vol.
**527**, pp. 86-101

- Check this out Cohl,
Sun and
Tohline's original Poisson
solver paper on the web. Wow. TECHNOLOGY...,
Check it out.
*"Parallel Implementation of a Data-Transpose Technique for The Solution of Poisson's Equation in Cylindrical Coordinates."*

- The twenty fifth of July. It's hard to keep yelling Hurray all the time, whew...., Hurray! Keep checking out functions. I keep making incremental progress, one day it will live up to its expectations, I assure you. Unless the heavens erupt and Tsunamies engulf us like Lovecraftian towering walls erasing all signs of habitation on the nearby lands and us, well, let's just say, I'm glad this server is in Mississippi, so I live on somehow. In fact, if I did hear that a tsunami was coming toward the east bay, I'd be moving like hell away from here. My house would get thrown around quite a few times, it wouldn't be a pleasant sight.

- Check out the manuscript that
Eric Barnes
who recently got his Ph.D.!! go Eric!!!,
has prepared a draft manuscript on how
Joel Tohline's
LSU Hydro group.
Eric Barnes,
who is starting a postdoc this fall with
Jerry Sellwood in New Jersey to learn the crafts associated
with orbital dynamics. He is the senior yout' member currently on-site at the
LSU Astrophysics Theory Group.
The LSU LSU
Astrophysics Theory Group
is strategizing for their future theoretical explorations, as
**Movies**. This is a critical step on our way to build HCE**(->->click<-<-)**

environments which both stimulate and makes curious the unsuspecting observer. In HCE we capture the full essence of what we are trying to describe in a such a way that even lay observers can get the full perspective. We speak in such a language that hopefully everything can be built up from a centralized viewpoint. I will be doing my best to keep everybody up to date. This is e-radio, live at 8 PM PST. - New restructuring!!!! If you're familiar with the old
one, you'll love the new one!
Check it out as DAD or
ME. I put my resume stuff at the bottom! : )

- The twenty second of July. Hurray! Check out the Francis John Welsh Whipple (1876-1943), Meteorology, Mathematics and superintendent of the Kew observatory (1925-1939). Well anyways, I think that's the guy, I think he worked with G. N. Watson and they did some neat stuff in England together regarding hypergeometric transformations which I am going to look onto more. His Whipple formulae when looked at in toroidal (anchor ring) coordinates. This is a presentation I brought forward on these interesting formulae.
- Check out an HTML version of our
Astronomische Nachrichten paper!
I did this back in 00. It's entitled,
*Developments in determining the gravitational potential using toroidal functions."*It's not perfect though and some of the equations got garbled in the LaTeX2HTML conversion. If you are someone who understands these kinds of think, please get help! Or help me figure out how to master the LaTeX2HTML craft. If you are interested there is the journal AN in your local University library, or contact me and I'll send you a copy. - Check out
*"The Potential of a Point."*These pieces are presented as an evolving work and are always welcome to debate. Constructive criticism is always welcome. : ) Here we discuss the various harmonic aspects of gravity and the Coulomb -- BTW: Did you know that the man was originally interested in Astronomy and Mathematics was Charles Augustin de Coulomb (1736-1806) interaction and the amazing properties associated with special function manifestations of the natural variation which we observe to exist in the universe on very small scales associated with electromagnetism or on extremely large distance scales for gravity. We explore the very soul of harmonic theory, the harmonic functions.

- I am going to be staying for one full week at the University of Chicago, Department of Mathematics, researching Mathematical developments in the classical theory of binary fission ( Maclaurin, Dirichlet, Dedekind, Riemann, Jacobi, Chandrasekhar, ...). This effort is mainly due to the gratitude and expertise of Norman Lebovitz, and I thank him a lot for this opportunity.
- If you're interested, there are some photographs of Eduard Heine that I came across on the University of St. Andrews "MacTutor Archive" site. There is also a *short* history given therein. Some mathematicians suppose he might have wanted to be called Eduard because he might be often mistook by others by, what some literary people have said might have been "Germany's greatest poet" Heinrich Heine(1797-1856) who lived and was prolific at about the same time as Eduard (1821-1881).
- I will be giving a talk at the
University of Chicago,
Department of Mathematics,
CAMP/Nonlinear PDE's seminar on
**Wednesday June 27th.**