marijke's
home page

Latest -- our solutions
for the 'hundred digit'
SIAM challenge 2002

www.silicon-alley.com

The lair of silicon alley where you can download the ideosyncratic math-oid freeware and shareware i write. The site also harbors some notes on writing web pages, the budding incomplete dictionary of filename extensions project, and some of my favorite links.

www.maxwellian.demon.co.uk

Maxwellian Demon (this site), jointly with Gian Vasta and James Baugh. A site focusing on the interface between physics and information theory. This site is still far from equilibrium - aren't we all?

www.silicon-alley.com/amp/

A Mathematicians' Paradise, a spanking new effort determined to put everything that's wonderful about mathematics out on the web, for you, for free! Jointly with a number of mathematicians across the 'net. Early days yet. Have a look!
Read how you can contribute and how you can support the site by buying your books and stuff from amazon.

PGP public key:

Type Bits/KeyID    Date       User ID
pub  1728/3C2392D5 1999/09/02 marijke <marijke@silicon-alley.com>

-----BEGIN PGP PUBLIC KEY BLOCK-----
Version: 2.6.3ia

mQDlAjfN2YkAAAEGwLtExcww+yhqx1sW4CSnwaPW/gIHY3pxFMMh0cdnVJSx818i
0GyTfepdYInTVlJFZ8DpinoxKhL24yekb7N1z0mnqA2N7IlQFLPtJ2/yW+1HTe/I
slGt1Xau1dltmG54e6EZmw/4eMpBlGWQ5mMeFiVWuk5rq8WbNNzM+VyJ4qeDYGa9
sN51/Lng1aNFBLPnLYxhZcpHxgbbPspcxHC10I6MGwgcaglQb1SonrlP4IBH1G5u
Tor+pY380BiZ24l08nheExn4evSQk8fSzd+W8/+w/f8CPCOS1QAFEbQjbWFyaWpr
ZSA8bWFyaWprZUBzaWxpY29uLWFsbGV5LmNvbT6JAO0CBRA3zdmKsP3/AjwjktUB
AYBeBr9pA8J7BWA+LB3JbfAS2fpiqKRTweeiIzc/COxpJzmEezOtEGXCVaToIKlA
WRZtL2SqeyJDzRgHtVcgwa7x/FIzxB+L3+hgAazall+GfJ/BRVBlnKIwJkuQIugl
6uhGQTCk77PhR5qDUi2/tUk6k9fmB9VWme9+8BZW0xVP/250q/DTSG+/iHBu2HP/
KoOzGXVJQGyZJWFDPkEcvnZUlM0bSpoo0sEQ6v/ajEQjltuYdl531X4LtqlGG/E+
L/BZyW6TiUstLvX+COeirxNtvrmTHE80EKWraPI=
=tw7A
-----END PGP PUBLIC KEY BLOCK-----

fractional powers of the Fourier transform (HTML)

A very short introduction to this mathematical oddity. I have also written freeware Windows program to explore this transform.

timespace rotations, an introduction to special relativity (HTML pages plus diagrams)

There are some essay here already, more being written as we speak, arranged in ascending order of prerequisite math (article 0: none, 1: arithmetic, 2: trig and ideally vector spaces). Each of these is quite suitable to be read on its own, and even readers well versed in relativity are gently nudged to go and read Do slopes add? -- you may enjoy it!

States & Statements
HTML 31 K, T_EX 26 K, dvi 28 K

Projection operators of the form |b><b| are discussed, and a case is being made for the feasibility of using them in stead of kets or bras to identify states. The second half of the article is a Quantum Logic primer.

Fermion statistics and generalised determinants
HTML 22 K, T_EX 22 K, dvi 24 K

A generalisation of the determinant is derived. The Boolean statement representation of states is extended to cover ensembles of identical fermions in the state space for one such particle, using the generalised determinant in the expression for transition probabilities. Curiously, Fermi-Dirac statistics drops out of this "for free" as a consequence of matrix arithmetic.

The Bayes Fisher Shannon metric,
\/¯information as a path integral
HTML multipage, T_EX ?? K, dvi ?? K

This paper is a belated write-up of some stuff i worked out in 1989-1991. It links a Bayesian view of probability to Shannon information, and links the latter, and Fisher quadratic measure, to a metric on the manifold of probability distributions, whose tangent spaces are Hilbert spaces, and which is examined here in a coordinate-free perspective. The paper ends with a foray into quantum information.

Last updated 02·05·26