HDTenEightyP/NetNews huggingface dataset:
From: jake@skatter.usask.ca
Subject: Re: Axiom (was ScratchPad II)--one more word.
Organization: University of Saskatchewan
Date: Thu, 5 Nov 1992 22:32:40 GMT

From article <Bx8p1o.3nK@news.cso.uiuc.edu>, by Richard J. Gaylord <gaylord@ux1.cso.uiuc.edu>:
>  btw - the ibm risc 6000 machine that axiom runs on costs  $26,500. 
>  [ i was told that there is no intention to port it to the mac (boo,
> hiss) but that it will go to other unnamed machines eventually.  
> 
> (btw - the new issue of byte mag has a comparision of workstations [ibm
> risc 6000, next, sun, sgi iris, apple quadra, etc] which might be of
> interest to symb. math program users.)

I might add that the next is rather unfairly compared in this review.

jake
--
Jason C. Breckenridge 				jake@skatter.usask.ca

One of the really amazing things is the number of times an almost-empty
toothpaste tube can be forced to give up "just enough".
Newsgroups: sci.math.symbolic
From: maeder@inf.ethz.ch (Roman Maeder)
Subject: Re: Question about programming in mma
Reply-To: maeder@inf.ethz.ch (Roman Maeder)
Organization: Theoretical Computer Science, ETH Zurich
Date: Thu, 12 Nov 1992 15:01:53 GMT

In article <1992Nov11.211405.27798@mlb.semi.harris.com> gsp@mlb.semi.harris.com writes:
> Can someone tell me how to pass symbols as parameters
> in mathematica. (like nlambda or macros in lisp)
> 
> For example, I want to define a function "dropCar" that
> takes a symbol as a parameter and has the side-effect of setting the 
> symbol's value to the "rest" of it's list.
> 
>     dropCar[ symbol_ ] := Block[ {},
>         symbol = Rest[ symbol ] 
> 	]
>         
...

This is simple: special forms correspond the definitions for functions
with attribute HoldFirst:

    In[1]:= SetAttributes[dropCar, HoldFirst]
    
    In[2]:= dropCar[ symbol_ ] := symbol = Rest[ symbol ]
    
    In[3]:= y = { 1.1, 2.2, 3.3 }
    
    Out[3]= {1.1, 2.2, 3.3}
    
    In[4]:= dropCar[y]
    
    Out[4]= {2.2, 3.3}
    
    In[5]:= y
    
    Out[5]= {2.2, 3.3}

Roman Maeder
Newsgroups: sci.math.symbolic
From: aicklen@utdallas.edu (Greg Aicklen)
Subject: Problem with Mma Notebook I/F (Windows)
Organization: Univ. of Texas at Dallas
Date: Fri, 6 Nov 1992 15:48:30 GMT

I am running Mma 2.1 for Windows, Student Edition.  I have noticed that
the Notebook I/F aborts with a memory protection fault a few operations
(Notebook operations, that is) after I make any error attempting to change
the cell style of any cell from Input to Text (other combinations may also
cause this problem, but I haven't checked).

If I don't select the cell using the cell bracket on the right (for example,
if I select the text directly or if no cell is selected), then any attempt
to change the cell style aborts the Notebook frontend.

ANybody else seen this?

Greg Aicklen
aicklen@utdallas.edu
From: kpw105@phys.anu.edu.au (Ken Wessen)
Newsgroups: sci.math.symbolic
Subject: Mathematica package for tensors?
Followup-To: sci.math.symbolic
Date: 7 Nov 1992 01:04:31 GMT
Organization: Theoretical Physics, Australian National University
Distribution: world
NNTP-Posting-Host: 150.203.15.19

Is there a mathematica package floating around that extends the available
functions for manipulating tensors?
If anyone knows of a specific package, or an ftp archive I can search,
please let me know.
Thanks
Ken
Organisation: Westfaelische Wilhelms-Universitaet, Muenster, Germany
Date: Thursday, 12 Nov 1992 16:28:58 MEZ
From: Georg Woeste <WOESTE@DMSWWU1A.UNI-MUENSTER.DE>
Newsgroups: sci.math.symbolic
Subject: Re: What About OCRing Math?
Distribution: world

This seems to be an interessting idea! A database of the
most important mathematical formulars could be interessting
for all persons, which need only results.
the persons, which need only results.

Regards

Georg Woeste
Newsgroups: sci.math.symbolic
From: katherle@daisy.uwaterloo.ca (Kate Atherley)
Subject: Re: MathCad: A front End to Maple???
Organization: University of Waterloo
Date: Thu, 5 Nov 1992 15:32:57 GMT

In article <1992Nov4.143925.27919@news.acns.nwu.edu> williams@casbah.acns.nwu.edu (Gus Williams) writes:
>
>I just recieved a propaganda :^) mailing from MathCad.
>In it they state that the symbolic manipulation in Mathcad is done
>by the "core of Maple's symbolic algebra functionality".
>
>Currently we are looking at purchasing a math package.  The
>notebook interface to Mathcad (I use an SGI workstation) looks
>more appealing than the interface to Mathematica.  
>
>My question is; Is MathCad a basic front end to the symbolic
>capabilities of Maple???

MathCad contains approximately 80 of Maple's over 2000 symbolic
routines.

If you have further questions, please mail us at info@maplesoft.on.ca .

Kate
Waterloo Maple Software Technical Support
support@maplesoft.on.ca
Newsgroups: sci.math.symbolic
From: lars@gsblas.uchicago.edu (Lars Andreas Stole)
Subject: Mma routines for Control, Calculus of Variations, Hamiltonians? 
Reply-To: lars@gsblas.uchicago.edu (Lars Andreas Stole)
Organization: University of Chicago Computing Organizations
Date: Wed, 11 Nov 1992 17:22:55 GMT

I'm looking for a Mathematica notebook or package that finds optimal  
functions to solve a standard control problem.  Are there any out there?   
Thanks in advance.



--
Lars A. Stole 
University of Chicago, GSB 
(312) 702-7309  
lars@gsblas.uchicago.EDU (NeXTMail)
Xref: sparky sci.math:14878 sci.math.symbolic:2959
From: watson@madvax.uwa.oz.au (David Watson)
Newsgroups: sci.math,sci.math.symbolic
Subject: Re: ......  examples of voronoi/dirichlet tesselations ....
Date: 13 Nov 1992 00:59:27 GMT
Organization: Maths Dept UWA
Distribution: world
NNTP-Posting-Host: xanthorrhoea.maths.uwa.oz.au

In article <1992Nov10.031248.4862@cs.wayne.edu>, 
uds@trace.eng.wayne.edu (Seetamraju Udaybhaskar) writes:
|> 
|> qn.1  :	What is a piece of a region that has been `effected' by 
a (voronoi) tessellation ?
|> 	Is it called a `tessel' ?

It may be called a tile, a polygon or polyhedron or polytope depending on the
dimension, a Voronoi neighborhood, a Dirichlet region, or a Thiessen
area-of-influence.  Tesselations may be regular or irregular and based on any
shape or collection of shapes that will fill space locally.
 
|> qn.2  : Are there any other type of tesselations or equivalent terms ?

A triangulation is a type of tesselation (sometimes tessellation) where all the
tiles are triangles.  A simplicial complex is a tesselation of simplices in
any dimension.  A Penrose tiling is a non-periodic tesselation of fixed shapes.
 
|> qn.3  : Could someone please give me a few `one-line' examples where voronoi
|> 	tesselations are popularly used.   I shall look up further on that.

Tesselations are used when spatial aggregates are considered.  A common example
concerns multivariate interpolation and one of the most general approaches to
the generation of representative manifolds such as topographical surfaces uses
the Voronoi tesselation as a basis for natural neighbor interpolation.  We use
that approach here for the study of chaotic behavior in higher dimensions. 

A classic reference for Voronoi tesslations and Delaunay triangulations is
Rogers, C.A., 1964, Packing and covering, Cambridge University Press.

Dave Watson                          Internet: watson@maths.uwa.edu.au
Department of Mathematics            
The University of Western Australia               Tel: (61 9) 380 3359
Nedlands, WA 6009  Australia.                     FAX: (61 9) 380 1028
Newsgroups: sci.math
From: schiller@prl.philips.nl (schiller c)
Subject: Axioms of set theory, infinity and R. Rucker
Originator: schiller@prl.philips.nl
Organization: Philips Research Laboratories, Eindhoven, The Netherlands
Date: Fri, 6 Nov 1992 13:31:38 GMT



In the definition of a set, one axiom is the existence
of infinity. It is one of the usual Zermelo-Fraenkel
axioms.

Reading the book "infinity and the mind" by Rudy Rucker
(by the way, it is delighting), one learns that
there are many different types of infinities which
exist, of different "size". 

Which of these is the infinity specified in the
axioms of set theory ? Is it important to decide this
question ? Does this have any effect on set theory ?



   Christoph Schiller
   
   schiller@prl.philips.nl
   

Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: What is a knot?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 11 Nov 92 21:41:13 GMT

In article <neil.721425760@dehn> neil@dehn.mth.pdx.edu (John Neil) writes:
>jbaez@riesz.mit.edu (John C. Baez) writes:
>
>>In article <COLUMBUS.92Nov6105242@strident.think.com>
>>columbus@strident.think.com (Michael Weiss) writes:
>
>>>How would one define a (tame) knot, intrinsically?  Definitions I am
>>>familiar with either involve modding out by ambient isotopy (in fact
>>there
>>>are subtle points here, I believe-- perhaps someone more knowledgeable
>>>would like to post), or by Reidemeister moves.
>
>>Well, a (tame) knot is just a circle embedded in R^3, or, if you prefer
>>something less intuitive, S^3.  But you seem to be speaking of the
>
>[stuff deleted...]
>
>Actually, if you are talking about a tame knot, you must be MUCH more
>specific than that.  All knots are embeddings of S^1 in S^3.  The tame
>variety are those embeddings which have a FINITE simplicial structure.
>A wild knot, while still an embedding of S^1 in S^3 will not have a FINITE
>simplicial structure.

Hmm - I am a smooth sort of guy, as opposed to a PL (or PC) sort.  So
when I said "embedding" I meant smooth as opposed to topological
embedding.  So my definition of tame knot is okay, no?  

The reason why I prefer working with smooth stuff, diffeomorphisms etc.
is that I am interested in relations of knot theory to gauge theory, not
just topology per se.
Xref: sparky sci.math:14927 alt.true-crime:255 alt.folklore.urban:28434
From: jack@dcs.glasgow.ac.uk (Jack Campin)
Newsgroups: sci.math,alt.true-crime,alt.folklore.urban
Subject: Re: a first year grad student freaks out.
Date: 13 Nov 92 18:46:50 GMT
Reply-To: jack@dcs.glasgow.ac.uk (Jack Campin)
Followup-To: alt.true-crime
Organization: COMANDOS Project, Glesga Yoonie

proberts@informix.com (Paul Roberts) wrote in sci.math:
> RVESTERM@vma.cc.nd.edu writes:
>> what's the deal with this thesis thing? what happens if you
>> simply cannot prove whatever your advisor assigned?
> Oh, you just hang about for ever and ever and eventually you walk into
> your advisors office and kill him with a hammer. They put you away for
> seven years or so (after all, it is *almost* justifiable homocide), you
> eventually get released, still muttering darkly about "other scores
> you still have to settle at Stanfo ...", ooops, at your ex-University.
> No big deal. This is a true story.

OK, I've heard of that one, but could somebody tell us the whole thing and
name names?

While we're at it, what *really* happened to Richard Montague?  (Strangled
in his bath with piano wire by a casual pickup, is the version I heard, but
that was only from one oral source).

[ Note the probably unprecedented crossposting.
  Followups will default to alt.true-crime. ]
-- 
--  Jack Campin    room G092, Computing Science Department, Glasgow University,
17 Lilybank Gardens, Glasgow G12 8RZ, Scotland   TEL: 041 339 8855 x6854 (work)
INTERNET: jack@dcs.glasgow.ac.uk or via nsfnet-relay.ac.uk    FAX: 041 330 4913
BANG!net: via mcsun and uknet     BITNET: via UKACRL    UUCP: jack@glasgow.uucp
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: Mercator Projection
Date: 10 Nov 92 18:51:18 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov10.020408.22139@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>In article <israel.721352141@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B. Israel) writes:
>>If you conformally map the sphere with the North and South poles removed, 
>>1-1 onto a cylinder, don't you have the Mercator projection up to 
>>translation and reflection?

>This would imply that the only conformations (is that the word?) of the
>cylinder onto itself are translations and reflections.  Is that true?

Yes.  The easiest way to see this is to go back to the sphere with poles
removed.  Let f be a conformal mapping of this 1-1 onto itself.  I assume
that f is orientation preserving (this may or may not be part of your
definition of "conformal" - if not, a reflection will fix it).  At the
poles (in the geographical sense), f can't have an essential singularity
because it's 1-1.  So f is a meromorphic function, i.e. extends to a
mapping of the whole sphere to itself.  This will either leave the poles
fixed or interchange them - if it interchanges them, apply a reflection
through the centre of the sphere (corresponding to 180 degree rotation of
the cylinder).  Now map the sphere with North pole removed to the complex
plane by stereographic projection, the South pole mapping to 0.  Then
f corresponds to an entire function with a pole (in the analytic sense)
at infinity, i.e. a polynomial.  Since it maps 0 to itself and is 1-1,
the only possibilities are f(z) = c z for constant, nonzero c.  This is
a two-dimensional, connected group of mappings, so it must correspond to
the translations on the cylinder (also a two-dimensional group of 
conformal mappings).

>-- 
>Vaughan Pratt
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: kanazawa@cs.ubc.ca (Keiji Kanazawa)
Newsgroups: sci.math.stat
Subject: Interface '93
Date: 11 Nov 92 21:41:53 GMT
Organization: UBC Department of Computer Science
NNTP-Posting-Host: miller.cs.ubc.ca


Could somebody please e-mail me a call for papers for Interface '93?

Thanks.

--

Keiji Kanazawa
kanazawa@cs.ubc.ca
From: rosy@cco.caltech.edu (Rosemary Macedo)
Newsgroups: sci.math.stat
Subject: help:  have forecast, need % probability
Date: 5 Nov 1992 18:22:47 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: alumni.caltech.edu

Please help this nonstatistician.

I have a forecast of y.  I know the historical distribution (mean &
st dev) of the forecasts of y, and I know the same for y itself.
How do I calculate the % chance, given FCST(y), that y > 0 or < 0 ?
I also know the mult R of my forecasts with the actual.

Please reply to rosy@alumni.caltech.edu
Thanks in advance for help.  (My access to reference books in statistics is 
rather  limited).r
From: ron@argus.lpl.Arizona.EDU (Ron Watkins)
Newsgroups: sci.math.stat
Subject: Correlations of small N (Jacknife???)
Keywords: Jacknife correlations
Date: 12 Nov 92 18:07:30 GMT
Distribution: usa
Organization: Lunar and Planetary Lab, U of AZ

Im looking for references to correlations of small numbers of numbers (small N).
I have heard the name Jacknife tossed about but I don't know of it nor do I
know of any references to it.
Can someone point me to sources of information about either of these topics?
I don't have a background in statistics and I don't know of any on-line
archives or other resources related to this topic either. Please direct
responces via e-mail to: ron@argus.lpl.arizona.edu
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ron Watkins    [ron@argus.lpl.arizona.edu]     /             _____      /
931 Gould-Simpson bldg.                       /             /    /     /
University of Arizona                        /             /____/     /
Tucson, AZ. 85721                           /             /          /
(602) 621-8606                             /_____ unar & / lanetary /_____ ab.
From: gdal@gdalsrv.sas.upenn.edu (GDAL Manager)
Newsgroups: sci.math.stat
Subject: Software for CART on PCs
Date: 12 Nov 92 18:27:06 GMT
Organization: Social Science Computing, University of Pennsylvania


  What DOS-based software packages are available to handle CART
(Classification And Regression Trees)? I'm aware of S-Plus. Is there
anything else?


George
-- 
gdal@gdalsrv.sas.upenn.edu		Social Science Computing
theall@gdalsrv.sas.upenn.edu		University of Pennsylvania
From: mikem@stat.cmu.edu (Mike Meyer)
Newsgroups: sci.math.stat
Subject: New StatLib entries for October 1992
Date: 6 Nov 92 02:57:16 GMT
Article-I.D.: war.9211061257.AA15531
Organization: Carnegie Mellon, Pittsburgh, PA

The following is a short list of the new or modified StatLib entries
for October 1992 (until 6 November 1992).

S		mclust		# Update
		sguide.ps1	# Update
		sguide.ps2	# Update
		boxmat		# boxplot matrices in S and lispstat

s-news		No new digests  :-(

datasets	sapa		# Time series from a book
		econdata	# Pointer to collection of econ data


general		xgobi.src	# Update
		mclust		# Update


jcgs		abstract.v1.1   # abstracts from issues
		abstract.v1.2   #  1 and 2

xlispstat	boxmat		# boxplot matrices in S and lispstat


To get started using StatLib, send the one line message
	send index
to statlib@lib.stat.cmu.edu

StatLib also has an anonymous FTP facility.
Use ftp to connect to lib.stat.cmu.edu and login with user name
"statlib".  PLEASE send your e-mail address as your password.  This
will enable us to notify you of changes to the software and notify the
contributors about who has requested the software.

A reminder that there is also an archive of SAS related material.
Send the message
	send sas from general
for details about the SAS-L archive.

Thanks to all the contributors -- please keep the contributions
coming! 

Mike Meyer, Carnegie Mellon.

================================================================
From: bateman@nsslsun.nssl.uoknor.edu (Monte Bateman)
Newsgroups: sci.math.stat
Subject: Thanks for the help!  (Re: Testing for Normality)
Date: 5 Nov 92 15:24:03 GMT
Article-I.D.: constell.1992Nov5.152403.15807
Organization: National Severe Storms Laboratory
Originator: usenet@kittyhawk.ecn.uoknor.edu

A couple months ago, I posted a question about testing for Normality in
a data set.  Thanks to the following for help:

	thompson@atlas.socsci.umn.edu (T. Scott Thompson)
	hrubin@pop.stat.purdue.edu (Herman Rubin)
	jerry@ginger.hnrc.tufts.edu (Jerry Dallal)
	chaas@coe.drexel.edu (Chuck Haas)
	rizzo@cbnewsf.cb.att.com (anthony.r.rizzo)
	gagnon@buma15.bu.edu (David Gagnon)
	jsvrc@rc.rit.edu (J A Stephen Viggiano)
	nichols@spss.com (David Nichols)
	alanm@cognos.com (Alan Myrvold)
	wvenable@algona.stats.adelaide.edu.au (Bill Venables)
	martin@biostat.washington.edu (Don Martin) 

Sorry for not responding sooner; I was busy finishing my dissertation.
Based on the advice I received, I used the Kolmogorov-Smirnov test for
fit to a normal distribution.

Thanks again!
Monte

--
===============================================================================
Monte Bateman, WB5RZX -- Physics PostDoc
Langmuir Laboratory for Atmospheric Research
New Mexico Institute of Mining and Technology, Socorro, NM

InterNet: bateman @ owl.nmt.edu
From: wvenable@algona.stats.adelaide.edu.au (Bill Venables)
Newsgroups: sci.math.stat
Subject: Re: Is the logarithmic transformation monotonic?
Date: 12 Nov 92 16:36:19
Organization: Department of Statistics, University of Adelaide
NNTP-Posting-Host: algona.stats.adelaide.edu.au
In-reply-to: mikef@dph1.health.su.OZ.AU's message of Thu, 12 Nov 1992 04:58:20 GMT

>>>>> "Michael" == mikef <mikef@dph1.health.su.OZ.AU> writes: 

Michael> I have needed to make comparisons between variances of some random
Michael> variable X, var(X). Specifically, I needed to know if var(X=a) >
Michael> var(X=b).  However, I was only able to compute var(lnX), and have
Michael> made the comparison between var(ln{X=a}) and var(ln{X=b}).

As it stands Michael this does not really make any sense.  However if your
question amounts to the following:

"Is it true that var[log(X)] > var[log(Y)]  implies  var[X] > var[Y]  where
 X and Y are positive random variables?"

then the answer is "No, it doesn't", (even though log(x) is indeed a
monotone increasing function for positive values of x).  

Just consider a simple sample case and put, say ,

		 X = {110, 120, 130} and Y = {10, 11, 12}.

Then var[X] = 100 and var[Y] = 1 so var[X] > var[Y].  

On the other hand var[log(X)] = .0069808 and var[log(Y)] = .008316 so
var[log(X)] < var[log(Y)].

It comes about because on the one hand var[c + X] is the same for all
constants c, whereas var[log(c*X)] is the same for all positive constants
c.  By trading these off one against the other you can make the direction
of the inequalities go either way.

Bill
--
___________________________________________________________________________
Bill Venables, Dept. of Statistics, | Email: venables@stats.adelaide.edu.au
Univ. of Adelaide, South Australia. | Tel: +61 8 228 5412  Fax: ...232 5670
Newsgroups: sci.math.stat
From: stdngohy@cicero.spc.uchicago.edu (Hang-Yue)
Subject: Re: Help With Statistics on "Compressed Data"
Keywords: statistics, compressed data,
Organization: U of Chicago, SSPPCC
Date: Thu, 5 Nov 1992 19:39:55 GMT


 Since there is threshold and you want normal errors, then you should
 use the truncated normal distribution.

 H.Y. Ngo
 ----------
 An sociology student who has some interests in Statistics.
Newsgroups: sci.math.stat
From: hauser@statrix2.wu-wien.ac.at (Michi Hauser)
Newsgroups: sci.math.stat
Subject: Re: generating correlated random numbers
Date: 5 Nov 1992 22:53:01 GMT
Organization: Wirtschaftsuniversitaet Wien
Distribution: all
NNTP-Posting-Host: statrix2.wu-wien.ac.at


You want a long series with a given autocorrelation structure.

Low order ARMA models are used to model the autocorrelation 
structure of weakly stationary processes. 

(1- a_1L - a_2L^2 - ... - a_pL^p) x_t =
        (1 - b_1L - b_2L^2 - ... - b_qL^q) u_t

u_t ... white noise

If you reverse the procedure and start with a special choice 
of the parameters you obtain a certain covariance structure. 
Cooose the parameters so that you end up with the desired C matrix. 
You find the formula in any times series book.

MA(q) processes have a C matrix with a (2q+1)-band structure,
AR(1) processes an infinte matrix with geometrically decreasing 
coefficients (c_i.) .
The actual generation by

x_t = a_1 x_(t-1) + ... + a_p x_(t-p) - 
           - u_t - b_1 u_(t-1) - ... - b_q u_(t-q)

needs starting values for x_(t-i) ,i=1,...,p  and some u_(t-j) .
The latter are white noise and no problem.

The effect of the x`s, however, should be neglegible.  
How quickly this starting value effect dies out depends on the 
roots of the AR polynomial:
roots close to the unit circle take a long time,
roots far away of the unit circle ( |z| >> 1 ) take only a short time.

E.g. AR(1): corr( x_t,x_(t-i) )= a_1^i  
( 0.1^10 = very small, 0.9^10=0.349 ! )

Remark:
For MA-type correlation structures there is no need to factorize 
the band matrix this method is equally exact.
 
Best wishes Michael

email: hauser@wu-wien.ac.at
From: atteson@grip.cis.upenn.edu (Kevin Atteson)
Newsgroups: sci.math.stat
Subject: exponential bounds for Markov chains, etc.
Date: 9 Nov 92 16:13:02 GMT
Distribution: usa
Organization: GRASP Lab, University of Pennsylvania


I'm interested in the speed of convergence of frequencies to probabilities
for Markov chains and possibly more general random processes.
Any general information concerning this subject would be apprecaited
but also I have the following specific question.
In the 2nd edition of the book "Probability and Random Processes" by
Grimmett and Stirzaker, at about the middle of page 452, they say
of Markov chains,

	"The convergence is rather fast, as the following
	(somewhat overcomplicated) argument indicates...skip about a page...
	Similar inequalities may be established by other means,
	more elementary than those used above."

I'd like to hear about these more elementary means.  Does
anyone know what they are referring to or how I can contact
the authors?

Please reply directly to me.

Newsgroups: sci.math.stat