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LaTEX -

- To use WebEQ, you must use a browser that can run Java applets. This immediately excludes a large fraction of your readers. Java is also known to pose security risks.
- The applet takes a long time to load. Upon visiting the WebEQ home page, it took 40 seconds for me to see one equation.
- You can't print any of the output from WebEQ.
- WebEQ isn't extensible or reconfigurable.
- WebEQ expects you to write your equations in a highly presentational language that is based half on TEX and half on the expired HTML 3.0 draft. It is not especially complicated, but it is tedious because there are no definitions for common mathematical constructs: you basically do the layout yourself. Moreover, the limited nature of the medium makes it difficult for your equation to be presented in a text-based browser or using a speech synthesis system.
- To put an equation into your document, you have to insert an APPLET element and then place PARAM tags within it to provide the expression, which increases typing and makes editing inconvenient. This combines with the presentational syntax to make for a lot of code even for the simplest expressions.

On the other hand, with MINSE, neither you nor your reader has to have any special software in particular. Right now MINSE can render equations to both GIF images and text -- you get two versions of the same document with no extra effort on your part! Even without a polymediator, MINSE expressions are simple enough that you can read them and figure out what they mean when they appear in an unmediated browser.

Here's an example of what you have to provide WebEQ.
This is the equation on the WebEQ home page at
`http://www.geom.umn.edu/software/WebEQ/`

:

This is how you would write the same thing for the MINSE mathematics context:<APPLET CODEBASE=bin CODE=WebEQ.class HEIGHT=90 WIDTH=285> <PARAM NAME=SIZE VALUE=36> <PARAM NAME=LINE1 VALUE=" f(ζ)=<BOX><BOX SIZE=SMALLER>1</BOX><OVER>"> <PARAM NAME=LINE2 VALUE="<BOX SIZE=SMALLER>2πi</BOX></BOX>"> <PARAM NAME=LINE3 VALUE="∫<SUB ALIGN=CENTER>γ</SUB>"> <PARAM NAME=LINE4 VALUE="<BOX>f(z)<OVER>z-ζ</BOX> dz"> </APPLET>

<se> f(?zeta?) = 1/(2*'pi*'i) * 'integ(f(z)/(z-?zeta?),z,?gamma?,) </se>

It gets more unfortunate when you want to include just a small equation fragment many times in a section of text. To produce a single Greek capital omega, we find the following on a page about graduate courses at Washington University:

With MINSE this would simply be<APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET>

In the original document, the above APPLET element has to appear many times, turning a single paragraph into the following mess:<se> ?Omega? </se>

<P>Next, we'll take up the Dirichlet problem: Given a continuous function f on the boundary of a domain <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET>, find a function u harmonic in <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET> and continuous on the closure of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET> which equals f on the boundary of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET>. Among the numerous methods for attacking this problem are Perron's method (Let u be the sup of a certain family of subharmonic functions), Dirichlet's principle (Let u be the function in the closure of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET> which equals f on the boundary of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET> and has minimal Dirichlet integral <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=35 WIDTH=70 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="∫<sub>Ω</sub>|∇ u|<sup>2</sup>"></APPLET>, and Brownian motion, (u(z) is the expected value of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=35 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="f(B_τ_)"></APPLET>), where <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=30 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="B_τ_"></APPLET> denotes two-dimensional Brownian motion started at z and stopped the first time it hits the boundary of <APPLET CODEBASE=../../bin CODE=WebEQ.class HEIGHT=25 WIDTH=20 ALIGN=top> <PARAM NAME=size VALUE=18> <PARAM NAME=color VALUE=0xffffff> <PARAM NAME=line1 VALUE="Ω"></APPLET>). Associated with the Dirichlet problem are <em>Green functions</em> and <em>harmonic measures</em> of domains.

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since Mon 17 Jun 1996