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i finally started another project: a math blog. the aim of this one is to write about mathematical things which interest me, for example things related to my research. the formulae will be rendered with latex; mathml is simply unuseable so far.
an example post shows a feature with i added to my wp-latex enhancer plugin: (primitive) environments for definitions, theorems, proofs, etc., including a very basic labeling system allowing hyperlinks which jump to the right environment; for example, here’s a link to a lemma in the post. the post features my favorite proof of the fundamental theorem of algebra, using complex analysis.

posted in: computer math www
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while updating some old posts with photos (just designwise, no content changed), i once again experienced a complete lockdown: the server became incredible slow and was floaded with apache processes, and i had to shut down and kill -9 all apache processes several times to be able to continue to do anything except waiting. this isn’t the first time this happend, but this time i had apache’s logging enabled (waiting for something like this) to see what was causing all the accesses. well, out of the 13.000 logfile entries (ranging over a week, i think), around 3.300 were by wordpress – and 99.9% of these happend in the last few hours, while i was updating the old posts. it seems that every time i updated a post, wordpress accesses all links and images in the post, also the local ones, and downloads them. yes, downloads them – also the big versions of panoramas. and if i’m updating posts with often 10–30 photos, some of them large, this clearly explains why the web server was dying. to put it that way, wordpress dosed itself. (the funny thing is that it did not first use a head first, to see what kind of link this is, but starts with a get to first download the whole thing. after downloading all links and images, it uses head on them.)
anyway. i don’t know at the moment what to do against that.
but another annoying thing is that the blog is loading rather slow. i also decided to see what is causing this. well, it turns out that the old main page was doing 298 sql queries. after disabling role scoper, this jumped down to 34, with loading times more or less the same. but then, i disabled the tag cloud. this just saved one query, but reduced the page generation time from around 10 to 2 seconds. wow. enabling role scoper again (i really need that one), i now have a bit less than 50 queries with maybe 4-5 seconds of page creation time.
well, still far from optimal, but already faster.

posted in: daily life thoughts www
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i was thinking on using latex in maybe some blog entries, maybe here or maybe somewhere else. so i decided to see what existing plugins there are. after a bit of searching, i stumbled over wp-latex, which is apparently also used by wordpress.com. unfortunately, it has a kind of clumsy syntax (“$latex formula$” instead of simply “$formula$”). and it has no support for display style formulae, i.e. something centered in its own line, as opposed to inline formulae which try to fit neatly into the text.

so i tried to fix that. and it worked out, and i can still use a “normal” $ by appending a blackslash in front of it. well, euler's identity is e^{i \pi} + 1 = 0, as simple as that. if you want to see something more complicated:

let K be a number field or an algebraic function field. then, we have the following commutative diagram with exact rows and columns:

\xymatrix{ & 0 \ar[d] & 0 \ar[d] & 0 \ar[d] & \\ 0 \ar[r] & \calO^* / k^* \ar[r] \ar[d] & \Div^0_\infty(K) \ar[r] \ar[d] & T \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / k^* \ar[r] \ar[d] & \Div^0(K) \ar[r] \ar[d] & \Pic^0(K) \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / \calO^* \ar[r] \ar[d] & \Id(\calO) \ar[r] \ar[d] & \Pic(\calO) \ar[r] \ar[d] & 0 \\ & 0 & H \ar@{=}[r] \ar[d] & H \ar[d] & \\ & & 0 & 0 & }

here, T simply denotes the cokernel of the map \calO^* \to \Div^0_\infty(K) which assigns to every unit \varepsilon \in \calO^* its principal divisor (\varepsilon); in particular, T \cong \Div^0_\infty(K) / (\Princ(K) \cap \Div^0_\infty(K)). finally, H denotes the cokernel of the degree map \Div(K) \to \G, where in the number field case, \G = \R, and in the function field case, \G = \Z.

this is written as follows:

 1 let \$K\$ be a number field or an algebraic function field. then,
 2 we have the following commutative diagram with exact rows and 
 3 columns: 
 4 \$\$\xymatrix{ & 0 \ar[d] & 0 \ar[d] & 0 \ar[d] & \\ 0 \ar[r] & 
 5 \calO^*  / k^* \ar[r] \ar[d] & \Div^0_\infty(K) \ar[r] \ar[d] & 
 6 T \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / k^* \ar[r] \ar[d] & 
 7 \Div^0(K) \ar[r] \ar[d] & \Pic^0(K) \ar[r] \ar[d] & 0 \\ 0 \ar[r]
 8 & K^* / \calO^* \ar[r] \ar[d] & \Id(\calO) \ar[r] \ar[d] & 
 9 \Pic(\calO) \ar[r] \ar[d] & 0 \\ & 0 & H \ar@{=}[r] \ar[d] & H 
10 \ar[d] & \\ & & 0 & 0 & }\$\$
11 here, \$T\$ simply denotes the cokernel of the map \$\calO^* \to
12 \Div^0_\infty(K)\$ which assigns to every unit \$\varepsilon \in 
13 \calO^*\$ its principal divisor \$(\varepsilon)\$; in particular, 
14 \$T \cong \Div^0_\infty(K) / (\Princ(K) \cap \Div^0_\infty(K))\$. 
15 finally, \$H\$ denotes the cokernel of the degree map \$\Div(K) \to 
16 \G\$, where in the number field case, \$\G = \R\$, and in the 
17 function field case, \$\G = \Z\$.

note that this example also shows a problem: namely, the vertical alignment of the inline formulae sucks bigtime. let's see how to fix this...

posted in: math www
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there was a new version of wordpress out, so i (finally) upgraded. the layout of the admin area completely changed; i already heard about that before. i don’t know if it’s better or worse than the old one, but i stumbled over one thing which is really annoying: in case you write private articles (like me) to ensure that in case the role scoper plugin stops working (or is simply disabled due to upgrades), nobody can see the private stuff (instead of everyone), you will find out that the new version of wordpress automatically publishes articles as soon as the visibility is set to private! this is pretty annoying, as i usually do that as one of the first things before writing (most of) the post itself.
another thing which got worse is the size of the tags field (for the simple tags plugin), which now resides in the right (narrow) column. before, it was prominently seated directly below the area where the post content itself is written (which is rather wide). as i often use a long list of tags, this makes things more confusing than they have to be.

posted in: www
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spielwiese moved to a new server today. it’s way faster now, as you might have already noticed. unfortunately, the ad rotator plugin which i used to display the random lyrics stopped working, probably it doesn’t like the php version running here. maybe i’ll replace it at some point…

today i cleaned up my blog a bit – at least on the technical side. i wrote a plug-in which encapsulates all my changes to wordpress, so the underlying wordpress is now a standard installation, making upgrading way easier.
moreover, as you might have noticed, i added a login box to the right margin. after playing around in the last days a bit, it seems that my goals can be partially resolved using role scoper. well, not perfectly, but at least to some extend. (so there’s still the need to write the optimal blog software.)

posted in: daily life www
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just found on xkcd, and its so right:

(copyright © 2008 xkcd.)

posted in: daily life thoughts www
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while i was searching for a plug-in which allows access control to posts based on users and/or user groups, i stumbled about many different plug-ins, some of them very promising, but either dead, not updated for a long time, or simply not exactly usable by producing a long list of php error messages already in the admin screen after activating them. grrreat. well, of course, i could also try to do it myself, as usual. but hey, that sucks: i’d be better of writing my own blog software.
well, i talked about the problem a bit with kornel, and we concluded that an optimal blog system would be a very slim piece of software, just providing the very basic features, i.e. managing posts, comments and pages, users and user groups/roles/whatever, and access privileges, while everything else—such as galleries, embedding videos, gadgets, comfortable post editors, …—is implemented as plugins.
anyone want’s to do this, and produce a well-documented, slim, bug-free blog system with a good plugin interface, together with a few standard plugins? :)

ever seen such advertisements?

“start making money entering data online!
work from home at your own time. anyone from any where in the world can do this job. available worldwide.
easily make $250+ per day!
fill out simple web forms at home
sign up here >>>>”

sometimes, i really wonder what people got to do if they sign up. my guess is that they are signing up to work as little spam bees: sit at home, surf the web, spam peoples forums, guestbooks, blog comments, … with spam!
let’s face it. during its lifespan, spielwiese got 310 spam comments so far, and blackness got 34 spam comments. and none of them ever got published; i never let them pass through. one would think that they’d maybe give up after some time, but it seems they don’t want to. maybe because they get paid for entering the spam over and over again?
as spielwiese is based on wordpress, which is a rather common blog software, it’s not surprising that there exists programs which feed wordpress based blogs with spam. so maybe the spam for spielwiese is automatically generated. but the software for blackness is completely self-brewn, so either someone is entering the spam manually, or someone adjusted their program to post spam there, too. or someone wrote a program which puts spam in basically everything which looks like a comment form. i’d guess it’s the latter, or some poor fellow gets paid to do it.
anyway.
spam is freaking annoying, both email spam, guestbook spam, forum spam, blog spam, and hopefully once our governments unite and will really try to do something against it. but then, i’d guess that won’t happen during my life…

while reading sp.on, i stumbled over a strange german easter tradition, called schwengellangziehen. apparently extincted in 1962, it apparently was revived this year. the idea is to take a group of young men (probably drunk or half-drunk), let them run in a circle next to a river, faster and faster, until the first ones fall into the river. then, continue with alcohole and partying. sounds… fascinating. what was really fascinating me is that this tradition is taking place in my hometown, lüdinghausen. and believe me, i’ve never heard about that before. never ever. anyway, if you’re curious, want to see some pictures, or read more, take a look at these links.

posted in: daily life www
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