<?xml version="1.0" encoding="utf-8"?>
<rss version="2.0" xml:base="http://oheric.com" xmlns:dc="http://purl.org/dc/elements/1.1/">
<channel>
 <title>Recent stories</title>
 <link>http://oheric.com/tracker</link>
 <description>Shows all new activity on system.</description>
 <language>en</language>
<item>
 <title>spec: generic sync plugin for Songbird</title>
 <link>http://oheric.com/share/shared_draft/spec_generic_sync_plugin_songbird</link>
 <description>	&lt;p&gt;I was going to whip up a python script to sync music to my mass-storage phone, but since I am using Songbird on all my platforms, the little extra effort to make a Songbird sync plugin will pay off big for me, and also be useful to lots of others. &lt;/p&gt;

	&lt;h3&gt;the spec&lt;/h3&gt;

	&lt;p&gt;Works with: &lt;span class=&quot;caps&quot;&gt;USB&lt;/span&gt; mass storage devices&lt;br /&gt;
Options:
	&lt;ul&gt;
		&lt;li&gt;select connected device (persist selection?)&lt;/li&gt;
		&lt;li&gt;select disk usage setting (min free space or total usage?)&lt;/li&gt;
		&lt;li&gt;select playlists (these are songbird playlists, and may be ie mp3 blogs or rss feeds)&lt;/li&gt;
	&lt;/ul&gt;&lt;/p&gt;

	&lt;p&gt;Behavior on sync:
	&lt;ul&gt;
		&lt;li&gt;remove oldest items&lt;/li&gt;
		&lt;li&gt;add newest items (so that disk usage is balanced among playlists or just so that newest items are available?)&lt;/li&gt;
		&lt;li&gt;optional renaming to maintain original playlist order (ie sequence-based naming)&lt;/li&gt;
	&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/share/shared_draft/spec_generic_sync_plugin_songbird&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/share/shared_draft/spec_generic_sync_plugin_songbird#comments</comments>
 <category domain="http://oheric.com/share/shared_draft">drafts</category>
 <pubDate>Tue, 16 Dec 2008 12:01:38 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">106 at http://oheric.com</guid>
</item>
<item>
 <title>Drupal as Open Architecture</title>
 <link>http://oheric.com/engineer/projects/drupal/drupal_open_architecture</link>
 <description>	&lt;p&gt;Wish I had seen &lt;a href=&quot;http://news.oreilly.com/2008/08/drupal-as-open-architecture.html&quot;&gt;this&lt;/a&gt; in August after &lt;span class=&quot;caps&quot;&gt;OSCON&lt;/span&gt;, but it really strikes a chord. I&amp;#8217;ve been a Drupal dev for a long time, and have recently been focusing on the newer &amp;#8220;agile frameworks&amp;#8221; in Python and Ruby, and I&amp;#8217;ve found the same shortcoming: there is no component architecture, at least not on the level of Drupal with its myriad callback hooks and &amp;#8220;monkey patching&amp;#8221; facilities. I&amp;#8217;ve been ruminating on the idea of following the Drupal architecture to build a similar framework on top of &lt;span class=&quot;caps&quot;&gt;WSGI&lt;/span&gt;.&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/engineer/projects/drupal/drupal_open_architecture&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/engineer/projects/drupal/drupal_open_architecture#comments</comments>
 <category domain="http://oheric.com/engineer/projects/drupal">drupal</category>
 <pubDate>Fri, 21 Nov 2008 00:21:16 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">105 at http://oheric.com</guid>
</item>
<item>
 <title>Personal Document Management</title>
 <link>http://oheric.com/organize/personal_document_management</link>
 <description>	&lt;p&gt;I hate the boxes of paper records I have to lug around. &lt;/p&gt;

	&lt;p&gt;Some of the types of documents in my life:&lt;/p&gt;

	&lt;ul&gt;
		&lt;li&gt;Records of:
	&lt;ul&gt;
		&lt;li&gt;Financial transactions&lt;/li&gt;
		&lt;li&gt;Taxes&lt;/li&gt;
		&lt;li&gt;Contracts&lt;/li&gt;
		&lt;li&gt;Business cards&lt;/li&gt;
		&lt;li&gt;Academic certificates&lt;/li&gt;
	&lt;/ul&gt;&lt;/li&gt;
		&lt;li&gt;Papers I&amp;#8217;ve written
	&lt;ul&gt;
		&lt;li&gt;Math&lt;/li&gt;
		&lt;li&gt;Creative writing&lt;/li&gt;
	&lt;/ul&gt;&lt;/li&gt;
	&lt;/ul&gt;

	&lt;p&gt;My goal is to put all my documents (paper and digital) into a single cross-referenced document management system with flexible metadata. Eric Blue &lt;a href=&quot;http://eric-blue.com/2008/05/18/document-management-systems-scan-smart-content-aggregation-and-navigation/&quot;&gt;recommends&lt;/a&gt;  &lt;a href=&quot;http://scan.sourceforge.net&quot;&gt;SCAN&lt;/a&gt;. From what I see, it looks simple and highly useful! I may start using this system and then convert to something else (probably a custom system based on &lt;span class=&quot;caps&quot;&gt;RDF&lt;/span&gt;). I just purchased a nice scanner, so I&amp;#8217;m going to implement this right away!&lt;/p&gt;

	&lt;p&gt;This fits into a larger goal of creating a unified model of all the entities I interact with, across all media.&lt;/p&gt;

	&lt;p&gt;Paper &amp;rarr; Image &amp;rarr; &lt;span class=&quot;caps&quot;&gt;PDF&lt;/span&gt; &amp;rarr; &lt;span class=&quot;caps&quot;&gt;SCAN&lt;/span&gt; metadata store&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/organize/personal_document_management&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/organize/personal_document_management#comments</comments>
 <category domain="http://oheric.com/organize">organize</category>
 <pubDate>Tue, 07 Oct 2008 16:42:38 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">103 at http://oheric.com</guid>
</item>
<item>
 <title>Panels for Django</title>
 <link>http://oheric.com/engineer/web/panels_django</link>
 <description>	&lt;p&gt;I &amp;hearts; &lt;a href=&quot;http://drupal.org/project/panels&quot;&gt;Panels&lt;/a&gt; (it does the simple layout on this blog, but it&amp;#8217;s capable of much more advanced usage).&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/engineer/web/panels_django&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/engineer/web/panels_django#comments</comments>
 <category domain="http://oheric.com/engineer/web">web</category>
 <pubDate>Mon, 06 Oct 2008 11:41:56 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">102 at http://oheric.com</guid>
</item>
<item>
 <title>Pro-tip: jEdit on network drive</title>
 <link>http://oheric.com/social_media/pro_tip_jedit_network_drive</link>
 <description>	&lt;p&gt;Most school networks provide users a personal network folder mounted as a Windows network drive and accessible from any campus workstation. This is primarily meant as a document folder, but executable programs can be stored here too. I have several useful programs in my network folder, but the most useful by far is jEdit.  The same copy runs on both Windows and Mac workstations, with the same plugins and configuration options. &lt;/p&gt;

	&lt;p&gt;To use jEdit in a network environment, just make sure that your jEdit user settings directory is stored on in your network folder by launching jEdit with &lt;/p&gt;

	&lt;blockquote&gt;
		&lt;p&gt;&amp;#8220;jedit.jar -settings=P:/ath/to/your/folder/.jedit&amp;#8221; &lt;/p&gt;
	&lt;/blockquote&gt;

	&lt;p&gt;via an application shortcut in windows, or a shell script on Mac/Linux (jEdit is an executable jar). Enjoy!&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/social_media/pro_tip_jedit_network_drive&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/social_media/pro_tip_jedit_network_drive#comments</comments>
 <category domain="http://oheric.com/social_media">share</category>
 <pubDate>Sun, 05 Oct 2008 20:24:25 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">101 at http://oheric.com</guid>
</item>
<item>
 <title>Can Paper Think?</title>
 <link>http://oheric.com/share/shared_draft/can_paper_think</link>
 <description>&lt;p&gt;An empty husk of a posting.&lt;/p&gt;
</description>
 <comments>http://oheric.com/share/shared_draft/can_paper_think#comments</comments>
 <category domain="http://oheric.com/share/shared_draft">drafts</category>
 <pubDate>Sun, 05 Oct 2008 13:59:45 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">100 at http://oheric.com</guid>
</item>
<item>
 <title>Portable Document Repository</title>
 <link>http://oheric.com/organize/portable_document_repository</link>
 <description>	&lt;p&gt;Microcontent can be easily transferred between infosystems. Simpler data formats are simply more portable.&lt;/p&gt;

	&lt;p&gt;By organizing your information as microcontent, you can easily implement various distributed workflows, including&lt;/p&gt;

	&lt;ul&gt;
		&lt;li&gt;local checkout of individual items&lt;/li&gt;
		&lt;li&gt;consolidation (aggregation)&lt;/li&gt;
	&lt;/ul&gt;

	&lt;p&gt;As the device market gets more complicated, .&lt;span class=&quot;caps&quot;&gt;NET&lt;/span&gt; and Java propose to achieve portability through homogeneity, but the browser remains the single (somewhat) universally available client platform. The key difference is that the web grew around portable data formats, not portable code.&lt;/p&gt;

&lt;p&gt;&lt;a href=&quot;http://oheric.com/organize/portable_document_repository&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/organize/portable_document_repository#comments</comments>
 <category domain="http://oheric.com/organize">organize</category>
 <pubDate>Sat, 04 Oct 2008 17:53:12 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">99 at http://oheric.com</guid>
</item>
<item>
 <title>Serving web content from flat files (RDF, Git, Textile, XHTML)</title>
 <link>http://oheric.com/social_media/serving_web_content_flat_files_rdf_git_textile_xhtml</link>
 <description>	&lt;p&gt;At the &lt;span class=&quot;caps&quot;&gt;OSCON&lt;/span&gt; Django meetup last Tuesday I asked some &lt;a href=&quot;http://www.vim.org/&quot;&gt;vim&lt;/a&gt; aficionados how they managed to keep their .vimrcs synchronized between different hosts. I myself prefer to use a network-aware editor like &lt;a href=&quot;http://jedit.org&quot;&gt;jEdit&lt;/a&gt; and &lt;a href=&quot;http://kde.org/&quot;&gt;KDE&lt;/a&gt;&amp;#8217;s &lt;a href=&quot;http://kate-editor.org/&quot;&gt;kate&lt;/a&gt; to avoid platform quirks.&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/social_media/serving_web_content_flat_files_rdf_git_textile_xhtml&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/social_media/serving_web_content_flat_files_rdf_git_textile_xhtml#comments</comments>
 <category domain="http://oheric.com/social_media">share</category>
 <pubDate>Sun, 27 Jul 2008 15:19:31 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">97 at http://oheric.com</guid>
</item>
<item>
 <title>Summer</title>
 <link>http://oheric.com/life/summer</link>
 <description>	&lt;p&gt;I won&amp;#8217;t be taking any other math classes this Summer (except 2 credit independent study), and the work I&amp;#8217;ll be doing is bound to be highly personal. We&amp;#8217;re talking, tricked out home site and portfolio, doing work with friends such as the relaunch of of Marjorie Bevis&amp;#8217; &lt;a href=&quot;http://www.marbledfabrics.com&quot;&gt;Marbled Fabrics&lt;/a&gt;, and perhaps the genesis of some sort of local peer-commerce/underground economy social networking site, which has been in conceptual stages among &lt;a href=&quot;http://heather.homelinux.org/&quot;&gt;my&lt;/a&gt; &lt;a href=&quot;http://xolotl.org/&quot;&gt;friends&lt;/a&gt;.&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/life/summer&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/life/summer#comments</comments>
 <category domain="http://oheric.com/wanderer">drift</category>
 <pubDate>Sat, 24 May 2008 14:25:57 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">62 at http://oheric.com</guid>
</item>
<item>
 <title>Nokia 770 Hackathon Notes</title>
 <link>http://oheric.com/nokia770/nokia_770_hackathon_notes</link>
 <description>	&lt;p&gt;Poky linux 3.1.
	&lt;ul&gt;
		&lt;li&gt;supports 770 with image&lt;/li&gt;
		&lt;li&gt;doesn&amp;#8217;t come with wifi driver, power mgmt&lt;/li&gt;
	&lt;/ul&gt;&lt;/p&gt;

	&lt;h3&gt;Wireless&lt;/h3&gt;

	&lt;p&gt;Chipset is &lt;a href=&quot;https://garage.maemo.org/projects/cx3110x/&quot;&gt;cx3110&lt;/a&gt; with &lt;a href=&quot;http://svn.o-hand.com/view/poky/trunk/meta/packages/cx3110x/&quot;&gt;bitbake recipe&lt;/a&gt; in poky. How to build this in an image?&lt;/p&gt;

	&lt;ul&gt;
		&lt;li&gt;power-management&lt;/li&gt;
	&lt;/ul&gt;</description>
 <comments>http://oheric.com/nokia770/nokia_770_hackathon_notes#comments</comments>
 <category domain="http://oheric.com/consumer/gadgets">gadgets</category>
 <pubDate>Tue, 08 Apr 2008 23:48:42 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">61 at http://oheric.com</guid>
</item>
<item>
 <title>Intro to Sage</title>
 <link>http://oheric.com/research/maths_0/intro_sage</link>
 <description>	&lt;p&gt;&lt;div style=&quot;float: right; padding:0 1em 0 1em;&quot;&gt;&lt;h4&gt;Useful Links&lt;/h4&gt;
	&lt;ul&gt;
		&lt;li&gt;&lt;a href=&quot;http://sagemath.org&quot;&gt;Sage&lt;/a&gt;&lt;/li&gt;
		&lt;li&gt;&lt;a href=&quot;http://sagenb.org&quot;&gt;Public Sage Server&lt;/a&gt;&lt;/li&gt;
		&lt;li&gt;&lt;a href=&quot;http://del.icio.us/ericdrex/sage&quot;&gt;Sage teaching materials and examples&lt;/a&gt; &lt;/li&gt;
	&lt;/ul&gt;&lt;/p&gt;

	&lt;p&gt;&lt;/div&gt;&lt;/p&gt;

	&lt;h3&gt;Sage is&amp;#8230;&lt;/h3&gt;

	&lt;ul&gt;
		&lt;li&gt;A general purpose &lt;strong&gt;symbolic computer algebra system&lt;/strong&gt; (&lt;span class=&quot;caps&quot;&gt;CAS&lt;/span&gt;) like Mathematica, Maple, Magma, etc.&lt;/li&gt;
		&lt;li&gt;Designed to be &lt;strong&gt;accessible and useful right away&lt;/strong&gt; for people with some math background.&lt;/li&gt;
		&lt;li&gt;Accessed through your browser.&lt;/li&gt;
		&lt;li&gt;Powerful, as we shall see&amp;#8230;&lt;/li&gt;
	&lt;/ul&gt;

	&lt;h3&gt;Why Sage? We have Mathematica&amp;#8230;&lt;/h3&gt;

	&lt;ul&gt;
		&lt;li&gt;Cost. &lt;/li&gt;
	&lt;/ul&gt;&lt;p&gt;&lt;a href=&quot;http://oheric.com/research/maths_0/intro_sage&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/research/maths_0/intro_sage#comments</comments>
 <category domain="http://oheric.com/scholar/maths">maths</category>
 <category domain="http://oheric.com/codify">wonder</category>
 <pubDate>Tue, 29 Jan 2008 16:53:02 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">59 at http://oheric.com</guid>
</item>
<item>
 <title>Homepage Dreams</title>
 <link>http://oheric.com/home/homepage_dreams</link>
 <description>&lt;p&gt;I would like to get my homepage in shape (easier than myself). I saw &lt;a href=&quot;http://therning.org/magnus/&quot;&gt;Magnus&#039; homepage&lt;/a&gt; and was inspired. Magnus is the author of the &lt;a href=&quot;http://therning.org/magnus/computer/epilicious&quot;&gt;Epilicious&lt;/a&gt;  extension for Gnome&#039;s Epiphany web browser.  I found his site while trying to file a bug report for same. He is interested in some of the same things as I am, but his site is well-organized, friendly to navigate, and full of content.&lt;/p&gt;
&lt;p&gt;&lt;a href=&quot;http://oheric.com/home/homepage_dreams&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/home/homepage_dreams#comments</comments>
 <pubDate>Fri, 18 Jan 2008 21:38:20 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">57 at http://oheric.com</guid>
</item>
<item>
 <title>Getting my hands dirty with MTH 421 ODEs</title>
 <link>http://oheric.com/research/maths_0/getting_my_hands_dirty_mth_421_odes</link>
 <description>&lt;p&gt;The author of my &lt;a href=&quot;http://en.wikipedia.org/wiki/Ordinary_differential_equation&quot;&gt;ODE&lt;/a&gt; text V.I. Arnold giving the modern (last 50 years) abstract mathematics curriculum a &lt;a href=&quot;http://pauli.uni-muenster.de/~munsteg/arnold.html&quot;&gt;sound flogging&lt;/a&gt;. Quite entertaining IMO.&lt;/p&gt;
</description>
 <comments>http://oheric.com/research/maths_0/getting_my_hands_dirty_mth_421_odes#comments</comments>
 <category domain="http://oheric.com/scholar/maths">maths</category>
 <category domain="http://oheric.com/codify">wonder</category>
 <pubDate>Wed, 16 Jan 2008 22:28:54 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">56 at http://oheric.com</guid>
</item>
<item>
 <title>PSU BS Mathematics Planner</title>
 <link>http://oheric.com/psu_bs_mathematics_planner</link>
 <description>&lt;p&gt;&lt;a href=&quot;http://www.mth.pdx.edu/programs/BS-major.asp&quot;&gt;BS Math requirements&lt;/a&gt;&lt;br /&gt;
&lt;strong&gt;Unfilled:&lt;/strong&gt;
&lt;ol&gt;
&lt;li&gt;Mth 256 or Mth 421: Differential Equations&lt;/p&gt;
&lt;li&gt;Mth 311, 312: Advanced Calculus
&lt;li&gt;Mth 344: Group Theory
&lt;/ol&gt;
&lt;p&gt;&lt;strong&gt;PSU BS Requirements:&lt;/strong&gt;
&lt;ul&gt;
&lt;li&gt;2 terms Foreign language&lt;/p&gt;
&lt;li&gt;Upper-division cluster (12 credits)
&lt;li&gt;Senior capstone (6 credits)
&lt;/ul&gt;
&lt;p&gt;Enroll in &lt;a href=&quot;http://www.mth.pdx.edu/programs/dept-honors.asp&quot;&gt;honors program&lt;/a&gt;?&lt;/p&gt;
</description>
 <comments>http://oheric.com/psu_bs_mathematics_planner#comments</comments>
 <pubDate>Fri, 21 Sep 2007 14:15:32 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">55 at http://oheric.com</guid>
</item>
<item>
 <title>Useful Drupal Links</title>
 <link>http://oheric.com/drupal/useful_drupal_links</link>
 <description>&lt;ul&gt;
&lt;li&gt;&lt;a href=&quot;http://api.drupal.org&quot;&gt;API Documentation for Drupal core&lt;/a&gt;&lt;/p&gt;
&lt;li&gt;&lt;a href=&quot;http://drupal.org/project/modules&quot;&gt;Contrib module project pages&lt;/a&gt;. Issue tracking, CVS browser, releases, documentation.
&lt;li&gt;&lt;a href=&quot;http://lists.drupal.org/listinfo&quot;&gt;Drupal Lists&lt;/a&gt;
&lt;li&gt;&lt;a href=&quot;irc://irc.freenode.net/drupal-support&quot;&gt;#drupal-support on freenode&lt;/a&gt;&lt;br /&gt;
&lt;p&gt;&lt;a href=&quot;http://oheric.com/drupal/useful_drupal_links&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/drupal/useful_drupal_links#comments</comments>
 <category domain="http://oheric.com/engineer/projects/drupal">drupal</category>
 <pubDate>Thu, 09 Aug 2007 12:37:27 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">53 at http://oheric.com</guid>
</item>
<item>
 <title>Back in Portland...</title>
 <link>http://oheric.com/life/back_portland</link>
 <description>&lt;p&gt;... for the third time this week, a record.&lt;br /&gt;
&lt;img src=&quot;http://oheric.com/sites/oheric.com/files/Photo 161.jpg&quot; alt=&quot;&quot; /&gt;&lt;br /&gt;
I&#039;m staying the night at the Washington Park Inn, an affordable option downtown since the NW Intl Hostel is full up. Hope to sleep long and sweet tonight. View of downtown, bridges, construction:&lt;br /&gt;
&lt;img src=&quot;http://oheric.com/sites/oheric.com/files/Photo 163.jpg&quot; alt=&quot;&quot; /&gt;&lt;br /&gt;
Dinner care of Fred Meyer&#039;s deli, leftovers in the mini-fridge.&lt;/p&gt;
&lt;p&gt;My things to do list is as follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Get cash (onpoint) since I left my debit card at Heather&#039;s.&lt;br /&gt;
&lt;p&gt;&lt;a href=&quot;http://oheric.com/life/back_portland&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/life/back_portland#comments</comments>
 <category domain="http://oheric.com/wanderer">drift</category>
 <pubDate>Sun, 29 Jul 2007 18:34:31 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">51 at http://oheric.com</guid>
</item>
<item>
 <title>My Friends</title>
 <link>http://oheric.com/home/my_friends</link>
 <description>&lt;p&gt;&lt;a href=&quot;http://akuatuta.freeservers.com/&quot; title=&quot;http://akuatuta.freeservers.com/&quot;&gt;http://akuatuta.freeservers.com/&lt;/a&gt;&lt;/p&gt;
</description>
 <comments>http://oheric.com/home/my_friends#comments</comments>
 <pubDate>Tue, 24 Jul 2007 16:02:28 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">50 at http://oheric.com</guid>
</item>
<item>
 <title>plant and animal sightings (and lichens)</title>
 <link>http://oheric.com/web/plant_and_animal_sightings_and_lichens</link>
 <description>&lt;p&gt;Me and Heather are going to make a website! We take lots of pictures of native plants, animals, lichens etc, and this will be a database of amateur sightings. Of course anybody can contribute their own sightings, and we will have a rating system so really neat pictures etc can float up.&lt;/p&gt;
&lt;p&gt;Todo:&lt;br /&gt;
- temp domain (can&#039;t login to dyndns.org?)&lt;/p&gt;
&lt;p&gt;collect:&lt;br /&gt;
- coordinates (or address)&lt;br /&gt;
- Photo&lt;br /&gt;
- species tags (free at first?)&lt;br /&gt;
maps&lt;/p&gt;
</description>
 <comments>http://oheric.com/web/plant_and_animal_sightings_and_lichens#comments</comments>
 <category domain="http://oheric.com/share/shared_draft">drafts</category>
 <pubDate>Sun, 08 Jul 2007 20:49:13 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">49 at http://oheric.com</guid>
</item>
<item>
 <title>The Continuing Quest for Freedom from Telco Tirany</title>
 <link>http://oheric.com/voice/continuing_quest_freedom_telco_tirany</link>
 <description>&lt;div class=&quot;rant&quot; style=&quot;background: #FFE; border: 2px solid orange; margin: 2em; padding 1em&quot;&gt;
&lt;h4&gt;Rant&lt;/h4&gt;
&lt;p&gt;Why is Skype evil? &lt;/p&gt;
&lt;p&gt;They choose to create their own proprietary network rather than interoperating with SIP, for the sole purpose of building a monopoly. Sure, it makes good business sense for them, since they are doubtless far more profitable than any public SIP service trying to compete in the same space. Can we blame them for wanting to make some dinero? No, I guess not. Will we fight them for control of the network? Duh of course!&lt;/p&gt;
&lt;p&gt;Anyway, I&#039;ve been using Skype for awhile since certain people I talk to also use it (there&#039;s the lock-in bit). Gizmo was pretty good, but not good enough (connection under bad conditions on public wifi etc was better under skype). Skype has its own cross-platform SIP client (using &lt;a href=&quot;http://www.trolltech.com&quot;&gt;Trolltech&lt;/a&gt;&#039;s excellent dual-license QT library of course), which is free as in beer, but not Free Software. Anyway big woop. It also doesn&#039;t do video.&lt;/p&gt;
&lt;p&gt;FF&lt;sub&gt;&amp;gt;&amp;gt;&lt;/sub&gt; 6 months, and now the market is starting to shift around a bit. &lt;a href=&quot;http://www.wengophone.com/&quot;&gt;Wengo&lt;/a&gt;, a France-based SIP provider, has produced a very interesting SIP client:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Actually&lt;/strong&gt; cross-platform (again via QT), unlike Skype which has a different and buggy version on each of Win, Lin and Mac.
&lt;li&gt;Open source, and using open components (big woop), unlike Gizmo or Skype
&lt;li&gt;Full-featured chat with all the major nets (MSN, AIM, Gtalk, IRC.....)
&lt;li&gt;Video! &lt;em&gt;Cross-platform&lt;/em&gt; video, fi-na-lly! Hallelujah!
&lt;li&gt;&lt;span style=&quot;color: pink&quot;&gt;Polished so it glistens. &lt;/span&gt;It&#039;s odd actually, the company clearly has enormously skilled and motivated engineers, but very poor marketing. They must have some other income source, perhaps in partnerships with Telcos.
&lt;/ul&gt;
&lt;/div&gt;
&lt;p&gt;The latest Wengophone release (2.1) claims to allow connections to other SIP providers. This is important because Wengo&#039;s service:&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;is in French / France
&lt;li&gt;doesn&#039;t include important features like a US call-in number
&lt;/ol&gt;
&lt;p&gt;So anyway I&#039;m thinking that Sipphone&#039;s service might be the perfect match for Wengo&#039;s client. Testing follows, this article to document results.&lt;/p&gt;
</description>
 <comments>http://oheric.com/voice/continuing_quest_freedom_telco_tirany#comments</comments>
 <category domain="http://oheric.com/consumer/voip">voip</category>
 <pubDate>Mon, 11 Jun 2007 22:46:53 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">47 at http://oheric.com</guid>
</item>
<item>
 <title>Wikipedia does spoken articles</title>
 <link>http://oheric.com/web/wikipedia_does_spoken_articles</link>
 <description>&lt;p&gt;&lt;a href=&quot;http://en.wikipedia.org/wiki/Category:Spoken_articles&quot; title=&quot;http://en.wikipedia.org/wiki/Category:Spoken_articles&quot;&gt;http://en.wikipedia.org/wiki/Category:Spoken_articles&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;I&#039;m listening to the &lt;a href=&quot;http://en.wikipedia.org/wiki/Lego&quot;&gt;Lego article&lt;/a&gt;, it&#039;s a good format to listen to while doing something else, not too distracting but you pick up interesting snippets here and there.&lt;/p&gt;
</description>
 <comments>http://oheric.com/web/wikipedia_does_spoken_articles#comments</comments>
 <category domain="http://oheric.com/share/shared_draft">drafts</category>
 <pubDate>Mon, 11 Jun 2007 13:04:14 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">46 at http://oheric.com</guid>
</item>
<item>
 <title>Perfect number finder in python</title>
 <link>http://oheric.com/idiomas/perfect_number_finder_python</link>
 <description>&lt;p&gt;In the interest of greater openness (sharing my inner life with the world and such), here is a bit of python I just wrote to find perfect numbers. After a few minutes of optimization, it is now quite fast and no longer brings OSX to its knees with memory-hungryness:&lt;/p&gt;
&lt;pre&gt;
from math import *
def is_perfect(a):
	sum = 1 
	for i in xrange(2, floor(sqrt(a))):
		if a%i == 0:
			sum = sum + i + a/i
	if sqrt(a)%1 == 0: sum += sqrt(a)
	return sum == a

def find_perfect(limit):
	results = []
	for i in xrange(1, limit):
		j=2**i*(2**(i+1)-1)
		if is_perfect(j):
			results.append(j)
&lt;p&gt;&lt;a href=&quot;http://oheric.com/idiomas/perfect_number_finder_python&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/idiomas/perfect_number_finder_python#comments</comments>
 <category domain="http://oheric.com/engineer/idiomas">idiomas</category>
 <category domain="http://oheric.com/scholar/maths">maths</category>
 <pubDate>Sun, 10 Jun 2007 02:00:23 -0700</pubDate>
 <dc:creator>root</dc:creator>
 <guid isPermaLink="false">45 at http://oheric.com</guid>
</item>
<item>
 <title>Uke stuff</title>
 <link>http://oheric.com/music/uke_stuff</link>
 <description>&lt;p&gt;I bought a ukulele a few months ago, the $20 China special at one of the 3 string shops in downtown Corvallis. I don&#039;t play any songs all the way through yet, but this guy&#039;s rendition of the (NES, Level 1-1) Mario Bros. theme on the uke should hold you over:&lt;br /&gt;
&lt;object width=&quot;425&quot; height=&quot;350&quot;&gt;&lt;br /&gt;
&lt;param name=&quot;movie&quot; value=&quot;http://www.youtube.com/v/32hrdrVXQFw&quot;&gt;&lt;/param&gt;
&lt;param name=&quot;wmode&quot; value=&quot;transparent&quot;&gt;&lt;/param&gt;&lt;embed src=&quot;http://www.youtube.com/v/32hrdrVXQFw&quot; type=&quot;application/x-shockwave-flash&quot; wmode=&quot;transparent&quot; width=&quot;425&quot; height=&quot;350&quot;&gt;&lt;/embed&gt;&lt;/object&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;I find this &lt;a href=&quot;http://www.sheep-entertainment.nl/ukulele/index.html&quot;&gt;ukulele chordfinder&lt;/a&gt; very useful. Also surf around their site, if you can figure out the wacky navigation. It&#039;s a media playground!&lt;/p&gt;
&lt;li&gt;My favorite &lt;a href=&quot;http://www.muffin.net.nz/&quot;&gt;ukulele tablature site&lt;/a&gt;.
&lt;li&gt;&lt;a href=&quot;http://www.theuke.com/print.php?content.7&quot;&gt;Article on relative tuning method&lt;/a&gt;
&lt;/ul&gt;
</description>
 <comments>http://oheric.com/music/uke_stuff#comments</comments>
 <category domain="http://oheric.com/node/music">music</category>
 <pubDate>Tue, 08 May 2007 20:10:54 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">42 at http://oheric.com</guid>
</item>
<item>
 <title>Summer of Code Proposal</title>
 <link>http://oheric.com/drupal/summer_code_proposal</link>
 <description>&lt;h3&gt;Motivation&lt;/h3&gt;
&lt;p&gt;In building a content-oriented website, people need a way to specify&lt;br /&gt;
structure (how the pages and content items of the site inter-relate)&lt;br /&gt;
and provide navigation based on the structure. &lt;/p&gt;
&lt;p&gt;Most existing tools for site-structuring and navigation in Drupal are problematic for two main reasons:&lt;/p&gt;
&lt;p&gt;&lt;a href=&quot;http://oheric.com/drupal/summer_code_proposal&quot;&gt;read more&lt;/a&gt;&lt;/p&gt;</description>
 <comments>http://oheric.com/drupal/summer_code_proposal#comments</comments>
 <category domain="http://oheric.com/engineer/projects/drupal">drupal</category>
 <pubDate>Sun, 25 Mar 2007 14:54:57 -0700</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">38 at http://oheric.com</guid>
</item>
<item>
 <title>HW #5: Spherical Coordinates, Duex</title>
 <link>http://oheric.com/differential_geometry/hw_5_spherical_coordinates_duex</link>
 <description>&lt;p&gt;This work is borrowed gratefully from Flanders 4.1.&lt;/p&gt;
&lt;p&gt;Position in &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/817bf0b094893b40c8332b418ca19e438c73841c.png&quot; alt=&quot;$ \Re^3 $&quot; /&gt; is given in terms of spherical parameters as:&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/88db8a0f77f4823c8ccc9d707659537265a5412b.png&quot; alt=&quot;\[ \vec{r} = &amp;amp;(r\sin{\phi}\cos{\theta}, r\sin{\phi}\sin{\theta}, r\cos{\phi}) \]&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p&gt;with basis &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/5cc341848e56afcf058c892125dfc65d4af51b38.png&quot; alt=&quot;$ \{\hat{i}, \hat{j}, \hat{k}\} $&quot; /&gt;. Applying the exterior derivative operator gives:&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/a0356925bfe254e5815c397ca0053a81ee52f132.png&quot; alt=&quot;\begin{align*} d\vec{r} = &amp;amp;(\sin{\phi}\cos{\theta}, \sin{\phi}\sin{\theta}, \cos{\phi})dr \\&lt;br /&gt;
&amp;amp;+ (r\cos{\phi}\cos{\theta}, r\cos{\phi}\sin{\theta}, -r\sin{\phi})d\phi \\&lt;br /&gt;
&amp;amp;+ (-r\sin{\phi}\sin{\theta}, r\sin{\phi}\cos{\theta}, 0)d\theta \\&lt;br /&gt;
= &amp;amp;dr\hat{r} + rd\phi\hat{\phi} + rd\theta\hat{\theta} \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p&gt;with&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/edce2b4892d583342062980f41376d36846bf647.png&quot; alt=&quot;\begin{align*} \hat{r} &amp;amp;= (\sin{\phi}\cos{\theta}, \sin{\phi}\sin{\theta}, \cos{\phi}) \\&lt;br /&gt;
\hat{\phi} &amp;amp;= (\cos{\phi}\cos{\theta}, \cos{\phi}\sin{\theta}, -\sin{\phi}) \\&lt;br /&gt;
\hat{\theta} &amp;amp;= (-\sin{\phi}\sin{\theta}, \sin{\phi}\cos{\theta}, 0) \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p&gt;Therefore, (&lt;strong&gt;answer part (a)&lt;/strong&gt;)&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/b35ded820015152c5cd3b1c9b2d855d6098edd00.png&quot; alt=&quot;\begin{align*} d\hat{r} = &amp;amp;(0,0,0)dr \\&lt;br /&gt;
&amp;amp;+ (\cos{\phi}\cos{\theta}, \cos{\phi}\sin{\theta}, -\sin{\phi})d\phi \\&lt;br /&gt;
&amp;amp;+ (-\sin{\phi}\sin{\theta}, \sin{\phi}\cos{\theta}, 0)d\theta \\&lt;br /&gt;
= &amp;amp;\hat{\phi}d\phi + \hat{\theta}d\theta \\&lt;br /&gt;
d\hat{\phi} = &amp;amp;(0,0,0)dr \\&lt;br /&gt;
&amp;amp;+ (-\sin{\phi}\cos{\theta}, -\sin{\phi}\sin{\theta}, -\cos{\phi})d\phi \\&lt;br /&gt;
&amp;amp;+ (-\cos{\phi}\sin{\theta}, \cos{\phi}\cos{\theta}, 0)d\theta \\&lt;br /&gt;
d\hat{\theta} = &amp;amp;(0,0,0)dr \\&lt;br /&gt;
&amp;amp;+ (-\cos{\phi}\sin{\theta}, \cos{\phi}\cos{\theta}, 0)d\phi \\&lt;br /&gt;
&amp;amp;+ (-\sin{\phi}\cos{\theta}, -\sin{\phi}\sin{\theta}, 0)d\theta \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
</description>
 <comments>http://oheric.com/differential_geometry/hw_5_spherical_coordinates_duex#comments</comments>
 <category domain="http://oheric.com/scholar/maths/differential_geometry">differential geometry</category>
 <category domain="http://oheric.com/scholar/maths">maths</category>
 <pubDate>Sun, 18 Feb 2007 22:31:23 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">37 at http://oheric.com</guid>
</item>
<item>
 <title>HW #3</title>
 <link>http://oheric.com/differential_geometry/hw_3</link>
 <description>&lt;ol&gt;
&lt;li&gt;
&lt;h3&gt;Hodge Dual in Minkowski Space&lt;/h3&gt;
&lt;p&gt;&lt;i&gt;Minkowski 4-space has orthonormal, oriented basis &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/0e4e1bfd869c5a11ce44a7ea196ee805ba8d8140.png&quot; alt=&quot;$ \{dx,dy,dz,dt\} $&quot; /&gt; with volume element (choice of orientation) &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/b40579dcf026d88f56bd6625e61a431c23e79405.png&quot; alt=&quot;$ \omega=dx\wedge dy \wedge dz \wedge dt $&quot; /&gt; and inner product &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/b4e1c648ab4bbff5332e72af52e68b38c6da6eb0.png&quot; alt=&quot;$ g(,) $&quot; /&gt; defined by&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/cab948dece4158dfcf91e0117df297c453fb3c41.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
g(dx,dx)&amp;amp;=1 \\&lt;br /&gt;
g(dy,dy)&amp;amp;=1 \\&lt;br /&gt;
g(dz,dz)&amp;amp;=1 \\&lt;br /&gt;
g(dt,dt)&amp;amp;=-1 \\&lt;br /&gt;
g(d\alpha_i,d\alpha_{j\ne i})&amp;amp;=0 \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p&gt;&lt;/i&gt;&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;&lt;i&gt;Determine the Hodge dual operator * on all forms by computing its action on basis forms at each rank.&lt;/i&gt;&lt;br /&gt;
In general, the dual can be computed as (Equation 20, &lt;a href=&quot;http://oregonstate.edu/~drayt/Courses/MTH434/2007/dual.pdf&quot; title=&quot;http://oregonstate.edu/~drayt/Courses/MTH434/2007/dual.pdf&quot;&gt;http://oregonstate.edu/~drayt/Courses/MTH434/2007/dual.pdf&lt;/a&gt;):&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/ebc0a6c4463f6ce6b5df627d1ddf2012fb6b73bd.png&quot; alt=&quot;\[ \ast(\sigma^1\ldots\sigma^p)=g(\sigma^1,\sigma^1)\ldots g(\sigma^p,\sigma^p)\sigma^{p+1}\wedge\ldots\wedge\sigma^n \]&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p&gt;where &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/d21f9d6942d98ddd97e453ae7a63ce74ba07c1ea.png&quot; alt=&quot;$ \sigma^1\ldots\sigma^n=\omega $&quot; /&gt; is the volume element.&lt;br /&gt;
In particular:&lt;/p&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/6d5b7e594cfd5af3df5d4a0ece521a9a98f9b98d.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\ast 1=\omega&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/b9418af9ceda1119e721b824e953765e4feacbc6.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\ast dx &amp;amp;=dy \wedge dz \wedge dt \\&lt;br /&gt;
\ast dy &amp;amp;=(-dx \wedge dz \wedge dt) \\&lt;br /&gt;
\ast dz &amp;amp;=dx \wedge dy \wedge dt \\&lt;br /&gt;
\ast dt &amp;amp;=(-1)(-dx \wedge dy \wedge dz) \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/f78ef17a31b3e42ac76f6ce6b3a0f26a2418bb54.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\ast dx\wedge dy &amp;amp;=dz \wedge dt) \\&lt;br /&gt;
\ast dx\wedge dz &amp;amp;=(-dy \wedge dt) \\&lt;br /&gt;
\ast dx\wedge dt &amp;amp;=(-1)(-dy \wedge dz) \\&lt;br /&gt;
\ast dy\wedge dz &amp;amp;=dx \wedge dt) \\&lt;br /&gt;
\ast dy\wedge dt &amp;amp;=(-1)(-dx \wedge dz) \\&lt;br /&gt;
\ast dz\wedge dt &amp;amp;=(-1)(dx \wedge dy) \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/e91c631a5bf397a2cdacc173b60a110a69c5693c.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\ast dx \wedge dy \wedge dz &amp;amp;=dt \\&lt;br /&gt;
\ast dx \wedge dy \wedge dt &amp;amp;=(-1)(-dt) \\&lt;br /&gt;
\ast dx \wedge dz \wedge dt &amp;amp;=(-1)dt \\&lt;br /&gt;
\ast dy \wedge dz \wedge dt &amp;amp;=(-1)(-dt) \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/f8caafa560fba2cd2568dadb0518a5aadeadd910.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\ast \omega = -1&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;li&gt;&lt;i&gt;How does your answer change if the opposite orientation is chosen, namely &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/f657a5a4855507c103ae4fcc7a145bf86fb0e824.png&quot; alt=&quot;$ \omega = dt\wedge dx \wedge dy \wedge dz $&quot; /&gt;?&lt;/i&gt;&lt;br /&gt;
The sign of each dual would change, due to the additional odd number (3) of transpositions to the volume element. The sign of the number of transpositions required to transform one volume element into another is an invariant (independent of a particular permutation).
&lt;/ol&gt;
&lt;li&gt;
&lt;h3&gt;Spherical Coordinates&lt;/h3&gt;
&lt;p&gt;&lt;i&gt;Spherical coords in &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/6ff1fbbbb0fff68ec5fc0f49876741ded6609e13.png&quot; alt=&quot;$ E^3 $&quot; /&gt; with &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/6d7db21f929c70c00f7f4d23876f6478f838645a.png&quot; alt=&quot;$ \omega = r^2\sin{&lt;br /&gt;
\theta}dr\wedge d\theta \wedge d\phi $&quot; /&gt;&lt;/i&gt;&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;&lt;i&gt;Calculate the action of * on the basis elements of each rank.&lt;/i&gt;
&lt;li&gt;&lt;i&gt;Compute the dot- and cross-products of 2 arbitrary &quot;vector fields&quot; (1-forms) using the expressions:&lt;/i&gt;&lt;br /&gt;
&lt;table class=&quot;displaymath&quot;&gt;
&lt;tr&gt;
&lt;td class=&quot;dspleft&quot;&gt;&lt;img class=&quot;teximage&quot; src=&quot;/files/tex/52ae2875fbe1310cd7fda551a8fa662dd03d6665.png&quot; alt=&quot;\begin{align*}&lt;br /&gt;
\alpha\cdot\beta&amp;amp;=\ast(\alpha\wedge\ast\beta) \\&lt;br /&gt;
\alpha\times\beta&amp;amp;=\ast(\alpha\wedge\beta) \\&lt;br /&gt;
 \end{align*}&quot; /&gt;&lt;/td&gt;
&lt;td class=&quot;dspright&quot;&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;/ol&gt;
</description>
 <comments>http://oheric.com/differential_geometry/hw_3#comments</comments>
 <category domain="http://oheric.com/scholar/maths/differential_geometry">differential geometry</category>
 <category domain="http://oheric.com/scholar/maths">maths</category>
 <pubDate>Tue, 13 Feb 2007 15:35:31 -0800</pubDate>
 <dc:creator>eric</dc:creator>
 <guid isPermaLink="false">36 at http://oheric.com</guid>
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