Line Integral of a Vector Field

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Inspired by a discussion with my son regarding movement of a point-charge between two other charges I revisited the definition of the line integral. Wikipedia offers an excellent visualization of the definition of the line integral for a vector field. See animated graphic below: This is something…

Torricelli's Trumpet: Infinite Surface Area but Finite Volume

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Just read on Torricelli's trumpet in Wikipedia. This states that there is a body having infinite surface but finite volume! That sounds contradictory at first. Function in question is $$ y = 1 / x $$ from $x=1$ to $a$. Volume is $$ V = \pi \int_1^a \left({1\over x^2}\right)\,dx =…

The Attraction of Curves – Brian Koberlein

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Brian Koberlein wrote a very good introductory article on curvature of space and time in the vicinity of gravity: see The Attraction of Curves – Brian Koberlein.

Dramatic Faster Sorting in Linux Using Nsort

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Last year I used a drop-in replacement for the ordinary Linux sort command called nsort from Ordinal Technology. Ordinal's nsort is free but not open-source. One thing is clear, however, it is very fast. nsort was written by Chris Nyberg. The motivation for looking for a faster sort was as follows.…

Harddisk Drive Speed in MB/s

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Below picture is from Read Throughput Average in Tom's Hardware.

Proportion of Papers on hgpu.org

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hgpu.org contains links to reviews, tutorials, research papers, program packages concerning various aspects of graphics and non-graphics (general purpose computing) using of GPU and related parallel architectures (FPGA, Cell processors etc.). The majority is on NVidia, see picture below.

India is now the third largest Smartphone market in the world - Android Authority

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An article in Android Authority from 26-Jun-2013, India is now the third largest Smartphone market in the world, states that: There are 14 major carriers listed for India, including two state owned providers. None have over 180 million subscribers. The smartphone market in India is expanding at…

Inhibit Annoying Message of the Day in Ubuntu

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I find the motd annoying when you log in to a Ubuntu server machine. To get rid of this I do the following as root: cd /etc/update-motd.d mkdir klmDisabled mv ??-* klmDisabled Unfortunately, whenever the packages update-manager-core, landscape-common, base-files, update-notifier-common change,…

WordPress.com News and Numbers: The August 2013 Hot List

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As already posted last month, there are around 4 billion pageviews per month. This makes 1.4 pageviews per millisecond on the average. Each pageview incurs hundred of lines of PHP code executed, a couple of MySQL queries and updates.

China Built 600 Dams per Year Since 1950

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According Los Angeles Times (dead link) China built 600 dams per year on average. This trend will continue. According Wikipedia, or Jie Cai's Master Thesis (dead link), China has the largest potential for hydropower in the world and currently ranks first in hydroelectric generating capacity with…

Newer GPUGRID Tasks Keep GPU Really Hot

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Recent GPUGRID tasks, like I60R2-NATHAN_KIDKIXc22 or 27x0-SANTI_RAP74wtCUBIC really keep my NVidia GTX 560 hot, i.e., as warm as 70° Celsius or higher. Fri Sep 6 17:16:38 2013 +------------------------------------------------------+ | NVIDIA-SMI 5.325.15 Driver…

Using WordPress for 5 Years Now

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Saving URLs in del.icio.us Still Troublesome

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I have been using del.icio.us (dead link) since at least the year 2005. During that time del.icio.us (dead link) was sold to Yahoo, which didn't do very much with this bookmarking service. It simply worked. In 2011 the service was acquired by a company named AVOS (dead link), see Wikipedia for the…

Mark Twain Commentary on the MacBook Air

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Mark Twain's (1835-1910) words still relevant today for people who want to change established things hastily. From Ken Krugler on Mark Twain Commentary on the MacBook Air: One of my favorite posts to the Unicode mailing list came during a heated debate about “simplifying” certain character…

Copy Directories with Symbolic Links via ssh

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Although probably known in most circles, it is worth repeating that scp by itself does not honor symbolic links. To overcome this limitation just combine tar and ssh, i.e., tar on sending side, untar on receiving side: tar cf - /src/dir | ssh remotehost "cd /dst/dir ; tar xf -" Usually…

Average Size of Web Pages plus Prediction

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Average Size of Web Pages plus Prediction shows an exponential fitting to web-page sizes. From above article: As you can see, the 1/2 MB mark was cracked in 2009 and the 1 MB mark was cracked in 2012. Despite the seemingly random fluctuations, an exponential trend is clearly visible. The power…

SyncSort Sort is Not Stable

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A colleague of mine noticed some strange behaviours in his programs. It was later discovered that this is due to SyncSort not conducting a stable sort. Stable sort means that the sequence of elements in input is not changed if there is no strict need to change them. Unfortunately, the documentation…

WordPress.com by the Numbers: The July 2013 Hot List

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Some statistics from WordPress just for month July, 2013. These sheer numbers almost sound unbelievable: 1 million new blogs 7 Exabyte of data 1 billion pages accessed by mobile devices 9 million YouTube videos embedded 500.000 posts per e-mail 200 posts per voice

Design Notes on System for the Analysis of Order- and Stepsize Changes for Cyclic Composite Multistep Methods

, 2 min read

For the numerical solution of the ordinary differential equation, initial value problem $$ y'=f(t,y), \quad y(t_0)=y_0,$$ one can use a cyclic composite multistep method of the form $$ \sum\limits_{i=0}^{m} A_i Y_{k+i} = h \sum\limits_{i=0}^{m} B_i Y'_{k+i}, \qquad…

ssh and rsync for Android

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I got somewhat tired of using FTP with my Android, even with lftp. Keeping multiple folders in sync is simply very cumbersome. If I only had rsync working on Android! I found SSHelper, written by Paul Lutus, see also Arachnoid. SSHelper offers ssh, scp, rsync. You can ssh to your Android phone and…