My Dual-Boot Notebook

===========================
Thinkpad X61
===========================
I got my second notebook, Thinkpad X61, a few days ago. With a 12.1 inch screen and no CDROM attached it weighs only 2.2 lbs, which is great for traveling. I chose it because I was really not happy with the weight of my old HP notebook: 7.25 lbs without battery. Before I made the oder I also looked into most popular 9 inch netbooks, such as Asus EEE PC, Acer Aspire One, and Dell E netbook. But they all have some unsolved performance issues with their ATOM cpus and onboard hard drives. I didn't go for Mac Air as well because a notebook that expensive means the same as robbery to me and it also restricts the fun you can find from trying all kinds of software.

As my Thinkpad X61 arrived I found everything to be great except the notorious Windows Vista operating system. My dislike of Vista is not lone but shared by all my friends, by news reports, and even by Bill Gates. So my immediate decision was to reinstall the operating system from scratch for the new notebook. This blog then records all the steps I took for that purpose, most of which were dug out deep from the internet using Google.

I have to mention that Thinkpad X61 has an over-heating issue with its wifi card under the right palm. The issue is most severe with Linux because the system just can't manage the wifi card that well. It is even worse on my notebook since the madwifi wireless driver doesn't have support for power management for the Atheros chip. But the issue is not obvious under Windows XP and becomes zilch after turning off the wifi card in the BIOS.

MACHINE: Thinkpad X61 7675CTO
(Intel Core2 Duo CPU T8100 @ 2.1GHz x 2, 2G RAM, 100G 7200RPM Hard Drive)


===========================
Dual-Boot Systems
===========================
The reinstallation was then planned for a dual-boot system with Windows XP Professional and 64-bit Ubuntu Hardy Heron. The Windows system was setup first and the Ubuntu second. The original hard drive partition and the unseen Windows vista recovery partition were all deleted at installing the Windows system. About 85 GB hard drive space was allocated to the Windows system and was divided into three NTFS primary partitions of 25 GB, 30GB, and 30GB, respectively. The remaining 15 GB was late formatted as a 12 GB ext3 root system and a 2 GB swap space for the Linux system. This allocation seemed too stingy for the Linux system, but I didn't realize this after completed all the work and tried out the new systems for a couple of days. Now I have learned that at least 30 GB hard drive space is necessary for carrying out some basic computational work on the Linux system. What a pity!


(TO BE CONTINUED...)

WINDOWS SYSTEM: Microsoft Windows XP Professional SP3


LINUX SYSTEM: Ubuntu 8.04.1 Hardy Heron
(Kernel 2.6.24-19-generic, Gnome 2.22.3, I386x64)


===========================
Windows XP Setup
===========================



===========================
Ubuntu Hardy Setup
===========================
# powertop:
1. echo 1500 > /proc/sys/vm/dirty_writeback_centisecs

2. sysfutils->ships sysfs.conf which allows to conveniently set sysfs attributes change
cpu frequency scaling to ondemand

# wlan power management:
no power management on madwifi driver for atheros


# chinese
1. language support -> chinese
2. scim setup

# Wpa2
1. /etc/ssl/certs/ca-certificates.crt
2. not done

# LaTex
1. texlive
2. texmaker

# Terminal
1. devils pie
2. setup

# intel compilers
0. fix errors when you try an initial install
1. cce
2. fce
3. mkl

# wireless
remove network-manager
install wicd
remove wicd
intall network-manager
wireless not working
install latest madwifi by replacing its ath_hal with latest hal from people.freebsd.org/~sam
restart and stop wireless roaming
start wireless roaming and works.

# syslog-ng
replace klogd and sysklogd
send network-manager messages to /dev/null with permission change.

# hug log files
solved by deleting network profiles for wpa2

Bolzano-Weierstrass Property

I used here the proof of the Bolzano-Weierstrass Property from the book "Elementary Real Analysis" by Thomson et al.. Note this theorem is different than the Bolzano-Weierstrass Theorem.

\begin{theorem} A set of real numbers $E$ is closed and bounded if and only if every sequence of points chosen from the set has a subsequence that converges to a point that belongs to $E$. \end{theorem}

\begin{corollary} A set of real numbers $E$ is closed and bounded if and only if every sequence of $E$ has a point of accumulation that belongs to $E$. \end{corollary}

\begin{proof} Suppose that $\E$ is both closed and bounded and let $\{x_n\}$ be a sequence of points chosen from $E$. Since $E$ is bounded this sequence $\{x_n\}$ must be bounded too. We apply the Bolzano-Weierstrass theorem for sequences to obtain a subsequence $\{x_{n_k}\}$ that is both monotonic and convergent. If $x_{n_k}\rightarrow z$ then there is $K$ such that $|x_{n_k}-z|<\epsilon$ for all $k\geq K$ and any positive $\epsilon$ . Since all the points of this subsequence belong to $E$ the neighborhoods of $z$ contain infinite points belong to $E$. So, by definition $z$ is a point of accumulation of $E$. Now we see that $ z\in E$ since $\E$ is closed.

So the Bolzano-Weierstrass Property is really that every sequence of a set of real numbers has a subsequence that converges to a point, or has a point of accumulation, that belongs to this set.

In the opposite direction we suppose that there is a set E which has the Bolzano-Weierstrass property but we don't know in advance if $E$ is closed and bounded. Then E cannot be unbounded. For example, if $E$ is unbounded then there is a sequence of points $\{x_n\}$ of $E$ with $x_n\rightarrow \infty$ or $x_n\rightarrow -\infty$ and no subsequence of that sequence converges, which contradicts the assumption. Also, $E$ must be closed. If $E$ is not closed, there is a point of accumulation $z$ such that $z\ni E$. This means that there is a sequence of points $\{x_n\}$ in $E$ converging to $z$. But any subsequence of $\{x_n\}$ would also converge to $z$ and $z\ni E$, which contradicts the Bolzano-Weierstrass Property assumed for $E$. \end{proof}

References: Bolzano-Weierstrass theorem

~~~

Riemann or Lebesgue integration

Excerpt from Martin Davis and Matt Insall, "Mathematics and Design: Yes, But Will it Fly?", Nexus Network Journal, vol. 4, no. 4 (Autumn 2002).

At 06:39 AM 8/26/2002, Matt Insall wrote:

Personally, I think it is likely to make a difference whether Riemann or Lebesgue integration is used, but that the difference will only be noticeable provided that the designers rigorously adhere to the requirements that that particular integration theory be used for all the integrals. As soon as they revert to numerical approximations, instead of using calculus or analysis, they have muddied the waters so that no direct comparison between one integration theory and another can be made.

This is with reference to Hamming's quip about this difference not being significant for engineering design.

Functions that are Riemann integrable are automatically Lebesgue integrable and the values of the integrals will be the same. There are two ways in which a function can be Lebesgue integrable but not Riemann integrable. Any bounded measurable function is L-integrable, but not all of them are R-integrable. Some unbounded measurable functions are also L-integrable, but not Riemann integrable, since all R-integrable functions are bounded. An example: the function 1/sqrt(x) has the L-integral 2/3 on the interval [0,1]. Being unbounded in that interval, it has no R-integral there.

Of course, this function does have an "improper integral" (sometimes called a Riemann-Cauchy integral) in that interval with the very same value. Only functions having absolutely convergent improper integrals have Lebesgue integrals. The classical example is sinx/x on the interval [0,\infnty] which has the value \pi/2 but no Lebesgue integral. This fact is sometimes confusingly stated as a case where something is R-integrable but not L-integrable. But one can perfectly well define "improper"
L-integrals, so that this comparison is inappropriate. It's just that the definition of L-integration automatically includes cases that in the Riemann case require this extra limiting step for which the inappropriate term "improper" is used.

Hamming of course hadn't meant to be taken so literally. His aphorism was intended to say that the fine points of mathematical analysis are not relevant to engineering considerations. And, he was perfectly right.

In the long-ago days when I had occasion to be on committees administering an oral qualifying exam for the doctorate, I would often ask the hapless student why analysts prefer the L-integral. This was a trap question: students who fell for the trap would tell me that the function on [0,1] that is 1 on the irrationals and 0 on the rationals is L-integrable, but not R-integrable. The right answer is that the L-integral has useful convergence properties not enjoyed by the R-integral.

Now whatever did Mat Insall have in mind? sin x/x on [0,infty]? Surely not in any engineering analysis.