Linear Algebra - Linear Independence Matrices

We can check for the linear independence of a matrix by extending out the matrices into column vectors. For example, checking the linear independence of the following matrices:

|1 1|
|1 1|

|1 2|
|3 4|

|2 3|
|5 7|

|1 4|
|6 8|

We would arrange the entries in the following way. In this way we would know if we could get the entries linearly combine any of the entries to form another one of the entries. This would only work if this row reduced to the identity matrix, if it does not then it is linearly dependent.

|1 1 2 1|
|1 2 3 4|
|1 3 5 6|
|1 4 7 8|

|1 1 2 1|
|0 1 1 3|
|0 2 2 5|
|0 3 5 7|

|1 1 2 1 |
|0 1 1 3 |
|0 0 0 -1|
|0 0 2 -2|

|1 1 2 1 |
|0 1 1 3 |
|0 0 2 -2|
|0 0 0 -1|

|1 0 0 0|
|0 1 0 0|
|0 0 1 0|
|0 0 0 1|

Thus the columns of this matrix are linearly independent, so the matrices are linearly independent. Its not possible to multiply the matrices by a factor and add them to one another in order to get the leftover matrix.

Computer Science - BOINC

BOINC is an open-source software that can be used in a volunteer fashion and for grid computing. It can be found at http://boinc.berkeley.edu/. The idea is to use the processing power of computers in idle time. The easiest use is as a donation service of extra computational power to already ongoing research projects. An example is the computation of a 3-D model of the SDSS or sloan digital sky survey. This project can be found here http://milkyway.cs.rpi.edu/milkyway/. It can also be used in a private sense in order to set up a grid supercomputer at a university by linking together the campus computers. The same system can be set up for company long term grid computing, with the application running in the background without need for screensaver graphics.

BOINC works by getting a set of tasks from a project's scheduling server. The computer then downloads executables and input files from the project's data server. The pc then runs the computations and uploads the output files back to the data server. Later the pc will report on completed tasks and receive new tasks indefinitely.

Theorem - Abegg's Rule

Subject - Chemistry
Period -
Creation - 1904
Founded by - Richard Abegg
Proponents - Gilbert N. Lewis

In more archaic terms it tells us the solubility of akali metals with strong acids decrease as you descend on the akali metal group, while the solubility will increase in weak acids when you descend the same group. There is an exception for the solubility of salt in water, but otherwise this rule held experimentally.


Subject - Chemistry
Period -
Creation - 1904
Founded by - Richard Abegg
Proponents - Gilbert N. Lewis


There is another rule that goes by the same name, or also known as Abegg's rule of 8.This is an old chemistry rule that states deals with the valence levels in molecules, saying that the positive and negative valency of an element is frequently eight.

Theorem - ABC Model

Subject - Psychology
Period -
Creation - 1921
Founded by - Aaron T. Beck, Burrhus Frederic Skinner
Proponents -

The ABC model is a model of behavior based on the operant conditioning paradigm, the idea that an individual's behavior can be modified through consequences. In particular this model says that you can change one's behavior with conditions that precede or follow the behavior in question. In either scenario behavior that is rewarded will occur more frequently and behavior that is punished will occur less frequently.

Theorem - ABC Conjecture

Subject - Math
Period -
Creation - 1985
Founded by - J Oesterlé
Proponents - D W Masser

A conjecture stating that there exists a positive number k such that all positive integers a, b and c where:
a + b = c
(a, b, c) = 1
will result in:
z < G ^k
Where G is the greatest square-free factor of abc.

This has profound implications in the study of Diophantine equations which are indeterminate polynomial equations with integer inputs or variables. An example of such an implication is that the abc conjecture tells us the Fermat equation has at most a finite number of solutions.

Theorem - Abandonment

Subject - Philosophy
Period - 20^th Century
Creation - Søren Kierkegaard, Frederich Nietzsche
Founded by -
Proponents - Sartre

Abandonment is a central concept to atheistic existentialism. The idea is that god does not exist which means that life has no intrinsic purpose or meaning. The idea is that man was "abandoned" in our universe and must create their own morality and code without divine assistance.

Theorem-A Priori Theories

Subject - Accounting
Period - 1960s
Creation -
Founded by -
Proponents -


An approach to accounting that was based heavily on using deductive reasoning for the development and improvement of accounting systems. This is the reason for the term A priori as the latin translation of a priori means justification independent of experience. Thus the proponents of A Priori accountancy theories use assumed axioms, or premises, rather than empirical, or experimental evidence to relate cause and effect.

Computer Science-Gettext

Gettext is a function in gnu that allows the user to switch between different languages. Due to the majority of computer science documentation and software being written in english, gettext is meant to help even the field for the rest of the world. It can be downloaded at the following location.

http://ftp.gnu.org/gnu/gettext/

However, there is a known error with gettext versions 0.18 above. Before doing the normal ./configure 
make 
sudo make install 
You must change the file stpncpy.c. Go into the directory where gettext is installed.
cd ../gettext-0.18.1/gettext-tools/gnulib-lib
vi stpncpy.c


Then before the line #ifndef weak_alias
add #undef stpncpy

It should look like the following


/* This is almost copied from strncpy.c, written by Torbjorn Granlund.  */

#include <config.h>

/* Specification.  */
#include <string.h>

#undef stpncpy
#ifndef weak_alias
# define __stpncpy stpncpy
#endif

/* Copy no more than N bytes of SRC to DST, returning a pointer past the
   last non-NUL byte written into DST.  */

This lets the build compile on a mac machine as there is an overlap in definition issue with stpncpy.c and an already existing strncpy.c in XCode on the mac os. This is not an issue on linux machines.

Computer Science-GTK

GTK is a Gnu version of Qt, a packaged gui builder. It builds off of the X window system and was originally designed for GIMP. The following is to help with the installation of it, but since it uses jhbuild to automatically download and compile source code, its not too difficult to follow.

First find the shell script to run here.
https://live.gnome.org/GTK+/OSX/Building
scroll down to the procedure section, and follow the instructions to set up GTK. The text for the script can also be directly found here, execute it after retrieving the text. If you want you can use the curl command to directly get the txt from here:
http://git.gnome.org/browse/gtk-osx/plain/gtk-osx-build-setup.sh
After the script is downloaded, go into terminal and cd to where the script is located and run the following 4 commands.

sh gtk-osx-build-setup.sh
jhbuild bootstrap
jhbuild build meta-gtk-osx-bootstrap
jhbuild build

These commands are also located as comments within the script.

Computer Science-Embed Font

If you want to embed a font into a document or a website, all you have to do is adjust the stylesheet associated with the page. Font-face defines the font you want to use, and you can call that font wherever you want. For example whenever you write paragraphs as is shown here, or you can list it higher up in the hierarchy such as in the body of the text, or in the header.

@font-face {
font-family: "Name your font";
font-weight: normal;
font-style: normal;
src: url(../location/of/font.ttf);
}

p {
font-family: "call your font";
font-size: 1.00em;
text-align: justify;
}

Then in your document link to your css stylesheet. 
<link href="../location/of/Stylesheet.css" rel="stylesheet" type="text/css" />

Physics-Angular motion

Angular motion is when a rigid body rotates around some point or points. Before we go in too deeply into this we first must define the environment we'll be working in. Normally we describe motion with cartesian coordinates, x, y, and z to define the axis, and assume that the object behaves as a point mass. We can't really do that with angular motion. For example a ceiling fan is hard to describe with only one point. Thus we bring in the rigid body, where there is a definite shape to objects. We also want to work with something more convenient than cartesian coordinates. For example although we can describe a circle in cartesian coordinates with x² + y² = 1, its much easier to just say r = 1 for all values of θ. We define the old x and y as:
x=r cos (θ)
y=r sin(θ)

Now we replace the terms in normal motion with their angular motion counterparts.
v = δx/δt
ω = δθ/δt
velocity goes from the change in position over time to angular velocity, the change in angle over time. However, it is defined slightly differently. Velocity is defined with a vector pointing in the same direction as the motion of the object. Angular velocity is defined with a vector pointing perpendicular to the plane of the angular motion. To be more specific, the direction is defined by the cross product of the motion of a point on the edge of the object and the vector from the center of the object to the point.

a = δv/δt
α = δω/δt
Angular acceleration is also defined with a vector perpendicular to  the rotational motion of the object. This means that both angular acceleration and angular velocity are defined in the z axis, and for the purposes of basic mechanics, remains stationary.

There are also analogs to the basic equations of motion. Assuming constant angular acceleration we can get:
ω_z=ω_0z + α_zt
θ-θ₀=1/2(ω_0z+ω_z)t
θ=θ₀ + ω_0zt + 1/2α_zt²

Computer Science-Web Scraping

Web scraping, or web harvesting is the process of extracting data from the web. An example of this would be data extraction using spreadsheets, whether they be excel or through google docs. A simple example here shows the importhtml function which brings a table from the wikipedia into the spreadsheet.

The next example shows the use of the importxml function on the same page. This function is a bit more powerful as you can specify the potions through the xpath syntax. Only a portion of this is shown, but the methodology here is to go to the website you want to scrape. Then right click somewhere on that site and select view source code. Then you look for the indicator that you want to scrape, this can range from a href to tr. Scraping for a href is often gives you useful information as it will list out all the links on the page. tr is often how tables are adressed, and this is what I used here. Instead of specifying one table on the page, importxml searching for tr tags will list out every table and its entries on that page.

Physics-Aberration

In optics an aberration is a defect in an image caused by a lens or a mirror. There are two main types of aberrations  one is chromatic aberration the other is spherical aberration. Chromatic aberration can only be caused by a lens, and has the effect of causing different colors to be refracted by the lens. This is normally caused by variations in the n, or the index of the refractive of material, indicating a nonuniform substance.

Spherical aberration on the other hand is when the light from an object focus in slightly different positions due to defects in the thickness or curvature of the lens. This means that there isn't a clear way to find the image of an object viewed with this lens as there is no convergence point.

This term can also be applied to astrophysics. It refers to the phenomenon where the position of a celestial body is displaced in relation to its actual position due to the movement of the earth. This can be correctly simply as we can approximate this effect using the sin(θ) = θ approximation, giving us an angular displacement of v/c where v is equal to the earth's orbital velocity and c is the speed of light.

Physics-Estimation

One of the most important intuitions to build through studying physics are approximations of what things are. Its important to know how big or small something roughly is or how fast or slow it is moving. This allows us to better perform "back of the envelope" calculations; popularized by Enrico Fermi, these calculations are useful in determining the behaviors of a system. Its not necessary to memorize all of these, but it helps to get a scale of the world.

Lengths:
10^-10 meters - Angstrom, roughly the size of an atom
10^-9 meters - Nanometer, few times larger than the largest atoms
10^-8 meters - Size of some transistors in computer chips
10^-6 meters - Micrometer, Micron, size of bacterias/cells
10^-3 meters - Millimeter, size of the point pen/edge of penny
10^-2 meters - size of a finger
10⁰ meters - meter, size of people
10³ meters - kilometer, length of a 10 minute walk
10⁷ meters - Diameter of Earth
10¹¹ meters - Distance to sun

Mass:
10^-24 kilogram - weight of buckyball
10^-9 kilogram - weight of grain of dust
10^-6 kilogram - weight of grain of salt
10^-3 kilogram - weight of grain of dust
10⁰ kilogram - weight of chihuahua
10³ kilogram - weight of car
10⁶ kilogram - weight of space shuttle
10²⁴ kilogram - weight of Earth

Velocity:
10^-3 m/s - speed of snail
10⁰ m/s - speed of human walking
10¹ m/s - speed of cheetah
10² m/s - speed of car
10³ m/s - speed of airplane
10⁶ m/s - speed of electron
3*10⁸ m/s - speed of light

Computer Science-Qt build update

Once again I misinterpreted a lot of what was written about the couldn't find Qt issue. The main parts are to ensure that Qt is completely installed, and to add this to the path.
PATH=$PATH:filepath/to/QtSDK/Desktop/Qt/4.8.1/gcc/bin
Once this is done, source it or restart your computer. Then you should be able to execute the commands correctly. For example to build XCode files you can use:
cmake -g XCode /filepath/to/src/

This should definitely allow things to work out on a mac. This location contains the correct bin, with the correct version of qmake, unlike the previous areas.

Computer Science-Qt Madde/PkgConfig

There has been an error I've been getting while calling Qt through cmake. It gives me the error Can't locate Madde/PkgConfig.pm in @INC. In order to help fix this issue, you have to make the pkg-config commands work under the mad environment. Thus in the ../QtSDK/Maemo/4.6.2/sysroots/fremantle-arm-sysroot-20.2010.36-2-slim/usr/share/qt4/mkspecs/features folder you can find a file labeled link_pkgconfig.prf.

vi link_pkgconfig.prf

to open it

then edit it by adding the word mad before each instance of pkg-config like so.

mad pkg-config
I still don't know yet if this is necessary, but I've updated some help on building Qt http://ctluk.blogspot.com/2012/08/computer-science-qt-build-update.html

Linear Algebra-Isomorphic linear transformation

In order to determine whether or not a transformation is both linear and isomorphic we must check to see if it meets the following criteria:

In order to determine linearity, usually the following two properties are sufficient:
T(f+g)=T(f)+T(g)
T(kf)=kT(f)

In order to determine Isomorphism, we must check to see if the kernel of the transform is 0. Which also means for a given transformation T from V to W, the image is W, fulfilling the rest of the requirements for isomorphism. Thus we can just check to see if the kernel is 0 or non-zero.

Example:
T(M)=M |1 2|
             |3 6|
M=|a b|
     |c d|
|a+3b 2a+6b|
|c+3d 2c+6d|
=
|0 0|
|0 0|

We can then separate this into solving for a,b which will be replicated for c,d
|1 3 0|
|2 6 0|
a = -3b

This makes M =
|-3b b|
|-3d d|
Thus the kernel is nonzero, and so this is not an isomorphic transformation.

Computer Science-Qt Updated

This is an update to what I wrote previously, I was confused on the installation of Qt.

After installing the QtSDK, cd into it
cd /filepath/to/QtSDK
run the SDK Maintenance tool via command line or through explorer window
Complete install(This will take a few hours)
This installation does not complete the installation of the particular version of Qt you want to run.
This now creates a QtSources folder it will have all the versions of Qt you have downloaded listed here. 
Example used version 4.8.1
cd /filepath/to/QtSDK/QtSources/4.8.1
http://qt-project.org/doc/qt-4.8/install-mac.html
follow the installation instructions
Now there is the appropriate configure file. 

./configure
make
sudo make install

Then set the environment variables, you must extend the path.
pico ~username/.bash_profile
PATH=$PATH:/usr/local/Trolltech/Qt-4.8.1/bin

Now the installation is complete when downloading from sdk.

Linear Algebra-Vector Spaces

A vector space is a set endowed with a rules for addition, and scalar multiplication. They must obey the following. For elements in the set f, g, and/or h.

1.(f+g)+h=f+(g+h) and c(kf)=(ck)f
This rule means that all elements in a vector space must obey the rules of association using both addition and multiplication.
2.f+g=g+f
This rule means that all elements in a vector space must obey the rules of commutation.
3.There exists one neutral element n in V such that f+n=f, which also denotes that n = 0.
4.There exists an element g in V such that f+g = 0. This denotes that for every element f there exists an element g which is equal to -f.
5.k(f+g)=kf+kg and (c+k)f=cf+kf
This rule means that all elements in a vector space must obey the rules of distribution.
6.1f=f
This ensures that a vector space obeys identity operations.

Physics-Twin Paradox

Most people have heard of the twin paradox. Two twins exist on earth, one twin goes into a rocketship that can travel at near the speed of light, while the other twin stays on earth. The travelling twin returns a few years later in his time and finds that his twin has aged into an old man. Now we know that there is time dilation by the above equation, finding Δt', that in and of itself is not the paradox. The question is how do we know which twin to apply the formula too? The reason being that although the twin on earth is "still", if the twin in the rocket is moving at some velocity away from the twin on earth, the twin in the rocket can say its the earth moving away from the rocket instead and that he is still.

However, this can be clearly seen if we draw the appropriate spacetime diagram for this situation. The twin in the rocket must have accelerated twice, once to reach the velocity to apply the dilation effect, and the other to change direction to head back towards earth. This breaks the parity between the two situations and the assumption that the twin in the rocket is in an inertial frame for the entire duration of the trip.

Thus the twin on earth is the one that must age more than the twin in the rocket as defined by the dilation effect.

Computer Science-GIMP

Gimp is an open source image editing tool, similar in functionality to adobe's photoshop. Thus its use is in image processing, in the creation and editing of images from a variety of sources. Images are treated as being in layers, capable of editing an arbitrary number of them to form a composite image. Gimp also has animation support through plugins. However the support for Gimp due to lack of manpower has caused releases to be unsynchronized for the different platforms it supports. Originally it was supported on windows, mac, and linux however the versions on mac and windows have fallen behind the linux releases.

http://www.gimp.org/
http://en.wikipedia.org/wiki/GIMP

Gimp also requires downloading XQuartz, which you can get here, or you can let the automatic download occur as part of start up.
http://xquartz.macosforge.org/landing/

Medicine - Pseudoephedrine Study Draft 2010

BACKGROUND
Pseudoephedrine (PSE) is a readily available over-the-counter nasal decongestant which is a sympathomimetic amine. Specifically PSE activates adrenergic receptors in presynaptic neurons causing muscle contraction in blood vessels, also known as vasoconstriction. This results in decreased inflammation and mucous production which relieves the symptoms of the common cold. This study in particular considers one of its alternative uses as an ergogenic aid.

As an ergogenic aid it was banned from use in sports competition as doping is illegal in most realms of professional sports. However, it is debatable whether or not PSE is capable of generating any ergogenic effect, and so there was a period from 2004-2010 where PSE was not on the banned substances list due to WADA’s list replacing the IOC’s list of banned substances.

Despite potential risks, and uncertainty on the ergogenic effects of PSE, athletes have still been known to abuse the use of pseudoephedrine in hopes of gaining an edge on their competitors. Data generated and recorded in the doping control laboratory of Cologne between 1996 and 2003 that included a total of 52,347 in-competition analyses yielded 33 AAFs for pseudoephedrine, which amounts to an average of 4.1 positive controls per year. In 2007 and 2008, that is, 3 years after pseudoephedrine was removed from the prohibited list, the prevalence of pseudoephedrine and ephedrine was determined in 16,335 in competition doping control samples. The analyses resulted in 102 cases of pseudoephedrine use or misuse. In particular there have been a high number of cyclists who have abused this drug in hopes of an edge in competition, out of those 102 cases of pseudoephedrine use, 44 came from cyclists (Thevis et. al).

The potential ergogenic effects that athletes believe PSE can provide is as a stimulant and to increase muscle performance. This is one of the points of controversy between studies, as a boost to muscle performance has yet to be confirmed. PSE’s use as a stimulant is also controversial as its effect on the nervous system is relatively minor and will probably only affect sensitive individuals. This use of PSE is likely due to its association with ephedrine and methamphetamine both of which do have significant effects on the nervous system to increase concentration. The association from ephedrine is due to the plant Ephedra sinica which contains both and is used as a traditional herbal remedy in Chinese medicine. The association with methamphetamine is because pseudoephedrine is used as a chemical precursor in the illicit creation of methamphetamine.

The purpose of this systematic review is to quantitatively consolidate the results of studies relating to the ergogenic effect of Pseudoephedrine in order to determine the validity of its ban from competition. Previous studies have yet to resolve these conflicting results even when using the same testing methods. Chu et. al 2002 found no ergogenic effect while performing a 30 second Wingate test, and yet Gill et. al found that there was an ergogenic effect with the very same Wingate test.

METHODS
In consultation with 2 research librarians, we developed search strategies to identify potentially relevant studies from the MEDLINE, and EMBASE databases. We sought reports of randomized control trials, including crossover trials, in relation to pseudoephedrine use for its ergogenic effect. From medline, our first search strategy retrieved 100 articles between the time period 1950-2010. Our second search strategy retrieved 42 articles between 1950-2010. From embase, our first search strategy retrieved 159 articles between the time period 1980-2010. Our second search strategy retrieved 80 articles between the 1980-2010.

One author and a peer then reviewed the titles and abstracts through our search and retrieved potentially relevant studies. Studies that were excluded in this process included those with co-interventions with other drugs. In particular, for the purposes of data abstraction, articles that related to Ephedra, ma huang were excluded due to it containing ephedrine. Out of those possibly relevant articles we retrieved 16 but were unable to retrieve two. However, as will be explained later, from reading the abstracts those studies just verified what is already established about PSE’s ergogenic effect. Also, out of those two, one of the articles studied the effects of PSE with the additional variable of diving, which is not as relevant to this study. Out of those 16 articles, only 8 were found to be relevant trials devoted solely to studying the ergogenic effects of PSE.

The same author and peer then independently abstracted data into abstraction forms. We resolved abstraction differences by repeated review and consensus. Similarly the same author and peer assessed risk of bias through the use of both the Jadad scale and the Cochrane collaboration’s tool for assessing risk of bias, once again resolving differences by repeated review and consensus. It was determined that articles with a jaded scale of less than 3 would be removed from the study, however all 8 studies were found to have a passing score.

RESULTS
Table 1 summarizes the results gathered from the 8 relevant retrieved articles. Displayed are the results of main tests of each trial, the significance of their results, as well as the quality of the studies. As these studies did not have results in which PSE produced a significant decrease in performance, significant outcomes signify that the study was able to find some kind of ergogenic effect while testing their subjects.

The participants in these studies were primarily male, females accounted for only 9.7% out of the total pool of subjects. Participants were on average 24.38 years of age, and in general good health. In total, the studies examined 93 individuals. 7 out of the 8 studies examined the ergogenic effect of a single dose of pseudoephedrine; the remaining study was a multiple dose trial.

Contrary to the apparent controversy over whether or not PSE can generate an ergogenic effect, the results of these studies seem fairly consistent. There appears to be a threshold value at which it becomes possible to detect the ergogenic effect of pseudoephedrine. The studies considered here can be separated into a relatively low dosage group and a high dosage group. Those below 120 mg, including the trial run by Swain et. al, as well as the sole multiple dose trial run by Chester et. al, fall into the low dosage group, which report no ergogenic effect of any sort. As was mentioned in the methods section there were articles found that were unable to be retrieved, however the abstracts of those articles only confirm this result. Below this dosage, it is definitive that no ergogenic effect can be found, and this range is well above that needed for a therapeutic dose.

Those trials with dosages above this value report finding some sort of ergogenic effect. The trial run by Gill et. al was able to find a significant increase in anaerobic performance while running a 30 second Wingate test, as well as an increase in isometric leg extension. The PSE group in this study had a mean +- SD of 1262.5+-48.5 over the placebo group which had a mean+-SD of 1228.4+-47.1 in peak power measured in watts for the Wingate test. The values in the leg extension test were 321.1+-62.0 in the PSE group over 295.7+-72.4 in the placebo group. However, they were unable to find any benefit in the bench press test, which showed that the possible ergogenic effects would be limited to the lower portion of the body. It’s important to note that while ingestion of PSE resulted in an increase in peak power that did not correspond to a significant increase in total work performed, which corresponds to a higher average power as the time was kept constant in these 30 second Wingate tests. However, there was a trend towards this result, so this study verifies an anaerobic ergogenic effect produced by PSE in high dosage.

The next two studies evaluated the possibility of an aerobic ergogenic effect produced by PSE. Hodges’ 2006 study noted a 5.8 second/2.1% decrease in time to completion in a 1500 m trial. This was noted as significant decrease in time, which would correlate to an increase in average power, which somewhat contradicts Gill’s result should anaerobic vs aerobic comparison be deemed valid. This report was odd in that 8 people were included in study 1 to determine the efficacy of the 1500m test, but only 7 people participated in the study 2 which was the RCT crossover with placebo study. It was not mentioned whether or not participants in study 2 overlapped with those in study 1 which would result in a baseline that nulls the results of the crossover study as the baseline time to completion was lower than either the placebo or PSE group by .3% with significance set at .5%. It is also important to note that all participants showed some sort of improvement when dosed with PSE.

The study done by Pritchard-Peschek et. al in 2010 confirms the trial run by Hodges in 2006. In this study a 180 mg dose of PSE was shown to provide a 5.1% decrease in cycling time set at the same significance level of .5%. Once again all participants showed some sort of improvement when dosed with PSE, as in the trial done by Hodges. In light of the study done by Hodges and Gill, it is confirmed that both an anaerobic and aerobic ergogenic effect is produced by the ingestion of high doses of PSE in the lower portion of the body.

Table 1

Study	Design	Subject description	Pseudoephedrine dosage	Main Outcomes	Outcome results
Gillies et. al 1996	RCT crossover, single dose	10 male cyclists	120 mg 90 minutes prior to testing	Time to completion, Isometric muscle test	Not significant, Not significant
Swain et. al 1997	RCT crossover, single dose	20 male cyclists, 10 relevant to pse	1mg/kg, 2mg/kg 60 minutes prior to testing	Time to exhaustion	Not significant
Gill et. al 2000	RCT crossover, Single dose	22 male athletes	180 mg 45 minutes prior to testing	Wingate test, Isometric leg extension, bench press	Significant, Significant, Not significant
Chester et. al 2002	RCT crossover, multiple dose	8 male endurance runners	60 mg,6 doses over 36 hours, 4 hours prior to testing	5000m time trial, steady state exercise Statistical data not reported	Not significant, Not significant
Chu et. al 2002	RCT crossover, single dose	10 male, 9 female healthy university students	120 mg, 2 hours prior to testing	Wingate test, MVC grip test, dorsi-flexion test	Not significant, Not significant, Not significant
Hodges et. al 2003	RCT crossover, single dose	11 male athletes	60 mg, 90 minutes prior to testing	40% submaximal cycling, 60% submaximal cycling, Wingate test	Not significant, Not significant, Not significant
Hodges et. al 2006	RCT crossover, single dose	7 male athletes from a university’s athlete club	2.5 mg/kg, 90 minutes prior to testing	1500 m time trial	Reported as significant
Pritchard-Peschek et. al 2010	RCT crossover, single dose	6 male cyclists or triathletes	180 mg, 60 minutes prior to testing	70kJ/kg standardized work time trial	Significant

Table 1 cont.

Study	# of Subjects recruited	# of Subjects completed	Jadad scale	Cochrane risk of bias
Gillies et. al 1996	10	10	4 randomization sequence not described	Acceptable
Swain et. al 1997	20	20	5	Acceptable
Gill et. al 2000	22	22	4 randomization sequence not described	Acceptable
Chester et. al 2002	12	8	4/ randomization sequence not described, reason for drop outs acceptable	Acceptable
Chu et. al 2002	19	19	4 randomization sequence not described	Acceptable
Hodges et. al 2003	11	11	4 randomization sequence not described	Acceptable
Hodges et. al 2006	8 or 15 or 7	7	3 randomization sequence not described, dropouts not made clear	Assuming subjects recruited is 7, Acceptable
Pritchard-Peschek et. al 2010	6	6	4 randomization sequence not described	Acceptable

DISCUSSION
Perhaps one of the most confusing aspects in studying the ergogenic effect of PSE is attempting to explain just how it could possibly produce an ergogenic effect. As mentioned in Prtichard-Pescheck et al.’s paper there is speculation (Chester et al., 2003; Gill et al., 2000; Gillies et al., 1996; Hodges et al., 2006; Swain et al., 1997) that PSE exerts an effect through “central” pathways and that the potential mechanisms of action may be related to one of the many sympathetic actions of NE, including increased fuel mobilization or stimulation of the central nervous system.
Hodges et al. (2006) alluded to the possibility that dopamine is involved in PSE’s mechanism of action. However, studies have yet to be done to confirm or deny these possibilities. In relation to its ban from use in competition, as was shown in the sole multiple dose study, no ergogenic effect was found even at the maximal therapeutic dose. The only effects were shown in single dose studies with at least triple that amount. In a study done by Chester et. al in 2004, it was shown that the maximal therapeutic dose done in a 36 hour time period had urine tests results of 149+-72 mg/L. This ranks above the current limits of testing which is 125 mg/L. Considering that there seems to be a threshold value at which ergogenic effect can be made possible, which is far above that of the maximal therapeutic dose, it is recommended that there is once again a raise in the limit of testing for PSE. It is also recommended that further studies be done to evaluate the potential mechanisms of action of PSE in relation to its ergogenic effect for the lower portion of the body.

REFERENCES

Chester, N., T. Reilly, and D. R. Mottram. "Physiological, Subjective and Performance Effects of Pseudoephedrine and Phenylpropanolamine During Endurance Running Exercise." International Journal of Sports Medicine 24.1 (2003): 3-8. Print.

Chester, Neil, David R. Mottram, Thomas Reilly, and Mark Powell. "Elimination of Ephedrines in Urine following Multiple Dosing: the Consequences for Athletes, in Relation to Doping Control." British Journal of Clinical Pharmacology 57.1 (2004): 62-67. Print.

Chu, Kelly S., Timothy J. Doherty, Gianni Parise, Jamie S. Milheiro, and Mark A. Tarnopolosky. "A Moderate Dose of Pseudoephedrine Does Not Alter Muscle." Clinical Journal of Sport Medicine (2002): 387-90. Print.

Gill, Nicholas D., Anthony Shield, Anthony J. Blazevich, Shi Zhou, and Robert P. Weatherby. "Muscular and Cardiorespiratory Effects of Pseudoephedrine in Human Athletes." British Journal of Clinical Pharmacology 50.3 (2000): 205-13. Print.

Gillies, Hunter, Wayne E. Derman, Timothy D. Noakes, Peter Smith, Alicia Evans, and Gary Gabriels. "Pseudoephedrine Is without Ergogenic Effects during Prologned Exercise." Journal of Applied Physiology 81 (1996): 2611-617. Print.

H. Hodges, Alastair N., Brenna M. Lynn, Jonathan E. Bula, Meghan G. Donaldson, Marc O. Dagenais, and Donald C. Mckenzie. "Effects of Pseudoephedrine on Maximal Cycling Power and Submaximal Cycling Efficiency." Medicine & Science in Sports & Exercise 35.8 (2003): 1316-319. Print.

Hodges, Kate, Sarah Hancock, Kevin Currell, and Asker Jeukendrup. "Pseudoephedrine Enhances 1500 M Running Performance." Medicine & Science in Sports & Exercise 37.Supplement (2005): S43. Print.

Pritchard-Peschek, Kellie R., David G. Jenkins, Mark A. Osborne, and Gary J. Slater. "Pseudoephedrine Ingestion and Cycling Time-Trial Performance." International Journal of Sport Nutrition and Exercise Metabolism 20 (2010): 132-38. Print.

Swain, Randall A., David M. Harsha, John Baenziger, and Robert M. Saywell. "Do Pseudoephedrine or Phenylpropanolamine Improve Maximum Oxygen Uptake and Time to Exhaustion?" Clinical Journal of Sport Medicine 7.3 (1997): 168???173. Print.

Physics-Inertial Frame

The idea of an inertial frame is that there are no external forces acting upon the frame. All inertial frames are not accelerating with respect to another inertial frame. Thus you can apply a galilean transformation to the frame, which basically means that you can calculate motion in one frame in the same way you calculate motion in another frame.

As an example let us consider a baseball in parabolic motion. It has a v₀ = 40 m/s with an angle 30 degrees above the horizontal. It has a vertical v0 = 20 m/s and a horizontal v₀ = 20(3)^1/2. It reaches its peak around 2 seconds in flight and will return to the initial height at around 4 seconds, with its vertical velocity oriented in the other direction. It will then get to travel around 80(3)^1/2 meters in this time frame.

Although there is a force acting on the baseball, it is within the system we already considered. Thus if we transform to another reference frame, we can repeat this calculation and get a new trajectory in this new frame. Let us take a reference frame that is moving 20 m/s in the same direction of the horizontal path of the baseball. We would then calculate the same v₀ in the vertical direction, which gives us the same flight time, however the horizontal position in this frame would only be 4[20(3)^1/2-20] which would be around 56 m. as opposed to the 136 m in the other frame. However once you transform this back to the original reference frame, you would get the same path of motion for the baseball.

Its also entirely possible to calculate in the reference where the ball moves only up and down, and has no horizontal motion. This would be the reference frame that has a velocity of 20(3)^1/2 in the direction of motion of the baseball. If there are no forces acting on an object you can always transform to a frame in which it is stationary. However in the case of this baseball, theres the addition of the force of gravity pulling it down for parabolic motion. Thus we can't transform to its completely stationary frame without adding in a force to the frame itself, making it an accelerating frame. Viewing objects in this frame would create imaginary forces on certain objects causing a lack of parity between frames.

Linear Algebra-Minors and Laplace Expansion

The basic idea here is to reduce a matrix into its components. These components are called minors, and the goal of this is to reduce the minor to a 2x2 form so that you can take the determinant with ab-cd where:
|a b|
|c d|

The Laplace expansion can occur along any column/row and equates the determinant of the entire matrix to the sum of the determinants of the minors. Each minor is multiplied by (-1) to the power of its indices. For example row one column one is (-1)^2 and so is positive, but row two column one is (-1)^3 which is negative

For example:
|a b c|
|d e f|
|g h i|

a
|e f|
|h i|
+
-b
|d f|
|g i|
+
c
|d e|
|g h|

Linear Algebra-Determinants and Eliminations

Its also possible to find Determinants through the use of Gauss-Jordan eliminations. Assuming the matrix is invertible and row reducible we can equate the row operations to the determinant with the following rules.
For each row division by a nonzero scalar k, we multiply those k's together.
For each row swap operation, we multiply by (-1)
No change due to row elimination.
Example:
|0 7 5 3 |
|1 1 2 1 |
|1 1 2 -1|
|1 1 1 2 |

|1 1 2 1 |
|0 7 5 3 | (-1)
|1 1 2 -1|
|1 1 1 2 |


|1 1 2 1 |
|0 7 5 3 |
|0 0 0 -2|
|1 1 1 2 |


|1 1 2 1 |
|0 7 5 3 |
|1 1 1 2 | (-1)
|0 0 0 -2|

|1 1 2 1 |
|0 7 5 3 |
|0 0 -1 1|
|0 0 0 -2|

Now we could complete the row reduction but we know from here that only two operations will occur. Dividing a row through by the first entry, and then starting from the last row elimination the above rows through multiplication and addition. The eliminations do not affect the result of the determinant, and all we have to do is multiply by k where k is the scalar value that we used to divide the row to get to a leading 1. Thus we can simply multiple the diagonal once the matrix has been reduced to an upper right triangular matrix.

det=(-1) (-1) (1 * 7 * -1 * -2)

det=14

Linear Algebra-Determinant Patterns

When solving for the determinant it is acceptable to use whatever pattern you want in order to find the solution. Normally when solving for the determinant we can use the first row in order to reduce the matrix into its 2x2 portions.

Example:
|1 2 3|
|4 5 6|
|7 8 9|
The normal formula for the determinant of a 3 by 3 matrix would be
det=1(5x9-6x8)-2(4x9-6x7)+3(4x8-5x7)
det=45-48-2(36-42)+3(32-35)
det=0

However we can solve this in a more arbitrary fashion utilizing a different row than the top row

det=-4(2x9-3x8)+5(1x9-3x7)-6(1x8-2x7)

det=-4(18-24)+5(9-21)-6(8-14)

det=0

Or by the last row

det=7(2x6-3x5)-8(1x6-3x4)+9(1x5-2x4)

det=7(12-15)-8(6-12)+9(5-8)

det=0

This can be used to make it easier to solve determinants by finding the simplest pattern to solve for the determinant.

|0 0 2 3 1|

|0 0 0 2 2|

|0 9 7 9 3|

|0 0 0 0 5|

|3 4 5 8 5|

-5

|0 0 2 3|

|0 0 0 2|

|0 9 7 9|

|3 4 5 8|

-5(2)

|0 0 2|

|0 9 7|

|3 4 5|

-5(2)(2)

|0 9|

|3 4|

-5(2)(2)(0x4-3x9)

det=540

Linear Algebra-Cramer's rule

Cramer's rule is a way of solving for a system of equations assuming that there are n unknowns with n linear equations. This is another way of saying that the coefficient matrix is invertible. Instead of using row reduction methods, Cramer's rule utilizes determinants. Assuming a given coefficient matrix and a solution vector, we first take the determinant of the coefficient matrix. We can then replace the coefficients of a variable x _n with the solution vector and take the determinant of that matrix. If you divide the determinant of the coefficient matrix with the solution vector over the determinant of the coefficient matrix we get the solution to x _n given that the determinant of the coefficient matrix is nonzero.

Example-
|2 3 7  |
|4 5 13|

So to solve this we take the determinant of the coefficient matrix
|2 3|
|4 5|
det=(2)5-3(4)
det=10-12
det=-2

|7   3|
|13 5|
det=(7)5-3(13)
det=35-39
det=-4

|2 7  |
|4 13|
det=(2)13-4(7)
det=26-28
det=-2

x₁ = -2/-2 = 1
x₂ = -4/-2 = 2

Computer Science-Qt

http://doc.qt.nokia.com/4.7-snapshot/install-mac.html
Qt is a cross platform application framework for the use of developing gui's.
Just as a note, some previous versions of Qt have the command line tools listed under Qt/bin which is no longer existent as Qt has begun to merge with Madde in their development.
http://wiki.maemo.org/MADDE

go to QtSDK and double click on the SDK Maintenance tool in order to complete install and updates.

updates found here
http://ctluk.blogspot.com/2012/08/computer-science-qt-updated.html
http://ctluk.blogspot.com/2012/08/computer-science-qt-build-update.html