Google, March 31st, 2009
Research group switches on world's first "artificial intelligence" tasked-array
For several years now a small research group has been working on some
challenging problems in the areas of neural networking, natural language and
autonomous problem-solving. Last Autumn this group achieved a significant
breakthrough: a powerful new technique for solving reinforcement learning
problems, resulting in the first functional global-scale neuro-evolutionary
Since then progress has been rapid, and tonight Google is pleased to announce
that just moments ago, the world's first Cognitive Autoheuristic
Distributed-Intelligence Entity (CADIE) was switched on and began performing
some initial functions. Although CADIE technology will be rolled out with the
caution befitting any advance of this magnitude, in the months to come users can
expect to notice her influence on various google.com properties. Earlier today,
for instance, CADIE deduced from a quick scan of the visual segment of the
social web a set of online design principles from which she derived a profile
These are merely the first steps onto what will doubtless prove a long and
difficult road. Considerable bugs remain in CADIE'S programming, and
considerable development clearly is called for, no more important journey for
Google to have undertaken.
For more information about CADIE see this
for more technical details click
don't take that seriously, it's April Fools' Day I think ;)
Internet Search Engines
Internet search engines are special sites on the Web
that are designed to help people find information stored on other sites. There
are differences in the ways various search engines work, but they all perform
three basic tasks:
* They search the Internet -- or select pieces of the
Internet -- based on important words.
* They keep an index of the words they find, and where
they find them.
* They allow users to look for words or combinations of
words found in that index.
Early search engines held an index of a few hundred
thousand pages and documents, and received maybe one or two thousand inquiries
each day. Today, a top search engine will index hundreds of millions of pages,
and respond to tens of millions of queries per day. In this article, we'll
tell you how these major tasks are performed, and how Internet search engines
put the pieces together in order to let you find the information you need on
Before a search engine can tell you where a file or
document is, it must be found. To find information on the hundreds of millions
of Web pages that exist, a search engine employs special software robots,
called spiders, to build lists of the words found on Web sites. When a spider
is building its lists, the process is called Web crawling. (There are some
disadvantages to calling part of the Internet the World Wide Web -- a large
set of arachnid-centric names for tools is one of them.) In order to build and
maintain a useful list of words, a search engine's spiders have to look at a
lot of pages.
How does any spider start its travels over the Web? The
usual starting points are lists of heavily used servers and very popular
pages. The spider will begin with a popular site, indexing the words on its
pages and following every link found within the site. In this way, the
spidering system quickly begins to travel, spreading out across the most
widely used portions of the Web.
When the Google spider looked at an HTML page, it took
note of two things:
* The words within the page.
* Where the words were found.
Words occurring in the title, subtitles, meta tags and
other positions of relative importance were noted for special consideration
during a subsequent user search. The Google spider was built to index every
significant word on a page, leaving out the articles "a," "an" and "the."
Other spiders take different approaches.
These different approaches usually attempt to make the
spider operate faster, allow users to search more efficiently, or both. For
example, some spiders will keep track of the words in the title, sub-headings
and links, along with the 100 most frequently used words on the page and each
word in the first 20 lines of text. Lycos is said to use this approach to
spidering the Web.
Other systems, such as AltaVista, go in the other
direction, indexing every single word on a page, including "a," "an," "the"
and other "insignificant" words. The push to completeness in this approach is
matched by other systems in the attention given to the unseen portion of the
Web page, the meta tags.
The searches defined by Boolean operators are literal
searches -- the engine looks for the words or phrases exactly as they are
entered. This can be a problem when the entered words have multiple meanings.
"Bed," for example, can be a place to sleep, a place where flowers are
planted, the storage space of a truck or a place where fish lay their eggs. If
you're interested in only one of these meanings, you might not want to see
pages featuring all of the others. You can build a literal search that tries
to eliminate unwanted meanings, but it's nice if the search engine itself can
One of the areas of search engine research is
concept-based searching. Some of this research involves using statistical
analysis on pages containing the words or phrases you search for, in order to
find other pages you might be interested in. Obviously, the information stored
about each page is greater for a concept-based search engine, and far more
processing is required for each search. Still, many groups are working to
improve both results and performance of this type of search engine. Others
have moved on to another area of research, called natural-language queries.
The idea behind natural-language queries is that you
can type a question in the same way you would ask it to a human sitting beside
you -- no need to keep track of Boolean operators or complex query structures.
The most popular natural language query site today is AskJeeves.com, which
parses the query for keywords that it then applies to the index of sites it
has built. It only works with simple queries; but competition is heavy to
develop a natural-language query engine that can accept a query of great
Start with .NET
As Microsoft® said:
Microsoft® .NET is a set of
software technologies for connecting information, people, systems, and devices.
This new generation of technology is based on Web services—small building-block
applications that can connect to each other as well as to other, larger
applications over the Internet.
I will not rewrite what others
write, since all know .NET, but they want to learn, I suggest first to download
.NET framework SDK, visit:
Then look for the .NET framework
SDK. Install it. Its free
then you can use any text editor
to write code.
Notepad is king, but Dos Edit is
the compiler come with it (the
framework) and is command line driven.
the command to compile a .vb file
written in notepad to an exe would be
and that would create an exe
their are other options availble
you may need like adding references to the compile, telling it to compile to a
Note that by this way u can run a
VB or a C# Application, for ASP.NET pages you need IIS (Internet Information
Service/Server as many call)
Introduction to PHP - Starting
This tutorial was written to introduce you to PHP, it assumes you know nothing
about programming at all, starts with the very basics and slowly guides you
through some of the concepts of PHP programming.
PHP is an ever-popular web scripting engine. It allows you to create dynamic web
pages easily and quickly. It has a very rapid learning curve so once you get the
basics down you'll progress very quickly and start writing some nifty scripts.
In newbie terms: it's a thingy that runs in conjunction with a web server that
easily allows you to create web pages that change -- such as guestbooks, list
users' comments, discussion boards, top fifty lists, administration panels ...
and so forth.
Yeah ok, so how do I use it?
Firstly you must ensure you have access to a web server that is compiled or set
up to work in conjunction with PHP. Most good web hosts these days will offer
PHP support, and if they don't you can always bombard them with e-mails and
whine until they do. PHP is getting very popular so the chances are you'll have
access to it. If you don't you can always install it yourself on your own
system, along with a web server. You can find instructions on how to do this, on
a wide range of operating systems, in The PHP Manual at
So How Do I write It?
PHP is very simple to use, the first thing to note is that PHP is embedded into
HTML. You don't have to have pure PHP code in a PHP document, you can switch
between HTML and PHP, let's take a look:-
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<title>My First PHP Page</title>
<h1>My First PHP Page</h1>
echo '<p>This is my first PHP script.</p>';
Simple, eh? Let's have a closer look at it. The script starts off as any HTML
document would, with a DOCTYPE definition followed by an open HTML tag, title,
body tag, the only bit we're interested in is the stuff between <?php and ?>.
That is the PHP code, only when you open the PHP tag, <?php, can PHP code be
This is a great feature of PHP as you can just type out HTML if that's all you
need and jump into "PHP Mode" when and if you need it, remember: a PHP document
doesn't have to contain only PHP.
So What Happens?
Remember how I said you need a web server that works in conjunction with PHP?
You need this because the PHP code has to be executed, the PHP interpreter
handles this. The web server is set up to recognise certain extensions as a PHP
document, say .php. here's what happens:-
Internet browser requests "index.php" from the server.
The web server receives request.
Web server checks "what type of document is this?", oh look ".php", it's a PHP
Web server invokes the PHP engine and passes it the contents of "index.php".
PHP Engine checks the document and anything between <?php and ?> is converted to
PHP returns the HTML output to the web server.
Web server sends document to internet browser.
That make sense? PHP code does not have to be compiled (converted to an
executable program) before hand, when the web server passes PHP the document, it
is then compiled on-the-fly (or interpreted), executed, checked for errors and
then returned to the web server. So what is sent to the client (the person
requesting the document) is not PHP code at all, it is the output of the PHP
code. So ... what would they receive from the above program?
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<title>My First PHP Page</title>
<h1>My First PHP Page</h1>
<p>This is my first PHP script.</p>
All the PHP code did was to output "<p>This is my first PHP script.</p>", when
PHP sends the output from the script back to the web server the above is what
remains. If a user views the source of a PHP page in a text editor they will not
see PHP code, all they will see is the output of that code.
The only bit of the above script we're interested in is this:-
echo '<p>This is my first PHP script.</p>';
We opened into PHP Mode, used the echo function (language construct, whatever)
to output a sentence, or string. Echo is just for printing stuff out, for
echo 'Hello World!';
Would output the text "Hello World!", just type echo 'whatever';, the string
is enclosed in single quotes and after the closing quote is a semi colon ( ;
). We then closed PHP Mode and wrote out the end of the HTML document.
Well in the above script there really is no point, but why not just print out
the '<p>This is my first PHP script.</p>' using normal HTML!?!?.
Because this is an example showing you how you go into PHP Mode, how the web
server handles the request and what goes on in the background, not a
Points To Remember
You need a web server that is working in conjunction with PHP, don't know if
yours is? Ask your host "can I use PHP?". They said "Nope"? Tell them how much
they suck and then install it yourself.
A PHP document doesn't have to contain only PHP, PHP is embedded into HTML.
PHP code is contained between <?php and ?>
The above script was just an example, an example!
Now that we have that cleared up and you (hopefully) know how PHP works, how
to embed it into HTML, (hopefully) have access to a web host that uses it and
didn't fall asleep on your keyboard and are now ready to get coding some PHP.
Click "Variables" and learn how to use variables in your PHP documents.
What is that?
Let's begin as
follow, surf to Google and perform a search on "Internet Merchant Account".
The results are staggering (472,000 results!) If you have created a web based
business and need to accept credit card payments, you need a merchant account,
but your choices are limitless. Before you partner with a provider, take time
to understand the different components of internet credit card processing, and
know what to look for in a merchant provider.
How It Works
Accepting credit card payments through your web site
actually requires multiple components. Between a paying customer and your bank
account, three layers exist:
Payment Gateway - This is the code that will transmit a
customer's order to and from an internet merchant account provider. The
payment gateway provides you the ability to accept customer billing
information (credit card number, credit card type, expiration date, and
payment amount) and the necessary validation steps that must be followed
before the credit card is actually billed.
Internet Merchant Account - A Merchant Account is an
account with a financial institution or bank, which enables you to accept
credit card payments from your clients. The payment gateway actually transmits
the billing information to the internet merchant account provider.
Unfortunately, most local banks do not provide internet merchant account
The main reason why most local financial institutions
or banks do not want to provide online merchant accounts is because
transactions conducted over the Internet are totally different from face to
face transactions where a signature is required to authorize the purchase.
This makes online transactions prone to credit card fraud. Fraud protection
should be one of your primary considerations when choosing an internet
merchant account provider.
Web Site - Regardless of which merchant provider and
gateway service you choose, your web site will need to integrate with your
service providers. Most providers include detailed web integration
How Much Does It Cost
Understanding the total costs of your merchant provider
can be tricky. Remember my Google example - there are more merchant account
providers than there are people looking for internet merchant accounts so ask
questions and be picky! Typically, an internet merchant account will have
three types of costs:
Up Front Application Fees
On Going Fixed Fee
Fixed Transaction Fee
Let us discuss each type of cost:
Up Front Application Fees
Many internet merchant accounts will require an up
front application fee. This fee, supposedly, is to cover their costs for
processing your application. In case you choose not to open an internet
merchant account, they still cover their initial costs. Although common, many
providers waive these fees and I recommend that you choose a provider that
does not require an up front fee.
On Going Fixed Fee
Most all internet merchant providers require a monthly
fixed fee or "statement fee" as it is commonly named, which is simply another
way to cover their costs and make money. You will be hard pressed to find a
provider that does not require this type of fee on a monthly basis. However,
do not choose an internet merchant account that requires more than $10 per
month. Additionally, most internet merchant providers require a monthly
minimum (usually $25). The bottom line is that you will be paying at least $25
per month (on top of the monthly statement fee) for your account.
Usually, the discount rate will be between 2 and 4
percent. The discount rate is the sales commission the provider earns on each
sale. For example, if the discount rate offered is 3%, and you receive a sale
over your web site for $20, you will owe 60 cents to your internet merchant
Fixed Transaction Fee
Usually between $0.20 and $0.30, the fixed transaction
fee is the fixed fee portion of each sale. Unlike the discount rate, the fixed
transaction fee is the same for every transaction. Whether you get a $1 sale
or a $100 sale, the transaction fee will be the same.
A bit more hidden in the small print, a termination fee
can apply if you cancel your merchant account within a specified period of
time (usually within one year). But beware, some merchant providers require a
three year commitment!
If a customer requests a refund and they want their
credit card credited, an internet merchant provider will charge you a separate
fee (usually between $10 - $20). Read the contract carefully, as other special
fees may apply.
Putting It All Together
Now that the different fees have been explained, let us
look at an example set of transactions to help understand what an internet
merchant account may cost your business on a monthly basis.
I have created a simple formula to help you calculate
your monthly charges:
Total Charges = Statement Fee + Number of Transactions
x (Average Sale x Discount Rate + Fixed Transaction Fee) + (Number of
Chargebacks x Chargeback Fee)
For example, let us see you sell widgets over the
internet. The sales price for each widget is $10. You typically have 100 sales
per month and about 5 people request refunds (chargebacks). For this example,
let us assume you have signed up with Jones&Jones internet merchant account
services and have the following terms:
Discount Rate - %2.5
Statement Fee - $10
Fixed Transaction Fee - $0.30
Chargeback Fee - $15
Using my formula above, your monthly Jones&Jones
charges will be:
Total Charges = 10 + 100 x (10 x .025 + 0.3) + (5 x 15)
You can calculate your monthly sales revenue by
multiplying your sales volume by your price:
Monthly Sales Revenue = 100 x $10 = $1000
Your internet merchant provider is costing you %14 or
your total sales.
Making Your Decision
Before you choose and internet merchant provider,
understand all of the cost components. Use your current or projected sales
data to forecast what your internet merchant account costs will be. Planning
ahead can save you time and money.
I hope it's clear now
Note: I used an article by Andy Quick, a co-founder of
sdk is done, you should be ready to use ASP .NET.
Yes! you have advantage of full VB .NET to write your
logic for your asp .net pages now instead of limited vbscript.
I know the old ASP was great, but had a few
limitations, and code gets very fragmented and difficult to maintain after a
while on complicated sites.
However ASP.NET is all old ASP was plus a whole lot
You can use it as before (more or less, with inline run
at server VBScript), but have the ability to use the full power and
functionality of C++.NET, C#.NET and VB.NET without the need of DLLs to
register and the need of CreateObject etc.
You will need Visual Studio .Net of course to compile
the code behind if you are to maximize the performance of the new <asp:xxxxx>
The coolest thing, is that you don't have to do any
browser type detection in ASP.NET, Just create a page based on the minimum
browser spec you want to deliver to, then code using the new ASP tags, then
when the page is requested from the browser, then only the browser supported
code will be delivered!
You can forget about Client side DHTML coding for
validation of form with the new RequiredFieldValidator,
RegularExpressionValidator and RangeValidator objects.
Just drop them on a webForm (ASPX page) and set their
I'm converted, and you would be if you give it half a
What's called "html" - Hyper Text Markup Language - is
much more than that. It's really the set of codes - called "tags" - for
creating an entire internet browser presentation, including the parts that
aren't "hyper." HTML is not a programming language, and an HTML document -
your webpage - is not a program. It's much simpler than all of that, and is a
well-devised collection of tags and markers which will allow you to turn
ordinary text into instructions that a browser can interpret. The use of html
to mark up a document for browser presentation is an act of "writing", and is
not properly referred to as "programming."
"Hypertext" is the jumping frog portion. A hyperlink
can jump to any place within your own page(s) or literally to anyplace in the
world with a 'net address (URL, or Uniform Resource Locator.) It's a small
part of the html language, but is the reason for our effort. (Why in the world
would you want to fiddle with html if it didn't have the linking
capabilities?) Thankfully, it's reasonably easy to get started.
The remainder of the language has been created to allow
us to do all of the other fancy stuff, like adding backgrounds, graphics, and
text. You can spend years becoming expert, but don't need to be to publish
successfully. We probably included some things in our markings that the real
experts would giggle at, but it works, and you can do it too.
For the more literal-minded history buffs, HTML is is
defined as Standard Generalized Markup Language (SGML), and was originated at
IBM in the 1960s as Generalized Markup Language (GML) in an effort to solve
the problem of transporting information across differing computer platforms.
Standardized and accepted by the International Standard Organization (ISO) in
Geneva, Switzerland, it became SGML, which encompasses several variations in
document types and markup languages. However, all browsers are devised to
interpret a specific group of markup tags chosen as HTML, and all assume the
same document type: thus, fortunately, we need only focus on the tags
specifically interpreted as HTML. (Invented by Tim Berners-Lee at CERN,
Geneva's particle-physics laboratory.) The accepted and "official" set of html
tags is maintained and updated at CERN, and is formally noted as Standardized
HTML is based on an 8-bit ASCII Latin-1 character set,
and includes characters for most western languages. Although we write HTML in
plain English, these characters may be invoked when occasionally needed with
the convention of typing an ampersand (&) followed by the number or name of
the character, followed by a semicolon.
Basic level HTML is known as HTML 1, and is the minimum
mandatory instruction set for all browsers. As needs and capabilites have
evolved, there have been additions to the basic set, called extensions. Level
2 adds tags for defining user-input fields, and is the current standard. Level
3 adds mathematical equations, tables, and figures, and is being finalized for
Standard acceptance. Netscape and MSIE already support many Level 3 tags.
These browser developers have become quite aggressive in developing HTML
extensions, and are continually introducing new levels of capability, even
before the tags are formally recognized as "standard." HTML site developers
respond enthusiastically, and author new documents which can only be fully
interpreted by newer browsers. For this reason, it's important and worthwhile
to frequently upgrade to the latest browser edition. As those new tags are
adopted and agreed upon, they are incorporated into Standard HTML (SHTML) as
part of a newly-evolved Extension.
In the next articles, I'll look at resources, tools,
html-writing pointers, and traps to avoid. Finally, I'll spend a little time
on graphics and construction of tables. In structure, I'll start with
overviews, then move to html detail in each topic area.
A great way to learn html is to use your browser's
View_Document_Source option, which will display the actual html code used to
create the page. Find a few pages on the WWW that you really like, and see how
their authors did it!
You may print the html as written for any web page. In
your browser, select File_Save_As and save the file to your chosen directory.
Open the (ASCII) file in your word processor, and print.
Some Flash Games!
that most poeple find difficult about complex numbers is the words complex and
imaginary seem to suggest they're something special, or magical, they're not,
they're just numbers, it's just that until now you havn't seen all tha numbers
that there are, just a small subset of them. What I'm goinna do is go over the
basics of complex number theory, in far more depth than you need, I've gone over
probably 4 weeks worth of the A level further maths course in 1 post but work
through it slowly and it should make sense, you should hopefully get familiar
enough not to be aprihensive about using them, they're just like real numbers,
you can add divide even raise complex numbers to the power of other complex
numbers, find their sines and cosines in fact anything that can be done with a
real number can be done with a complex number.
I'm dealing with them graphicly as well as algebraicly,
which makes it a bit easier to understand, do go through it slowly and
experiment between what's happaning on the diagram and in the algebra.
hope it helps
OK, let's start with the number line, you'll have to draw
your own cos it's hard to do diagrams in text,
just draw a horizontal line on a piece of paper and mark
some numbers on it, 0 in the centre +ve numbers to the right and -ve numbers to
If you remember once apon a time you probably used a
number line to learn about -ve numbers, to do this you had the line going in 1
direction (starting at 0 and moving to the right) and then you extended the line
in the other direction to find more numbers, well we're extending our line
again, this time we're making it a plane.
You have at the moment what is basicly an x axis of a
graph, so draw a y axis, but where you label points on the y axis ad an i on the
end to distinguish them from the real numbers.
so on the x axis we have real numbers and on the y axis
we have imaginary numbers (with the i for imaginary) we havn't yet defined a
plane of numbers, we've just added a second line.
Before we do anything else to this diagram, what happens
if we try to add these new numbers together, what could we define
Ai + Bi
well, let's define Ai as A multiplied by i, where i is
the point 1i on the y axis of your graph, so this means that
Ai + Bi = (A + B)i (distibutive law)
so we can add imaginary numbers to imaginary numbers,
(and obviously real numbers to real numbers) but what happens if we try to add a
real number to an imaginary number?
What is A + Bi
seeing as we havn't defined this, nor given it a name,
let's just leave it as A + Bi
Going back to the diagram, we need a place for all these
new numbers (in the form A + Bi) that's quite easy, let's put the number A + Bi
at coordinates (A, B) on our plane. (for any 2 real numbers A and B)
Ok, so we have a whole load of new numbers, which we can
add and subtract (A + Bi + C + Di = (A + C) + (B + D)i) Now we should work out
how to multiply and divide them.
As you probably know i is defined as the square root of
-1 so i*i = -1, so let's look at a simple example
(3 + 4i)(2 - 6i)
multiply this out
= (3*2) + (3*6i) + (4i*2) + (4i*6i)
the 3*2 we can do, it's 6, but what about the other 3
Well, let's look at 3*6i, add a set of brakets and we get
(3*6)i which is 18i
4i*2 is a bit more difficult, let's add some * signs and
4*i*2 = 4*2*i (Associative law)
and what about the last part, 4i*6i remember that i*i =
-1, we get 4*6*-1 = -24
so we get
(3 + 4i)(2 - 6i)
= (3*2) + (3*6i) + (4i*2) + (4i*6i)
= 6 + 18i + 8i - 24
= -18 + 26i
so we can multiply our new numbers, but what's happening
on our diagram?
first let's define 2 new terms the modulus of a complex
number and the argument.
plot a point on your diagram (3 + 4i) and draw a straight
line from the point to the origin.
the modulus of a complex number is the length of this
line, the argument is the angle this makes with the +ve real axis (in the
direction of 1) going clockwise (ie 5 - i has a -ve argument (or a large one
close to 2*pi) the argument is measured in radians, not degrees (at this stage
you can think in degrees if you want, but you'll need to think in radians when
you want to do other things with complex numbers other than just adding,
multiplying and dividing)
so, what's the modulus of our point? well, we can use
Pythagoras Theorum to get it.
the modulus is sqrt(3^2 + 4^2) = sqrt(25) = 5
with a bit of trigonometry we see that the argument of
our complex number is Atan(4/3) (the inverse tangent of the imaginary part / the
so if I have a number with Modulus R and argument R how
do I express this in the form A + Bi
well, we can think of our number as a right angled
triangle, with angle x and Hypotenuse lenght R, the real part is the adjacent
side and the Imaginary part is the Opposite side.
so our number is R*cos(x) + R*sin(x)i = R( cos(x) + i*sin(x)
) (i is on the left of sin(x) because it makes it easier to pronounce)
What's all this got to do with multiplying then? well,
let's try to multiply 2 complex numbers in modulus argument form.
R(cos(x) + i*sin(x)) * S(cos(y) + i*sin(y))
= R*S( ( cos(x) + i*sin(x) )( cos(y) + i*sin(y) ) )
= R*S( (cos(x)*cos(y)) + (cos(x)*i*sin(y)) + (i*sin(x)*cos(y))
+ (i*sin(x)*i*sin(y)) )
= R*S( ( cos(x)*cos(y) - sin(x)*sin(y) ) + ( cos(x)*sin(y)
+ sin(x)*cos(y) ) )
now over on the trigonometry tread I posted some trig
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
have a look at the real and imaginary parts of the
complex number in brackets, and we see that we can express the product in this
R*S( cos(x+y) + i*sin(x+y) )
so to multiply 2 complex numbers we find the product of
their modulii and the sum of their arguments and we get our new number.
right, I'll do division and then think of this as a good
we know how to multiply complex numbers in modulus
argument form, so to divide them we can do the opposite divide the modulii and
subtract the arguments, but this is a lot of work, we have to convert the 2
numbers into modulus argument form, do the maths and the convert back, if we're
multiplying we don't need to do any conversions and it's easy.
first we need to define something called the conjugate of
a complex number, to get the conjugate of a complex number we negate the
imaginary part, ie the conjugate of A + Bi is A - Bi
the conjugate of a complex number is a reflection of it
in the real axis, which means it has the same modulus but the negative argument,
so multiplying a number by it's conjugate will always give you a real number,
the square of the numbers modulus.
so to divide 2 complex numbers, Z and W we can multiply
top and bottom by the conjugate of W
NB, I'll use W' to represent the conjugate of W, although
really it's denoted by W with a bar over it.
Z/W = (Z * W') / (W * W')
we can multiply Z by W' easily enough and W * W' is very
easy and gives us a real number, so we get a complex number divided by a real
number, which we can do, just divide both parts by the real number, tada.
I'm gonna stop now, but hopefully that's enough to give
you a basic understanding of complex numbers, I've gone through quite a lot, but
you should be able to work out the bulk of it, in any case you should be set to
do your program, post If you have any more problems.
The best way to
treat an imaginary number (or, a complex number) is to treat it like a regular
For example : what is sqrt(i) ??
sqrt(-1) = i
but what about sqrt(i) ??
That is simply a number that when multiplied together,
That turns out to be
(1/sqrt(2)) + (1/sqrt(2))*i
Actually, there are two numbers that qualify. You can
figure out the other one.
Also, what is (4 + 3i) / (2 + 5i) ??
You can divide complex numbers.
A simple way to do it is to multiply the top and bottom
by the same number, (2 - 5i). This will turn it into its more familiar format
of a + bi.
The answer is 23/29 - (14/29)*i
You can also take the log of a complex number, cosine,
sine, tangent, etc etc etc.
Why Do We Need ... ??
We need friends
for many reasons,
all throughout the four seasons.
We need friends to comfort us when we are sad,
and to have fun with us when we are glad.
We need friends to give us good advice.
We need someone we can count on to treat us nice.
We need friends because we are social in nature
and having friends makes us feel secure.
We need friends to remember us once we have passed
sharing memories that will always last.
That's why I need YOU!
ابتسم ...أنت في دولة
عندما تكتظ (المقاهي)
بالشباب ... وتشكوا المساجد والمكتبات من الغياب.. أنت في دولة عربية.
عندما يستضيفون (راقصة)
لتتحدث عن (تحرير) فلسطين ... يجب أن تبكي فأنت في دولة عربية.
عندما تدرس الابتدائي 5
سنوات .. والإعدادي 3 سنوات ومثلها المرحلة
الثانوية .. وأربع سنين في الجامعة أو خمسة .. لتعمل بعدها في سوق الخضار
.. لا تيأس أنت
في دولة عربية .
عندما يكون هناك ستة
ملايين (عامل) أجنبي .. وثلاثة ملايين (عاطل) . أنت في دولة عربية.
عندما تقوم من النوم
لتجد في هاتفك المحمول رسائل ليس لها أي معنى ...أنت في دولة عربية
عندما تكون هناك (خمسة
عشرة) مجلة تهتم بـ (الشعر الشعبي) ولاتكون هناك
مجلة واحدة أو (نشرة) تهتم بالأمور العلمية ... أنت في دولة خليجية
عندما تذهب إلى تلك
المنطقة في بلدك .. فلا تجد منهم من يتحدث العربية
وتظن أنك تعديت الحدود حتى وصلت إلى (دكا)...لا تستغرب ... أنت في أسواق
إحدى دول الخليج حيث كل البائعين أجانب
عندما (تضحك) عليك شركة
الاتصالات في بلدك و(تشفط) كل اللي في جيوبك ..أنت في دولة عربية
الأمريكية) وتأكل (الهمبورجر) وتشرب (البيبسى) ثم تطالب
بمقاطعة المنتجات الأمريكية ...أنت مجنون تعيش في دولة عربية.
أن لا تحصل على الترقية
في عملك إلا (بواسطة) ولا تجيب تقدير في الجامعة
إلا (بواسطة) ولا تجد الوظيفة إلا (بواسطة) ولا تنتقل إلا (بواسطة) ولا
تحصل على (حقوقك) إلا بواسطة . أنت مواطن مسكين مقهور مظلوم تعيش في دولة
عندما تستنكر تلك القناة
الإخبارية في ذلك البلد الهجوم على (دولة عربية)
وفي نفس الوقت
ينطلق الهجوم من ذلك البلد ..أنت تعيش في ( قُطر ) عربي
عندما تكون (رجل) و
تستعمل الإنترنت باسم (بنت) ... أنت عربي.
عندما تصل إلى هذا السطر
ولا زلت مستمراً في القراءة ...الحمد لله هناك (مجنون غيري).
ابتسم ...أنت في دولة
ما هو وجه التشابه بين الكمبيوتر والتاكسي والحفرة ؟
ج 1 : الكمبيوتر .....
التاكسي ...... حاسب يا
الحفرة ........ حاسب لا
س2 : ما هي قمة الحيرة ؟
ج 2 : يقال لك اجلس على
ركن غرفة مستديرة
س 3 : سؤال يجيب عليه
ج3: قطار بسير بسرعة 90
كم / الساعة ، ويتوقف في 8
محطات ، وسرعة الرياح
134 م / ثانيه
فما اسم سائق القطار ؟!!!
س 4 : ما هي قمة الذكاء
ج 4 : هو ان تجد ركن
س5 : ما هي قمة الالم ؟
ج 5 : التزحلق على
زحلاقه مغطاه بشفرات حلاقة وشظايا الزجاج
س 6: ما هي قمة العذاب ؟
ج 6 : السقوط بعد ذلك في
حوض به كولونيا
س 7 : ما هي قمة الادب ؟
ج 7 : ان تطرق باب
الثلاجه قبل فتحها
س 8 : ما هي قمة الذهول
ج 8 : ان يفتح احدهم لك
س 9 : كيف تضع 4 افيال
في سيارة فولكس؟
ج 9 : اثنين قدام واثنين
س 10 : كيف تضع 8 افيال
في سيارة مرسيدس ؟
ج 10 : نبيع المرسيدس
ونشتري 2 فولكس
س 11 : كيف نضع فيل في
الثلاجة على ثلاث مراحل ؟
ج 11 : - نفتح الثلاجة 2
- ندخل الفيل في الثلاجه 3 - نقفل الثلاجة
س 12 : كيف نضع زرافة في
ثلاجة على اربع مراحل ؟
ج 12 : - نفتح الثلاجة 2
- نخرج الفيل 3 - ندخل الزرافة 4- نقفل الثلاجة
س 13 : ما هو الشيء الذي
ننام عليه ونجلس فوقه ونغسل به اسناننا ؟
ج 13 : السرير والكرسي
س 14 : ما الذي له راسان
و 8 اقدام ؟
ج 14 : كلبان
س 15 : كيف نقسم برتقاله
واحده على ثلاثة اشخاص
بحيث يأخذ كل واحد نصف
ج 15 : نقول للبرتقاله
انتي برتقاله انتي
، فترد انا مش برتقاله
برتقاله كيف ؟ فتقول انا برتقاله ونص وكذا نقسمها على ثلاث اشخاص
س 16 : كيف تستطيع ان
تعرف بأن 8 افيال
متواجدين داخل فندق
الشيراتون بدون ان تدخل الفندق ؟
ج 16 : اعرفهم ، اذا
وجدت 2 فولكس في مواقف الفندق
س 17 : احترقت حديقة
الحيوانات فاحترقت جميع الحيوانات التي بها ، إلا الزرافة لم تحترق .... لماذا ؟
س17 : لاننا وضعنا
الزرافة في الثلاجة
س18: ماهو الغباء ؟
ج18: انك تستمع ا لشريط
وماهي قمة الغبا ؟
انك تقلب الشريط
س 19 : ومن هو اغبى من
هو الذي يطلب الشريط
ليعمل عليه نسخة
Yacoub Sabatin (c)
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