MAGIK & LOGIC OF A RUBIK CUBE

                  MAGIK & LOGIC OF A RUBIK CUBE 

Rubik's Cube is a famous puzzle cube invented by Ernö Rubik in 1974.

For those unfamiliar with the cube, the basic concept is that the cube is made up of 27 cubelets. The exposed faces of these each have a different colour. Rubik invented a mechanism whereby any layer of cubelets (i.e. 9 cubelets) can be rotated in a clockwise or an anticlockwise (counterclockwise) direction, independently of the other layers. By doing this many times at random, the colours displayed on the faces become jumbled up. The objective of the puzzle is to restore the initial position in which each side of the cube shows only one colour.

In the approach to solving Rubik's Cube described here, we use the colours and the visualization of the cube employed in Rube Cube, as found in BrainBoxFun from TopAccolades Limited.

In the version of Rube Cube found in BrainBoxFun you are able to see all six sides or faces. Initially, you see a completed cube, with red showing on the front face, blue on the right face and white on the top face. Projected behind, to the left and below the cube, you can see the other three faces, as if reflected in mirrors or as if the tiles on the three hidden faces have been lifted away; initially, the back side shows pink, the left side shows green and the bottom side shows yellow.

If you are new to the cube, you will soon learn that solving it is far from easy. This is hardly surprising since there are billions of permutations, and some people have taken decades to solve it (and most people who have started it have never completed it). Below, however, we show you an approach to going about this; not only that, but we hope that you will be able to remember how to solve it.

The approach to solving the cube is suitable for beginners, and uses the tools (also called algorithms or rotation sequences) that, we understand, were first developed by David Singmaster. David Singmaster also developed a widely-used notation for describing moves and solutions; however, here we use a notation devised by David Wolstenholme, as it results in word-like strings of letters that are easier to remember.

Wolstenholme notation

Face and layer notation

The six faces of the cube are each referred to by a single letter, as follows:

• F = Front
• R = Right
• T = Top
• B = Back
• L = Left
• D = Down

The same notation is used to refer to the layer of nine cubelets that include that complete face. These letters are also shown on the picture above.

Layer rotation notation

The notation for rotation of a layer consists of two letters: the letters F, R, T, B, L and D for the layers, as above, followed by another letter indicating the type of rotation, either: O, A, or I, where:

• O = Clockwise 90 degrees (remember Ordinary clock, or O'clock)
• A = Anticlockwise 90 degrees (also called counterclockwise)
• I = Inverse, i.e. a rotation of 180 degrees

So, FO means a clockwise rotation of the Front layer by 90 degrees, while BA means an anticlockwise rotation of the Back layer by 90 degrees, and RI means a rotation of 180 degrees (clockwise or anticlockwise - it makes no difference) of the Right layer.

On the picture above, you will also see some blue arrows, each with a two-letter label. The arrows indicate the rotation of the six layers that each include a complete face, while the labels specify the rotation in this notation.

Important: Please note that the terms clockwise and anticlockwise are always used to indicate the direction of rotation when facing that particular side or layer. This means that an anticlockwise rotation of the Back layer looks like a clockwise rotation when viewed from the front. That is why you will see that the arrows associated with labels FO and BA both appear to be showing a clockwise rotation when viewed from the front.

Cube rotation notation

As well as rotating a layer, we can also rotate the complete cube. We use a three-letter specification for cube rotations, in which we add the letter C to the end to signify that the entire cube is to be rotated. So, FOC means that the entire cube is to be rotated around the Front-Back axis in a clockwise direction when viewed from the Front. Note that the cube rotation FOC is the same as the cube rotation BAC. 

Tool/algorithm notation

A tool, or algorithm, is just a sequence of layer rotations and/or cube rotations.

In the tool sequences used in the approach described, we generally join two specifications of layer rotations together to form a 4-letter 'word'. So, ROTA specifies a clockwise rotation of the Right layer followed by an anticlockwise rotation of the Top layer.

As will be seen, these 4-letter words and the 3-letter cube specifications often form recognizable words or names, or maybe sequences of letters that sound like words. Examples include: FOTO, ROC, BAC, ROTA, RITA, ROTI, or RIFA. This is the primary reason for choosing the notation above, since we humans are good at remembering words and can build stories around them to help us remember them.

Later on, we also introduce names for the tools used. These names, and associated mnemonics, also form part of the notation.

The Basics

Remember that while the individual layers on a cube can rotate, the relative positions of the centre squares on each face will remain unchanged. In the Rube Cube version of Rubik's Cube,

• the red centre square will always be opposite the pink one;
• the white one will be opposite the yellow one; and
• the blue one will be opposite the green one.

Also, if you have the white centre square at the top and look down, you will find that the centre squares of the sides are always ordered red, green, pink and blue as you move clockwise. Please note that if you have a physical cube, the colours and their relative positions may be different.

We will refer to the centre squares of faces as centre squares, to pieces at the 8 corners, each of which displays three different colours, as corner pieces, and to the remaining pieces (those in the middle of the edges, each of which displays two different colours) as edge pieces. Because the centre square is fixed in position relative to the other centre squares, we will also, for example, refer to the layer containing the white centre square as the white side, even though not all the pieces may be displaying white on this side at the time.

When trying to solve the cube, it is not enough just to get the pieces into the correct position; the pieces also have to have the correct orientation (that is, the colours have to be facing the correct way). Next we introduce two concepts concerned with orientation of the pieces.

Edge Flips

You will often find that you would like to 'flip' an edge piece. By this, we mean that we would like to take an edge piece that has a certain colour on one side and do something so that it ends up with the other colour on this side.

Corner Twists

You will often find that you would like to 'twist' a corner piece. By this, we mean that we would like to take a corner piece that has a certain colour on one side and do something to it so that a different colour ends up on this side. Because it shows three colours, the effect of doing this is that the three colours appear to have twisted round, either clockwise or anticlockwise

The diagram below shows an anticlockwise twist (see how the blue colour has moved anticlockwise from the Right side to the Top side).

Top-layer Tools

A tool is a sequence of rotations that is designed to achieve a certain result. There are four basic tools described here, where their broad objectives are shown in brackets,

• Flipper (Orientate edge pieces)
• Swapper (Position corner pieces)
• Twister (Orientate corner pieces)
• Looper (Position edge pieces)

These four tools are not only useful but also easy to describe, since they have an impact on the Top layer only. The bottom two layers end up unchanged by the application of these tools, so you can make use of them safe in the knowledge that only the Top layer is affected.

Many tools can, of course, be used in more than one way: a screwdriver, for example, can be used not only to tighten a screw, but also to untighten it, i.e. to reverse or undo the impact. These tools can also be used in reverse. Essentially, the reverse of a tool is just the same set of rotations as the main tool, but carried out in reverse order and with the direction of rotation reversed. So, if the main sequence of rotations is FOTO ROTA RAFA, as for Flipper, then the first rotation for the reverse will be on the same layer as the last rotation of the basic sequence, i.e. on the F layer, but in the O direction instead of A, i.e. FO. The next rotation will be on the R layer, but this time in the O direction. The complete sequence for the reverse of Flipper is: FORO TORA TAFA. Note that the I direction remains unchanged, since a 180 degree rotation requires another 180 degree rotation to reverse it. To distinguish the uses of the tool, we add the word Reverse in front of the name when it is used in reverse, e.g. Reverse Flipper.

You only have to remember the main set of sequences, since you can always work out the reverse sequence from that, as above.

These tools will be used at most stages of solving the cube, so we will describe them all now. You will see associated with each tool, and its reverse, an icon that describes the impact. This summarizes the impact by pointing out which corners have been twisted, and in which direction, which edges have been flipped, and which pieces are moved to another location. The intensity of colours is also important: the intense colours and black signify the primary impact we are looking for, while the less intense colours mean that these changes take place but they are not of primary importance - they are just side-effects.

Note: Always consider that the movement occurs after other changes, such as twists and flips, have been made. So, a piece shown as being flipped but also with an arrow on it means that the piece initially at this position is flipped but is also then moved in the direction of the arrow. So, if the Front-Right corner is blue and has an arrow pointing to the Back, this means that the piece initially in this position is twisted clockwise, but ends up located in the Back-Right corner.

Note: The arrow states in which direction the piece moves. This is always unambiguous, as corner pieces must end up at other corners, and edge pieces at other edges.

Name	Sequence	Impact	Primary purpose	Secondary effects
Flipper	FOTO ROTA RAFA		Flip the edge pieces on the Right and Front sides.	The Back-Right corner is twisted clockwise, the Front-Right corner is twisted anticlockwise. The three rightmost edge pieces move around one place clockwise. The Back two corners swap places, as do the Front two.
Reverse Flipper	FORO TORA TAFA		Flip the edge pieces on the Back and Front sides.	The Back-Left corner is twisted anticlockwise, the Front-Left corner is twisted clockwise. The three rightmost edge pieces move around one place anticlockwise. The Back two corners swap places, as do the Front two.
Swapper	LOTA RATO LATA ROTI		Swap the positions of the two Right corner pieces.	All corners except the Back-Right one are twisted clockwise. All four edge pieces move around one place clockwise.
Reverse Swapper	TIRA TOLO TARO TOLA		Swap the positions of the two Right corner pieces.	All corners except the Front-Right one are twisted anticlockwise. All four edge pieces move around one place anticlockwise.
Twister	RATA ROTA RATI ROTI		Twist three corner pieces (all except the Back-Left corner) anticlockwise.	The three rightmost edge pieces move around one place anticlockwise.
Reverse Twister	TIRA TIRO TORA TORO		Twist three corner pieces (all except the Back-Left corner) clockwise.	The three rightmost edge pieces move around one place clockwise.
Looper	RITA FOBA RIFA BOTA RI		Move the three rightmost edge pieces around one position anticlockwise, as if looped together. Back->Front->Right->Back	None.
Reverse Looper	RITO BAFO RIBO FATO RI		Move the three rightmost edge pieces around one position clockwise, as if looped together. Front->Back->Right->Front	None.

Overall strategy

The overall cube-solving strategy employed here is: Fix the four corners of the first layer; then fix the edge pieces in the first two layers of each of the sides; and, finally, solve the last layer.

Fix the four corners of the first layer

We will use white as the first layer. Our objective is to correctly position and orientate all the corner pieces that have a white side - with the white side displayed on the side with the white centre piece.

This is the easiest part of solving the cube, since you do not need to worry about how you disturb the other layers. You can try positioning and orientating the corner pieces with a white side using your own set of rotations, as described next, where the white centre square is positioned on the Top.

First, bring up one of the corners with a white side so that it has its white side on Top. Then rotate the Top so that colours of the sides of the corner piece match the colours of the centre square on the sides. In the image below, the white/red/blue corner, circled, has its sides correctly matching up with the white, red and blue centre squares.

Then bring the other Top corners into the correct position, with their white sides on Top and their side colours matching the centre squares of the sides.

If you're having problems, our recommended approach is to bring the corner piece you wish to position into the Top layer to the Front-Right-Down corner, directly beneath the corner in the Top layer into which it should move. The following demonstrates some moves that should help; these are fully described afterwards.

This shows the most difficult situation at A, where the last corner piece (red/green/white), shown circled, is at the Front-Right-Down corner, directly beneath the corner it needs to move to. However, the white side is pointing downwards, so this means we can't just rotate the Front or the Right side to bring it to the Top and find that it is correctly orientated, as the white will not be on the Top. We therefore take steps that will bring the corner back to the same place, but twisted. First, we rotate the Down side (DA) to bring the piece to the Front-Left-Down corner, then do an LA rotation, which moves it up to the Front-Left-Top corner. However, this also moves the two leftmost Top corners so that their white sides are now on the Back side. We can then turn the Front 180 degrees (FI) to bring the piece back into its original corner, followed by an LO rotation to restore the corners on the Left with their white sides on Top.

Position B, where we are now, shows that the three Top corners are back to their correct places, and that the piece in the Front-Right-Down corner has been twisted clockwise compared to its position in A, so that the white side is now on the Front. We can now bring the piece up to the corner above by first doing a BO rotation to move the back two white-topped corners out of the way, then doing an RO rotation to bring the corner to its correct position, and then a final BA to restore the two corners at the Back, so that we now have all four corners in their correct positions.

In the above we have covered the cases where the white side of the Front-Right-Down piece is on the bottom (position A) and on the Front (position B). If you're trying to place the corners and find that the white side is on the Right side, you do similar moves to the last three, but on the Front and Left sides, namely: LA, FA and LO.

Alternatively, instead of making your own set of rotations, you can make use of the Swapper and Twister tools as follows. First, put the face with the white centre square to the Back. Second, identify where the corner pieces with a white side are, and use rotations of the Front and Back layers and the Swapper tool to bring all of them to the Front (if they're at the Back in the wrong place).

Then, rotate the cube so that the Back-Top-Right corner doesn't have the correct piece in it, rotate the Front layer so that corner piece that should go at the Back is at the Front-Top-Right corner, then use Swapper to push it to the Back. Finally, and if needed, use either the Twister or Reverse Twister tool, as appropriate, to orientate the Back-Top-Right corner piece. Rotate the cube around the Front-Back axis, and deal with another corner piece. Repeat until all the corner pieces on the white side are correct.

Fix the edge pieces in the first two layers

Once the corners of the first, white layer have been fixed, we can see that to complete the top two layers (the white layer and the one between white and yellow) we just need to put the eight edge pieces in these layers into their correct positions with correct orientation.

To do this, we will use the Looper and Reverse Looper tools as our main tools, supported by the Flipper and Reverse Flipper tools and some easy rotations to get the pieces in the correct starting positions for using these tools. We operate on one of the side colours (all but white and yellow) at a time. To begin doing this, we always start off by putting the first, white layer at the Back if it's not already there.

Our basic approach is that we work on the Top layer and use the Looper to push the edge piece we want to have at the Back edge from the Front to the Right edge, then use the Looper again to push the piece we want to have at the Right side from the Front to the Right, which also moves the piece that was there to the Back edge where we want it.

To demonstrate this, the image below shows our starting position for doing this on the blue side, where we have the blue/white edge piece (circled in black) at the Front (blue on Top). Running the Looper tool pushes this piece to the Right edge. We then move the piece we finally want to be positioned here, the blue/pink piece, which is circled in pink, to the Front at the Top with a simple FA rotation. Finally, we run the Looper tool again which results in both the Right and Back edge pieces on the blue side in their correct positions.

This is a neat use of the tool, since we move the two edge pieces into position with two uses of Looper. However, we had the ideal starting position in this example, where both edge pieces were already at the Front and correctly orientated. Often we find that the required edge pieces are not at the Front, and, once moved there, they are not both correctly orientated. So, we need to move edge pieces forward to the Front layer, and to flip incorrectly orientated pieces.

Bringing edge pieces to the Front layer

If the edge piece you are interested in is in the Back layer or the layer between the Back and the Front, and needs to be brought to the Front layer ready for use of the Looper as just described, simply use the Looper or Reverse Looper to bring it forward.

In this example, we want to place edge pieces in the red side. We see that both the red/white piece, circled, and the red/blue piece are in the middle layer between the Front and the Back. This means we need to bring both forward to the Front layer. We can bring the the red/white piece forward by bringing the green side to the Top, then use the Reverse Looper, which brings it to the Front.

We also need to bring the red/blue piece to the Front layer, which we can do by bringing the pink side to the Top (FOC) then using the Reverse Looper, as before. As both the pieces are correctly orientated (the red sides of the pieces are not on the Front), no flipping is required so we can insert them into the red side in the correct positions as before.

If we now focus on the green side, where we're interested in the green/white and green/red edge pieces, we find that the green/white piece, circled, is in the Back layer on the pink side. To bring this forward, we rotate the cube so that the pink layer is at the top, then use the Looper tool, to brings it to the Front.

However, we're not yet ready to use the Looper to move the pieces into their correct positions on the green side, as the green/red piece has the green side on the Front, so it needs to be flipped.

Flip incorrectly orientated pieces

To flip pieces, first rotate the cube so that the white side is on the Down side. Then rotate the Top layer so that the piece you want to flip is in the correct position for flipping by the Flipper or Reverse Flipper (and make sure that any pieces you don't want flipped aren't in a position to be flipped as well). In this case, we start off with the green/red piece, circled, at the Front. We could now use either the Flipper or Reverse Flipper to flip the piece. However, we notice that the pink/green piece will also need to be flipped for completing the pink side, so, as the Reverse Flipper will flip both, we use this.

Obviously, if both pieces for a particular side need to be flipped, you can always position them to be able to flip both with one use of the Flipper or Reverse Flipper.

In our example, we are now ready to use the Looper on the green side, and then to use these techniques to complete the pink side, leaving us with the first two layers complete.

Solve the last layer

Once the first two layers are complete, only one layer needs to be solved: the layer that should display yellow on its main side. To solve this we first bring the yellow side to the top.

The last layer is solved in four stages:

Each stage makes use of only one of our four tools. You may have noticed that the four tools vary significantly in their side effects, from Flipper, which has many, to Looper, which has none. As we move through the stages we use a more refined tool.

The order in which the tools are used and their names have the same initial letter, which helps you to remember them: First - Flipper; Second - Swapper; Third - Twister; Last - Looper. Their primary focus (e.g. Flipper is concerned with edge piece orientation) helps you to remember what you need to do in these stages:

1. Orientate edge pieces
2. Position corner pieces
3. Orientate corner pieces
4. Position edge pieces

1. Orientate edge pieces

To begin the last layer, now on the Top, we first form a yellow cross by ensuring that the four edge pieces have yellow showing on the Top. It is important to note that we don't, at this stage, care whether or not they're in the correct positions (i.e. whether their side colours match up with the centre squares of the sides).

Clearly, if some of them are not displaying yellow on the top, we need to flip them using Flipper or Reverse Flipper. Now, you will find that you begin with one of the following scenarios:

• the cross is already formed, in which case there's nothing to do at this stage;
• two of the edge pieces are showing yellow
• none of the edge pieces are showing yellow

If two of the edge pieces are showing yellow, we simply use either Flipper or Reverse Flipper to flip the two that aren't showing yellow, making sure that we rotate the Top to get them in the correct positions. In our example, there are already two edge pieces showing yellow on the Left and at the Back, which just happens to be correct for using Flipper, since this flips the Right and Front edges, so we use this.

If there were two edge pieces showing yellow and these were opposite each other, you would rotate the Top so that these were on the Left and Right sides, then use the Reverse Flipper.

If none of the edge pieces were showing yellow, you would first run Flipper, which results in two yellow edges opposite each other, then rotate the Top 90 degrees (TO or TA) and run Reverse Flipper.

We now have the yellow cross (edge pieces correctly orientated but not necessarily correctly positioned), so we can move to the next stage.

2. Position corner pieces

Now we rotate the Top to see whether we can get all the corners in their correct positions, regardless of the fact that they may not have yellow showing on the Top. So, we're looking to position the red/blue/yellow corner in the corner where the red, blue and yellow sides meet, for example. If you find that you can rotate the Top so that all four are correctly positioned, then this stage is complete.

If the four corners aren't all correctly positioned, then we need to look to find two that can be correctly positioned, leaving the other two incorrectly positioned. This often seems difficult to do, due to the fact that corners may be twisted, but do persevere and you will find two that can be correctly positioned.

In our example, we are lucky in that we can see that the two corners at the Back are correctly positioned, even without rotating the Top, while the Front two, one circled in black and one circled in pink, are not.

Once you have found the two corners that are correctly positioned, you need to swap the positions of the two that aren't. If the two that need swapping are on one side, as they are in our case, we just rotate the cube to bring them to the Right side and use the Swapper, as shown below.

If the two that need swapping are diagonally opposite each other, just use Swapper to swap over any two corners. After doing that, you will find that you then have two corners that need swapping on one side, so you can just rotate the cube to get these on the Right side and use Swapper again.

We now have the edge pieces correctly orientated and the corner pieces in their correct positions, but not necessarily correctly orientated.

3. Orientate corner pieces

Now that the corners are in their correct positions, you will probably find that some of them are not correctly orientated and need twisting. If you're lucky enough to find that they're all correctly orientated, just move on to the last stage.

Check each corner in turn to see what sort of twisting is required to orientate it, if any, and count up the numbers needing clockwise and anticlockwise twists. Clearly you're going to use the Twister or Reverse Twister tool, but it is not always easy to work out how to use them. If you think about what they do you should be able to work out how to use them, but the following guide gives details.

Three clockwise rotations required

Rotate the cube so that the corner that doesn't need twisting is in the Back-Left corner, then use Reverse Twister.

Three anticlockwise rotations required

Rotate the cube so that the corner that doesn't need twisting is in the Back-Left corner, then use Twister.

Two clockwise and two anticlockwise rotations required

Rotate the cube so that one of the corners that needs an anticlockwise twist is in the Back-Left corner, then use Twister. This will leave you with three corners requiring anticlockwise twists, so do as instructed above.

One clockwise and one anticlockwise rotation required

Rotate the cube so that the corner that needs a clockwise twist is in the Back-Left corner, then use Twister. This will leave you with three corners requiring clockwise twists, so do as instructed above.

In our example, where corners needing a clockwise twist are circled in black, while those requiring an anticlockwise twist are circled in pink, we see that the Back-Right corner needs a clockwise twist, while the Front-Left corner needs an anticlockwise twist; the other two are already correctly orientated. So, we rotate the cube so that the one requiring the clockwise twist is in the Back-Left corner and run Twister. This produces the situation where three corners need a clockwise twist, so we rotate the Top (TI) to put the correctly orientated corner in the Back-Left corner. Then we run Reverse Twister to give us all corners correctly orientated. It also happens to complete the final layer, so a simple rotation completes the cube.

4. Position edge pieces

In our example, we've been lucky to have achieved the ideal outcome from orientating the corners: all the edges are in the right position. However, in other cases we may find that 3 or 4 edges are in the wrong position. We'll show you how to deal with the worst case of 4 wrongly positioned edges, which also involves handling 3 edges in the wrong position.

In our starting position, A, there are four incorrectly positioned edges. We therefore apply Looper, which results in three incorrectly positioned edges. To handle this, we need to bring the correctly positioned side to the Left (TIC cube rotation).

We're now at position B, the situation in which we deal with three wrongly positioned edges. Looking at their layout, we see that the edges need to move clockwise (red needs to move to where pink is, for example). Running Reverse Looper corrects the positions and completes the puzzle.

Here its over the funniest and worst head eater is broken out..................................................................

INTERNET CONNECTION SHARING

Sharing one Internet connection among several computers

Sharing one Internet connection among all the computers on your home network saves time because you have to set up only one connection. And it saves money because you don't have to buy an individual Internet account for each computer.

There are two ways to set up Internet connection sharing: by using a router, or by using Internet Connection Sharing (ICS).

Using a router

How it works: Each computer connects to a router (sometimes called an Internet gateway device). The router, which can be wired or wireless, connects to a broadband (DSL or cable) modem, and the modem connects to the Internet. The router and modem can also be purchased as a single device.

A network using a router and modem

Make sure your router has a built-in firewall. A firewall can help stop unwanted connections to your network from the Internet.

Using ICS

How it works: One computer on the network is designated as the host computer. The host computer connects to the Internet and the other network computers share that Internet connection.

A network using Internet Connection Sharing (ICS)

This method is a bit less convenient because it requires the host computer to be turned on all the time. However, it's the best method if you have a dial-up Internet connection, or if you use a modem with a USB connection.

Share Your Mac's Wired Internet Connection via Wi-Fi.

Many of us these days have more than one device that we'd like (or need) Internet connection for -- smart phones and tablets, laptops and mobile Internet devices. Hefty tethering charges and fees for wi-fi hotspot access when you're away from home or travelling can add up for all those devices; it isn't always economical to pay to have all of them connected. Thankfully, there's free software called Connectify that can turn your Windows 7 laptop into a wi-fi hot spot or wi-fi access point of sorts, sharing its Internet connection over wi-fi with any other nearby wireless devices (any wireless-capable device, running Windows 7 or not). Here's how to use Connectify to get wi-fi Internet access on multiple devices through your Windows 7 laptop.

Note: If you have a wired Internet connection (e.g., one Ethernet connection in your hotel room) or a 3G cellular data modem for your computer, you can also use Internet Connection Sharing, a built-in Windows feature to share an Internet connection. See How to Share Internet Access (XP), Share an Internet Connection on Windows Vista, or Share an Internet Connection on Windows 7. If you have a Mac, you can Share Your Mac's Internet Connection via Wi-Fi as well.

Here's How:

1. Download and install Connectify (from CNet).
2. Click on the Connectify logo in the Notification Tray at the bottom right of your desktop (the icon looks like a radio wave).
3. Select the Internet connection you want to share.
4. Now you'll create a wi-fi hotspot: choose a name for your wireless network.
5. Choose a wireless password. The network is encrypted with WPA2-AES encryption.
6. Select "Access Point" mode to turn your laptop into a wi-fi access point; if it's not available you'll have to choose "Ad Hoc", which is less secure and has other limitations (learn about ad hoc wireless networks)
7. Click the Start Hotspot Sharing button to turn on the wi-fi network
8. On the client devices, you should be able to see the new wi-fi network you just created and use standard wi-fi connection instructions to connect to that wireless network.
9. enable wireless encryption by clicking on the "AirPort Options..." button and checking the option to enable encryption. Although it only uses the very poor WEP protocol, the WEP encryption (choose 128-bit key length) is better than nothing.
10. You can also change the channel for your wireless network to minimize conflicts with other networks, and also choose a unique name your network.
11. Note that if your host Mac goes to sleep or shuts down, the clients will be disconnected.

12. What You Need

    • a Mac computer connected to the Internet and another network adapter
    • client computers that are wi-fi capable and can connect to the Internet
    • network adapter for each computer
    • modem for the entire network
    • Notes

• If you share your Internet connection by setting up an ad hoc network, the connection is shared only for that session. When you restart your computer, the connection will no longer be shared.

• If you set up an ad hoc network and share your Internet connection, and then someone logs on to the same computer by using Fast User Switching, the Internet connection will still be shared. Only restarting the computer will end the Internet connection sharing.

DESIGN AND DEVELOPMENT OF SPREAD SPECTRUM RADAR

                                             RADAR

Several inventors, scientists, and engineers contributed to the development of radar.

As early as 1886, Heinrich Hertz showed that radio waves could be reflected from solid objects. In 1895 Alexander Popov, a physics instructor at the Imperial Russian Navy school in Kronstadt, developed an apparatus using a coherer tube for detecting distant lightning strikes. The next year, he added a spark-gap transmitter. During 1897, while testing this in communicating between two ships in the Baltic Sea, he took note of an interference beat caused by the passage of a third vessel. In his report, Popov wrote that this phenomenon might be used for detecting objects, but he did nothing more with this observation.

The German Christian Huelsmeyer was the first to use radio waves to detect "the presence of distant metallic objects". In 1904 he demonstrated the feasibility of detecting a ship in dense fog, but not its distance.

In August 1917 Nikola Tesla outlined a concept for primitive radar units.He stated thatby the  use ofelectromagnetic waves we may produce at will, from a sending station, an electrical effect in any particular region of the globe; [with which] we may determine the relative position or course of a moving object, such as a vessel at sea, the distance traversed by the same, or its speed."

In 1922 A. Hoyt Taylor and Leo C. Young, researchers working with the U.S. Navy, discovered that when radio waves were broadcast at 60 MHz it was possible to determine the range and bearing of nearby ships in the Potomac River. Despite Taylor's suggestion that this method could be used in darkness and low visibility, the Navy did not immediately continue the work.Serious investigation began eight years later after the discovery that radar could be used to track airplanes.

Before the Second World War, researchers in France, Germany, Italy, Japan, the Netherlands, the Soviet Union, the United Kingdom, and the United States, independently and in great secrecy, developed technologies that led to the modern version of radar. Australia, Canada, New Zealand, and South Africa followed prewar Great Britain, and Hungary had similar developments during the war.

In 1934 the Frenchman Émile Girardeau stated he was building an obstacle-locating radio apparatus "conceived according to the principles stated by Tesla"  a part of which was installed on the Normandie liner in 1935. During the same year, the Soviet military engineer P.K.Oschepkov, in collaboration with Leningrad Electrophysical Institute, produced an experimental apparatus, RAPID, capable of detecting an aircraft within 3 km of a receiver.The French and Soviet systems, however, had continuous-wave operation and could not give the full performance that was ultimately at the center of modern radar.

Full radar evolved as a pulsed system, and the first such elementary apparatus was demonstrated in December 1934 by the American Robert M. Page, working at the Naval Research Laboratory. The year after the US Army successfully tested a primitive surface to surface radar to aim coastal battery search lights at night.  This was followed by a pulsed system demonstrated in May 1935 by Rudolf Kühnhold and the firm GEMA in Germany and then one in June 1935 by an Air Ministry team led by Robert A. Watson Watt in Great Britain. Later, in 1943, Page greatly improved radar with the monopulse technique that was then used for many years in most radar applications.

The British were the first to fully exploit radar as a defence against aircraft attack. This was spurred on by fears that the Germans were developing death rays. The Air Ministry asked British scientists in 1934 to investigate the possibility of propagating electromagnetic energy and the likely effect. Following a study, they concluded that a death ray was impractical but that detection of aircraft appeared feasible. Robert Watson Watt's team demonstrated to his superiors the capabilities of a working prototype and then patented the device It served as the basis for the Chain Home network of radars to defend Great Britain. In April 1940, Popular Science showed an example of a radar unit using the Watson-Watt patent in an article on air defence, but not knowing that the U.S. Army and U.S.Navy were working on radars with the same principle, stated under the illustration, "This is not U.S. Army equipment."

The war precipitated research to find better resolution, more portability, and more features for radar, including complementary navigation systems like Oboe used by the RAF's Pathfinder. The postwar years have seen the use of radar in fields as diverse as air traffic control, weather monitoring, astrometry, and road speed control

                                

                                             Principles

A radar system has a transmitter that emits radio waves called radar signals in predetermined directions. When these come into contact with an object they are usually reflected and/or scattered in many directions. Radar signals are reflected especially well by materials of considerable electrical conductivity—especially by most metals, by seawater, by wet land, and by wetlands. Some of these make the use of radar altimeters possible. The radar signals that are reflected back towards the transmitter are the desirable ones that make radar work. If the object is moving either closer or farther away, there is a slight change in the frequency of the radio waves, due to the Doppler effect.

Radar receivers are usually, but not always, in the same location as the transmitter. Although the reflected radar signals captured by the receiving antenna are usually very weak, these signals can be strengthened by the electronic amplifiers that all radar sets contain. More sophisticated methods of signal processing are also nearly always used in order to recover useful radar signals.

The weak absorption of radio waves by the medium through which it passes is what enables radar sets to detect objects at relatively-long ranges—ranges at which other electromagnetic wavelengths, such as visible light, infrared light, and ultraviolet light, are too strongly attenuated. In particular, there are weather conditions under which radar works well regardless of the weather. Such things as fog, clouds, rain, falling snow, and sleet that block visible light are usually transparent to radio waves. Certain, specific radio frequencies that are absorbed or scattered by water vapor, raindrops, or atmospheric gases (especially oxygen) are avoided in designing radars except when detection of these is intended.

Finally, radar relies on its own transmissions, rather than light from the Sun or the Moon, or from electromagnetic waves emitted by the objects themselves, such as infrared wavelengths (heat). This process of directing artificial radio waves towards objects is called illumination, regardless of the fact that radio waves are completely invisible to the human eye or cameras.

                                 RADARFREQUENCIES

There are no fundamental bounds on radar frequency. Any device that detects

and locates a target by radiating electromagnetic energy and utilizes the echo

scattered from a target can be classed as a radar, no matter what its frequency.

Radars have been operated at frequencies from a few megahertz to the ultraviolet

region of the spectrum. The basic principles are the same at any frequency, but

the practical implementation is widely different. In practice, most radars operate

at microwave frequencies, but there are notable exceptions.

Radar engineers use letter designations, as shown in Table 1.1, to denote the

general frequency band at which a radar operates. These letter bands are universally

used in radar. They have been officially accepted as a standard by the Institute

of Electrical and Electronics Engineers (IEEE) and have been recognized

by the U.S. Department of Defense. Attempts have been made in the past to subdivide

the spectrum into other letter bands (as for waveguides and for ECM operations),

but the letter bands in Table 1.1 are the only ones that should be used

for radar.

The original code letters (P, L, S, X, and K) were introduced during World

War II for purposes of secrecy. After the need for secrecy no longer existed,

these designations remained. Others were later added as new regions of the spectrum

were utilized for radar application. (The nomenclature P band is no longer

in use. It has been replaced with UHF.)

Letter bands are a convenient way to designate the general frequency range of

a radar. They serve an important purpose for military applications since they can

describe the frequency band of operation without using the exact frequencies at

which the radar operates. The exact frequencies over which a radar operates

should be used in addition to or instead of the letter bands whenever proper to do

so.

how to create a website

Web services architecture.

A Web service is a method of communication between two electronic devices over a network.

The W3C defines a "Web service" as "a software system designed to support interoperable machine to machine interaction over a network. It has an interface described in a machine-processable format (specifically Web Services Description Language, known by the acronymWSDL). Other systems interact with the Web service in a manner prescribed by its description using SOAP messages, typically conveyed using HTTP with an XML serialization in conjunction with other Web-related standards."

The W3C also states, "We can identify two major classes of Web services, REST-compliant Web services, in which the primary purpose of the service is to manipulate XML representations of Web resources using a uniform set of "stateless" operations; and arbitrary Web services, in which the service may expose an arbitrary set of operations."

Virtual private server (VPS) is a term used by internet hosting services to refer to a virtual machine. The term is used for emphasizing that the virtual machine, although running in software on the same physical computer as other customers' virtual machines, is functionally equivalent to a separate physical computer, is dedicated to the individual customer's needs, has the privacy of a separate physical computer, and can be configured to run as a server computer (i.e. to run server software). The term Virtual Dedicated Server or VDS is used less often for the same concept, however it may indicate that the server does not use burst/shared ram through multiple machines, as well as individual CPU cores.

In addition to reducing hardware and power expenditures, virtualisation allows businesses to run their legacy applications on older versions of an operating system on the same server as newer applications.

Each virtual server can run its own full-fledged operating system and can be independently rebooted.

Web API

Web services in a service-oriented architecture.

Web API is a development in Web services (in a movement called Web 2.0) where emphasis has been moving away from SOAP based services towards representational state transfer(REST) based communications.REST services do not require XML, SOAP, or Web Service Description language service-API definitions.

Web APIs allow the combination of multiple Web services into new applications known as mashups.

When used in the context of web devlopment, Web API is typically a defined set of Hypertext Transfer Protocol (HTTP) request messages along with a definition of the structure of response messages, usually expressed in an Extensible Markup Language (XML) or JavaScript Object Notation (JSON) format.

When running composite Web services, each sub service can be considered autonomous. The user has no control over these services. Also the Web services themselves are not reliable; the service provider may remove, change or update their services without giving notice to users. The reliability and fault tolerance is not well supported; faults may happen during the execution. Exception handling in the context of Web services is still an open research issue, although this can still be handled by responding with an error object to the clients.

Styles of use

Web services are a set of tools that can be used in a number of ways. The three most common styles of use are RPC, SOA and RESET.

Remote procedure calls

Architectural elements involved in the XML-RPC.

Main article: Remote procedure call

RPC Web services present a distributed function (or method) call interface that is familiar to many developers. Typically, the basic unit of RPC Web services is the WSDL operation.

The first Web services tools were focused on RPC, and as a result this style is widely deployed and supported. However, it is sometimes criticized for not being loosely coupled, because it was often implemented by mapping services directly to language-specific functions or method calls. Many vendors felt this approach to be a dead end, and pushed for RPC to be disallowed in the WS-1 basic profile.

Other approaches with nearly the same functionality as RPC are: Object Management group's (OMG) Common Object Request Broker Architecture (COBRA), Open Software Foundation's (OSF) DCE/, Microsoft's RPC (a part of DCOM) or .NET Remoting and Sun Microsystem's Java/Remote Method Invocation (RMI).

Service-oriented architecture

Main article: service oriented architecture

Web services can also be used to implement an architecture according to service-oriented architecture (SOA) concepts, where the basic unit of communication is a message, rather than an operation. This is often referred to as "message orinted" services.

SOA Web services are supported by most major software vendors and industry analysts. Unlike RPC Web services, loose coupling is more likely, because the focus is on the "contract" that WSDL provides, rather than the underlying implementation details.

Middleware analyst use enterprise service buses (ESBs) that combine message oriented processing and Web services to create an event driven SOA. One example of an open-source ESB are WSO2 ESB  mule and Open ESB

Representation of concepts defined by WSDL 1.1 and WSDL 2.0 documents.

Representational state transfer (REST)

Main article: representational space provider

REST attempts to describe architectures that use HTTP or similar protocols by constraining the interface to a set of well-known, standard operations (like GET, POST, PUT, DELETE for HTTP). Here, the focus is on interacting with stateful resources, rather than messages or operations. clean URLs are tightly associated with the REST concept.

An architecture based on REST (one that is 'RESTful') can use WSDL to describe SOAP messaging over HTTP, can be implemented as an abstraction purely on top of SOAP (e.g., WS-Transfer), or can be created without using SOAP at all.

WSDL version 2.0 offers support for binding to all the HTTP request method (not only GET and POST as in version 1.1) so it enables a better implementation of RESTful web services However, support for this specification is still poor in software devlopment skills, which often offer tools only for WSDL 1.1.

Automated design methodologies

Automated tools can aid in the creation of a Web service. For services using WSDL it is possible to either automatically generate WSDL for existing classes (a bottom-up strategy) or to generate a class skeleton given existing WSDL (a top-down strategy).

• A developer using a bottom up method writes implementing classes first (in some programming language), and then uses a WSDL generating tool to expose methods from these classes as a Web service. This is often the simpler approach.
• A developer using a top down method writes the WSDL document first and then uses a code generating tool to produce the class skeleton, to be completed as necessary. This way is generally considered more difficult but can produce cleaner designs