We all live and love on this big blue marble, but how many of us actually care about what we are doing to it? If we all showed some concern with the pollution, maybe we could change the way we live. You would not drink a glass of water that was murky, so why do all agree to breathe air that is hazy. Hazy is not a weather element it is from pollution. That is why I decided to run my car on water, it leaves nothing but water in emissions. If everyone drove a “green” vehicle, it would be easier to breathe.
When my husband told me he wanted to convert our cars, my first thought was oh no. But I did come around and I wanted to know what it would take to run my car on water. I did not even know that was possible. My husband explained the process to me and showed me a website about it. He even showed me how much money it would save us in the long run. We could pay down our debt with the amount we would be saving in the long run. I agreed that it was a good idea and I watched the savings start rolling in.
Gaming laptops used to only be attainable from specialist companies. Though they didn’t shift a significant deal they still made the most in relation to other styles of notebook. Surely I could confidently say everyone wanted one though. They were like the pinnacle of what was capable with notebook computer technology, the best laptops about. They would create a lot of excitement but I don’t believe many people would go out and buy laptops at high prices. Things look set to change though because now the gaming notebooks sector has attracted the attention of bigger brands.
These are certainly high margin notebook computers for the global brands and they are aware of it. It is certainly a good way to larger profits. In addition they are aware they can sway us to buy laptops like these more easily than small companies. I reckon smaller system builders are extremely perturbed regarding this. The high end technology will quickly forge its way into the view of the everyday customers. In my opinion if anybodies decided to part with a lot of money the established brand always comes out on top.
The companies new laptops are receiving a large amount of praise as being the best laptops from the media. This is one opportunity the local system builders should utilise to their advantage. This is a massive sales proposition that must be mentioned. These purchasers have the technical know how and can decide which notebook computers are best. The tech specs are of great significance for this type of buyer. All gamers concur that it is a favourable situation. I would predict a few price wars taking place in this market after the early stages. Even though that’s my take on it, its just my opinion and probably not what will occur. Technology is always getting better and the new units should normally be high priced on launch. I reckon we will have to see whether this overcrowding produces any big benefits for gamers.
Notebooks seem to be the current trendy thing this year. Manufacturers are trying to keep up with this but have issued warning that supplies could be limited. This is one trade which in my opinion will not be affected with all the financial peril that seems to be going on. Also with notebook computers now it seems like every couple of months or so the technology is already taken over with something different.
With all the latest advances in technology gaming notebooks have benefitted a great amount in my opinion. I feel gaming notebooks have never been at such low prices. You can hunt down some extremely good bargains out there that will get you playing games. The speed of gaming notebooks has greatly enhanced and its really a viable means of gaming. Even more indredible these days In my opinion is how sleek the cases are getting especially when you think about much speed is in them. Extreme gaming enthusiasts will always be more partial to their desktop gaming machines for speed and rightly so but it’s the functionality notebooks give that influences people compromise on frame rates. I wouldn’t give it too long before we see ultra lightweight gaming notebooks on the shelves.
Talking of gaming notebooks, the most choice are aquirable when they are custom built. Ram and hard disks are usually high performance engineered components in custom notebooks which extreme consumers like. Specifying what you require simply is the major advantage. Prebuilt notebook computers are targeted for common tasks and not upto doing more intensive activies. Power users need custom notebooks for this reason. There are plenty of resellers selling custom notebooks, with great customer support. To a couple of people this means a lot.
Next gen notebook computers do seem like an appealing proposition. The tiny $500 notebooks are selling like crazy at the moment. Its insane how technology designed for the developing nations have become hyped in the 1st world nations. People would prefer to have large screen ultra portables if that makes sense. Rigid housing needed for such notebooks are still too expensive. I can guess its not too long before we begin experiencing gaming laptops that are weightless. Even though notebook technology follows plans there is forever going to be a idea that changes all that.
Cell phone and PDA cell phone combo users are downloading, buying, and playing more and more add-ons than ever before. From cell phone wallpaper (backgrounds and images) to games and ringtones, it seems cell phone users just cannot get enough!
There are also even newer software and information packages that come as add-ons to the PDA/cell phone market. You can download software that tells you how to mix any drink imaginable and even tells you which types of glasses to use for each drink.
You can purchase and download golf software applications of all kinds. And let’s not forget the multitude of Bible ebooks that are available almost the instant a new PDA model is available!
Ringtones are always a major pull online and tens of thousands of them are downloaded every day from places like Cell-Phone-Nation.com and hundreds of sites like it.
Many PDA phones are coming out with Adobe PDF readers that make reading an “ebook” the same as reading online at home from your desktop computer.
Marketers are picking up on this booming market and scurrying to supply more choices in topics and information to this hungry, under served market.
Already there are some applications coming out to organize recipes, mixed drinks, gold scores, sports betting and virtually anything else you can imagine. But only if the creators of these products make them available for specific platforms like Blackberry.
Podcasting is a major topic now among marketers. With the ability to get online with your cell phone, you can easily surf to a site that makes audio and even video presentations, commercials, and seminars available for download instantly to your phone.
The market for cell phone software, ringtones, podcasted audio and video, and myriad other files, photos and games is wide open and ready for smart marketers to pounce on for major profits in a relatively brand new industry.
To date, you can only buy and download one sales and marketing related ebook at Sprint.com, out of about ten selections for your Blackberry PDA Cell Phone. The other selections? The Bible and a bartender software.
The market is truly in its infancy. Moving now on this market will be a cash cow for smart marketers looking for fertile ground for increased profits. If you are not actively seeking out spots in the podcasting and PDA software market, you are losing money as we speak.
When I bought my Blackberry, the first thing I did was go to the add-ons and third party applications to get cool stuff to put on it. The selection was miserable. After downloading an ebook on marketing, there was nothing left for me to purchase.
Many people will feel the same way until they are given real choices in the software and information they can purchase as add-ons to their new toys.
To discover a glaring void in the market the size of this one is unheard of in this day and age. For the marketers who seize its potential and start actively supporting the market with choices, the sky is the limit for increasing reach and profits.
Jack Humphrey is a contributing editor for http://cell-phone-nation.com
mail is an experiment in a new kind of webmail, built on the idea that you should never have to delete mail and you should always be able to find the message you want. The key features are:
*
Search, don’t sort.
Use Google search to find the exact message you want, no matter when it was sent or received.
*
Don’t throw anything away.
2192.020031 megabytes (and counting) of free storage so you’ll never need to delete another message.
*
Keep it all in context.
Each message is grouped with all its replies and displayed as a conversation.
*
No pop-up ads. No untargeted banners.
You see only relevant text ads and links to related web pages of interest.
About the Author
vivek gupta
vsworx
Primes:
Randomness and Prime Twin Proof
Martin C. Winer
martin_winer@hotmail.com
Referring sites:
I’m greatly appreciative of sites that have found my work interesting and have linked to me: Most Notably, I appreciate:
Google Directory
Google Prime Directory
DMOZ Open Directory Project
DMOZ Open Directory
H. Peter Aleff @ recoveredscience.com
Recovered Science
Introduction
Overview
The purpose of this work is to look into some long pondered questions. First, is the distribution of primes across the number line random? Next, what is random anyways? Finally the theories and axioms derived are used to solve the long discussed “Prime Twin Problem” to show possible applications of the understanding of what it means to be random.
Sieves and Patterns
Consider all odd numbers starting at 3.
Mark a 1 on the number line where the number is a product of 3, (including 3×1), 0 otherwise. We get a pattern (sieve) such as:
1 0 0 1 0 0
3 5 7 9 11 13
1)The pattern is 100…
2)Note that the numbers corresponding to the zeros between 3 and 3^2=9 are also prime (5 and 7).
3)The length of the pattern is 3
Consider the pattern formed by 3 and 5:
1) the pattern is 110100100101100…
2) Note that the numbers that correspond to zeros between 5 and 5^2=25 are also prime (7,11,13,17,19,23)
3) The length of the pattern is 3×5=15
Definition of P(x) [The Xth Prime]
In general
If we let P(x) be the xth prime starting from 3 such that
P(1)=3, P(2)=5, P(3)=7 and so on, we can consider the patterns on a larger scale.
Definition of Pat(n)
Suppose we define a function Pat(n) which will produce the string of ones and zeros as defined above from P(1) to P(n).
I.e. Pat(1) = 100…
Pat(2) = 110100100101100… (That’s the pattern or sieve of 3 and 5)
In such a case,
(1) The pattern will consist of 1’s and zeros corresponding to the products and non-products of the n composing prime factors,
(2) The numbers corresponding to zeros between P(n) and P(n)^2 are guaranteed to be prime
[Why? because a number is either a prime or a product of primes. A zero means that it’s not the product of any prime below it. The first unique contribution a prime factor gives to the number line occurs at P(n)^2 = P(n)xP(n) because below that at say P(n)xP(n-1) can be rewritten as P(n-1)xP(n) and thus is already accounted for in the number line. Thus a zero between P(n) and P(n)^2 is not a product of primes and must therefore be prime.]
(3) The length of the pattern will be:
P(n) x P(n-1) x P(n-2) x … x P(1)
Unique Contributions of P(x)
Description
As we build iteratively build Pat(n)’s over time, each successive prime adds to our knowledge of which numbers are prime and which numbers are not. In the case of the prime number 3, we know that 3 is prime and that all (other) multiples of 3 are not prime. However, when we come to the prime number 5, 5 does not ADD to our knowledge that all multiples of 5 are not prime. For example 15 is a multiple of 5, but we already knew that this number was not prime because of the prime number 3. Therefore, the unique contribution to our knowledge as we build Pat(n)’s that a given prime (P(x)) provides us is given below:
Definition uniqueContribution(P(x))
For any prime, P(x), define
UniqueContribution(P(x)) = {P(x)*k; k is odd, k>=P(x), primeFactorization(P(x) contains no primes < P(x)}
In English…
The uniqueContribution a prime number (P(x)) gives us as to which numbers are not prime while building successive Pat(n)’s is a function of all odd multiples of P(x) such that the odd multiples have no primes less than P(x) in their prime factorizations
Examples:
Consider the prime 5.
5*5 = 25 is a unique contribution of 5
5* 15 = 5*3*5 = 75 is NOT a unique contribution because it has 3 in its prime factorization. Ie, we already knew that 75 was not prime thanks to the prime number 3.
5*5*5 = 125 is a unique contribution.
Powers of a prime
It turns out that powers of primes (greater than the first power) are unique contributions.
Important Notes on uniqueContribution(P(x))
For larger P(x), uniqueContribution(P(x)) becomes increasingly difficult to calculate and more complicated. The unique contribution becomes more random as P(x) increases.
General Notes on Randomness
Axioms of Randomness
1) All truly random patterns must be infinite length
2) A pattern is said to be random if there is an infinite supply of complexity
Black Box Pattern Paradox
It can only ever be said that an infinite length pattern follows a pattern for a certain finite length. Suppose you have a machine that spits out 1’s and 0’s and it spits out 1010101010… for a certain number of times you make the attempt. You can only say that it follows the patter 10… for the number of attempts you made because on the next attempt, the pattern may change. Thus it is impossible to ever say that an infinite length pattern follows a certain pattern unless you are aware of the algorithm that generates it.
On Randomness of Primes
Measure of Randomness in a Binary Pattern
Let’s define a measure of randomness (mr) for a binary pattern to be the number of smallest repeating units in the lowest reducible pattern.
Definition of Lowest Reducibility:
A pattern is reducible if it can be rewritten in a simpler, shorter form, such as:
11111111… is reducible to 1…
10101010101010… is reducible to 10…
Definition of Smallest Repeating Units
Take the pattern:
Pat(2) = 110100100101100…
This repeats every 3rd and every 5th. Note it repeats every 9th as well but that’s not the smallest repeating unit because the every 3rd subsumes the every 9th. Thus the mr of this pattern is 2.
Some Examples for Clarity
So,
100000000… is no more or less random than
100…, or
100000000000000000000000…
(Because in all cases mr = 1)
However,
110100100101100… (every 3rd and 5th) is more random than those above since mr=2.
Some other interesting examples for clarity:
110… has mr = 2 because it has two repeating units of size 3, (the second offset by 1)
101… has mr = 2 because it has two repeating units of size 3, (the second offset by 2)
111… has mr = 1 because this is a reducible pattern, reducing to 1…
The latter is an important example because one might be tempted to say this pattern repeats every 3rd, every 3rd offset by 1 and every 3rd offset by 2, but this pattern reduces to 1… therefore, the mr is calculated on the lowest reducible pattern.
Examining Pat(n) re: Randomness with increasing n
So as we take higher n in Pat(n), the number of smallest repeating units increases. In fact it exactly equals n. For any given n, Pat(n) isn’t absolutely random, but P(n+1) is more random than Pat(n).
Model of Lim(x->inf) (1/x) = 0
Examine the model of:
let f(x) = 1/x
At no x, is f(x) = 0, however
closenesstozero(f(x+1))>closenesstozero(f(x))
and the
lim(x->inf)f(x) = 0
Likewise, for no x is Pat(x) a random pattern, however
The mr(Pat(n+1))>mr(Pat(n)), and then the
Important Identities
(4a) lim(n->inf) mr(Pat(n)) = inf (i.e. grows infinitely complex)
(4b) lim(n->inf) uniqueContribution(P(n)) = random set
(4c) lim(n->inf) Pat(n) = random binary pattern (i.e. absolute random)
Definition of Random in English
Pat(n) always produces patterns in the lowest reducible form (ask me for a proof if you like). Pat(n) has n smallest repeating units (we know this because the units are prime). Therefore as you create Pat(n) with greater and greater n, you produce lowest reducible patterns of greater and greater complexity (higher mr). Each individual P(n) as n increases, has a more and more complicated uniqueContribution, leading to more complexity in the resulting Pat(n)’s, hence more randomness. As you do this without bound, you create complexity based on previous complexity, resulting in infinite complexity = random.
So what can we do with this knowledge?
Solution to prime twin, triple, quadruplet problem
Well it solves the prime twin, triplet, and quadruplet problems in a shot…
From 2 above, we know that the zero’s between P(n) and P(n)^2 are prime. A prime twin will occur in this region whenever you see the pattern 00 (two adjacent prime candidates). Can one predictably say that there exists a certain Prime P(K) after which, there will never be a 00 in the pattern between P(k+q) and P(k+q)^2?
An examination of pattern combinatorics reveals that there is a 00 in the base case P(1) (100..). As we combine patterns, there will always be a 00 somewhere in the pattern Pat(n) (ask me for the proof if you like). The trick is, will it be between P(n) and P(n)^2.
Well the pattern subtended by P(n) and P(n)^2 is a subset of the pattern Pat(n) and grows without bound as n does. You can tell me less and less about it as n grows without bound. By (4) I can let n grow without bound until it is a truly random pattern at which time you can no longer tell me that you can predictably state that there won’t be a 00 in the pattern between P(n) and P(n)^2. At the time that there is a 00 between P(n) and P(n)^2, a new prime twin will occur.
This is true of all prime triples, quadruplets etc that are allowable.
Why do they keep finding patterns in primes?
This becomes evident knowing that we only have a finite list of primes in our knowledge. The patterns produced by a finite list of prime factors are never absolutely random, just relatively random, or ’sufficiently complex to avoid simple categorization’. Statistical tools, depending on their power, will find a pattern in those patterns not produced by an infinite number of prime factors (the number line).
Interesting Patterns in Non-Primes
There are some interesting patterns in non-primes that emerge from this work.
Define:
LowMarker(n) = 3 + 2(P(1)xP(2)x…x(P(n)),
HighMarker(n) = 3 + 2(3×5x…xP(n)), and
Offset(n) = P(n) - 3
We can say conclusively, thanks to pattern combinatorics that numbers in the ranges:
LowRepeater(n) = [LowMarker(n),LowMarker(n)+Offset(n)] and
HighRepeater(n) = [HighMarker(n),HighMarker(n)+Offset(n)] are non-prime (product of primes)
Moreover they follow a similar pattern to the base pattern that spawned them.
Example
Let’s work an example:
Examine Pat(4) at the start of the pattern
Examine the numbers
{3,5,7,9,11}
3 is a product of 3,
5 is a product of 5,
7 is a product of 7,
9 is a product of both 9 and 3,
11 is a product of 11
Recall P(4) = 11
Let’s examine the numbers in the ranges, LowRepeater(4) and HighRepeater(4)
Examine LowRepeater(4)
LowRepeater(4) = {2313,2315,2317,2319,2321}
2313 is a product of 3,
2315 is a product of 5,
2317 is a product of 7,
2319 is a product 3, and necessarily, not a product of 9 (this could only occur in HighRepeater)
2321 is a product of 11
Examine HighRepeater(4)
HighRepeater(4) = {20793, 20795, 20797,20799, 20801}
20793 is a product of 3,
20795 is a product of 5,
20797 is a product of 7,
20799 is a product of both 9 and 3,
20801 is a product of 11
LowRepeater(n,k) and HighRepeater(n,k)
LowRepeater and HighRepeater repeat over the number line
Adding a factor k to the previous functions we get:
LowMarker(n,k) = 3 + 2k(P(1)xP(2)x…x(P(n)),
HighMarker(n,k) = 3 + 2k(3×5x…xP(n)), and
Offset(n) = P(n) - 3
Then,
LowRepeater(n,k) = [LowMarker(n,k),LowMarker(n,k)+Offset(n)] and
HighRepeater(n,k) = [HighMarker(n,k),HighMarker(n,k)+Offset(n)] are non-prime (product of primes)
All, where k>=0 and k is an integer.
Interesting observation about the difference between LowMarker(n,k) and HighMarker(n,1)
For a fixed n, and HighMarker’s k=1, LowMarker’s k = the product of the non-primes between P(1) and P(n).
The following table will clarify:
LowMarker(3,1)
=
HighMarker(3,1)
LowMarker(4,9)
=
HighMarker(4,1)
LowMarker(5,9)
=
HighMarker(5,1)
LowMarker(6,9*15)
=
HighMarker(6,1)
LowMarker(7,9*15)
=
HighMarker(7,1)
LowMarker(8,9*15*21)
=
HighMarker(8,1)
Questions? Comments?
martin_winer@hotmail.com
© Martin C. Winer, 2004
Posted to the web on Mar 16, 2004 after years of being ignored 
About the Author
Martin Winer is a computer scientist by day, working on www.rankyouragent.com and an amateur mathematician by night. For a formatted version of this article, please view:
http://members.rogers.com/mwiner/primes.htm
The first microscope was created hundreds of years ago. In the passing centuries, microscopes evolved into powerful, precise tools that allow scientists to view tiny objects at a level of detail that seems unreal. There are a wide array of available microscopes, from the compound microscopes commonly found in high school science classrooms to powerful scanning tunneling and electron microscopes used by Nobel Prize winners.
Most historians agree that two Dutchman made the first microscope in 1590. Zaccharias Janssen and his son Hans were two eyeglass makers who experimented with putting multiple lenses together in a tube. They found that objects under the tube were greatly enlarged. Over the next hundred years, scientists Robert Hooke, Anton van Leeuwenhoek, and others further refined the work of the Janssens and used microscopes to examine insects, blood, and other items. Scientists have continued microscopes into the present day. Now, microscopes can show tiny particles that are unseen by the naked eye in extremely exact detail.
Microscopes operate on several principles. Most common microscopes have two different lenses. Viewers look through the ocular lens, also known as the eyepiece. There is another lens, called the objective lens at the end of the ocular lens. The objective lens is a sphere shaped lens located above the stage of the microscope. People place the object they want to examine on the stage and can adjust the lenses to bring the object into focus. Most microscopes have an adjustment knob for coarse focus and one for fine focus. Many microscopes have several objective lenses with different strengths for users to choose from. The lenses are arranged on a circular platform that can be rotated to have the different lenses put into place under the ocular lens. Microscopes also need a light source of some kind underneath the stage. Most commercial microscopes have a light bulb, but many high-end microscopes use lasers or electrons for illumination.
Microscopes have been used to make countless vital scientific discoveries. They are invaluable tools used in a variety of scientific fields that enable researchers to make discoveries that would be impossible with the naked eye.
About the Author
Microscopes Info provides detailed information about electron, compound, stereo, digital, video, and scanning tunneling microscopes, as well as an explanation of the different parts of a microscope, and more. Microscopes Info is affiliated with Business Plans by Growthink.
