khaled

Lets say that we have the set [math]P = { 2, 3, 5, 7, ... }[/math], where [math]P[/math] is the set of all prime numbers ... The series [math]P_1 + P_2 + P_3 + ...[/math] does it converge or diverge ..? [math]\sum_{P_i \in P} P_i \; = \; ?[/math]

In general, Random Walk is an algorithm that progress stochastically ... First, the stochastic part can be modeled either by using a statistical distribution over a PRNG if it's linked to a real-system, otherwise you use PRNG directly ... Second, how you model progress in your system, using the stochastic resource ... Third, how you constraint your random walks in your system ... Finally, you make tests, and analysis ... The most simple example of random walks is random walking in the coordinate system, you simply have this recursive function: [math]X_i = X_{i-1} + Random(X) \; , \;\; Y_i = Y_{i-1} + Random(Y)[/math] Now since you mentioned, "if i want to move from one node to another", you might want to know how to use Random Walks in a Linear Search, given a problem [math]P = \langle \; S, \; F, \;\; f_i \; \rangle[/math] where [math]S[/math] is the state-space (a graph which vertices are states) of the problem P, [math]F[/math] is the set of final-states (solutions of the problem), and [math]f_i[/math] is a function over state i (node i) where [math]S_i \in S[/math] known as the expansion function, [math]f_i = G[/math] such that there is an edge from state [math]S_i[/math] to [math]S_j[/math], [math]\forall S_j \in G[/math]. In linear search, you only keep 1 node, you search path is linear .. and so to make a Random Walk in a Linear Search, you can use the following algorithm, Transition Algorithm: ___________________________ Input: Node i Output: Node j 1. Use Expansion Function to Obtain Neighbor States: [math]G \leftarrow f_i[/math] 2. Obtain a Random number using a PRNG: [math]r \leftarrow Random() \;\;\; {\bf mod} \;\;\; |G|[/math], where [math]|G|[/math] is number of elements in G 3. Return a Randomly chosen neighbor state: [math]G_r[/math] ___________________________ good luck,

Now if an atom shatters, it will result in smaller atoms and some rays, as what happen in an atomic explosion, But what if an atom lose all of its electrons, and remain like that .. is that possible, and what would happen next ?

I just imagined a 3-dim circular curve that takes the shape of a ball,

I think that when you travel at the speed of light, the time doesn't stop otherwise, how come that photons change position with time, and have change of energy, ..etc but maybe because photons are too fast, everything else seem relatively very very slow, and speaking about observing other things at that speed, it might be impossible,

First, Highly Sync Social Community idea is neither new nor came from facebook .. and google is not an improvement for facebook I know hundreds of websites that are copy-cat to facebook, http://mashable.com/2007/07/11/10-facebook-clones/ If you are unsatisfied, you can read more about Information Theory, and Social Communities

I simply told you to read Q.M basics, because your speech earlier sound like you don't understand reality of Q.M, in Q.M, there is only 1 universe, 1 cat, 1 object .. but with no observation that object can change move into a new state as time progress, and if we observe the state, we get the reality of the object in time, otherwise we extend current superposition to contain all possible states. Sorry for the assumption,

there is only 1 universe, multiple universes is the superposition of the universe, and it's a paradox, we don't talk about "orthodox" which is related to Christianity religion ... I suggest you read about basics of Quantum Mechanics, the superposition, and the Uncertainty,

Actually, the two are different, since an operation has been done over its elements, So, there's no essence in relating the sum of one to the other ...

Nope. It is defined as 0, in measure theory.

1: [math]\frac{1}{(\frac{1}{0})} = 1 \times \frac{0}{1} = 0[/math], 2: [math]\frac{1}{(\frac{1}{0})} \;\; \approx \;\; \lim_{x \to 0} \frac{1}{(\frac{1}{x})} \;\; = \;\; \lim_{x \to \infty} \frac{1}{x} = 0[/math] .. in terms of limits what do you think ?

They are both experts, and they know what they talk about. It's your problem that you ask for a high-level atomic physics question, without the decent knowledge in atomic physics ... There is no such thing as "the force that prevents", we have two forces on the object, each have the inverse direction, and the same power. Consider them like two vectors, a vector and its inverse, when they add up, we get Zero. This is a physics forums, we are not talking about mathematics. Even though, without mathematics, you can't work in physics .. Mathematics is not based on concepts from physics, it has its own roots in history, Wikipedia:History of Mathematics ... Moreover, Quantum theory is based on having a hidden object, and observer (that can observe something about the object), the object's real state, and the object's state from our perspective (superposition) over time. A simple example to understand is Wikipedia:Schrodinger's cat. The hidden object is the cat, the observer for example is opening the box, the real state is either life or dead, the superposition is alive and dead.

In theoretical physics, you can know the total energy in the universe .. The zero energy theory, since we have symmetries that cancel each others, we get a total energy of Zero .. when we say the total energy is Zero, some people think it's wrong, but the expansion for one to understand this is that there are amounts of positive and negative energies, NOT that it means there is no energy in the universe! Also, scientists found clever methods to calculate things that are difficult to think about, such as total energy in the universe, total matter in the universe, and even the energy of nothing! they didn't have to go measure it, they took the other way in ...

I think that ajb and swansont tried their best to understand your question, If you are trying to understand how electrons move around. You should think about the works such as Einstein Relativity, which explain how planets orbit around a star just like how it explain how electrons orbit around a nucleus ... 2 forces inverse to each others' directions which are orthogonal to the tangent, one pulls it down to the nucleus, and one pulse it away .. in symmetry they keep it in its orbit, if one of the two forces exceed, then it either is pulled away or pulled down ... hard enough to understand ..?

this doesn't make any sense, Facebook and Google+ are independent projects, and each one is designed using different strategy and technologies ... I use gmail, google maps, google search, google scholar, google code, and google groups .. but Google+ doesn't seem complete nor interesting,

That gave me an idea, if [math]\frac{1}{(\frac{1}{0})} = 1 \times \frac{0}{1} = 1 \times 0 = 0[/math], then we have [math]\frac{1}{(\frac{1}{0})} = {(\frac{1}{0})}^{-1} = (\frac{1}{0})^{-r} = 0[/math], besides [math](\frac{1}{0})^{0} = \frac{1^0}{0^0} = \frac{1}{?} = ?[/math] we still get [math]\frac{1}{0} = {(\frac{1}{0})}^{+r} = {((\frac{1}{0})^{-1})}^{-1} = {0}^{-1} = \frac{1}{0} = ?[/math] for any [math]-r \in \mathcal{R}^{-}[/math], and [math]+r \in \mathcal{R}^{+}[/math] ...

Just a curiosity, photon is a boson or a fermion ?

normally [math]\frac{1}{(\frac{1}{0})} = \frac{1}{?} = ?[/math], but if you apply limit, then we have: [math]\lim_{x \to 0} \frac{1}{ (\frac{1}{x}) } \approx \lim_{x \to \infty} \frac{1}{x} = 0[/math], I don't know if using limits would help finding the answer ...

Google+ is nothing more than a new sharing service between google users ...

This is from Wikipedia, a figure that illustrate the different levels of cloud computing ... SaaS is in the application level, service layer ... You have to be aware that when you are working in Cloud computing, you are not dealing with physical parts of any device .. you simply work in a cloud, the only thing you can see is resources, storage resources, processing resources, ..etc .. you utilize number of resources to provide some service in your case, Your work will be either that you build a Cloud Service, that requires you to learn how to work in a cloud system of your choice, or you find an existing cloud service, and improve it ... .. good luck

First of all, try to put your codes inside [math] [ code ] .. [/ code ] [/math] brackets, Let me simplify this for you, your program is not the only one processing on your machine, you can use platform-dependent functions to raise the priority of your program in the system, but that's stupid since your program doesn't deserve such thing ... anyway, why'd you want to create 200 programs, it sound futile .. if you want to see the upper limits of your machine, there are tools that can tell you that, those tools won't go create 200+ programs, they will just use equations over resources ... Also, about your code, you are trying to create 200+ copies of a visual application, this will make your environment lag too ...

Lava AD-AWARE is the top-rated anti-spyware by CNET group ... download: LAVE:AD-AWARE good luck,

Tutorials: C: http://www.iu.hio.no/~mark/CTutorial/CTutorial.html C++: http://java2s.com/Tutorial/Cpp/CatalogCpp.htm Java: http://www.java2s.com/Tutorial/Java/CatalogJava.htm References: C\C++: http://www.cplusplus.com/ Java: http://download.oracle.com/javase/6/docs/api/overview-summary.html

I think that it depends on both the planet's distance from its star (the gravitation point that keeps it in orbit), and its size ...