khaled

You are right, and again .. we use it as a short form I thought you know better than me, it's not about jargons .. solve and calculate have different meanings, verify is not check Can you revise your informations, checking an answer can be a problem itself you know, it's not using a calculator to check the result of an equation. The input is the problem, the verification algorithm check if there exist at least 1 solution for the given problem. there is a difference between asking "are there blue balls in the box ?" (verification), "is this a blue ball ?" (checking), and "bring me a blue ball from the box." (solving) 1. P=NP is an open problem, currently, computer scientists assume that P≠NP since no one have ever came up with a P algorithm to solve an NP problem, so it's not because I said "non-polynomail" instead of "non-deterministic polynomial", that was a short form we use 2. computer scientists use P and NP in general, technically we use the Big O notation, the classes are literature 3. when I say "verification is a decision problem in which we return TRUE if there exist at least 1 solution for the given problem", don't assume we make things happens in a flash, the verification itself is a problem too

just a simple question: what if the sword blade is padded by a substance that keep the steel temperature really down, will that make the bindings in the structure stronger ?

You can do it the brute force way, which is NP (takes huge amount of time), But if you want to do it the smart way, you can use Intelligent Search, Dynamic Programming, or Combinatorial Constraint Satisfaction

Your note is right, but my definition is not wrong, we use the term "non-polynomial" as a short term in computer science ... we use the terms "solve" and "verify\decide" instead of "calculate" and "check", it's an algorithm not an evaluation Problems can be either solved or verified .. the optimal solution to a problem tell us if it's P, or NP .. verification of a problem is a decision problem that returns TRUE if there exist a solution, FALSE otherwise ------------------ Note that Problems are solvable or unsolvable .. Solvable Problems are either decidable or undecidable .. the complexity for verification of a problem is always less than or equal the complexity of solving

[math]P \neq NP[/math] Here we have [math]P[/math] denotes Polynomial Time Algorithm, and [math]NP[/math] denotes Non-Polynomial Time Algorithm, -- The statement above is interpreted "there exist no polynomial time algorithm to solve a non-polynomail problem" A Polynomial Time Algorithm is an algorithm with a Time Complexity that progress slow according to a huge input size [math]N[/math] A Non-Polynomial Time Algorithm is an algorithm with a Time Complexity that progress fast, Polynomial Time Complexity examples: [math]O© \;[/math], [math]\; O(log N) \;[/math], [math] \; O(N^c) \;[/math], [math] \; O(\sqrt{N}) \;[/math] ... These complexities are bounded by polynomials on the form [math]O(\sum_{i=0}^{k}{c_i N^i})[/math] So basically any complexity that is not bounded by (progress faster than) polynomials as mentioned above, is a Non-Polynomial, :: It's like saying "anyone that runs slower than Tom is in group Tom, others are in group Non-Tom" .. so "Tom is a bound for members of group Tom". Non-Polynomial Time Complexity examples: [math] \; c^N \;[/math], [math] \; N^N \;[/math], [math] \; N ! \;[/math] ... -- where [math]c[/math] is a constant, Note: the above definitions are unofficial, they are to help understand. Also notice that the question: [math]is \;\; P \; = \; NP[/math] is still an open problem in Computer Science and Mathematical Logic, which ask if there exist a polynomial time algorithm that can solve an NP problem

It seem you don't need Transliteration .. you need a Data Representation Scheme, which is simple here is an example: using char in C++, which preserves a single byte, we can caste it to int to deal with it as a decimal, for a data representation scheme for a byte, we need a 1-dim table of size [math]2^8 = 256[/math] cells // define your own schema, where data value X is represented as schema[X] char * schema [256] = { "alpha","beta","gamma", .. "OMEGA" }; // this is a simple function that takes a string of data bytes, represent it using our schema void myDataRepresent ( char * data ) { int i = 0; while ( data [ i ] != '\0' ) { cout << schema [ (int) data [ i ] ] << " "; } cout << endl; } ---------------------------------------- Note: Unlike transliteration schema, data representation schema doesn't have to be a unique mappings .. so for example two or more values can be mapped to the same representation.

"0010 0001" is known as data (as represented in Binary), data which is stored over a medium (memory), A data representation is a function, that maps a domain of data to a range of outcomes, A data-type preserve a fixed amount of memory, with a built-in data-representation. Data is what is stored in memory, can be represented differently through different data representations. Data-Representations [C++]: Binary Code, Hexadecimal Code, Octal Code, Decimal Code, Ascii Code, Unicode, ..etc Data-Types [C++]: Boolean (bool), Integer (short, int, long), Real (float, double), Character (char), String (char*), ..etc ------------------ About your question: Yes you can, in computer science it's called Transliteration, where you represent same information using same representation, but with different scheme .. the method is simple, you need to define two things: the map table and the transliterate function .. the map table, is a table of size K x 2, symbols are paired with their mappings, the transliterate function takes data, and transliterate it, note that transliteration is not symmetric.

If you love to learn by going from Tutorials to Examples .. I recommend this website: Java2S

I'm not really good in physics, but when you said that "photons are timeless" .. feels like "From the moment a photon was born, it traveled observing everything else halt"

do you think it's possible to use Quantum Entanglement to create Perfect Clocks, where time is exactly the same among all clocks ?

It seem that Statistical Mechanics of Stock Markets are modeled using Mathematical Physics Models, I know mathematics and physics, but what is mathematical physics ?

Imagine quantum entangled clocks, they will be the perfect clocks in nature!

That reminds me of this mind game: Gopherwood:Entanglement

I had a class on Probability & Statistics, and another on Simulation & Modeling. So I need to learn these integrals, and what else should I learn in order to be able to build a model ? Actually, I'm writing a software for my father, my father wants simple functionality which will be considered in the first version. The software is simple it keeps stocks price data, but I want to add more analysis functionalities to the software.

I was reading about "Quantum Entanglement" .. and one explanation was saying that if we have two dices that are quantum entangled, if we roll one for N times and it result in N ordered outcomes, if we roll the other N times, we will get the exact same outcomes ... Not only I'm shocked by that example, but also confused .. my question is simple: what is quantum entanglement exactly ?

Greetings, I'm working on a project where Stocks data are managed in order to be analyzed for an investor, 1. what statistical distribution\s should I use for this type of data ? 2. should I only consider the final price of the stock during the day, or include more detailed variables ?

I think you people confuse programming languages with data representation

If you have a Mac, you can do this: - Insert the music CD - Open iTunes - If iTunes ask you to "import the CD" click "Yes" - Else you can find "import" in the top menus The "import the CD" process will load tracks from the music CD, to your iTunes Library Note also, that you can highlight anything in your iTunes and copy them If you want to copy them manually, then you have to ask experts at the Mac Forums

I think your code is messy, besides that you should use tags You should take care of what should be done the first time this code runs, and what things that should run on every update, which progress your animation

I've once read "Observe .. Think .. Propose a theory .. prove your theory" .. and "there exist facts that we know they're true, but we can't prove them" One theory says "anything that can happen, will happen" which was proved under the scope of nature .. but if we interpret it mathematically, we get that "there exist no event with 0 % probability" which I really don't know how to start thinking how to disprove .. I remember taking the class on Probability, Statistics, and Modeling .. where normalized probability space is where we have an assumption that initially "everything happened once".

If you math experts tell me that things I'm told by my math professor are wrong, and you are making jokes, rather than clearing up things and saying "what is wrong" .. how can I know what is right then ?!

This what I get when simplifying your statement: = { [ (p^q) V (p^r) ] V (q^r) } ^ ~[(p^q) ^ r] = { (p^q) V (p^r) V (q^r) } ^ { ~p V ~q V ~r } = { (p^q) V (p^r) V (q^r) } ^ ~{ p ^ q ^ r } So, it's just as DrRocket mentioned, Check: Wolfram|Alpha:Solution

Did I say something wrong, maybe I should've used the word "depends" rather than "based" .. I've just modified my post Still I can't understand why would a mathematician tear off his hair, on what I've said.