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Mathematical Theorems, Conjectures and Guesses

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Mosteller's Theorem in Probability

Posted by ICUQB4UQRU, Dec 9 2008, 04:22 PM

"I know who you are Mr. Mosteller, you that girl from that Korean Tea place are you not?"
Mrs. Knoitall

It is the opition of Mr. Who that he have Mr. Mosteller's permission to post his problem.

"Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girl friend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is first delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain."

Here is an example of the Mosteller's sequence that terminate: Can one deduce it traffic time? From that can one deduce its city working population? From that can one deduce the probable city this is in?...Using previous deductions, can one deduce who is Marvin?

[Opened mail]

More Hint: Marvin get off work on an unspecific time. Therefore, it is likely that he work five-days a week. Thus, in this 20 days he worked Y days? Base on current design of subway terminal, he can only enter the left or the right and then stuck there since it is likely he did not cross the subway base on rationality. Hence, the decision is made outside before he enter the subway since it is also assume that the gap between incoming train is less than X minutes. It is also safe to assume that incoming train is slower or equal to outgoing train at this time of "rush-hour."
Final Hint: Mosteller's Theorem on Random "Events"
Under certain condition, random event can be switched with informative event.

This is also an example of the union of two disjoint or more logic base in a certain sense:

Person A: The writer of this problem must have include some kind of non-mathematical trick. I must therefore think ways around it. Perhaps the subway is specially designed with crossing. Maybe the answer is just somekind of estimation. Let added extra assumptions.

Person B: The writer of this probem intended an exceptional challenge for someone, it is what it is and the solution is a clear precise answer.

What you see above it certain "same logic" with different base. This problem is independent of whether you cheated and assumpt there is crossing within the subway or honorably solved it, the answer still the same if an two different "type" of mathematician solved it.


A Method for Solving Partial Differential Equation

Posted by ICUQB4UQRU, Dec 9 2008, 03:52 PM

"Selfishness, it's just human nature."

[Mr. Who]This can be generalizes, let E be a P.D.E. with 2-dimesional real domain and is 1-time differentiable; let C be its initial conditon with Cardİ bigger or equals to some natural number, say, N. There exists a solution F in the sense that it can predict the surface emulated by E within a neighborhood which is dependent on N.

Hints:

f1 _|
f2___|_
f3 ___|_
f4 ____|_
f5 _____|_
f6
.
.
.

[Opened mail]


A Conjecture Regarding The Distribution of Prime

Posted by ICUQB4UQRU, Dec 9 2008, 03:03 PM

"For the Lord had love the world so much that he gave his only son as its savior."

[Mr. Who]Let the set N be all prime numbers up to a large prime number p and let M > p. There exist a computer program that uses Real Analysis to increase the level of effieciency in finding primes between p and M as the difference between them increases.

Hint: Index N (which is from a discreet space) to form a series that emulate wave form in the continuous space use a combination of stastics and probability techniques to form a set of normal like distributions with high peak...somethings like that I don't really remember due to my execellent memory.

[Opened mail]


An Infamous Theorem From Diophantine Analysis

Posted by ICUQB4UQRU, Dec 9 2008, 02:38 PM

"Don't hate the player; hate the game."
--Magic Johnson's wife 1:28 min into his first game, in regards to her love of "the game"

[Mr. Who]Let a < c < d with the following condition: For any polynomial with real coefficients, the Riemann intergal of this intergant from a to a + 1 is equals to its intergation from c to d. Then we have, c is irrational if and only if d is irrational.

Hints: consider Fermat's Last Theorem.

O.k. this is an silly one so here the proof.
Lemma:
let class(k)=n-root((a+k)^n+a^n), then we have class(k) < class(k+1) < class(k) +1. Note also that class(k+2) and class(k+1) are elements of the open interval between class(k+1) and class(k+1) +1.

F.L.T. and this lemma proves it.

[Opened mail]


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