Amr Morsi

I think, SarK0Y, that there must be 2 loops as you are finding the multiplication of "2" elements of n elements of the set.

For sure there is a partial continuum between strings for the same particle. But, it is not closed. In other words, it may lose or gain energy.

An example of this continuum is a particle moving in circular motion and not radiating energy; the strings of 2 dimensions (or 3 to be accurate) are exchanging energy, depending upon velocity in each dimension.

Well, I am not an expert in arrays.

But, I can say that: Since the difference between successive products is minimum, then you can get the smaller 4 numbers from the array and distribute them on the 2 subsets (4 numbers as 2 for each subset) by calculating the min difference in product. And, then get the following smaller 2 numbers and distribute them on the 2 subsets by making |MIN(0)-(X(1)-Y(1))| a minimum..... and so on.

This may work out.

I really don't know what does "Newton's method" imply?

The former integral you introduced in the first post gets vanished. Just substitute with phi1=phi+pi and integrate from phi1=0 to phi1=2pi. The derivative will cancel out with the integration.

Or, you may use the definition you posted before in another thread:

[math]

\frac{d^2|\phi|}{d\phi^2}=2(\delta(\phi)-\delta(\pi-\phi))

[/math]

I think you can get the Taylor Series.

Try to get d(theta)/ds, theta'', theta''', .......etc from the relation given with s=0.

Tn=nth-derivative * s^n /n!

Is there a certain array in question? Or, it is a general problem?

If W is only a function of phi, then it will turn to something like the formula written by alejandrito but divided by r^2*(sin(theta))^2...........

Merged post follows:

I think that "compact inetrnal space" defines the path.

I haven't got your question, SarK0Y. Is it how to split a given array into two subsets?

Also, what do you mean by MIN(n)? Does it mean the nth minimum product?

May be the below is following this criteria, ajb:

"Minimum surface area, generated by rotating a curve between 2 fixed points around a fixed axis, doesn't imply that the curve is a straight line, although the shortest distance between two fixed points is a straight line."

Do you know the equation of the path? Or, it is simply r*phi?

If so, are you sure that the bounded integral is zero?

It's all right, Tacobell.

O.K. Michel. Let's say as Plank's constant.

But, have you ever asked yourself why Pi has this value. It is a property of the universe, although it is a geometric one. I think it is similar to what we are saying here.

You are welcome, Farsight. It is a good question.

I think that we must differentiate between Field Energy (Energy per unit volume) and Potential Energy (Energy per unit mass). The later is not included in the Einstein Field Equation, I admit that. But, the former can be derived from the spacetime curvature (the metric tensor).

We can look to electromagnetism to have an idea. Maxwell's Equations, which describes the EM field, can define EM Energy density totally away from Lorentz Force Equation. However, the Potential Energy is not included. I think the situation is similar here.

Much electromagnetic radiation is prisoned on the inner side of the event horizon of a black hole. They can't reach it. How light can enter the event horizon, in special cases.

When a mass is lost, due to electromagnetic radiation, gravitational waves get emitted, resulting also in the changing the gravitational field outside.

Contraction only, if symmetrical, doesn't produce gravitational waves, there must be mass to energy transfer.

The gravitational wave can be either a radiation, that extends to r=infinty, or a furnituring; which changes the gravitational field around a mass density.

Any reduce in mass, which is the source of the spacetime curvature, is accompanied with reduce in total energy. And due to the law of conservation of energy, energy carried by gravitational waves must account for the decrease in energy.

I think, Intesaruddin, you will have to open another thread in the computer section.

timo, have you considered the first equality in your calculations? I think we should use 4,6,8 for a,b,c and 4 for x.

asinh(theta) contains a ln function which cannot be solved with "theta * sqrt (1 + thetaˆ2)". So, I think the inverse function will not be a closed form.

Maybe, the strings are able to sustain the frequency because they're continuously interacting with each other, creating sort of a continuum, and with the surroundings.

For sure, strings are interacting with each others and are exchanging energy with each others. But, I don't think that this is the main reason. I think it has to do with the medium (or the surroundings); radiation and potential energy.

The main equation is E=sqrt((p*c)^2+(m*c^2)^2).

When the particle is at rest, p is zero, and then you get E=m*c^2. It is called the Rest Energy. And it is the total energy confined in mass m.

When m is in Kgs and c in m/s, the unit for E is Joule.

So as not to get confused, make the equation as follows:

Total momentum before=Total momentum after.

Note that it is not a must for the change in momentum to be negatively equal. They only moved together.

O.K. Bignose. Sorry for that.

Thanks.

"Compact interval" is not involved here. It is a separate point.