Nope. Good question, but when fusion occurs in stars it often takes more than one atom to create the next. So if you were to take 100 atoms (say hydrogen) and put them through the process of fusion, you'll end up with 50 heavier atoms (Helium). But the heavier atom doesn't actually have the same...
I have searched the Internet for quite some time now, but the best bounds I could find were the ones you linked to that Dusart published. I had heard mention on a similar sight that Dusart had proven the tighter bound I mentioned before, but no reference was given. That's why I thought of asking...
Hello,
I remember reading somewhere that Dusart proved that ##\theta (x)<x## for very large ##x##. Where ##\theta (x)## is the first Chebyshev function (the sum of the logarithms of all primes less than or equal to ##x##). I couldn't find any source for this and was wondering if anybody had...
Hello! So let's say that you have a sequence ##a{_n}## and the limit as ##n->{\infty}## gives the finite number ##b## not equal to zero. If ##a{_n}## is known to be irrational, and ##a{_n}{_+}{_1}## can be shown to be irrational, does it follow by induction that ##b## is irrational? Is there any...
The partial derivatives are positive in the regions ##x>a## and ##y>b##. They could be positive everywhere, but the above is what I think is important to proving that inequality. I could be wrong, though.
Hello!
Say we have an inequality that says that ##f(x, y)>c## where ##f(x, y)## is a function of two variables and ##c## is a constant. Assume that we know this inequality to be true when ##x=a## and ##y=b##. If you show that the partial derivatives of ##f(x, y)## with respect to ##x## and ##y##...
Hello! What I'm wondering is if you want to prove an inequality, let's say ##a<b## and you already know that ##a>c## is true. If you are able to prove that ##c<b## is true, would that go on to imply that ##a<b## is true also? If this is correct, is it known as a theorem?
Thank you!
Thank you for the link bcrowell, I'll have to look over that paper for the next couple of weeks as it does seem interesting. Also thank you samalkhaiat, I didn't know Hamiltonian in those papers was what we now consider the Lagrangian Density. I guess that is another way in which the notation is...
bcrowell, I actually didn't know that the constraint on the determinant was a hindrance, so thank you for that info. I guess you could say these papers are very archaic (interpreting the notation is really difficult being so different from what is used now). I'm reading them mostly out of...
Hello! I have recently bought the book The Principle of Relativity by Einstein (Along with Minkowski, Lorentz and Weyl). This book is simply a collection of papers published by Einstein (along with the other three scientists mentioned) concerning the development of Special and General...
The simple answer is because the Earth rotates on an axis that is almost vertical (can't remember what angle it is tilted at). Because of this you can reach a maximum North and maximum South, meaning if you are at the South pole, no matter where you turn you can only go North, not more South...
Net work does not tell you if there was a change in potential energy, it tells you about a change in kinetic energy. The work done by a conservative force is equal to the negative of the change in potential energy. That means even if the net work is zero, since gravity did work there was a...
To the best of my knowledge the net work is the change in kinetic energy. When you lift an object at constant velocity there is the gravitational force pushing it down, and a normal force pushing up. Both these forces do an equal amount of work, one negative work, the other positive. These to...