Questions Given the function defined by: $$ \oint e^{S(k,x)} \frac{\partial \ln(\frac{\int_0^\infty e^{-t} y^k dt }{ \int_0^\infty e^{-t} y^{(k-n-1)} dt})}{\partial k} dk = \frac{\partial S(n,x)}{\partial x}$$ Can this be used in the Borel summation sense for divergent series? If so, when ...

I am a bit rusty on my statistics so the following may not be the most precise. Why is the range $\theta_{12}\in[31.42^o−36.05^o]$ called a $3σ$ range? Does it mean that the probability that $\theta_{12}$ lies between $31.42^o$ and $36.05^o$ is 0.9973? Yes. I have more commonly seen either ...

During the breakfast with my colleagues, a question popped into my head: What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon? A qualitative answer would be nice, but if we could find a mathematical model or even better make the experiment (we don't h...

Other day, I bumped my bookshelf and a coin fell down. This gave me an idea. Is it possible to compute the mass of a coin, based on the sound emitted when it falls? I think that there should be a way to do it. But how?

This question is based on a discussion with a 10-year old. So if it is not clear how to interpret certain details, imagine how a 10-year old would interpret them. This 10-year old does not know about relativistic issues, so assume that we are living in a Newtonian universe. In this model, our un...

Four-legged chairs are by far the most common form of chair. However, only three legs are necessary to maintain stability whilst sitting on the chair. If the chair were to tilt, then with both a four-legged and three-legged chair, there is only one direction in which the chair can tilt whilst ret...

I have this problem from University Physics with Modern Physics (13th Edition): The inside of an oven is at a temperature of 200°C (392°F). You can put your hand in the oven without injury as long as you don't touch anything. But since the air inside the oven is also at 200°C, why isn't your ...