We know that the force that opposes the rolling of an object exists due to the deformation of the body's surface at the point of contact which creates a decelerating torque on the body. What if the object is perfectly rigid such that it doesn't deform even a little? In ....

Let $P$ be a polynomial having integer coefficients (and degree $\geq 3$), and let $\mathscr P_P$ be the set of prime numbers dividing some value $P(n)$ with $n \in \mathbb Z$. Is it true that $\sum_{p \in \mathscr P_P} \frac1 p$ diverges? The case of polynomials with degree $2$ can ....

I have been working on a project for almost a year now. This project involves the implementation of a computational method to calculate material properties and the application to different material systems. I have also done original modifications to the method during the course of the implementation. At the moment ....

I'm trying to understand the empty universe model. My first textbook (which doesn't cover the empty universe) gives the Friedmann equation as $$\left^{2}=\frac{8\pi G}{3}\rho-\frac{kc^{2}}{R^{2}}$$ Am I right in thinking all I need do is put $\rho=0$ so $$\frac{dR}{dt}=\pm c$$ for $k=-1$ and then say $$R=\pm ct$$ for an expanding or ....

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I'm a potter. I find what I think are iron concretions in a deep red local clay. I fired these iron concretions to cone 6 (about 2100F) and when I removed it from the kiln (room temp) they were then magnetic. I tested for magnetism before and after firing just ....

I know this might be a silly question but I am confused with different answers of internet. My question is: Molar conductivity is given as: Molar conductivity = $\frac{\kappa}{M}$. S.I. unit of : $\kappa$ is $\pu{Sm}^{-1}$ & $M$ is in $\mathrm{mol \, m^{-3}}$. Thus, Molar conductivity in S.I. is $\mathrm{S ....

If we look at our solar system we have the sun which has planet orbits and planets have moon orbits. If we look at the possible size difference from hypergiants to small asteroids why shouldn't it be possible to nest orbits to an astounding degree: supergiant orbit a hypergiant, star ....

I am trying to write a program to compute the advection equation. $$u_t +u_x = 0$$ I use the spectral method for the spatial derivative $u_x$ and the leapfrog method for the time derivative $u_t$. That will give the an equation for the next time step: $$u_{j}^{k+1} = u_{j}^{k-1} - ....

When trying to import some files into my Mathematica notebook, I wanted to use ToString to specify the file path. Consider the following MWE, where we export some expression to the directory of the notebook, and immediately import it back: In:= Export]<>"output.txt", 2020]; import1 = Import]<>"output.txt"] Out= "2020" This works ....