"until" as used in this sentence
Does "until [date]" mean "before that date"?
Why is inductance (L) proportional with turns-square (N²)? We start from the   $$ \mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0. $$  We take surface integration of both sides, for the surface (\$s\$) inside the mean path (\$c\$) of the core.  $$ \int_s \left( \mathbf{\nabla} \times \mathbf{B} \right) \cdot d\mathbf{s} = \mu \int_s \mathbf{J} \cdot d\mathbf{s} $$  We use the  to rewrite the left hand side; where \$c\$ is in the same direction with the magnetic flux \$\Phi\$.  $$ \oint_c \mathbf{B} \cdot d \mathbf{\ell} = \mu N I $$  (The integral on the left hand side results \$NI\$, because there are \$N\$ different wires on the winding.)  The magnetic field density inside these kind of cores are considered to be uniform. So, we can write  $$ B \ell_c \overset\sim= \mu NI \implies B = \dfrac{\mu NI}{\ell_c}; $$  where \$\ell_c\$ is the mean path lenght of the core.  We can find magnetic flux from the magnetic flux density we have found by using the cross sectional area of the core \$A_c\$.  $$ \Phi = BA_c = \dfrac{\mu NIA_c}{\ell_c} $$  By definition, inductance is the amount of magnetic flux generated per applied current, that is  $$ L \overset\triangle= \dfrac{\Phi}{I}. $$  So, we find inductance of the system as  $$ \boxed{ L = \dfrac{\Phi}{I} = \dfrac{\dfrac{\mu NIA_c}{\ell_c}}{I} = \dfrac{\mu NA_c}{\ell_c} }. $$  But, all other sources () give inductance of an inductor like this as  $$ L = \dfrac{\mu N^2A_c}{\ell_c}. $$  What is the mistake I did in my derivation? Please explain in detail. Why is 'that' sometimes optional before dependent clauses? ${!FOO} performs a double substitution in bash, meaning it takes the (string) value of FOO and uses it as a variable name. zsh doesn’t support this feature.  Is there a way to make this work the same in bash and zsh?  Background:  I’ve got a list of environment variables, like  PATH MAIL EDITOR   and want to first print the variable names and afterwards their values.  This works in bash but not zsh:    for VAR in LIST do         echo $VAR         echo ${!VAR} done   It should be somehow possible “the old way” with eval, but I can’t get it to work:  for VAR in LIST do         echo $VAR         echo `eval \$$VAR` done   I’m never going to understand why I can’t simply do arbitrary deep substitutions like ${${VAR}} or even ${${${VAR}}} if need be, so an explanation for that would be nice, too. As far as I understand, whatever can be done using DeclareMathOperator can also be achieved using newcommand, but not the other way around. If this is the case, what are the circumstances where DeclareMathOperator is the better choice? When should I take solely newcommand?  I found a question regarding , and I wonder what other aspects should be taken into consideration when it comes to choosing which method to use when defining math operators. I find myself repeating a lot of:  mkdir longtitleproject cd longtitleproject   Is there a way of doing it in one line without repeating the directory name? I'm on bash here. How do I remove the OneDrive folder from my File Explorer folder tree in Windows 10? I don't use or want to use OneDrive, but after upgrading to Windows 10 it's been installed automatically and added to the sidebar of every explorer window:    I can't seem to figure out how to get rid of it. I can't uninstall it like a normal app, and I can't seem to unpin it in Explorer's options.  I tried following  to getting rid of it, but that seems to only remove stored OneDrive files.  I've also tried following another  and , but I can't seem to edit group policies on my computer (maybe because I upgraded from Win7 Home Premium?).  All I would really like is to be able to remove the OneDrive shortcut from my explorer sidebar, though being able to uninstall OneDrive would be a bonus.  I'm not sure what I should try now. Is there a way to remove OneDrive from Windows 10? bash history for current session Maybe I'm overlooking something but is there a way to get your current bash history for the current session you are using like  if i run  ssh host $ pwd $ ls $ cd /tmp   I just want to see those 3 commands and nothing else How do I find the right size of filters for a lens? I was looking to get a circular polarizing filter and an UV filter for my Canon 550D, 18-135mm lens. When I checked online I found these filters came in different sizes, like 62mm, 67mm, 72mm, 77mm. How do I know which is right?  Also, will there be any degradation of photo quality if I put both these filters on the lens? Diffeomorphism & Weyl transformations in the 2D worldsheet of string theory and the existence of conformal gauge D. Tong's , chapter 5 (), feature the following in introducing the symmetries used in the Faddeev-Popov method:     We have two gauge symmetries: diffeomorphisms and Weyl transformations. We will schematically denote both of these by $\zeta$. The change of the metric under a general gauge transformation is $g \rightarrow g^{\zeta}$. This is shorthand for,   \begin{equation} g_{\alpha \beta} (\sigma) \rightarrow g_{\alpha \beta}^{\zeta} (\sigma)= e^{2\omega (\sigma)} \frac{\partial \sigma^{\gamma}}{\partial \sigma'^{\alpha}} \frac{\partial \sigma^{\delta}}{\partial \sigma'^{\beta}} g_{\gamma \delta} (\sigma) \end{equation}   In two dimensions these gauge symmetries allow us to put the metric into any form that we like — say, $\hat{g}$. This is called the fiducial metric and will represent our choice of gauge fixing.   Is there a proof available that shows that the combined symmetry allows us to "put the metric in any form (locally, of course)?" Is this property restricted to two dimensions? How do you uninstall wine 1.5? How do I enable the "Universe" repository? How do I get to the Universe Repository in supported versions of Ubuntu? What happens to the holes in the skull where teeth were developing? In Skeptics.SE, a question regarding the skulls of children arose. Depicting a scary skull where the permenent teeth are "hidden" inside the jaws and the milk teeth are in the their place.  After all milk teeth fall out, and the permanent teeth "rise", do the holes left by them filled up, or do we go around with holes in our jaws?    The picture: Recently I ran across the sentence:     "Just why the law prescribed thirty-nine lashes instead of forty or forty-one and so on, must needs remain unanswered."   How did a plural verb like "needs" wind up as an adverb?  Is it alone in this phenomenon, or are there other examples that appear to be an odd misplacement of a second verb, but are actually adverbs as well? Is there a single word to describe a solution that hasn't been optimized? I am working with some code, and I would like to describe the difference in its performance when it is optimized versus when it is not optimized. Unfortunately, I can't find a word to describe the code before it is optimized; "sub-optimal" might work, but I want to emphasize that this is the first iteration of the code. If "unoptimized" were a word, I would use that, but I haven't found any references to it in any dictionary.  Perhaps "raw" or "original"? "Least Astonishment" and the Mutable Default Argument NIST randomness test p values I have a binary sequence of length $2^{20}$. I am using the NIST statistical test, assess.   What should be taken for ./assess and  How many bitstreams? in this test? In the final Analysis report, what p-values should be there to pass this test? Better way of saying "those who are curious"? What is $dx$ in integration? 1) Alex's house      2) Alex' house     When the noun ends with the letter 's' or 'x', do I need to put 's' after an apostrophe or not?  I remember I read some rules related to this in my school grammar book, but now I've forgotten it. Can someone explain __all__ in Python? I have been using Python more and more, and I keep seeing the variable __all__ set in different __init__.py files.  Can someone explain what this does?