If the first Death Star had the weakness installed on purpose
Were there any improvements to the second Death Star (other than the change in exhaust port) that we know of?
Using a transistor as a switch I am attaching a motor to an ATmega32 chip. I want to build an H-bridge but before doing that, I want to control the motor using the chip. I bought few NPN Transistors from RadioShack. I have 5V running though the breadboard. I attached Vcc to the Collector, Base to the Pin, and Emitter to the motor. And other wire of motor is hooked up to Ground. Unfortunately, the power coming out of the transistor is too low, the motor is barely moving (As opposed to when I hook up my motor straight to 5V). What is wrong? Do I need a different transistor or is my setup wrong? If it is the transistor, can you please recommend the right one, I am not too good at those. Permission denied to change gid(group) of a file I own It appears I still miss some things about the way permissions work. I am on a debian 7 system btw. just now I have this file of which I downloaded and it belongs to myuser:myuser, that is both user and group are set to me. It also resides in my $HOME directory since that is where I downloaded it to.  So far so good. Now I want to share this file with some other users of the pc and for that I want to switch the group ownership of the file to group "users". however that fails:  nass@quarx:~/xmas_carol$ chgrp -R users *  chgrp: changing group of movie.mov': Operation not permitted   And the contents of the folder are:  -rwxr-xr-x 1 nass nass 2482411461 Feb  6 03:57 movie.mov   I am fuzzy about what is going on with the permissions. Can someone explain In eevee, shadows are clipped by camera distance As shown in the gif, the shadow in eevee is clipped by the camera distance. The same is true for F12 rendering. Where are the options to improve this issue? Is the space $\mathbb{N}$ is a baire spaces ? yes/No Is  the  space $\mathbb{N}$  is a  baire  spaces ?  My attempts :   No ,  It  will not form a  baires  spaces ,  let $C_n= \mathbb{N}\setminus\{n\}$. This is open (since $\{n\}$ is closed in $\mathbb{R}$, hence in the induced topology of $\mathbb{N}$) and dense, since every open ball with center in $\mathbb{n}$ intersects ${C_n}$. But  $$\bigcap_{n\in\mathbb{N}} {C}_n = \emptyset$$  So $\mathbb{N}$ is not a baires  spaces because for  Baire Space the intersection of a countable family of open dense sets must be dense.   Is  Its correct or not ? Manually installing a program on Debian I have installed Debian on my pc, but the problem is that at the moment I have no Internet connection to this pc. So, to install a program I have to manually downloaded from a pc with internet and then install it to the linux-debian computer.  The question is this: Is there a standard way to make the installation manually? Note that when I connect a usb flash with the program I want to install(that is:   cdparanoia_3.10.2+debian-10.1_i386.deb) and I try opening it I get the message:     Failed to execute child process “ar” no file or directory. Why can't you use the keyword 'this' in a static method in .Net? I'm trying to use the this keyword in a static method, but the compiler won't allow me to use it.  Why not? What price should I charge for design services? I was hoping I would find some people in the industry that could help me decide what's the best price to charge to design (in this case) business cards.  What are standard prices for professional designers?  From a firm point of view? From a freelancer?  I don't want to overcharge clients but I don't want to ruin the industry by underselling my services. Number of points on a line in a finite projective plane I've been reading some proofs regarding finite projective planes of order n, and often they start out by assuming that each line contains n+1 points. Is this a fact that follows from the axioms for finite projective planes? Or does this relate to the order of the finite field being projected? (for example in the Fano plane, does the fact that each line contains 3 points follow from the fact that there are 3 elements {0,1,2} in Z_2?) I haven't been able to find a clear explanation of this (clearly I do not yet have a solid understanding of how such planes are constructed). If someone could enlighten me that would be excellent. Determining likely relationship based upon autosomal DNA shared cM Given two tests that share some cM of autosomal DNA, how can I easily find the predicted relationships that such shared cM would suggest? For example, a 2,200 cM match suggests it could be either: grandparent, half-sibling, or grandchild. Help with footer always to bottom How can one differentiate between "who" and "whom"? Many times, I've been asked the difference between "who" and "whom". I myself know the difference, but it is hard to explain to others. What is the easiest way to explain it to those with a basic understanding of English? A mnemonic (if possible) would help. Let $A$, $B$ be two reduced $k$-algebras. Then if an element of the form $$\sum a_{i}\otimes b_{j}$$ is nilpotent, we can compose it with any $k$-homomorphism $f$ from $A$ to $k$ to get a homomorphism from $A\otimes B$ to $B$. This map's image is $$\sum f(a_{i})\otimes b_{j}$$must be nilpotent as well. So if we assume $b_{j}$ is linearly independent in the first place, we may reason that $f(a_{i})=0$. This showed that $a_{i}$ are in the Jacobson radical of $A$. However, we only know $\mathrm{Nil}(A)=0$, and it is not clear to me how to pass from the Jacobson radical to the nilradical without using some commutative algebra machinery.   Here is what I think that might work. If $A$ is of finite type, then by Nullstellensatz we can assert the above is true. But if $A$ is not of finite type, then I can write $A=k[x_{1},...,x_{n}][X]$, where $n$ is the transcendence degree of $k(A)$ and $k[X]$ is finite over $k$. Then I should be able to pass from $k[X]$ to $A$ by inductive argument on the transcendental degree of $k(A)$, since prime ideals are maximal in a UFD (I am working with $k[x]$ by introducing $[x]$).   The proof I have for the case of finite type is not satisfying. Given $I\subset k[X]$, using Nullstellensatz one can show that $$I_{X}V_{X}[I]=\sqrt{I}$$ where $V_{X}[I]$ is the set of all points in $X$ on which $I$ vanishes, and $I_{X}(V_{X}[I])$ be the ideal in $k[X]$ which vanishes on $V_{X}[I]$. Granting this, let $I=(a_{i})$, then we want to show $I=0$, which is $V_{X}[I]=X$. This follows since if $U\subset W$, then $V_{X}[U]\supset V_{X}[W]$. Since $V_{X}[I]\supset V_{X}[m_{x}]$ for all maximal ideal corresponding to points, it must be $X$. This proof is unnecessarily winding by using the ideal-variety correspondence. Ideally I should be able to construct a pure algebraic proof.   The thing not clear to me is whether the above strategy really works. Namely I am not sure if I can really induct on the transcendental degree of $k(A)$. To make matters simple assume we showed the statement holds for $A$ with transdental degree $&lt;n$. For $A$ with transdental degree $n$ we can thus write it as $k[A'][x]$. Then any maximal ideal $m'$ of $k[A'][x]$ must correspond to a maximal ideal $m=m'\cap k[A']$ in $k[A']$. But it seems not possible to show that any prime ideal is maximal. Indeed considering the simple example of $k[x,y]$, where $(x)$ is a prime ideal but not maximal since $k[x,y]/(x)=k[y]$ is not a field. The problem is in the inducting process the base ring is not neccessarily a field, and so this strategy cannot work.   I am thinking maybe I can show $m'=m[f(x)]$ with $f(x)$ some irreducible polynomial in $k[A'][x]$. Because we know $k[A'][x]$ is noetherian by Hilbert's basis theorem, so in particular $m'$ must have a finite generating set. And we can reduce the number of irreducible polynomial to 1 since $m'$ is a maximal ideal. But I still do not know how to use this to finish the proof. How to call a constructor on an already allocated memory? How can I call a constructor on a memory region that is already allocated? Spacing issue for newenvironment wrapper of equation environment If I create a custom environment based on the equation environment, I get a spacing issue: the next line of text after my environment closes doesn't start on the left margin.  Example code:  \documentclass{article} \begin{document} \newenvironment{myenv}{\begin{equation}}{\end{equation}} \noindent $| \leftarrow$ this is the left margin. \begin{myenv} e ^{i \pi} + 1 = 0 \end{myenv} $| \leftarrow$ this isn't the left margin. \end{document}   Output:    Removing the newline after \end{myenv} solves the spacing problem, but the resulting code is not readable.  Of course, in this example I could just use the equation environment itself. My real issue involves a more complex custom environment that suffers from the same problem, and which also includes an equation environment within it. Java: Why does if statement never resolve to true? Please add a system to allow file uploads attached to questions and answers Show this equality (The factorial as an alternate sum with binomial coefficients). If gravity isn't a force, then why do we learn in school that it is? Left and right subscript / superscript I am trying to put two subscripts at the left and right of a character. For example, something like:  _{t} p_{x}  where p is in the middle. How do you do this? How did Vader saving Luke turn him to the good side? Couldn't Vader save his son and continue being a Sith Lord? Couldn't he have let Luke go and basically become the Emperor and have the Galaxy to himself? I don't think killing the Emperor to save your son will automatically convert you to the light side. Enlighten me.