How do I get my winsxs folder to be smaller on windows 7, above and beyond all of the standard disk clean up?
Why does the /winsxs folder grow so large, and can it be made smaller?
Kept back upgrade of fwupd What's wrong now with fwupd? It was OK since May 1st, 2020 on newly installed Ubuntu 20.04 The following packages have been kept back:    fwupd  0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded. Attaching towel rail to drywall In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual? I've read in several places that one motivation for category theory was to be able to give precise meaning to statements like, "finite dimensional vector spaces are canonically isomorphic to their double duals; they are isomorphic to their duals as well, but not canonically."  I've finally sat down to work through this, and -  Okay, yes, it is easy to see that the "canonical isomorphism" from $V$ to $V^{**}$ is a functor that has a natural isomorphism (in the sense of category theory) to the identity functor.  Also, I see that there is no way that the functor $V\mapsto V^*$ could have a natural isomorphism to the identity functor, because it is contravariant whereas the identity functor is covariant. My question amounts to:     Is contravariance the whole problem?   To elaborate:   I was initially disappointed by the realization that the definition of natural isomorphism doesn't apply to a pair of functors one of which is covariant and the other contravariant, because I was hoping that the lack of a canonical isomorphism $V\rightarrow V^*$ would feel more like a theorem as opposed to an artifact of the inapplicability of a definition.  Then I tried to create a definition of a natural transformation from a covariant functor $F:\mathscr{A}\rightarrow\mathscr{B}$ to a contravariant functor $G:\mathscr{A}\rightarrow\mathscr{B}$. It seems to me that this definition should be that all objects $A\in\mathscr{A}$ get a morphism $m_A:F(A)\rightarrow G(A)$ such that for all morphisms $f:A\rightarrow A'$ of $\mathscr{A}$, the following diagram (in $\mathscr{B}$) commutes:  $$\require{AMScd}\begin{CD} F(A) @&gt;m_A&gt;&gt; G(A)\\ @VF(f)VV @AAG(f)A\\ F(A') @&gt;&gt;m_{A'}&gt; G(A') \end{CD}$$  This is much more stringent a demand on the $m_A$ than the typical definition of a natural transformation.  Indeed, it is asking that $m_A=G(f)\circ m_{A'}\circ F(f)$, regardless of how $f$ or $A'$ may vary. Taking $\mathscr{A}=\mathscr{B}=\text{f.d.Vec}_k$, $F$ the identity functor and $G$ the dualizing functor, it is clear that this definition can never be satisfied unless $m_V$ is the zero map for all $V\in\text{f.d.Vec}_k$ (because take $f$ to be the zero map). In particular, it cannot be satisfied if $m_V$ is required to be an isomorphism.     Is this the right way to understand (categorically) why there is no natural isomorphism $V\rightarrow V^*$?   As an aside, are there any interesting cases of some kind of analog (the above definition or another) of natural transformations from covariant to contravariant functors?  Note: I have read a number of math.SE answers regarding why $V^*$ is not naturally isomorphic to $V$. None that I have found are addressed to what I'm asking here, which is about how categories make the question and answer precise. ( was closest.) Hence my question here. On the iPod Touch/iPhone, since it is tied to your iTunes account, I am quite sure you can have your bought apps on multiple devices you own (can't test though, iPod Touch was stolen).  However, now I have the Motorola Droid, and am waiting for a tablet, and am considering getting a Nook and rooting it to run my own apps.  Question is, if you buy an app on the marketplace, how is the security done:   Is it tied to your Gmail account so you can share it between devices you own? Is it tied to the device? (Don't break/replace your phone!) As long as it's installed, you're OK? (If you uninstall, or wipe your device, it's gone).   I assume 3 is highly unlikely, though a possibility, so leaving it here as a potential answer to my question. In the tense of present perfect, Are 'recent past' and 'hot news' the same? Optimization when Cost Function Slow to Evaluate What's the difference between "uname -r" and "uname -v"? Prove that negative absolute temperatures are actually hotter than positive absolute temperatures Could someone provide me with a mathematical proof of why, a system with an absolute  (such that of a spin system) is  than any system with a positive temperature (in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system). Reset post score to 0 on migration How do I list all available shell builtin commands? We know bash supports number of  buitin commands  like:  $ type type cd help command type is a shell builtin cd is a shell builtin help is a shell builtin command is a shell builtin   I want to get list of all available shell builtin commands. How do I do that by command-line? How would you explain covariance to someone who understands only the mean? ...assuming that I'm able to augment their knowledge about variance in an intuitive fashion (  ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units, we take the square root to keep the units same and that is called standard deviation.  Let's assume this much is articulated and (hopefully) understood by the 'receiver'. Now what is covariance and how would one explain it in simple English without the use of any mathematical terms/formulae? (I.e., intuitive explanation. ;)  Please note: I do know the formulae and the math behind the concept. I want to be able to 'explain' the same in an easy to understand fashion, without including the math; i.e., what does 'covariance' even mean? Are fractions with prime numerator and denominator dense? So the question is in the title. And I mean dense in positive real numbers ofcourse. Somehow I cannot grasp if this is very trivial or not. The prime numbers aren't that dense, but are there enough of primes to make the fractions constructed from them dense? There is a type and search drodown which will appear after user type in the value. I need to click on the dropdown which contains the name of the drop down field.   The problem here is that there is no unique attribute present (No unique class, no unique name) &amp; the id keeps on changing after every login so cannot take id also. How do I set bold and italic on UILabel of iPhone/iPad? Earth moves how much under my feet when I jump? If I'm standing at the equator, jump, and land 1 second later, the  Earth does NOT move 1000mph (or .28 miles per second) relative to me,  since my velocity while jumping is also 1000mph.   However, the Earth is moving in a circle (albeit a very large one),  while I, while jumping, am moving in a straight line.   How much do I move relative to my starting point because of this? I  realize it will be a miniscule amount, and not noticeable in practise,  but I'd be interested in the theoretical answer. gedit: search and replace with regular expressions I want to replace this with gedit:   1299465 |  2003415 | 2015-09-06 05:35:34.59662+02  1299449 |  2009400 | 2015-09-06 05:35:32.301683+02  1299450 |  2008465 | 2015-09-06 05:35:32.451393+02  1299457 |  2015211 | 2015-09-06 05:35:33.451049+02   to that:  2003415 2009400 2008465 2015211   How can I do this with gedit?  Background: I want to do it with gedit and not sed/python/.... since the replace needs to be done interactive. Why on average does each bootstrap sample contain roughly two thirds of observations? How to use maths symbols in text mode? I try to add a center dot with \circ but it fails to compile. How to use maths symbol in text mode? The error message is   ovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorbian,  welsh, loaded. (/usr/local/texlive/2012/texmf-dist/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/local/texlive/2012/texmf-dist/tex/latex/base/size10.clo)) (./untitled-1.aux) ! Missing $ inserted. &lt;inserted text&gt;              $ What happens to options held during a reverse stock split? I held 1 put option for 100 shares of USO that expires on May 8. Yesterday, USO underwent an 8:1 reverse stock split. My options are now for USO1 instead of USO, but what does that mean?  The strike price hasn't changed, so does that mean that my option will expire worthless as it's unlikely the stock will drop (significantly) to back below the strike price? Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$ This was an assertion made in our textbook but I have no idea how to show that either statement is true.  Also would like to show that that $\mathbb{Q}(\sqrt{2})$ is strictly larger than $\mathbb{Q}$, which was the second part of the assertion.