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Why does Stack Exchange use Imgur over Amazon S3 or Azure? What benefit does  offer over , , etc. for image hosting?   Is it the simplicity of integration? The cost model? What's better about using a "gateway"? Why does the base-emitter voltage of a BJT decrease with temperature? According to Sedra/Smith Microelectronic Circuits, \$v_{BE}\$ changes by \$-2\text{mV}/\text{°C}\$. I cannot understand how this could possibly be the case given the equations I am familiar with.  With all currents kept constant, we have:  \$\large{i_E = \frac{I_s}{\alpha}e^{v_{BE}/V_T}}\$  To keep \$i_E\$ constant, any change in \$V_T\$ would have to be accompanied by a change of the same factor in \$v_{BE}\$, otherwise \$\alpha\$ or \$I_s\$ would have to change, which as far as I understand is not possible.  So, how can \$v_{BE}\$ be inversely proportional to \$V_T\$? This appears to be a css bug which (I think) has recently been introduced. It's most visible when viewing questions on Stack Exchange sites using mobile devices (the full site with responsiveness, not the mobile site) but can easily be reproduced by resizing a browser window on a question where the combined width of the tags is large. A couple of example questions show this behaviour:  On Meta Stack Overflow:   On Meta Stack Exchange:     Using the Meta Stack Overflow question to demonstrate (as the total width of the tags is larger):  At 1100px, the tags just about fit into their containing div.     At 800px, the tags appear on top of related questions:     At 450px, the tags are now wider than the view (the last tag is completely off the screen), causing scroll bars to appear:      This doesn't happen to lists of questions - the tags flow onto multiple lines:     Reproduced on: { Firefox 81, Chrome 84, Edge 84 } on Windows 10, and Chrome 85 on Android 11. fitch style proof problem regarding rule of inferences Okay I have the following fitch proof almost figured out, from here I know I have to move forth in conlcuding but I don't know what I am missing  (2 premises)  S → (R ∨ P)  P → (¬R → Q)   my work below  new scope assume S   Rule: > elim  R ∨ P  New scope assume R  Q∨R     Rule: V intro  End scope – (new scope assume P)  ¬R → Q         Rule: > Elim  my confusion comes where I go from here  Q∨R            rule Taut Con ??  Goal:├ S → (Q ∨ R) Finding my house in minecraft I wandered too far to go look for sheep and now I'm on a completely different island.  How do I find my way back to my house? Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$ Random plot based on a specific random seed Render every Nth frame of an animation I want to render every Nth frame of an animation, in this case every 12th frame. This way I can play back the animation at 2fps and see if everything is going correctly.  I'm a real novice with Blender Python and cobbled this together:  import bpy  for f in range(startframe,endframe,NthFrame):     bpy.context.scene.frame_current = f     bpy.ops.render.render()     bpy.data.images['Render Result'].save_render(filepath="" + str(f) + '.png')    This kind of works, the right images are rendered and saved. However it completely freezes up Blender, and after about an hour it crashes on windows due to being unresponsive I guess. How can I fix this? Preferably I'd like it to work like rendering an animation normally works, i.e. being able to still use Blender and seeing the progress of each rendered frame. I accidentally opened too many menus (or windows) and I want to reset them to default.  It is really annoying, and effecting my animation.  Thanks Gravatar profile image not showing sometimes It seems that with some profiles the Gravatar image is broken. I am not sure if this is an issue with SE or Gravatar, or both, so posting here.  As an example,  shows an error on , which shows a HTTP 500 on Gravatar.  Profile image on SO:        Image on Gravatar:        Switching to the MSE profile of the user, the image is working (but has a different hash).  Is this a bug on the SE side? Can anything be done to make Gravatar fix this?    Update 2016-10-04:  It happened to me again two times today. The last user profile was . Calling the service two or three times fixes the issue. What is the difference between can and could in 'Can/could you please explain this to me?' Multiple (diamond) inheritance compiles without "virtual", but doesn't with What is the formula for Real vs Apparent Depth, when not looking perpendicular to the interface?   I know the formula $$\frac{\text{real depth}}{\text{apparent depth}}=n$$   but I'm not looking for this. How to do line optical illusion art effects? I was wondering how I can do this type of optical illusion. Is it done manually or is there a quicker way to do it. Thanks ahead of time. Why doesn't Ubuntu 16.04 in Windows have ubuntu.exe? How to clone a Windows 10 dell onto an SSD I've recently bought a Dell Inspiron 3650, and would like to clone the disk onto a samsung SSD I have bought for it, in order to speed up boot times etc.  Samsung provide a clone tool called "Samsung data migration", which I've had success with in the past for cloning a system from a HDD to SSD.  Having tried it on the dell, the disk is not bootable, Leaving me with an error that no bootable media can be found. I've tried using a recovery usb to fix any boot system errors, but this fails with an error.  Booting into windows on the old HDD, the system recognises the disks have the same ID and disables the SSD, so it looks like the clone was successful.  I've tried disabling secure boot in the bios and then doing the clone, but this doesn't make a difference.  What else should I try? The system has Windows 10 home installed and is brand new, straight out of the box. Why is my attempt at downloading Big Sur failing? I am currently using a MacBook Pro 13&quot; Mid 2018 with Touch Bar. Today macOS Big Sur was released and I tried to download it but it's getting stuck at 484.4 MB. Initially, it shows 16-17 minutes left, but as soon as it reaches 484.4 MB it's stuck and the timer goes till 10 hours! My Wi-Fi is totally stable with a speed of 100 Mbps. I tried to restart my Mac but it still gets stuck. Earlier there were similar issues in the App Store (even now they are). The issue was I was not able to download an app unless I connect to the US VPN. I even contacted support but they were not able to help out. It wasn't a big deal as a VPN could be used. But now even with VPN, it gets stuck. OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" .  Based on evidence gathered to-date, it appears that the universe is both , as evidenced by observations and the . This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time."   Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles.  However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle:  Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic?  It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?   For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)?  Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise. Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$ Let $f$ be a real, continuous function defined for all $0\leq x\leq 1$ such that $f(0)=1$, $f(1/2)=2$, and $f(1)=3$. Show that  $$\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$$  exists and compute the limit.  Attempt:   Since $f$ is real-valued continuous on $0\leq x\leq 1$ and the boundaries $f(0)=1$ and $f(1)=3$, $f$ is bounded on the interval  and the integral $\displaystyle\int_0^1 f(x^n)dx$ exists for any positive $n$. Thus, we can interchange the limit and the integral and compose the limit, \begin{align*} \lim_{n\rightarrow\infty} \int_0^1 f(x^n)dx&amp;=\int_0^1\lim_{n\rightarrow\infty}f(x^n)dx\\ &amp;=\int_0^1 f\left(\lim_{n\rightarrow\infty} x^n \right)dx\\ &amp;=\int_0^1 f(0)dx=1. \end{align*}  Questions: So, my first question concerns whether interchanging the limit and the integral is correct. It seems it would be justified by the dominated convergence theorem, where $f(x^n)$ is dominated by a function $g(x)=\displaystyle\sup_{0\leq x\leq 1} f(x^n)$ and $f_n(x^n)$, on $0\leq x\leq 1$, converges pointwise to a function $f$ that takes value 1 for $x\neq 1$ and 3 for $x=1$.  My next question is whether the interchange between the limit and composition of the function is allowed. Since the function is continuous and the limit exists at that point, it seems the interchange would be justified. This post is in reference to the following blog post:   To start off, a quick introduction of myself; my name is Jascha Drel, Product Manager for Advertising at Stack Overflow. In this role, I am part of ’s organization.   Our team is continuously making improvements to the ads experience on our sites. One of the changes we’re excited about sharing is the new Report this Ad feature now available on some of our sites. We want to continue to give our communities more native control over their ad experience. We needed a quantifiable way to receive feedback and this feature will allow that.  We enforce strict  on the types of advertisers we work with but cannot fully control what is shown due to how advertising delivery works. However, being able to hear from our users about problematic ads will be a huge benefit as we can address those problems faster and with more accuracy. The Report this Ad feature will allow us to quickly see and investigate ads reported by you which matters to us because we want to hear your thoughts.  Furthermore, this new feature ensures that the members of our communities have a built-in way to report ads they consider problematic when we test any new ad formats/solutions.  We are launching this feature on 5 sites initially (, , , , and ) to get a good understanding of what we can expect in terms of numbers of reports whenever launching this to the entire network. Prior to launching it network-wide, we’ll share general results we’ve seen here.  What happens once an ad is reported?  All reports will be consolidated into a dashboard that the team will look at several times per week to spot irregularities in terms of the total number of reports, report categories, and on an advertising campaign basis. We will not be replying to individual reports, but we will reach out to our advertisers, to share feedback or notify them if the ad being reported does not fit our guidelines. We may also evaluate our policies in response to large numbers of reports not covered by them. Since we don’t have a baseline for the number of ads that are going to be reported using this new feature, we will consider reevaluating the process if the current process doesn’t scale.    We’d like to share an update on the progress of this feature:   We've launched this feature on 5 SE sites (Server Fault, Database Administrators, Arqade, Game Development, and Unix &amp; Linux) initially for logged in users only, and for anonymous users afterward. The report this ad button was shown several million times (of which roughly 65% paid ads and 35% house ads). We showed several dozens of different ad campaigns. So far we have received 0 reports. We've tested the feature several ways, found some minor bugs (which have been/are being fixed), however, in the vast majority of the scenarios the feature works well (we’re happy to be ).   We’re currently graduating this feature and are releasing it network-wide this week. Feel free to comment below if you have any questions/comments.