Why is the azimuth resolution in Sentinel (SAR sensor) worse than the range resolution?    The table in this  gives the resolution for SLC products aquired in the different aquisition modes. In all of them the range resolution is better than the azimuth resolution.    Note: This question is totally different from my , as the latter tackles the effects of the incidence angle on the ground resolution (range resolution + azimuth resolution), and this doesn't explain why sometimes the range resolution is better than the azimuth resolution.
On this link (Sentinel1  for a SLC product), the resolution is written as a range from the highest corresponding to low incidence angle, to the lowest resolution corresponding to high incidence angle.  My question is how is the resolution related in general to the incidence angle? And if they are really related, why is the resolution affected by the change in the incidence angle?
Add Item to Finder Sidebar Can I still use logistic regression if some variables are not applied to all the observational units? Some of the variables are questions that are not being asked to every single person in the questionaire depending on how they answered previous question(s). So would I still be able to use a logistic regression if some of the questions (the independent variables) are only measuring the responses of SOME of the respondents? Why is the ##UserID## parameter not populated in Data Explorer anymore? Environment I'm logging in using the OpenID from  and using Chrome 31.0.1650.57 m if that matters. Steps to reproduce: Log in to  and , for example, like: DECLARE @MyUserID INT = ##UserID:int##  SELECT TOP 1     Id AS [Post Link],     Score AS [Score],     CreationDate AS [Creation Date] FROM     Posts WHERE     OwnerUserId = @MyUserID AND     PostTypeId IN (2, 3) ORDER BY     CreationDate DESC  Then press the Run Query button and see if the UserID field is filled with your own user ID like shown in the below screenshot:  Question: Did something changed on the ##UserID## parameter (for example, that it's not supported anymore)?  If so, then there is an outdated  paragraph about it (What's the point of logging in). If not, it is a bug which is there about three days (I've been waiting since I noticed that you were going to do some changes to Data Explorer, but it remains there, hence my question). How do I complete the square from the point I have left off at, and is this correct so far?   I have a normal prior for $\beta$ of the form $p(\beta|\sigma^2)\sim \mathcal{N}(0,\sigma^2V)$, to get:  $p(\beta|\sigma^2)=(2\pi\sigma^2V)^\frac{p}{2}\exp[-\frac{1}{2\sigma^2}\beta^T\beta]$  where $\beta^T\beta$ is   $\sum\limits_{i=1}^p \beta_i^2$.  My likelihood has a normal distribtuion for the data points y of the form $p(y|\beta,\sigma^2)\sim\mathcal{N}(B\beta,\sigma^2I)  $  $p(y|\beta,\sigma^2)=(2\pi \sigma^2V)^\frac{n}{2}\exp[-\frac{1}{2\sigma^2}({\bf y}-{\bf B}{\bf \beta})^T({\bf y}-{\bf B}{\bf \beta})]$  (Note that $\beta$ is a matrix/vector too, \bf does not work.)  To get my posterior for $\beta$ I combined the above, took the exponential parts only, and then expanded to get:  $\exp[-\frac{1}{2\sigma^2}({\bf y}^T{\bf y}-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta)]\exp[-\frac{1}{2\sigma^2}({\bf \beta}^T{\bf B})]$.  I dropped the $({\bf y}^T{\bf y})$ term, as is not a function of $\beta$.  Putting into one expression without the exponential:  $-\frac{1}{2\sigma^2}(-{\bf y}^T{\bf B}\beta-\beta{\bf B}^T{\bf y}-\beta^T{\bf B}^T{\bf B}\beta+{\bf \beta}^T{\bf B})$.  I know I need to combine the similar terms and get into the form of the multivariate normal distribution, which is what I am aiming for, but I am unsure how to do this? I probably have to add an extra term to the expression to get it into the correct form?  Note: This is not homework, it's a project, but my Bayesian working knowledge is not good at all and so I need to understand the working out. I intend to integrate out the $\beta$ and then the $\sigma^2$ after getting into the multivariate form. Helpless after exhausting daily limit for reviewing Suggested Edits I have faced this problem earlier. But today I got to face this problem twice in a span of couple of minutes.. I have unfortunately finished my daily quota of reviewing Suggested Edits. But I want to further edit a post for which an edit has already been suggested by another user having less than 2000 Reputation.  I come across a post and it says that an edit has already been suggested which is pending for Review:   I click on edit (1) and a pop-up of Suggested Edit appears:    However, the problem is this Suggested Edit doesn't thoroughly deal with the post. It just fixes some capitalization and nothing else — no grammar fixes, no sentence restructuring to make it more clear, no code formatting, no dividing it into lists, etc. — in short, perfect candidate to be rejected. (The image for the suggested-edit I have uploaded didn't have those problems - however, there were those problems in the edits that I encountered earlier.) The problem before me is that I am helpless. I can't approve, reject or improve the edit since I have already gone past my daily quota of Reviewing them. Neither can I make the edits to the post since this suggested edit is pending review. I am completely helpless!! Whats the opinion of the community in this matter?  Should we (those with more than 2000 Rep) be able to edit them? Don't count it in our Review Progress obviously - not sure what should be done with the suggested edit already proposed.  Or, Let it be, someone else would come and edit them and other Reviewers would deal with the Suggested Edit appropriately.  Or, Something else.    Note: This might not be much of a problem for Stack Overflow since the Review Queue is very busy here. However, this is a bit of a problem for smaller sites. So, treat it as a question posted at Meta.SE and not so much at Meta.SO.  Dirty Hack: Ah... found a dirty hack to work around this situation. However, this shouldn't be used unless absolutely necessary. Credit goes to  in . To edit a post enter this link in your browser: http://${site_url}/posts/${post_id}/edit. So, to edit this particular post one would enter: http://meta.stackoverflow.com/posts/171129/edit. I repeat, the hack shouldn't be used unless necessary. Is empty set element of every set if it is subset of every set? This problem is from Discrete Mathematics and its Applications  My question is on 9b. I know that the sign represents an element is a member of. (from book)  I know that the O with a slash across it is the empty set which &quot;is a special set that has no elements&quot;. From , I got that the empty set is a subset of all sets, meaning that every member of the empty set(nothing) is also a member of any other set. Based on all of this, for 9b, would {0} contain the empty set because it fundamentally has the elements that consist of the empty set(nothing) or does it physically have to have the empty set? Get Last Friday of Month in Java Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$ Today, we had a math class, where we had to show, that $a_{100} &gt; 14$ for  $$a_0 = 1;\qquad a_{n+1} = a_n + a_n^{-1}$$  Apart from this task, I asked myself: Is there a closed form for this sequence? Since I didn't find an answer by myself, can somebody tell me, whether such a closed form exists, and if yes what it is? Position of "only" in “We 𝒐𝒏𝒍𝒚 have two possibilities” Is there any difference in meaning between the three following sentences?   We only have two possibilities. We have only two possibilities. We have two possibilities only.   I have already read  and I know that the position of only and the emphasis (written or oral) may change the meaning of some sentences, but I am not sure if it does here.  Note: It is clear that “only we have two possibilities” has a different meaning. My question is restricted to the sentences I’ve listed above. I saw her dance/dancing? I saw a flash of lightning strike/striking? I caught her steal/stealing? What is the correct way to pluralize an initialism in which the final word is not pluralized by adding the letter "s"? Rules for refreezing food What is the name of this kind of character illustration? MacBook Pro stuck in gray screen when booting I've got a Late-2011 15" MacBook Pro stuck in the gray screen when booting AFTER login. I've tried removing the drive (it's non-retina) and booting from a working bootable Yosemite installer, no luck. (it sees the startup USB drive, the progress bar progresses, but stuck at the gray screen again even without a drive.  Tried NVRAM reset (cmd option P R), it has reset (the login sound's volume changed) but nothing changed.  Tried holding D on startup, AHT doesn't start, instead, it tries to boot into the OS.  Tried Cmd V, it sometimes works and displays the verbose output, sometimes, it acts like I haven't even pressed. Again, stuck after login.  Tried booting again from USB, I select USB (after seeing both drives correctly), but no luck, it's also stuck.  I've stumbled upon this:    I've tried booting into single user mode with Cmd S, it worked ONCE, I've disabled the graphics extensions just as shown at that post, restarted, but again, nothing changed.  More weirdly, now the Cmd S doesn't work either. It just takes me to login screen without showing the terminal, just as I haven't pressed anything.  Why would this happen? Why would a Mac refuse to enter hardware test mode, single user mode, or refuse to boot from a working bootable Yosemite drive both with or without the main drive installed?  UPDATE: I've run the AHT and got an error:  4MEM/66/40000000: 0x84e0ec98  It looks like a memory issue, but I'm not sure.   UPDATE 2: I've tried reinserting the RAMs and the the problem is not reported anymore. However, the Mac still won't boot. Is the W statistic output by wilcox.test() in R the same as the U statistic? I've recently been reading about the Mann-Whitney U test. It turns out that to carry out this test in R you actually need to run a Wilcoxon test!  My question: is the W statistic of wilcox.test in R identical to the U statistic? Looking for a short story about a robot evolving to have supernatural powers apt install "*" method in Ubuntu 20.04 does not work Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero? How does the Golden Ratio/Spiral Work? Is it useful with Logo Design? Was this an oversight?  Or is it to do with the JVM?