I understand the difference between the PASSID number and the Global Entry number, what I'm not sure about is which one I'm supposed to give the airline for international travel?   Do they only need the PASSID number or do I need to give them the Global ID number instead?
There are two 9-digit numbers on the back of the Global Entry card. The one on the upper left corner is the Known Traveler Number or PASSID. But on the upper right hand corner there is another 9-digit number, slightly larger than the PASSID. What is the purpose of this second 9-digit number?
Placeholder for body off in Android app The placeholder for the body field (the word "Body") is strangely placed in the Android app, seems a bit too high:    Could reproduce using:   Samsung Galaxy 4a.  Android version 4.4.2  App version 1.0.54 Moto X (2013), Android 4.4.4 App version 1.0.60 When would you use a voltage regulator vs a resistor voltage divider?  Are there any uses for which a resistor divider is particularly bad? Why are map tiles being repeated? Using MapServer and Openlayers How can I figure out what's slowly eating my HD space? Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer? Why would a journal accept my previous paper for publication, but reject latest manuscript due to being "outside of the journal's scope?" I submitted a manuscript last year to an IEEE journal, and the paper was accepted for publication. I recently submitted a new manuscript to the same journal, but, this time, the paper was rejected, and I was told that I should submit to another journal since my paper was not within the journal's scope. The two papers both target similar applications. Furthermore, the second paper uses some work in the first paper, making substantial improvements at solving a much more difficult problem. Based on the reviewer's comments (and my own personal assessment), I do not believe that the work presented in the second paper was "incremental" in nature. Far from it. Two of the three reviewers gave positive reviews. The third reviewer, however, mentioned the "outside of journal's scope" issue and the associate editor and editor-in-chief both sided with the 3rd reviewer, and the paper was stopped dead in its tracks.  I'm scratching my head trying to come to terms with how in the world my first paper could be accepted by this journal, but the second paper focused on the same application space and achieving substantial improvements on a much more difficult problem (backed up with measured results) could be rejected. Any ideas? Prove $\dfrac{\csc\theta}{\cot\theta}-\dfrac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$   So, LS= $$\dfrac{\csc\theta}{\cot\theta}-\dfrac{\cot\theta}{\csc\theta}$$ $$\left(\dfrac{1}{\sin\theta}\cdot \dfrac{\tan\theta}{1}\right)-\left(\dfrac{1}{\tan\theta}\cdot \dfrac{\sin\theta}{1}\right)$$ $$\dfrac{\tan\theta}{\sin\theta}-\dfrac{\sin\theta}{\tan\theta}$$ Now, considering the fact that I must have a common denominator to subtract, would this be correct: $$\dfrac{\tan^2\theta}{\tan\theta\sin\theta}-\dfrac{\sin^2\theta}{\tan\theta\sin\theta}\Rightarrow \dfrac{\tan^2\theta-\sin^2\theta}{\tan\theta\sin\theta}$$ I feel like I'm close to the answer because the denominator is the RS of the OP. Please help. Do not give me the answer. White regions in DensityPlot — is this a bug with ColorFunctionScaling? If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use?  For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is important especially since I am trying to couple this with a limit toward infinity. Consider the integral equation $\phi(x)-\frac{e}{2} \int_{-1}^{1} x e^{t} \phi(t) d t=f(x) .$ Then  there exists a continuous function $f:[-1,1] \rightarrow(0, \infty)$ for which solution exists there exists a continuous function $ f:[-1,1] \rightarrow(-\infty, 0)$ for which solution exists for $f(x)=e^{-x}\left(1-3 x^{2}\right)$, a solution exists for $f(x)=e^{-x}\left(x+x^{3}+x^{5}\right),$ a solution exists  what I tried $f(x)=f(x)+\frac{e}{2} \int_{-1}^{1} x e^{t} \phi(t) d t$ $\phi(x)=f(x)+\frac{e x}{2} \int_{-1}^{1} e^{t} \phi(t) d t$ $ \begin{array}{l}L e t \quad c=\int_{-1}^{1} e^{t} \phi(t) d t \\ \Rightarrow \phi(x)=f(x)+\frac{x e}{2} c\end{array} $ $c=\int_{-1}^{1} e^{t}\left(f(t)+\frac{c e}{2} t\right) d t$ $c=\int_{-1}^{1} e^{t} f(t)+\frac{\operatorname{ce}}{2} \int_{-1}^{1} t e^{t} d t$ $c=\int_{-1}^{1} e^{t}f( t)+\frac{\operatorname{ce}}{2}\left[t e^{t}-e^{t}\right]_{-1}^1$ $c=\int_{-1}^{1} e^{t} f(t)+\frac{c e}{2}\left(2 e^{-1}\right)$ $c=\int_{-1}^{1} e^{t} f(t) d t+c$ $\int_{-1}^{1} e^{t} f(t) d t=0$ Option (3) and (4) satisfies this Relation so, (3) and (4) seems true  to me.is i am right? I am stuck  for option (1) and (2)  is there any result or theorem ? "more than one does" or "more than one do"? However, if no x satisfies the equation or more than one x does—that   is the solution is not unique—the problem is said not to be well   posed.   In the line(source: ) above it uses "more than one does", but logically and intuitively it should be "more than one do" since "more than one" means two or more, then it is plural. I have tried my best to interpret it as it is, but hardly can I convince myself to make "more than" collocate with "does" as an adv., which may only make it make sense. For each of the following, give an example of a sequence of functions $f_n$ that converges to f  A. uniformly but not in the mean square sense.  B. in the mean square sense but pointwise nowhere.  I know that for part A the domain of the function cannot be bounded but other then that I'm not sure how to go about the problem EDIT:  The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.  The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the   $(0,0)$ Representation $(\frac{1}{2},0)$ Representation  $(0,\frac{1}{2})$ Representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation $(\frac{1}{2},\frac{1}{2})$ Representation infinite dimensional Representation? How does Cantor's diagonal argument work? I'm having trouble understanding Cantor's diagonal argument.  Specifically, I do not understand how it proves that something is "uncountable".  My understanding of the argument is that it takes the following form (modified slightly from the  article, assuming base 2, where the numbers must be from the set $ \lbrace 0,1 \rbrace $):  \begin{align} s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In this case, the diagonal number is the bold diagonal numbers $(0, 1, 1)$, which when "flipped" is $(1,0,0)$, neither of which is $s_1$, $s_2$, or $s_3$.  My question, or misunderstanding, is: When there exists the possibility that more $s_n$ exist, as is the case in the example above, how does this "prove" anything?  For example:  \begin{align} s_0 &amp;= (1,0,0,\mathbf{0},\dots)\ \ \textrm{ (...the wikipedia flipped diagonal)}\\ s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ s_4 &amp;= (0,1,1,\mathbf{1},\dots)\\ s_4 &amp;= (1,0,0,\mathbf{1},\dots)\ \ \textrm{ (...alternate, flipped } s_4\textrm{)}\\ s_5 &amp;= (1,0,0,0,\dots)\\ s_6 &amp;= (1,0,0,1,\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In other words, as long as there is a $\dots \text{ continues}$ at the end, the very next number could be the "impossible diagonal number", with the caveat that it's not strictly identical to the "impossible diagonal number" as the wikipedia article defines it:     For each $m$ and $n$ let $s_{n,m}$ be the $m^{th}$ element of the $n^{th}$ sequence on the list; so for each $n$,      $$s_n = (s_{n,1}, s_{n,2}, s_{n,3}, s_{n,4}, \dots).$$      ...snip...      Otherwise, it would be possible by the above process to construct a sequence $s_0$ which would both be in $T$ (because it is a sequence of 0s and 1s which is by the definition of $T$ in $T$) and at the same time not in $T$ (because we can deliberately construct it not to be in the list). $T$, containing all such sequences, must contain $s_0$, which is just such a sequence. But since $s_0$ does not appear anywhere on the list, $T$ cannot contain $s_0$.      Therefore $T$ cannot be placed in one-to-one correspondence with the natural numbers. In other words, it is uncountable.   I'm not sure this definition is correct, because if we assume that $m = (1, \dots)$, then this definition says that "$s_n$ is equal to itself"&mdadsh;there is no "diagonalization" in this particular description of the argument, nor does it incorporate the "flipping" part of the argument, never mind the fact that we have very clearly constructed just such an impossible $T$ list above.  An attempt to correct the "diagonalization" and "flipping" problem:  $$s_n = (\lnot s_{m,m}, \lnot s_{m,m}, \dots) \quad \text{where $m$ is the element index and} \quad\begin{equation}\lnot s_{m,m} = \begin{cases}0 &amp; \mathrm{if\ } s_{m,m} = 1\\1 &amp; \mathrm{if\ } s_{m,m} = 0\end{cases}\end{equation}$$  This definition doesn't quite work either, as we immediately run in to problems with just $s_1 = (0),$ which is impossible because by definition $s_1$ must be $ = (1)$ if $s_1 = (0)$, which would also be impossible because...   Or more generally, with the revised definition there is a contradiction whenever $n = m$, which would seem to invalidate the revised formulation of the argument / proof.  Nothing about this argument / proof makes any sense to me, nor why it only applies to real numbers and makes them "uncountable". As near as I can tell it would seem to apply equal well to natural numbers, which are "countable".  What am I missing? Sum of two uniform random variables I have the age-old problem of a div wrapping a two-column layout. My sidebar is floated, so my container div fails to wrap the content and sidebar.  &lt;div id="container"&gt;   &lt;div id="content"&gt;&lt;/div&gt;   &lt;div id="sidebar"&gt;&lt;/div&gt; &lt;/div&gt;   There seem to be numerous methods of fixing the clear bug in Firefox:   &lt;br clear="all"/&gt; overflow:auto overflow:hidden   In my situation, the only one that seems to work correctly is the &lt;br clear="all"/&gt; solution, which is a little bit scruffy. overflow:auto gives me nasty scrollbars, and overflow:hidden must surely have side effects. Also, IE7 apparently shouldn't suffer from this problem due to its incorrect behaviour, but in my situation it's suffering the same as Firefox.  Which method currently available to us is the most robust? Can't find wifi drivers for 0bda:f179 Realtek Semiconductor Corp I'm trying to install wifi drivers for a particular mini wifi card i bought. The output of lsusb is:  0bda:f179 Realtek Semiconductor Corp   I've searched everywhere for drivers, but could not find anything. Any help?  Thanks When mounting an NFS share manually using mount and a path of the form &lt;domain/ip&gt;:&lt;path&gt;/&lt;path&gt; or &lt;domain/ip&gt;:/&lt;path&gt;/&lt;path&gt;, umount fails to find the path in /proc/mounts, despite the fact that the path is in fact listed in /proc/mounts.  This is the same problem as in this question:   Steps to reproduce:  # mount --version mount from util-linux 2.24.1 (libmount 2.24.0: debug, assert) # mkdir mountpath # mount 192.168.2.101:/devices mountpath # umount mountpath /home/.../mountpath was not found in /proc/mounts # grep mountpath /proc/mounts 192.168.2.101://devices /home/.../mountpath nfs4 rw,[snip],addr=192.168.2.101 0 0   How can I unmount this mount? "ORA-01950: no privileges on tablespace 'SYSTEM' " : What error is it? Earlier I created a user :  SQL&gt;create user suhail identified by password SQL&gt;User created. SQL&gt;Grant create session,create table to suhail; SQL&gt;Grant Succeeded.   but when I login as suhail and try to create a table I get an error saying ORA-01950: no privileges on tablespace 'SYSTEM' .  What error is it ? Why does it occur ?    SQL&gt; connect suhail Enter password: Connected. SQL&gt; create table suhail_table(name char(10)); create table suhail_table(name char(10)) * ERROR at line 1: ORA-01950: no privileges on tablespace 'SYSTEM'   I am using Oracle Database 11g Express Edition Release 11.2.0.2.0 Possible point location algorithm How to find and replace a string by increasing its numerical part?