The stamp on my passport got smudged a little bit due to rainwater going in. But the information page is still intact without any damage. Also, there is a valid German visa on this passport, where I will be travelling to in October. Will this passport be considered as damaged?  [
My Indian passport book cover is detached from the main book, but all other information, as well as the book is fine. I am traveling to India in 2 days. What should I do? Will there any problem at the airport?
Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$ Let $\{ a_n, n\geq 1\}$ be a sub-additive sequence, i.e. for any $m,p\geq 1$ $$ a_{m+p} \leq a_m + a_p. $$ .Prove that $$\lim_{n\to\infty} \frac{a_n}{n} = \inf_n \frac{a_n}{n}.$$ I guess the first step is to state $$a_{n} = a_{mp+q} \leq a_{mp} + a_q$$ but I'm not sure where to go from here.... Send email using the GMail SMTP server from a PHP page A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing. I would like to prove the statement in the title.  Proof: We prove that if $f$ is not strictly decreasing, then it must be strictly increasing. So suppose $x &lt; y$.  And that's pretty much how far I got.  Help will be appreciated. If "clearly evident" is redundant, what word or phrase suggests being indisputable but not readily apparent? A  asks whether the modifier "clearly" changes the meaning of "evident". I would have said, prior to examining a few dictionaries, that evident did not necessarily mean readily apparent, but to my surprise it does.  This brings me to ask what word or expression would mean something can be taken as a true fact, but not through an easily constructed (not obvious or readily apparent) rationale?   For example, if Sherlock Holmes says something is true while everyone else is still sitting on their hands, then it is evident to Holmes, but not to the rest of the world. So, from everyone else's point of view, it is not readily apparent, and (by definition) apparently it is not evident, clear, or clearly evident at all, based on the dictionary definitions. But (let's stipulate) it is true and deducible from the observable evidence. What would we call this?  Update  An update is highlighted above. I can see from some of the answers and comments that I may have gone off my mark with the phrase "not through an easy-to-follow rationale”, and I have modified the question to correct this. I understand that there can be rationales, arguments, or proofs that, once explained, may or may not be easy to follow. What I intend is that the rationale to support the indisputable conclusion is not (initially) easy to recognize or construct (not readily apparent) in the first place. I apologize for the confusion. (The original can be seen in the change history.)  Update 2  Shortly after offering a bounty to this request, I recalled a single word that I now believe is a very good match to the parameters specified in this inquiry as it is stated above. That word has not yet been suggested (or approached) by any answer or comment (active or deleted) at the time of this edit. This request is changed to a single word request. (However, if you feel a single word fits well but not without some additional supporting words, please offer your thoughts in an answer.) While my curiosity for the term has already been met, the request and bounty remain as an open challenge. I will post my own answer once the bounty has expired and been awarded. Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$ Assume $T \in \mathbb{R}^{d\times d}$. Let $\rho(T)$ be the spectral radius of $T$ and $\rho \ge 0$. Prove that  $\rho(T) &lt; \rho$ if and only if there exists a $P \succ 0$ satisfying $T^TPT - \rho^2 P \prec 0$.  I can prove the Necessity: If $P = I$, for any $x \in \mathbb{R}^d$,   \begin{equation} x^T T^T P T x - \rho^2 x^T P x = \| Tx \|^2 - \rho^2 \| x\|^2 &lt; 0 \end{equation} so $T^T PT - \rho^2 P \prec 0$  I get stuck in proving the Sufficiency. In a project the customer wants the images of the WMS to be secured against unauthorized access.   What are the common solutions to realize that?   Are they compatible with the OGC-standards? How can I move files into subdirectories by count? I have around 100,000 files in a directory. As you can imagine, that's not an ideal situation, and I'd like to split the directory up into subdirectories. But the filenames aren't such where I can put them into subdirectories based on their names or anything, so I'd like to create, say, 10 directories and put about 1000 files in each. Is there an easy bash command or loop that would do this? In Iron Man 3,      When the real villain kidnapped the President of the United States,   it is never explained why none of the other Avengers came to help, or why Tony didn't call them. The only explanation so far is: "it was an Iron Man movie...", but an in universe answer would be good. I have a tag in my html like this:  &lt;h1&gt;My Website Title Here&lt;/h1&gt;   Using css I want to replace the text with my actual logo. I've got the logo there no problem via resizing the tag and putting a background image in via css. However, I can't figure out how to get rid of the text. I've seen it done before basically by pushing the text off the screen. The problem is I can't remember where I saw it. Load Excel data sheet to Oracle database I am looking for a free tool to load Excel data sheet into an Oracle database. I tried the Oracle SQL developer, but it keeps throwing a NullPointerException. Any ideas? Interpreting spline results I was wondering. If I have a bilinear symmetric form, it is easy to find its matrix. But, when I have a quadratic form, which is the procedure to do that?  I heard that one possibility is: If $q$ is my quadratic form, then $$f(x,y) = \frac{1}{4}q(x+y) - \frac{1}{4}q(x-y)$$ is the bilinear symmetric form associated, so the method reduces to find the matrix of $f(x,y).$   The point is that seems a little noising... How to find, in practice, the matrix of quadratic form?  Thanks in advance. I have been playing around with camera tracking and I'm happy enough with the tracking and alignment of the markers with the footage when viewed through the camera.    The problem is, when I am not looking through the camera I can see that the grid isn't aligned to the camera.    How do you correctly align the grid to this tracked camera? I have set a floor and two points for scale, also clicked setup tracking scene, but this just added cube and plane which were on the grid. How do I debug permissions? How do I debug permissions in Drupal 7?  I use core reporting, error logs, devel module error logs, backtrace and node access permission block but sometimes it is not enough. What else should I check to find out why certain fields, views or blocks are not showing to a user?  I also found there is a  for reporting on permissions called  but it is not available for Drupal 7.  I am using various permission related third-party modules:   - devel node access 7.x-1.x-dev   - fast permissions administration 7.x-2.0  - organic groups access control 7.x-1.x   - profile2 group access 7.x-1.x-dev   - ur-node access 7.x-1.x-dev Is it safe to use file's hash as IV? I'm encrypting some files using AES in CBC mode.    I'm also using file's digest (SHA-1) to check that data is decrypted correctly (so I need to store it with file).  Is it safe to use this digest as AES's IV and store it in the header of file? Or it has security issue? How can I get Firefox to open torrent files with Transmission? Every time I download a torrent file (.torrent), Firefox thinks I should open it with a text editor. How can I get it to open with Transmission? In Edit -> Preferences -> Applications, there's no setting for torrent files, and no apparent way to add a new filetype. How does an attacker's reach interact with the Mounted Combatant feat's ability to force an attack against the mount to target the rider instead? Help me understand adjusted odds ratio in logistic regression I've been having a hard time trying to understand the use of logistic regression in a paper. The paper available  uses logistic regression to predict probability of complications during cataract surgery.   What is confusing me is that the paper presents a model that assigns odds ratio of 1 to baseline described as follows:     A patient whose risk profile was in the reference group for all risk indicators (ie adjusted OR=1.00 for all in Table 1) may be regarded as having a ‘baseline risk profile’, and the logistic regression model indicates a ‘baseline predicted probability’ for PCR or VL or both=0.736%.   So the probability of 0.00736 is presented with odds ratio of 1. Based on the transformation from probabilities to odds ratios: $o=\frac{p}{1-p}$, this can't be equal to 1:  $0.00741=\frac{0.00736}{1-0.00736}$.  It gets even more confusing. The composite odds ratios that represents multiple covariates having values different than the baseline is used to calculate predicted risk.      ...the composite OR from Table 1 would be 1.28 X 1.58 X 2.99 X 2.46 X   1.45 X 1.60 = 34.5, and from the graph in Figure 1, we see that this OR corresponds with a predicted probability of PCR or VL or both of around 20%   The only way to arrive at the values the paper is giving as examples is to multiply the baseline probability with composite odds like this: $0.2025=\frac{(34.50\ \times\ 0.00736)}{1\ +\ (34.50\ \times\ 0.00736)}$.  So what is going on here? What is the logic for assigning odds ratio 1 to a baseline probability that is not 0.5? The update formula I've came up with above comes up with the right probabilities for examples in the paper but this is not the direct multiplication of odds ratio I'd expect. What is it then? appears to have been question banned because of two unpopular Meta suggestions. (He says so in )  Look at the two contributions that appear to have gotten him banned. Like those of many others, they may not be of perfect quality, but they are not actively harmful to the site, either. As it stands, you can get question blocked on Meta simply for asking questions that aren't popular with the Meta crowd.  Why does the team insist on keeping the question ban active on Meta?  Why can't real problem users be dealt with through manual moderator action? Don't tell me it's a problem of scale; as far as I can see, actually toxic users are very rare on Meta.  People will frequently complain that Meta actively discourages the expression of unpopular viewpoints and suggestions. With the threat of question bans in place, I find those complaints difficult to refute. I hate that. I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong