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How to combine two strings together in PHP? I understand that the first point release of Ubuntu 18.04, namely 18.04.1 is now available and that my system should now offer it as an update.  My current OS version is 16.04.5 LTS. In System Settings/Software and Updates I have set 'Notify me of a new Ubuntu version' to 'For long term support versions'. I have tried both the main server and the server for United Kingdom, neither offers an update when Software Updater is clicked or via the Ubuntu Software icon.  Can anyone please tell me why I don't get the option of updating to 18.04?  Edit:  I don't remember the details exactly, but I think that my last LTS point release update was offered automatically a lot sooner after the published release date than where we are now with 18.04.1.  Edit 10th August  It appears that there has been some problem with the update process and that it should be fixed next week, see:    Edit 14th August 18.04.1 LTS now available from UK server, I need a binary search algorithm that is compatible with the C++ STL containers, something like std::binary_search in the standard library's &lt;algorithm&gt; header, but I need it to return the iterator that points at the result, not a simple boolean telling me if the element exists.  (On a side note, what the hell was the standard committee thinking when they defined the API for binary_search?!)  My main concern here is that I need the speed of a binary search, so although I can find the data with other algorithms, as mentioned below, I want to take advantage of the fact that my data is sorted to get the benefits of a binary search, not a linear search.  so far lower_bound and upper_bound fail if the datum is missing:  //lousy pseudo code vector(1,2,3,4,6,7,8,9,0) //notice no 5 iter = lower_bound_or_upper_bound(start,end,5) iter != 5 &amp;&amp; iter !=end //not returning end as usual, instead it'll return 4 or 6   Note: I'm also fine using an algorithm that doesn't belong to the std namespace as long as its compatible with containers. Like, say, boost::binary_search. Is it possible to do something like this  #ifdef SOMETHING #define foo // #else #define foo MyFunction #endif   The idea is that if SOMETHING is defined, then calls to foo(...) become comments (or something that doesn't get evaluated or compiled), otherwise it becomes a call to MyFunction.  I've seen __noop used, but I don't believe I can use that.  EDIT(s):  I don't think I can really use a macro here, because MyFunction takes a variable number of arguments.  Also, I'd like to make it so the arguments are NOT evaluated!  (So doing something like commenting out the body of MyFunction doesn't really give me what I need, as the arguments will still be evaluated) $A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected Let $X$ be a topological space. Let $A$ and $B$ be two subsets of $X$ such that: $A$ and $B$ are closed, $A \cup B$ is connected, $A \cap B$ is connected     Prove that $A$ and $B$ are connected.   Thoughts:  Suppose that $A$ is disconnected. Since $A$ is closed, there are two non-empty, disjoint, closed sets $E$ and $F$ in $X$ such that $A = E \cup F$. Then I attempted many things but all were not really useful.  Please help. Thanks. Where is Jon going? At the end of S08E06 of Game of Thrones, Jon Snow along with Tormund and others of the Night's Watch      leave the Night's Watch.   and go into the woods.  Where are they going? And why? How to prove floor identities? So I have this word problem and I’m a bit confused about it. I have the answer and explanation but I still don’t understand: The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?     A. Less than 5730 years      B. Approximately 5730 years      C. Significantly greater than 5730 years, but less than 11460 years      D. Approximately 11460 years  Correct Answer: A Explanation: Because the half-life of carbon-12 is essentially infinite, a 25 percent decrease in the ratio of carbon-14 to carbon-12 means the same as a 25 percent decrease in the amount of carbon-14. If less than half of the carbon-14 has deteriorated, then less than one half-life has elapsed. Therefore, the sample is less than 5730 years old. Be careful with the wording here—the question states that the ratio is 25% less than the ratio in nature, not 25% of the ratio in nature, which would correspond to choice (D). How is the ratio of the carbon isotopes relevant to half-lives? What is the purpose of saying the half-life of an isotope is infinite? What is meant by “the normal ratio in nature”? Just based on the answer, it seems like the question said “25% of a carbon sample decayed, how old is this sample?” Obviously it’s younger than 5,730 years (the time for its first half life) because if only 25% decayed that means half a half-life has passed. I don’t see how isotopes and ratios would change this problem at all. Edit: Every answer here was very informative and helpful. It was tough to pick a best answer. I picked Cosma’s because it clicked with me. If you’re reading this and want to understand radiocarbon dating, look at every answer because there is some useful information in every answer Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$ Studying from Roman's Advanced Linear Algebra, I want to prove that $$U^* \otimes V^* \cong (U \otimes V)^* \cong \hom(U,V;\mathbb{F})$$ The author proves that $U^* \otimes V^* \cong (U \otimes V)^*$ by showing that there is an unique linear transformation   $$\theta:U^* \otimes V^* \to (U \otimes V)^*$$  defined by $\theta(f \otimes g)=f \odot g$ where $(f \odot g)(u \otimes v)=f(u)g(v)$  I want to prove that $U^* \otimes V^* \cong \hom(U,V;\mathbb{F})$. I tried to use the universal property by fixing $f \in U^*, g\in V^*$ and defining $S: U^*\times V^* \to \hom(U,V;\mathbb{F})$ as $S(f,g)=F_{f,g}$, where $F_{f,g}(u,v)=f(u)g(v)$, but I got stuck. Statement: $[a, b] \cap \mathbb{Q}$ in $\mathbb{Q}$ is not compact. Thus the interior of all compact subsets of $\mathbb{Q}$ is $\emptyset$.   I am trying to understand the first sentence. I read that a closed subspace of a compact space is compact, so for example, consider the unit interval $[0, 1]$ which is a compact space. Take a closed subspace $[0, 1] \cap \mathbb{Q}$ of $[0, 1]$. This set is closed since it just consists of all the rational numbers in between $0$ and $1$, including $0$ and $1$. So it is a closed subspace of a compact space. But why isn't this compact? How to pick one number from each sorted list so that the difference between the minimum and maximum is as small as possible? If you look at this picture, how would you describe the mood and the eyes of the character?  I would not say she's angry. I would say she is concentrating to cut the object. However there are many kinds of concentration, and thus the eye expression can differ. This one gives me the feeling that she doesn't accept the existence of the object, and thus must kill it. Develop rich API exposing Stack Overflow functionality I would love to see an actual native iPhone app for Stack Overflow, Server Fault, Super User, etc.  I've actually developed a number of iPhone apps myself, and would certainly be interested and willing in doing the bulk of the legwork, but it would be necessary for the SO team to expose a real API, instead of simply RSS feeds.  Maybe if there's enough demand behind this, we can convince the SO team to build a rich API, which could be useful for many other applications, not just an iPhone app. Resistor in series needed with LED string? How do JavaScript closures work? How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help. I need to package my Python application, its dependencies and Python into a single MSI installer. The end result should desirably be:   Python is installed in the standard location the package and its dependencies are installed in a separate directory (possibly site-packages) the installation directory should contain the Python uncompressed and a standalone executable is not required Comment authors are not getting migrated How to make the Navigation Bar of an UINavigationController display at the bottom? Contraction mapping in the context of $f(x_n)=x_{n+1}$.