In class we are currently covering upper/lower bounds, big Oh and omega and the like. I am pretty good on the "typical" functions one would do, but at a complete loss at "general" statements. This ons function, for example:  $$\forall f\in\mathcal{F}: \lfloor \sqrt{\lfloor f(n)\rfloor }\rfloor \in O(\sqrt{f(n)}).$$  the domain F by the same is all natural numbers that return a real positive number when inputted. My first instinct with something like this is to remove the floors, the general strategy I though to solve this is remove the outer floor, then get rid of the square root, and then the inner floor. But I have no idea how to go about this or if this is even the right way to do it.  Help please? Thanks in advance.
In class we are currently covering upper/lower bounds, big Oh and omega and the like. I am pretty good on the "typical" functions one would do, but at a complete loss at "general" statements. This ons function, for example:  $$\forall f\in\mathcal{F}: \lfloor \sqrt{\lfloor f(n)\rfloor }\rfloor \in O(\sqrt{f(n)}).$$  the domain F by the same is all natural numbers that return a real positive number when inputted. My first instinct with something like this is to remove the floors, the general strategy I though to solve this is remove the outer floor, then get rid of the square root, and then the inner floor. But I have no idea how to go about this or if this is even the right way to do it.  Help please? Thanks in advance.
How do I copy a property from an active object to selected objects? I have been using the Copy Attributes add-on to copy some properties from active object to selected objects. This add-on is not enabled by default and must be explicitly enabled. But its a very useful workflow enhancing tool.    There is a limitation though. Not all properties can be copied and even those that can be copied are copied in groups (Its hard-coded in to the add-on).  My question is if there is a built-in feature or any another other way to copy any property from the active object to the selected objects? This is a somewhat bizarre question. My objectives are to understand the language design decision and to identify the possibilities of reflection in C++.   Why C++ language committee did not go towards implementing reflection in the language? Is reflection too difficult in a language that does not run on a virtual machine (like java)? If one were to implement reflection for C++, what will be the challenges?   I guess the uses of reflection are well-known: editors can be more easily written, program code will be smaller, mocks can be generated for unit tests and so on. But it would be great if you could comment on uses of reflection too. Custom 500 Error page: Is there a way to theme a fatal error? In /core/includes/errors.inc, when there is a fatal error it outputs a response with the message "The website encountered an unexpected error. Please try again later." and a back-trace, if error_level is set to verbose, and without the back-trace otherwise.  It seems like at this point, there's no way, with an event subscriber to capture the response and alter it.  Is that correct?  Or is there a way to wrap the output from line 268 of errors.inc in Drupal 8.4 with markup?    Note, there's another , but that doesn't offer a complete solution.  Also, I looked into .htaccess and Apache ErrorDocument directive, but that . Once Apache passes off to PHP, it can no longer use that directive.  That's for real server errors. How to use mirror ball to light a scene? I can prove the converse of it, but I cannot do this one. Here is the problem:     Prove that the implicit function theorem implies the inverse function theorem. I have been working on a Java project for a class for a while now. It is an implementation of a linked list (here called AddressList, containing simple nodes called ListNode). The catch is that everything would have to be done with recursive algorithms. I was able to do everything fine sans one method: public AddressList reverse()      ListNode:    public class ListNode{   public String data;   public ListNode next; }   Right now my reverse function just calls a helper function that takes an argument to allow recursion.  public AddressList reverse(){   return new AddressList(this.reverse(this.head)); }   With my helper function having the signature of private ListNode reverse(ListNode current).  At the moment, I have it working iteratively using a stack, but this is not what the specification requires. I had found an algorithm in C that recursively reversed and converted it to Java code by hand, and it worked, but I had no understanding of it.  Edit: Nevermind, I figured it out in the meantime.  private AddressList reverse(ListNode current, AddressList reversedList){   if(current == null)        return reversedList;   reversedList.addToFront(current.getData());   return this.reverse(current.getNext(), reversedList); }   While I'm here, does anyone see any problems with this route? How can I restart a Windows 7 computer without screen or mouse? How many ways to arrange people on a bench so that no woman sits next to another woman? I have this graphic. I need to change the color of the graphic to hex color: 1485cc...is there a way to make this graphic match that particular hex color hue...without me having to have to re create the graphic. Login required moving to Super User on iPad When moving around the sites on Stack Exchange using Safari on my iPad (not the Stack Exchange App), I am fine when moving to any site other than SuperUser.  When logged in, I can switch sites and stay logged in, but when I switch to Super User I need to log in again. If I choose not to log in and switch to another site, I am logged in there. Is there a problem with the login handling for Super User? If it helps, I log in with a Stack Exchange account, not through Facebook or Google. Update After getting fed up with the problem, I took the advice given in the answer below which was to use Chrome, and the problem still exists. The same goes for Firefox. Have I missed something?  As you can see from the screenshots below, there are no cookie settings to be found. Chrome for iOS settings page  Privacy settings page  Content settings page  Google app settings page How to determine if string contains specific substring within the first X characters I want to check whether Value1 below contains "abc" within the first X characters. How would you check this with an if statement?  var Value1 = "ddabcgghh";  if (Value1.Contains("abc")) {     found = true; }   It could be within the first 3, 4 or 5 characters. How do I check if a file exists in Java? I tried to update Grub so I run:  sudo update-grub  Generating grub configuration file ... Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported.   What exactly this warning wants to be changed? (I upgraded from 12.04 to 14.04 before)  This is my /etc/default/grub file:  GRUB_DEFAULT="0" GRUB_HIDDEN_TIMEOUT="0" GRUB_HIDDEN_TIMEOUT_QUIET="true" GRUB_TIMEOUT="10" GRUB_DISTRIBUTOR="`lsb_release -i -s 2&gt; /dev/null || echo Debian`" GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX="" Parameterize an SQL IN clause How do I parameterize a query containing an IN clause with a variable number of arguments, like this one?  SELECT * FROM Tags  WHERE Name IN ('ruby','rails','scruffy','rubyonrails') ORDER BY Count DESC   In this query, the number of arguments could be anywhere from 1 to 5.  I would prefer not to use a dedicated stored procedure for this (or XML), but if there is some elegant way specific to , I am open to that. Given that $\displaystyle{a+b\sqrt[3]{2} +c\sqrt[3]{4} =0}$, where $a,b,c$ are integers. Show $a=b=c=0$  Do I use modular arithmetic? We have a SBS 2011 server with 16GB memory that runs Exchange, WSUS and File Sharing for approx 20 users. The server also gives 2GB memory to a virtual machine running in Hyper-V so 14GB left for the rest.  When the server first boots Store.exe consumes about 500MB memory, WSUS and IIS consume some as well, but we generally are only at 60% capacity. During the course of the working day Store.exe consumes 8GB memory and the server sits at approx 97% capacity.  This makes using the server very slow, logging on via RDP is slow, general server admin is slowed down.  Is this normal? I have read that Exchange will consume lots of memory that it does not neccessarily need and then releases it back to other applications that need it. I have also checked that all mailboxes are opened in cached mode. We do have some external uses who connect via Outlook Anywhere or OWA.  If it's deemed to be "normal" is there some way I can restrict it using ALL available memory and leave a little bit for SBS to use for server admin? I have seen some articles regarding setting a high and low memory flag but rumours that this does not work with update rollup 5 which we have installed.  Am I expecting a single server to do to much with only 14GB memory?  Thanks What is the relation between the Higgs field and chirality? Wikipedia  that the spontaneous breaking of chiral symmetry "is responsible for the bulk of the mass (over 99%) of the nucleons".  How do the nucleons gain mass from the spontaneous breaking of chiral symmetry? Why don't leptons gains mass from it? What is the role of the Higgs field in this all? Here at the Genealogy and Family History Stack Exchange we see many questions about relationship mapping which is also known as:   relationship calculation kinship terminology etc   If you are just trying to understand how to calculate "cousins and removes" then  provides an excellent guide.  However, if you are seeking an English term for a more complicated relationship between two members of an extended family, rather than asking a question like:          site users are encouraged to first review the answers below.    Note: This Q&amp;A arises from  and is set to  to help make it canonical. What is the noun for someone who receives a referral? When a referrer (noun) gives a referral (noun) to another person, what is the term (noun) used for the recipient of the referral? "The referred" may work, but am I missing another term? "Referred" indicates past-tense, but I intend to use the term in future and present tense as well. How to troubleshoot unwanted white spaces smartly?