Looking for a way to choose the proper modules for the system, I reviewed all my notes taken in class.    I know looking is present participle, but I feel it is improper to be used in this meaning. The participial phrase functions as an adjective modifying I (the subject), but the meaning expressed in this sentence is not like an adjective. I think it is clearer if expressed in adverbial clause of purpose.
My case here is that I was writing something for school, and my teacher explained an error which I really can't see. She referred to articles about &quot;dangling participles&quot;, which was previously unknown to me. I find it hard to relate the examples I've found about it to my situation. So this is a text I've written and the bold part is where the problem arises: (You could read only the bold part if you please)  Wandering, and lost in his thoughts, there is a deep despair occupying the mind of this man. He is barely aware of his surroundings, except for those few moments when the loud blissful voices break through the protective barriers, developed by his immense sadness and grave frustration, into his mind. ”How can they all possibly be so happy?” he thinks to himself. Staring blindly, with his head low, as he walks in a slow pace, whispering ”Mary, Mary, my Mary,” over and over again. Yesterday was her funeral. She had passed away from a severe type of cancer, at a relatively young age. It was his wife. They had been together since high school and were greatly attached to each other. Having spent nearly half his life by her side, we cannot but imagine his grief. Indeed, he could hardly picture a life without her. So, alone he roams in the midst of all the seemingly incessant cheering and noises, drowned by his sorrow.  Her comments on that part was:  we is slightly out of place here – see my comment below These few sentences are about him and his emotions, so ‘we’ seems out of place. If the sentence starts: ‘Having spent nearly half his life by her side’, the reader expects it to continue: ‘he’. After all we have not spent half our lives by her side.  Is she right? If so, could anyone try to explain why?
Is there a way to install a newer version than in the repository?  Ubuntu installs vagrant 1.4.3 at the moment, but I need at least 1.5 New York is a great place to live. New York is a great place to live in.  I've seen the former usage a lot and I've started wondering what the grammar aspects of it are. The main question I'm asking involves the grammar when the preposition in the end of the sentence is deleted. Is it equally formal or correct to omit it? What are the grammar properties of this? Some more examples of similar usage:  This organisation is a great place to work. This is a great place to stay/sit/study/travel/go.  Just to show that 'live' isn't special in this case. Note: I'd posted the same question  before, but the answers were not satisfying enough (the answers there did not seem to provide the precise grammar aspects of this, those that could be in a serious grammar book), so I'm posting this here to get some more views on the question. I hope it is acceptable. Exact sequence of sheaves with non exact sequence of global sections Let $X$ be some topological space. By $\mathcal{F}_i$ we denote some sheaves of abelian groups on $X$. The sequence of sheaves and morphisms  $$\mathcal{F}_1\longrightarrow \mathcal{F}_2\longrightarrow \mathcal{F}_3\longrightarrow... $$ is said to be exact if for each $x\in X$ the corresponding sequence of stalks $$(\mathcal{F}_1)_x\longrightarrow (\mathcal{F}_2)_x\longrightarrow (\mathcal{F}_3)_x\longrightarrow... $$ is exact. However if the sequence of sheaves is exact than the sequence of global sections is not necessarily exact! (The most famous example is the sequence of sheaves $$0\longrightarrow\mathbb{Z}\hookrightarrow \mathcal{O}\stackrel{\exp}{\longrightarrow} \mathcal{O}^*\longrightarrow0$$ considered as sheaves on $\mathbb{C}-\{0\}$, where $\mathcal{O}$ is a sheaf of holomorphic functions, $\mathcal{O}^*$ is a sheaf of holomorphic functions with no zeros).  So, could you give me some easy examples of such phenomenon ? I'm currently working on some logging code that supposed to - among other things - print information about the calling function. This should be relatively easy, standard C++ has a type_info class. This contains the name of the typeid'd class/function/etc. but it's mangled. It's not very useful. I.e. typeid(std::vector&lt;int&gt;).name() returns St6vectorIiSaIiEE.  Is there a way to produce something useful from this? Like std::vector&lt;int&gt; for the above example. If it only works for non-template classes, that's fine too.  The solution should work for gcc, but it would be better if I could port it. It's for logging so it's not so important that it can't be turned off, but it should be helpful for debugging. PHP: Static and non Static functions and Objects Bold italic vectors I am trying to display vectors as bold and italic. The command \mathbf sets the letters non-italic. I also googled a bit and stumbled upon \mathbf{\em y} or \mathbfit{y}, which all didn't work.  I hope someone can help me on this. How do I convince gdal2tiles to output pngs with transparency? How do I generate random integers within a specific range in Java? I am on a multiplayer Minecraft realm in 1.16 and I was wondering if there was any way to set a chest's Items to a player's entire Inventory including the offhand and armor slots. Using data modify &lt;chest coordinates&gt; Items set from entity &lt;player&gt; Inventory, I was only able to copy over the hotbar and the top two rows of a player's inventory. I honestly don't care if it takes 50 command blocks, any response is gladly appreciated. I'm trying to make a material node setup to set final render colors, regardless of lighting conditions. Is such a setup possible? If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$ Why is the PHP version different in phpinfo() and CLI? I realized that there is a miss matching between the PHP version reported by phpinfo() and php -v (in the CLI).  phpinfo():  5.5.24 php -v: 5.6.9   I am working on a Mac OS X 10.10 (Yosemite) and installed a library (php-version) to try to manage the PHP versions.  It reports me 3 different versions installed on my laptop:    5.4.41   5.5.25 * 5.6.9   I would like to set the same version of PHP in both Apache and CLI.  How can I tell Apache which PHP version use?  I tried to write this line in my httpd.conf:  LoadModule php5_module    /usr/local/opt/php56/libexec/apache2/libphp5.so   Then:  sudo apachectl restart   But all this not solve the problem… In my PHP info I still have: 5.5.24 Due to the implementation of Java generics, you can't have code like this:   public class GenSet&lt;E&gt; {     private E a[];      public GenSet() {         a = new E[INITIAL_ARRAY_LENGTH]; // error: generic array creation     } }   How can I implement this while maintaining type safety?  I saw a solution on the Java forums that goes like this:  import java.lang.reflect.Array;  class Stack&lt;T&gt; {     public Stack(Class&lt;T&gt; clazz, int capacity) {         array = (T[])Array.newInstance(clazz, capacity);     }      private final T[] array; }   But I really don't get what's going on. Why use gradient descent for linear regression, when a closed-form math solution is available? I am taking the Machine Learning courses online and learnt about Gradient Descent for calculating the optimal values in the hypothesis.  h(x) = B0 + B1X   why we need to use Gradient Descent if we can easily find the values with the below formula? This looks straight forward and easy too. but GD needs multiple iterations to get the value.  B1 = Correlation * (Std. Dev. of y/ Std. Dev. of x)  B0 = Mean(Y) – B1 * Mean(X)   NOTE: Taken as in   I did checked on the below questions and for me it was not clear to understand.      The above answers compares GD vs. using derivatives. I'm using Drupal seven. I want to make the options in a select list be dependent on the value chosen in another select list in a form.  I'm sure this has been asked many times before, but I am having difficulty finding a clear answer for how to do this.  The form is for users to enter a work history.  They need to select a squadron which is a node reference to the squadron field type, and this is in a drop-down list.  However, the squadron, is dependent upon a city drop-down list.  Users first need to select a city which will then filter the options for the squadron.  In the squadron content type, I created a taxonomy for city which gets tagged to the squadron.  I would be very grateful for any pointers as to the best way (simplest?) to go about this, or for any useful resources online which would help. How can I download this flash game for offline play? is one of the best flash games ever.    Is there some way to download it, so that I can play it offline? The result set has no current row while using JDBC I am using the following code in selenium, but I am not able to retrieve data from database. I am getting the errors "The result set has no current row"  My code is   public class Auto {      public static void main(String[] args) throws InterruptedException, SQLException, ClassNotFoundException, InstantiationException, IllegalAccessException     {           Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");         System.out.println("Driver loaded");           Connection con=DriverManager.getConnection("jdbc:sqlserver://192.168.*****\\SQLEXPRESS/*****_DW/EPS:****;user=******;password=******; ");          System.out.println("Driver loadedd");       java.sql.Statement stmt= con.createStatement();     ResultSet rs=stmt.executeQuery("select * from [*****_DW].[dbo].dim_grantee ");      System.out.println("Query executed");      while (rs.next());     {         String Name=rs.getString("NAME");          System.out.println("Name is");     }   } Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$ Let $\varphi(n)$ be Euler's totient function, the number of positive integers less than or equal to $n$ and relatively prime to $n$.    Challenge: Prove  $$\sum_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}.$$   I have two proofs, one of which is partially combinatorial.    I'm posing this problem partly because I think some folks on this site would be interested in working on it and partly because I would like to see a purely combinatorial proof.  (But please post any proofs; I would be interested in noncombinatorial ones, too.  I've learned a lot on this site by reading alternative proofs of results I already know.)  I'll wait a few days to give others a chance to respond before posting my proofs.  EDIT: The two proofs in full are now given among the answers. Text won't appear in interface? There is one problem, it seems that text won't appear on my program. The three images show the errors and also my laptop specs (I believe I just have very small amount of laptop power that makes Blender glitch).  Everything else works fine (zooming, panning, rotating, etc.) and the buttons are still there and do what they're supposed to do, but the text just won't appear.  Might anybody know how to fix this?        The drive update didn't help either. I know a way around it though, does anybody know a page which shows screenshots of more or less the buttons on blender Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$ I want to show that for $\gcd(a,b) = 1$ $a,b \in Z$   $\gcd(a+b, a-b) = 1$ or $\gcd(a+b, a-b) = 2$ holds.      I think the first step should look something like this:      $d = \gcd(a+b, a-b) = \gcd(2a, a-b)$   From here I tried to proceed with two cases. 1: $a-b$ is even, which leads to $\gcd(a+b, a-b) = 2$ 2: $a-b$ is odd, which leads to $\gcd(a+b, a-b) = 1$  My main problem I think is, that I do not know how I should include $\gcd(a,b) = 1$ in the proof.  Any help is appreciated. Thx in advance. Cherio Woltan