What prepositions to use in a sentence with "Know where I stand..."
How do I choose between "as to", "on", "of", and "about"?
What is the minimum $ \sigma$-algebra that contains open intervals with rational endpoints What are the minimum $\sigma$-ring and $\sigma$-algebra on $\mathbb R$ which contain the open intervals with rational endpoints?  Is there a relation between this $\sigma$-algebra and Borels? Explanation behind Second Derivative of a Parametric Equation Formula I am looking to find out how the second derivative formula works.  I can blindly apply it but I don't have a grasp of what is going on or why. The first derivitive has the formula $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$. I told this was because if you divide them you cancel out the dts and get dy/dx. The second derivative has the formula $\frac{d^2y}{dx^2} = \frac{d}{dx} \left(\frac{dy}{dx}\right) = \frac{ \frac{d}{dt}\left(\frac{dy}{dx}\right) }{\frac{dx}{dt}}$. Is this something that can be explained with only a knowledge of calculus or is this something I would have to take on faith until I learn more. Any help would be greatly appreciated. How can I combine two plots? How to create a timer using tkinter? How to open Nautilus (File Manager) preferences? A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix $e^A$, where $A= \begin{bmatrix} 0 & \omega \\ -\omega& 0 \end{bmatrix}$ $\omega&gt;0$, Then Compute the matrix:          $e^A$,     where $A= \begin{bmatrix} 0 &amp; \omega \\ -\omega&amp; 0 \end{bmatrix}$      I have never seen any problem like this. So Please help me solving this. Any link for theoretical reading is welcome. Which fruits and vegetables should be kept in a fridge, and which outside? What is the best (idiomatic) way to check the type of a Python variable? I need to know if a variable in Python is a string or a dict.  Is there anything wrong with the following code?  if type(x) == type(str()):     do_something_with_a_string(x) elif type(x) == type(dict()):     do_somethting_with_a_dict(x) else:     raise ValueError   Update: I accepted avisser's answer (though I will change my mind if someone explains why isinstance is preferred over type(x) is).  But thanks to nakedfanatic for reminding me that it's often cleaner to use a dict (as a case statement) than an if/elif/else series.  Let me elaborate on my use case.  If a variable is a string, I need to put it in a list.  If it's a dict, I need a list of the unique values.  Here's what I came up with:  def value_list(x):     cases = {str: lambda t: [t],              dict: lambda t: list(set(t.values()))}     try:         return cases[type(x)](x)     except KeyError:         return None   If isinstance is preferred, how would you write this value_list() function? Can I keep the Rueful Axe and get Clavicus Vile's Mask? Is there a way to keep the Rueful axe and get Clavicus's Mask?  I thought you could kill Barbas after receiving the mask, but he is a statue now.  Did I miss my chance? Can someone help me elucidate the definition of "income" from a tax perspective? More specifically, if Joe is paid for his work in avocados instead of dollars, then would Joe be exempt from paying any income tax for the year? Or would the value of avocados earned for the year be translated into dollars which would then be considered Joe's annual income? If so, what guidelines would one use to make this translation? (Make the assumption that Joe does not sell the avocados (for dollars) at a later date and either eats them or trades them for other real property)  What if he was paid in gold instead of avocados? Why the principal value of complex number argument is taken within $(-\pi,\pi]?$ Why the principal value of complex number argument is taken within $(-\pi,\pi]?$ What is the harm in considering similar other intervals like $[0,2\pi)$ for the purpose? Can I include the completion of Udacity and Coursera classes I have attended in an academic CV? Can I include in my academic CV that I have attended and completed the  and  classes I have been taking? I understand that these are not anything major, but the courses definitely gives a good overview and starting formal study on the subject becomes less cryptic. If I can include them without any negative impacts, then under what section should I include them? When I install a simple program it often uses make &amp;&amp; make install and doesn't often even have an uninstall target.  If I wish to upgrade a program, is it standard protocol to assume it just rewrites seamlessly over the old program?  How do I keep track of these programs; do most people just 'fire and forget' and if no uninstall target is given do I have to manually delete everything? What are metaclasses in Python? In Python, what are metaclasses and what do we use them for? With \setbeamercovered{transparent} covered parts of a slide are displayed transparently. If there is a (small) picture among the text, it is shown as it is. Beamer has only this picture, so it shows this picture. My question: How can I give a gray version of the picture to beamer such that in covered parts of a slide, this gray version is used? "Do you know where's Linda?" vs "Do you know where Linda is?" How to protect website from bulk scraping /downloading? Pagination broken when merging search results with additional WP_Query On the search results page (search.php) I would like to perform an additional WP_Query to keep a specific order of search result types e.g. search results from authors should always be shown before the other results -  The first few pages should hold the author results, the other results should be shown on all the following pages only (not mixed on each page).  global $wp_query; //holds the results of the initial search query  $authorposts = $wp_query-&gt;posts;     $query = new WP_Query( 'year=2012&amp;monthnum=12&amp;day=12' ); $otherposts = $query-&gt;posts;  $wp_query-&gt;posts = array_merge( $authorposts, $otherposts  ); $wp_query-&gt;post_count = count( $wp_query-&gt;posts );  if ( have_posts() ) : while ( have_posts() ) : the_post(); ?&gt;   //show results loop...   The problems appear with the behaviour of pagination - while the $authorposts seem to paginate correctly i.e. correct page numbers for author posts and pagination works as only those where existent. But the $otherposts on the other hand are shown at the bottom of each page, right under the author posts. And they are the same on every page! Also the page count reflects the count of the first query only.  I have also tried to merge with the plus operator:  $wp_query-&gt;posts = $authorposts + $otherposts;   but in this scenario the $otherposts don't show up at all and the page count stays the same (page count for author posts).  All the examples with similar goals using two separate queries I've seen looked quite the same -  So I'm wondering if the my way of extending the original search query results with that additional WP_Query is sufficient or if I'm missing some $wp_query fields to be populated (correctly)? What's the correct way doing this?  Update: It should be noted that I'm using the WP-PageNavi plugin to paginate but this should not be relevant in the first place as the first page is already rendered wrong. And it's also initialized with the query object: wp_pagenavi( array( 'query' =&gt; $wp_query )); Boundary condition with spatial derivative is ignored by NDSolve