Performance difference of constraint placement in SQL join-on
SQL JOIN - WHERE clause vs. ON clause
So this has been an on-going saga the last few days, and I've already posted several related questions here, and I am feeling quite defeated.  I have/had a beautiful 16" cast iron dutch oven from Cabelas. I took it out for a test spin the other night (I had completed all seasoning steps that the Google Gods recommended). Then:   I tried (and failed spectacularly) to cook a pork roast in it, but cooked it at way too hot a temperature and burned/charred/fused the animal fats/juices into the oven, whereby it basically baked into the cast iron (related question ) I tried cleaning/scrubbing it with coarse-grained salt -> did nothing Then I tried cleaning it with dishwashing liquid + salt -> did nothing Then I let the whole thing soak in a vat of a 50/50 mixture of water + white vinegar -> took all the tarry slude off, stripped some seasoning off (revealing bare iron), but in 80% of the burned/charred areas, still did nothing Then I went to town on it with a steel wool and salt and dishwashing liquid and was left with some smooth, properly seasoned surfaces, and some more areas stripped down to bare metal I decided to just re-season it. So I scrubbed it one last time (about 1 hour ago) with a steel wool and some water, got all the rust and remaining crud off (finally), and built a fire. I placed it on the hot coals of the fire and let it sit there for 15 mins. My intention (whether misled or not) was to burn off all the remaining water from when I had previously washed/scrubbed it, then let it cool off, then season it with oil, and then bake it for a few hours.   So I just took the oven off the fire and opened the lid...and the entire inside is covered in rust. An hour ago there was none. When I put the oven into the fire 15 mins prior, there had been none (yes, I checked) This just came out of nowhere.  I'm ready to give up, unless anyone can offer some concrete set of steps for me that will salvage this $100 rust bucket. How can I get rid of the rust and then re-season this before more rust sets in? Meh... Finding inverse of polynomial in a field I'm having trouble with the procedure to find an inverse of a polynomial in a field. For example, take:     In $\frac{\mathbb{Z}_3[x]}{m(x)}$, where $m(x) = x^3 + 2x +1$, find the inverse of $x^2 + 1$.   My understanding is that one needs to use the (Extended?) Euclidean Algorithm and Bezout's Identity. Here's what I currently have:  Proceeding with Euclid's algorithm:  $$ x^3 + 2x + 1  =(x^2 + 1)(x) + (x + 1) \\\\   x^2 + 1 = (x + 1)(2 + x) + 2$$  We stop here because 2 is invertible in $\mathbb{Z}_3[x]$. We rewrite it using a congruence:  $$(x+1)(2+x) \equiv 2 \mod{(x^2+1)}$$  I don't understand the high level concepts sufficiently well and I'm lost from here. Thoughts?  Wikipedia has a page on this we a , but it's still not clear in my mind.  Note that  has almost the same title, but it's a level of abstraction higher. It doesn't help me, as I don't understand the basic concepts.  Thanks. Equation number enclosing parentheses misplaced with Polyglossia+Hebrew+amsmath I'm using the plugin  which registers it's own post type but the capability is assigned to "post".   I want to change it to "manage_options".  Is there a correct way without altering the plugin to do that? Calling a hook, a function or whatever?   public function register_post_type() {      $labels = array (         'name'               =&gt; _x( 'Custom Code', 'post type general name' ),         'singular_name'      =&gt; _x( 'Custom Code', 'post type singular name' ),         'menu_name'          =&gt; _x( 'Custom CSS &amp; JS', 'admin menu' ),         'name_admin_bar'     =&gt; _x( 'Custom Code', 'add new on admin bar' ),         'add_new'            =&gt; _x( 'Add Custom Code', 'add new' ),         'add_new_item'       =&gt; __( 'Add Custom Code' ),         'new_item'           =&gt; __( 'New Custom Code' ),         'edit_item'          =&gt; __( 'Edit Custom Code' ),         'view_item'          =&gt; __( 'View Custom Code' ),         'all_items'          =&gt; __( 'All Custom Code' ),         'search_items'       =&gt; __( 'Search Custom Code' ),         'parent_item_colon'  =&gt; __( 'Parent Custom Code:' ),         'not_found'          =&gt; __( 'No Custom Code found.' ),         'not_found_in_trash' =&gt; __( 'No Custom Code found in Trash.' ),     );     $args   = array (         'labels'              =&gt; $labels,         'description'         =&gt; __( 'Custom CSS and JS code' ),         'public'              =&gt; false,         'publicly_queryable'  =&gt; false,         'show_ui'             =&gt; true,         'show_in_menu'        =&gt; true,         'menu_position'       =&gt; 100,         'menu_icon'           =&gt; 'dashicons-plus-alt',         'query_var'           =&gt; false,         'rewrite'             =&gt; array ( 'slug' =&gt; 'custom-css-js' ),         'capability_type'     =&gt; 'post', // &lt;--- I want to manipulate this         'has_archive'         =&gt; true,         'hierarchical'        =&gt; false,         'exclude_from_search' =&gt; true,         'menu_position'       =&gt; null,         'can_export'          =&gt; false,         'supports'            =&gt; array ( 'title' ),     );      register_post_type( 'custom-css-js', $args ); }   The above code is in custom-css-js.php lines 200-239. What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$ I would like to evaluate the sum  $$\sum_{n=0}^\infty \frac{1}{an^2+bn+c}$$  Here is my attempt:    Letting    $$f(z)=\frac{1}{az^2+bz+c}$$  The poles of $f(z)$ are located at   $$z_0 = \frac{-b+\sqrt{b^2-4ac}}{2a}$$  and  $$z_1 = \frac{-b-\sqrt{b^2-4ac}}{2a}$$  Then  $$ b_0=\operatorname*{Res}_{z=z_0}\,\pi \cot (\pi z)f(z)= \lim_{z \to z_0} \frac{(z-z_0)\pi\cot (\pi z)}{az^2+bz+c}= \lim_{z \to z_0} \frac{\pi\cot (\pi z)+(z_0-z)\pi^2\csc^2 (\pi z)}{2az+b} $$  Using L'Hopital's rule. Continuing, we have the limit is  $$ \lim_{z \to z_0} \frac{\pi\cot (\pi z)+(z_0-z)\pi^2\csc^2 (\pi z)}{2az+b}= \frac{\pi\cot (\pi z_0)}{2az_0+b} $$  For $z_0 \ne 0$  Similarly, we find  $$b_1=\operatorname*{Res}_{z=z_1}\,\pi \cot (\pi z)f(z)=\frac{\pi\cot (\pi z_1)}{2az_1+b}$$  Then   $$\sum_{n=-\infty}^\infty \frac{1}{an^2+bn+c} = -(b_0+b_1)=\\ -\pi\left( \frac{\cot (\pi z_0)}{2az_0+b} + \frac{\cot (\pi z_1)}{2az_1+b}\right)=  -\pi\left( \frac{\cot (\pi z_0)}{\sqrt{b^2-4ac}} + \frac{\cot (\pi z_1)}{-\sqrt{b^2-4ac}}\right)= \frac{-\pi(\cot (\pi z_0)-\cot (\pi z_1))}{\sqrt{b^2-4ac}}= \frac{\pi(\cot (\pi z_1)-\cot (\pi z_0))}{\sqrt{b^2-4ac}} $$  Then we have  $$\sum_{n=0}^\infty \frac{1}{an^2+bn+c} = \frac{\pi(\cot (\pi z_1)-\cot (\pi z_0))}{2\sqrt{b^2-4ac}}$$    Is this correct?  I feel like I made a mistake somewhere.  Could someone correct me?  Is there an easier way to evaluate this sum? What vintage movie had this blue floating holographic head talking to some kind of military installation? What do you recommend as an optimal point and orientation for mounting a rear-view mirror? I'm open to handlebar-, glasses-, or helmet-mounted.  Some of the considerations, as I understand it, are:   Ease of mounting. View provided. Vibration. Likelihood of breaking. Robustness for repeated off and on (for glasses-mounted).   I've got a hybrid bike with flat handlebars.  I'd also welcome specific product recommendations and recommendations about other aspects to look for in a mirror. Forcing smoothness of regression coefficients I can only move the origin point of the mesh that I selected in object mode, but not the whole mesh Did I set anything up by accident? Why use Chef/Puppet over shell scripts? New to Puppet and Chef tools. Seems like the job that they are doing can be done with shell scripting. Maybe it was done in shell scripts until these came along.  I would agree they are more readable. But, are there any other advantages over shell scripts besides just being readable? Suppose I have two tables that don't have many columns (3, for example). How can I position them side by side? how to make a regex string reject a blank field The most common way to refer to non-immediate family? Make clear which profile data is visible to whom How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$. How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor=\left\lfloor\frac{x}{n}\right\rfloor$.  So we want to prove $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\ge\left\lfloor\frac{x}{n}\right\rfloor$ and $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\le\left\lfloor\frac{x}{n}\right\rfloor$  Since $\lfloor x\rfloor\le x$, we can just start from here and prove  $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\le\left\lfloor\frac{x}{n}\right\rfloor$  But for $\left\lfloor\frac{\lfloor x\rfloor}{n}\right\rfloor\ge\left\lfloor\frac{x}{n}\right\rfloor$, I have no idea how to start. Using apt-get how to check have installed latest version ? Hello im just new for Linux   I know that  sudo apt-get   is for installing application   but how I would know that I have installed the latest version of the application   for example apt-get install sun-java6-jdk   is there an option to upgrade or see the latest version   or its ok to install an old version the application and Linux will upgrade it for me ? Implementing i18n string translation in a custom module? I have a custom module I've built which essentially acts as a repository of custom CTools keywords that users can arbitrarily define. The issue I'm facing is I need to be able to translate these user-defined strings, so I think I need to implement string translation using the i18n_string module.  I have never worked with translation or localization before, so I'm a bit lost with regards to going about how to implement this. I think I'm on the right path with i18n_string though. Can someone experienced with i18n provide examples that I can look at so I can learn the proper way to implement this? I recently updated my profile bio (from Arqade) and clicked 'Save and copy changes to all public communities'. This appears to have broken/reset my profile picture on all but Arqade. Note that I did not update my profile picture as part of my changes. Arqade:  Meta SE for comparison:  I haven't touched my profile picture in years. Is this a bug?  Update: It appears my profile pic across all communities has been set back to 'Identicon'. I went on to Stack Overflow and changed my profile picture back to 'Gravitar' and clicked 'Save and copy to all communities' again, but this did not update my profile picture anywhere but SO. (I did the same on Sustainability to be doubly sure). Update 2: This is a persistent bug - I had changed most of my SE communities back to my 'Robotnik' display pic over the past little while. Today I edited my profile again on Arqade, Clicked 'Save and copy' - and the display pic reverted back to identicon again across all sites. Update 3: I have re-uploaded my profile picture and the 'Save and copy' function worked. It appears that this is actually a bug to do with the old images from Gravatar. Is there a word or phrase for something that one might wish exists, but most certainly doesn't? The Python docs say:     re.MULTILINE: When specified, the pattern character '^' matches at the beginning of the string and at the beginning of each line (immediately following each newline)... By default, '^' matches only at the beginning of the string...   So what's going on when I get the following unexpected result?  &gt;&gt;&gt; import re &gt;&gt;&gt; s = """// The quick brown fox. ... // Jumped over the lazy dog.""" &gt;&gt;&gt; re.sub('^//', '', s, re.MULTILINE) ' The quick brown fox.\n// Jumped over the lazy dog.'