Representation of the delta distribution as an element of the dual of $H^1$
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
Version of the app: 1.0.51. (It is up to date at the time of writing according to Google Play.)  This started happening after the network problem that happened earlier this morning. Both my tablet and my phone are popping up notifications for events (comments, and probably edits too) that happened prior to the network issue. I had received notifications for these events already and had already cleared them before the network issue happened.  The repeated notifications do not show up in the bar displayed at the top of the Stack Exchange sites. In other words, I get notified again in Android but do not get notified again on the SE web sites. Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$. How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? I work sometimes till 4 am and my friends and the rest of the world obviously don't know in advance that I don't want to be called at 8 am.  Is there an app or setting that can allow me to have an emergency override list of people I need to be woken up for if a possible emergency arises but ignore all other calls until I wake up?    I'm familiar with the Do Not Disturb option, but it has limitations that it blocks all calls. What if there is an emergency at night?  What if I want to allow certain callers during the Do not Disturb time? Is there a way to have an emergency list that allows calls during silent? How do Horcruxes work? A few questions regarding the Horcruxes.   Had Voldemort actually succeeded in using a Horcrux, would he come back the same age (biologically and/or aesthetically) he was when he made the Horcrux, or the age he would biologically be if he had never died (half died)? If Harry was a Horcrux, then in the graveyard, when Wormtail added Harry's blood to the potion to bring Voldemort back, didn't that technically use up the Horcrux inside of Harry? So in Deathly Hallows when Voldemort kills Harry, shouldn't Harry have actually died rather than just have the Horcrux inside him destroyed, seeing as it was technically used in the Goblet of Fire? I am creating a GUI frontend for the Eve Online API in Python.  I have successfully pulled the XML data from their server.  I am trying to grab the value from a node called "name":  from xml.dom.minidom import parse dom = parse("C:\\eve.xml") name = dom.getElementsByTagName('name') print name   This seems to find the node, but the output is below:  [&lt;DOM Element: name at 0x11e6d28&gt;]   How could I get it to print the value of the node? How to find out why "context is incorrect"? How do you Xforward windows using ssh? Which packages should be loaded after hyperref instead of before? How do I remove my "page not found" pages from Google's index? I have a wordpress site that has had a large number of blog posts removed. How can i ask google to remove all these 404 page not founds, but leave the active blog posts. I see the removal tool in google webmasters but it doesnt say if it will just remove the 404s. I understand 404s naturally are removed from the index, but i want to expedite this. Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$ Let $(a_n)_{n=0}^{\infty}$  be a sequence of real numbers satisfying $\sum_{1}^{\infty} |a_n - a_{n-1}| &lt; \infty$   Which of the following conclusions must then be true?  The series $\sum a_nx^n$ converges   Nowhere on $ \mathbb{R}$ Everywhere on $  \mathbb{R}$ On some interval containing $(-1,1)$ Only on $(-1,1)$   What I have tried is Make an inequality with $|a -b| \leq |a| +|b|$ .. but i cant proceed further .. Any sort of help will be deeply appreciable . I'm curious how USB device recognition works in Windows. I imagine it's something like this:   When you plug in a device, it tells Windows "here's my device ID to tell you what I am" Windows looks to see if any drivers have been installed that match that device ID. The driver probably tells Windows what the device should be called - like "BlackBerry Curve" or "Canon Printer" If so, it somehow associates that device with that driver Otherwise, it looks for a matching driver online (if you let it)   Am I right? If so, that still leaves some questions.   When you install drivers, where do they go? Are they files in a folder, or do they get added to the registry? What is Windows doing when it first recognizes the device, thinks, and finally says "your new device is installed and ready to use?" Where does Windows look for missing drivers? Is it in their own database? Do device manufacturers submit drivers to Microsoft for inclusion there?   Can anybody explain how this process really works? Also, do other OSes do this differently? Allow horizontal scrolling of long math expressions Stack Exchange formats math, but often the formatted math is wider than the screen. It would be nice if formatted math were scrollable the same way that formatted code wider than the screen is scrollable. Preimage of codimension one subspace of the quotient $g/D^1 g$ I am trying to prove the following.  Proposition Let $g$ be a Lie algebra such that the first derived algebra $Dg$ is a proper ideal of $g$. Consider the quotient $g/D^1 g$, and show that the preimage of any codimension 1 subspace is   an ideal, and has codimension 1.   I could show that the preimage is indeed an ideal, but I need some help with the part about the dimensions:  So suppose that $\phi: x \mapsto [x]$ is the quotient projection. And write $[h] + Dg$  for a codimension 1 subspace of $g$ (here $h\subset g$). Then the preimage of this subspace is just the linear span $h+Dg\leq g$. Let $y+z \in h+Dg$ with $y\in h$ and $z\in Dg$. Let $x\in g$. We want to show that $[x, y+z]\in h$, ie that $h + Dg \lhd g$. We can write $x$ as $x_0+x_1$ for $x_0 \in Dg$, $x_1\not\in Dg$. Then  $$[x,y+z] = [x_0, y+z] + [x_1, y] + [x_1,z] \in h + Dg$$  The inclusion follows since $Dg$ is an ideal so the first and third terms belong $Dg$; and $[x_1, y] \in D_g$, as $g/Dg$ is abelian. How do I use a C# keyword as a property name? Using asp.net MVC I'd like to do this inside a view:  &lt;%= Html.TextBox("textbox1", null, new { class="class1" }) %&gt;   This statement does not compile because class is keyword in C#. I'd like to know how I can escape the property names such that this compiles.  It is possible to get this to compile if I change the "class" property to "Class" (uppercase C). But this is not suitable because strict xhtml says that all attributes (and element) names must be lowercase. What is the difference between a tatkal and premium tatkal ticket in Indian Railways? Optimal way to ignore duplicate inserts? Background  This problem relates to ignoring duplicate inserts using PostgreSQL 9.2 or greater. The reason I ask is because of this code:    -- Ignores duplicates.   INSERT INTO     db_table (tbl_column_1, tbl_column_2)   VALUES (     SELECT       unnseted_column,       param_association     FROM       unnest( param_array_ids ) AS unnested_column   );   The code is unencumbered by checks for existing values. (In this particular situation, the user does not care about errors from inserting duplicates -- the insertion should "just work".) Adding code in this situation to explicitly test for duplicates imparts complications.  Problem  In PostgreSQL, I have found a few ways to ignore duplicate inserts.  Ignore Duplicates #1  Create a transaction that catches unique constraint violations, taking no action:    BEGIN     INSERT INTO db_table (tbl_column) VALUES (v_tbl_column);   EXCEPTION WHEN unique_violation THEN     -- Ignore duplicate inserts.   END;   Ignore Duplicates #2  Create a rule to ignore duplicates on a given table:  CREATE OR REPLACE RULE db_table_ignore_duplicate_inserts AS     ON INSERT TO db_table    WHERE (EXISTS ( SELECT 1            FROM db_table           WHERE db_table.tbl_column = NEW.tbl_column)) DO INSTEAD NOTHING;   Questions  My questions are mostly academic:   What method is most efficient? What method is most maintainable, and why? What is the standard way to ignore insert duplication errors with PostgreSQL? Is there a technically more efficient way to ignore duplicate inserts; if so, what is it?   Thank you! How do I see the type of a variable whether it is unsigned 32 bit, signed 16 bit, etc.?  How do I view it? I have made a fancy title page using titleformat and tikz, but I now face the following problem. The \chaptertitlename command returns \chaptername or \appendixname. I would like to spread the letters of the text returned by \chaptertitlename to a given length.  For example I would like to be able to call: \mycommand{\chaptertitlename}{3cm} in order to space the letters of \chaptertitlename on a total length of 3cm. How to do that ?  EDIT: This example illustrates a nearly working thing:  \documentclass[11pt]{article} \usepackage{fontspec} \newcommand{\spreadletters}[2]{\makebox[#2][s]{#1}}  \begin{document} \spreadletters{m y w o r d}{3cm} \end{document}   How to convert myword to m y w o r d ?  EDIT 2: Can someone explain me why the first work and not the second one (and how to make it work) ?  \documentclass[11pt]{book} \usepackage{fontspec} \usepackage{seqsplit} \usepackage[explicit]{titlesec}  \newcommand{\spreadletters}[2]{\makebox[#2][s]{\seqsplit{#1}}}  \begin{document} \chapter{First} \spreadletters{myword}{10cm} \linebreak % This is working \spreadletters{\chaptertitlename}{10cm} % This is not working \end{document} How do I bulkify queries for directly or indirectly related records?