I would like to add a search box to the Google search results, just like Stack Overflow . I have been trying for several days but no luck. How can I add this to my own site?
Observe the following results for searching the text "dictionary" on Google:    Notice that there is a custom search box at the bottom of the listing for dictionary.reference.com. Is there any documentation floating around that explains the criterion by which Google decides to display such a search box?
Cut one side of a rectangle node in TikZ I would like to draw two consecutive rectangle nodes (one is next to the other with an intersected edge). How to cut one side of a rectangle node in TikZ so that the intersected side looks like others?   Consider the example below, I don't want the "duplicated" edge between node 1 and 2.   \begin{tikzpicture}    \node [style={draw, inner sep=0pt, minimum size=0.5cm}]           (1) at (0, 0)  { $1$ };   \node [style={draw, inner sep=0pt, minimum size=0.5cm}]           (2) at (0.5, 0)  { $2$ };  \end{tikzpicture} If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true? In the book of first order logic I'm reading they say that if $(\varphi_1,...,\varphi_n)$ is a proof from a set of formulae $\Sigma$, then so is $(\varphi_1,...,\varphi_n,\forall x \varphi_j)$ for all $1\leq j \leq n$. They assume that as an axiom but it doesn't make sense to me. Why if $\varphi$ is true then so is $\forall x \varphi$? For example if $\varphi$ is $x=1$ that wouldn't mean that $\forall x : x=1$ , or would it?  Maybe what I don't understand is: why $(\Sigma \vdash \varphi \implies \Sigma \vdash \forall x \varphi)$ is true but $(\varphi \implies \forall x \varphi)$ is not true?  The book is this: What is the Euler Totient of Zero? Wolfram MathWorld defines the Euler Totient function as follows:  The totient function phi(n), also called Euler's totient function, is defined     as the number of positive integers &lt;=n that are relatively prime to (i.e., do  not contain any factor in common with) n, where 1 is counted as being  relatively prime to all numbers   By this definition would $\phi(0)=0$? In Excel, the window can be frozen in place in such a way that you can always see the name of the column even though you go way down below the 'fold' of the screen.  On SE, when you scroll, the whole page goes up (or down). This means the top navigation bar is scrolled off screen. I'm not sure if it would be a good idea or not to fix the top navigation to the top of the screen and let the rest of the content scroll.  What do you think about this, in terms of pros and cons?  [Update]  With the new Top navigation bar, kudos to the design team, I think this question becomes relevant again. I'm aware of the busload of downvotes, but still.  The top navigation bar doesn't occupy much space and has two notification areas:   Inbox Achievements   Having these two notifications visible at all times would be nice, IMO.  [Update]  I've just noticed that I haven't used the word "optional" in this discussion... My bad. In Excel, the Freeze function is controlled by the user. You can optionally Freeze part of the interface, and you can eliminate the Freeze at will. Why can a function modify some arguments as perceived by the caller, but not others? I'm trying to understand Python's approach to variable scope. In this example, why is f() able to alter the value of x, as perceived within main(), but not the value of n?  def f(n, x):     n = 2     x.append(4)     print('In f():', n, x)  def main():     n = 1     x = [0,1,2,3]     print('Before:', n, x)     f(n, x)     print('After: ', n, x)  main()   Output:  Before: 1 [0, 1, 2, 3] In f(): 2 [0, 1, 2, 3, 4] After:  1 [0, 1, 2, 3, 4] Displaying intersecting roads and creating multiple labels for long roads in QGIS? I am new to GIS and I am using QGIS 1.7.3 on Windows.  Can any one tell me how to display a map from line shapefile with these two characteristics:   Roads are displayed with borders at the sides and intersect at crossroads Name label for long roads are duplicated at specified intervals   Here is the link to an image that illustrates my idea:    (The map was taken from underdark's blog)  This is the best I can achieve by drawing lines with two overlapping simple line, one slightly bigger than the other: My husband is a teacher in New Jersey; 61 years of age. He has a pension plan listed on w-2 in box 14 (other). It is coded as 414(h). He asked the tax advise person at the school if he could still contribute maximum yearly amount to an individual Ira and was told yes. An accountant we know told us this was incorrect. Can he deduct the amount placed in individual Ira? An inequality for a sum of sine functions I want to show for $x\in\mathbb{R}$, the following inequality holds. $$ \left|\sin x\right|+\left|\sin (x+1)\right|+\left|\sin (x+2)\right|&gt;8/5. $$ This trigonometric inequality has been verified by Mathematica using the Plot commend. However, using the sum formula for the sine function seems doesn't work, and I cannot give a rigorous proof of it. Any suggestion, idea, or comment is welcome, thanks! How to deal with cross-thread access exceptions? I just want Telegram to be run and I have added it to startup apps. The point is that I need it to be minimized. Any commands? I want to use Windows 7 or 8 but I don't know to install a software like VirtualBox which we have to do with the use of terminal. I don't want to use Windows as a main OS so I want to use it in VirtualBox. Can you tell me how to install downloaded files in Ubuntu. I once installed java runtime but don't know the meaning of the lines which I have written in terminal, I just did as the blog posted by a man says. Definition of $\mathbb{R}^\infty$ I want to have a vector with a superscript:  \vec{o}^t   But this gives very bad results: the t is overlapping with the vector arrow. How do I fix this (and why does this give bad results in the first place) ? When I visit the reputation tab of my profile, I see a lot of stuff. I can make out some of it, but not all.   What do all the event types mean? Why do some events show an odd reputation gain or not show any reputation change at all? Why are some events sometimes highlighted in yellow? My reputation suddenly dropped, but I don't see anything. What happened? Why do some events disappear from my reputation history? I have a query going that gets data for an ID for the last 3 months.  I need to tweak it so I get the highest value for each of the three months.  I've tried a couple of things with the aggregate function MAX, but I'm not getting anywhere.  I'm trying to get the max value for each of the past months ....  Here's the data from the query, currently sorted by date (asc):   ID      Date               Value 12410   01/03/2017 12:17    0.000178 12410   01/10/2017 11:36    0.000186 12410   01/17/2017 11:27    0.000189 12410   01/24/2017 13:09    0.000182 12410   01/31/2017 10:37    0.000169 12410   02/07/2017 11:03    0.000214 12410   02/14/2017 11:52    0.000176 12410   02/21/2017 10:51    0.000200 12410   02/28/2017 12:29    0.000194 12410   03/07/2017 08:39    0.000206   Here's the query:   select AnalysisID as "ID" , AnalysisDateTime as "Date", AnalysisValue as "Value" from AnalysisValueTbl where AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -3, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-3, getdate())) or AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -2, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-2, getdate())) or AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -1, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-1, getdate())) order by AnalysisValue desc How to display Toast in Android? Repeat String - Javascript What is the best or most concise method for returning a string repeated an arbitrary amount of times?  The following is my best shot so far:  function repeat(s, n){     var a = [];     while(a.length &lt; n){         a.push(s);     }     return a.join(''); } Convergence to a Uniform Distribution $\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} $  Show that if $P(X_n = i/n)=1/n$ for every $i = 1,...,n$, then $X_n$ converges in distribution to a uniformly distributed random variable $X$.  Convergence in distribution is defined as   $$P(X_n \leq x) \rightarrow P(X \leq x)$$  and I have that a uniform distribution with parameters $a$ and $b$ implies that  $$P(X \leq x) = \frac{x-a}{b-a}$$  I cannot go any further however. I feel like I don't know anything about $X_n$ - I don't even know if it is continuous or discrete. What I can just say is that   $$P(X_n \leq x) = \sum_{i=1}^\floor{x} \frac{1}{n}$$  where $\floor{x}$  means rounding $x$ to the closest lower integer. How to get text under mouse in any open window Boy Born on a Tuesday - is it just a language trick?