Independence of $x = z_1^2 + z_2^2$ and $y = z_2 / z_1$, with $z_1, z_2$ having a standart normal distribution
Independence of Gaussian variables
Permanent Redirect (WWW to non WWW) Find executable files recursively I have got the directory called Test and a few directories inside it. Both Test and the directories inside it have executable files. I'd like to print them with ls. I'd use this command.  ls -l `find Test/ -perm /u=x,g=x,o=x -type f`   Is this a good/right/quick command or not?  My solution is:  find Test/ -executable -type f -exec ls -l {} \;   and got the same result as warl0ck and pradeepchhetri offered. Does someone falling into a black hole see the end of the universe? This question was prompted by . Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone falling into the black hole reaches the event horizon, so could that person see the universe age by an infinite time?  To be more precise, suppose the observer starts falling from rest at time $t = 0$ and some initial distance $r &gt; r_s$. If we wait for some time $T$ then shine a light ray at the falling observer. Will the light ray always reach the falling observer before they cross the event horizon? If not, what is the formula for the longest time $T$ that we can wait and still be sure the ray will catch the observer? If $T$ is not bounded it implies that observer could indeed see the end of the universe.  I can think of a qualitative argument for an upper limit on $T$, but I'm not sure how sound my argument is. The proper time for the observer to fall to the event horizon is finite - call this $\tau$. The proper time for the light ray to reach the horizon is zero, therefore the light ray will reach the observer before they cross the event horizon only if $T &lt; \tau$. Hence $T$ is bounded and the observer won't see the end of the universe.  I think a more rigorous approach would be to determine the equations of motion (in the Schwarzschild coordinates) for the falling observer and the light ray, and then find the condition for the light to reach the falling observer at some distance $\epsilon$ from the event horizon. Then take the limit as $\epsilon \rightarrow 0$. In principle this seems straightforward, but in practice the algebra rapidly defeated me. Even for a light ray the radial distance:time equation isn't closed form (Wolfram claims it needs the $W$ function) and for the falling observer the calculation is even harder. Continuous extension of a real function Related;    This is the theorem i need to prove;  "Let $E(\subset \mathbb{R})$ be closed subset and $f:E\rightarrow \mathbb{R}$ be a contiuous function. Then there exists a continuous function $g:\mathbb{R} \rightarrow \mathbb{R}$ such that $g(x)=f(x), \forall x\in E$."  I have tried hours to prove this, but couldn't. I found some solutions, but ridiculously all are wrong. Every solution states that "If $x\in E$ and $x$ is not an interior point of $E$, then $x$ is an endpoint of a segment of at most countable collection of disjoint segments.". However, this is indeed false! (Check Arthur's argument in the link above)  Wrong solution Q4.5;    Just like the argument in this solution, i can see that $g$ is continuous on $E^c$ and $Int(E)$. But how do i show that $g$ is continuous on $E$? When I get exceptions, it is often from deep within the call stack.  When this happens, more often than not, the actual offending line of code is hidden from me:  tmp.rb:7:in `t': undefined method `bar' for nil:NilClass (NoMethodError)         from tmp.rb:10:in `s'         from tmp.rb:13:in `r'         from tmp.rb:16:in `q'         from tmp.rb:19:in `p'         from tmp.rb:22:in `o'         from tmp.rb:25:in `n'         from tmp.rb:28:in `m'         from tmp.rb:31:in `l'          ... 8 levels...         from tmp.rb:58:in `c'         from tmp.rb:61:in `b'         from tmp.rb:64:in `a'         from tmp.rb:67   That "... 8 levels..." truncation is causing me a great deal of trouble.  I'm not having much success googling for this one:  How do I tell ruby that I want dumps to include the full stack? Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?    It seems to me like they are equal definitions in a way.    Can you give me a counter-example?    Thanks Java conditional compilation: how to prevent code chunks from being compiled? Don't display pending edit counter if you've exhausted your suggested edit votes an "X is an X is an X" what does this mean? Batch Requests/sec reported by DMV millions of times larger than Activity Monitor I have verified through SQL Server Profiler that my request per-second are around 30 request/s as is corroborated by SSMS Activity Monitor but sys.dm_os_performance_counters is reporting hundreds of millions/s.  Any idea what might be causing this gross discrepancy?  Query:  SELECT     RTrim(LTrim(object_name)) as object_name,     RTrim(LTrim(counter_name)) as counter_name,     cntr_value FROM     sys.dm_os_performance_counters  WHERE      instance_name IN ('', '_Total')     and counter_name IN (         N'Batch Requests/sec'         , N'SQL Compilations/sec'         , N'SQL Re-Compilations/sec'         , N'Transactions/sec')   Results:  object_name counter_name    cntr_value SQLServer:Databases Transactions/sec    191721399 SQLServer:SQL Statistics    Batch Requests/sec  242955426 SQLServer:SQL Statistics    SQL Compilations/sec    42048371 SQLServer:SQL Statistics    SQL Re-Compilations/sec 1200947 The integral $\int_0^8 \sqrt{x^4+4x^2}\,dx$ How can I set up password-less SSH login? Get rows with most recent date for each different item Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction? Repeated Iteration of a 2x2 matrix Suppose I am given a $2$x$2$ matrix $A=$ \begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix}  And an initial vector $x_n$ = \begin{pmatrix} x_0 \\ y_0\end{pmatrix}.  Under repeated iteration $x_{n+1} = Ax_n$, we find that $x_{n+1}$ converges to a line in the direction of the $eigenvector$  of $A$ of the form $X$= $[u,mu]$ where $m$ is the slope of the line.  I know that this process somehow also involves the largest $eigenvalue, \lambda,$ of $A$, though I am unsure how it connects.  My question is: How does the largest eigenvalue connect to this repeated iteration, how do I find the slope of the line of convergence $m$, and what is meant by the "direction of the eigenvector"? There are a few examples of pairs of words ending with -ee/-er like employee and employer or advisee and adviser. What I was curious about is if there was any rule that would describe the relationship of the objects in a pair like this and situations when it's appropriate to create a counterpart for a given word.   I'll give you an example. It's relatively common in the computer programming world to see the word dragee, which describes an object that is being dragged with a mouse. I understand that this is a relatively new word and could not be found in any dictionary (I've tried). Is that acceptable to make up words like this one or is it just bad English? Trying to keep track of the updates to all the great, user-developed add-ons is fairly frustrating (at least for me). Is there currently a centralized resource where all these amazing add-ons are kept and updated in one location?  If there isn't such a resource, would it be possible to have blender query the collection of installed add-ins and then iterate through on-line references looking at version #'s for add-ins?  Since, as far as I know, it hasn't been done...I have to ask if there are any major flaws in the concept. Of course, in my dream scenario, there would be a "voting" front-end that would allow users to see what the most popular and useful add-ons are and where you don't have to read pages (and pages) of threads. Changing text applied when duplicating file in Finder When duplicating files in the finder, OS X attaches a space followed by 'copy' to the file name. This can lead to some file alphabetizing problems and the copies may appear out of order (not directly subsequent to the original). Is there a way to change the appended text? I would prefer that it says '_1' or _copy. Thanks. I think this is just something I've grown used to but can't remember any proof.  When differentiating and integrating with trigonometric functions, we require angles to be taken in radians. Why does it work then and only then? The lines wrap so much on v1.0.85 that only a few items can be displayed.  Edit: This is on the world's most low end tablet, Azpen A727.  Screenshots of the old:    and new, showing loss of quality