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How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$? Flag indicator present on Meta, but no flags visible Training on the full dataset after cross-validation? Function ereg() is deprecated How to set a proxy for terminal? I am looking to set a proxy for terminal. What I need is I want to send all terminal communications to the internet through a proxy, say tor.   I tried to set a system wide proxy set up. But Terminal doesn't obey the system wide proxy configuration.  Is there any other way to do this? stab(S) is isomorphic to $ S_k \times S_{n-k} $ Show that the group $S_n$ (right) acts on the set of subsets of $\{1,2,\ldots n\}$ by $\rho(S,\sigma)=S\sigma$. Show that there are $n+1$ orbits, one for each possible value of $|S|$. Show that if $|S|=k$ then $\mathrm{Stab}(S)\cong S_k\times S_{n-k}$.  I have shown that there are n+1 orbits but now I am stuck with the last bit. my initial thought is that if I let $S =\{1,2,3,...,k\}$ then $\mathrm{Stab}(S)$ would involve $(1)(2)(3)...(k)$ i.e. mapping to itself and then $k+1$ to $n$ mapped in any ways ($S_{n-k}$) I feel like $\mathrm{Stab}$ is isomorphic to $S_{n-k}$ what am I misunderstanding here? How would I prove the last part? Thanks a lot Command-line completion from command history So, I've looked at history and at Ctrl+R, but they are not what I thought I knew. Is there a way that I can type in the beginning of a command, and cycle through the matches in my history with some bash shortcut?  # mysq(some shortcut key)   Gives me:  # mysqldump  --add-drop-table -e -q -n -C -u  (some shortcut key) #  mysql -u ben.dauphinee -p Is it "me" or "I" and why? How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? Command for creating a directory and navigating into it directly? Is there a formula for $(1+i)^n+(1-i)^n$? Taking the * of these two large shapefiles   locally using ArcMap takes appr. 10 min.   Over the last few weeks, I've tried to obtain the same results using other, open-source approaches without success. I am curious why only ArcMap seems to generate results in a reasonable amount of time without errors.   The approaches I've tried so far:  QGIS  The most straight-forward alternative. There are two "union" functions available in QGIS. One default (part of vector overlay), one based on SAGA. Both functions create the desired results on smaller samples but fail to run (or take forever) on my shapefiles. I tried running union for 30 minutes after which the progress bar was at appr. 4%    PostGIS  I've ingested the shapefiles on an AWS RDS instance running postGreSQL with PostGIS enabled. The approach is not so straight forward and requires a hideous long SQL query to obtain the same result. Most importantly, the query did not create a meaningful result on the full datasets. It did run properly on a sample though.   See separate question   CREATE TABLE test.sqlislelijk AS  -- input data with polys1 AS (   SELECT      pfaf_id as df1,     geom as g   FROM hybas06_v04 ), polys2 AS (   SELECT      aqid as df2,     geom as g   FROM y2018m11d14_rh_whymap_to_rds_v01_v01 ), -- intersections intersections AS (   SELECT df1, df2, ST_INTERSECTION(a.g, b.g) i, a.g AS g1, b.g AS g2    FROM polys1 a, polys2 b WHERE ST_INTERSECTS(a.g, b.g) ), -- per-row union of intersections with this row diff1 AS (   SELECT df1, ST_UNION(i) i FROM intersections GROUP BY df1 ), diff2 AS (   SELECT df2, ST_UNION(i) i FROM intersections GROUP BY df2 ), -- various combinations of intersections pairs AS (   SELECT df1, df2, i AS g FROM intersections   UNION ALL   SELECT      p.df1,     NULL,     CASE       WHEN i IS NULL THEN g        ELSE ST_DIFFERENCE(g, i)     END   FROM polys1 p LEFT JOIN diff1 d ON p.df1 = d.df1   UNION ALL   SELECT     NULL,     p.df2,     CASE       WHEN i IS NULL THEN g       ELSE ST_DIFFERENCE(g, i)     END   FROM polys2 p LEFT JOIN diff2 d ON p.df2 = d.df2   ) SELECT    df1 as pfaf_id,   df2 as aqid,   g as geom FROM pairs WHERE NOT ST_IsEmpty(g);   Google BigQuery  Google's GIS extension for BQ looks promising but I experienced weird behavior and internal errors, probably due to mixing of GEOMETRY and GEOGRAPHY objects. Also, the syntax is similar to PostGIS and a command of 1 line in geopandas takes >20 lines in SQL.   GeoPandas  Probably my favorite approach. The out-of the box approach does't give any results after running it for several hours. My latest approach includes tiling the shapefiles, use multiprocessing on each tile and merge them. Not very straight forward and one 10x10 degree tile till takes 40+ minutes to calculate.   See   It is the first time in my career that I am impressed by the performance of ArcMap. It seems that ArcMap handles this use-case much, much better than anything else. The issue seems persistent over all solutions I've tried so far. Is there something wrong in the underlying libraries of the open-source/alternative solutions?    Note that Union in ArcMap means something different than in the Shapely / PostGIS world. NullReferenceException in Unity Since many users are facing the NullReferenceException: Object reference not set to an instance of an object error in Unity, I thought that it would be a good idea to gather from multiple source some explanation and ways to fix this error.  Symptoms I am getting the error below appearing in my console, what does it mean and how do I fix it?  NullReferenceException: Object reference not set to an instance of an object How to send emails and avoid them being classified as spam? This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating? What is the antiderivative of $x^{x^{x^{x...}}}$? What is $\int{x^{x^{x^{x^{\dots }}}}dx}$? I managed to get it down to a complicated series after using $u$-substitution, but I want to see other methods of approach, or if my answer was right.   First I let $$u=x^{x^{x^{x^{\dots }}}}$$, and $du$ would be, in terms of $u$, $$du=  \frac{u}{\frac{1-ln(u)}{u}e^{ln(u)/u}}$$ This makes the integral of $$\int{x^{x^{x^{x^{\dots }}}}dx}=\int \frac{1 - ln(u)}{u}{e^{ln(u)/u} }du$$ Now making $w = ln(u), dw$ becomes $1/u$ and the integral becomes $$\int e^{w/e^{w}}(1-w)dw$$ From there, I distributed and made $2$ integrals of series, using the Taylor polynomial for $e^x$. From there, I integrated and back substituted. I was only trying to find the indefinite integral.   I'm still a junior in high school, so let me know if the answer is beyond my scope of understanding. How do you compute negative numbers to fractional powers? I found some articles related to this, but they were not sufficient for me. I want to know how the localhost works and why is it the same on many different machines?   How does the localhost block the access to the website when we use it in the host file to block the website? Will Windows 10's reset delete my Linux partitions? How to determine the size of a package while using apt prior to downloading? When using apt-get install &lt;package_name&gt;, and there are dependencies that need to be downloaded, the terminal outputs names of additional packages and total size, and asks for confirmation before downloading.   But, when dependencies are satisfied and nothing but the named package needs to be downloaded there is no size output and no confirmation.  When using Synaptic, I can see the total size that new packages that will use after installation but no way to see the size that needs to be downloaded, except to go from package to package and use properties to see the compressed size.  I would like to know if there is a way to see the size of a package(s) in terminal and Synaptic prior to downloading and installing it/them? One thing I've noticed about the relatively new sitewide layout is that I can't find a quick way to get back to www.stackexchange.com without finding StackExchange in the sites list. As a result, I am typing stackexchange in my toolbar a whole lot more often now. In particular, I tend to enjoy browsing the hot questions list and my own personal feed quite often so visit these pages on a daily basis. Is there an easy link to them that I'm missing?  (On the android app, there is a feed in the menu that I really appreciate, something like that on the desktop would be ideal!)