Why use plural form here?
Are collective nouns always plural, or are certain ones singular?
Move object in inches instead of feet? Whenever I move an object in blender in unit mode(Imperial), it always make it in feet. For example, if I type G Y 12, it will move 12 feet. How can I make it move 12 inches instead? Consider $\mathbb R^{[0,1]}$ the space of all functions from $[0,1]$  to $\mathbb R$  and the cylindrical sigma algebra $\mathcal B$  on it. The question is: how to prove that $C[0,1]\notin \mathcal B$. Sometimes you see a video of a fan or a propeller spinning very fast, and the apparent rotation is distorted. The fan can appear to be moving in the opposite direction of rotation, or even stationary. This optical illusion is known as the wagon-wheel effect. If I understand correctly, this occurs because the camera framerate is slower than the frequency at which the fan makes one rev, so stroboscopic effects should be expected.   Does the wagon-wheel effect occur only in videos, or can we observe it just with the eye? Graphing y=x^2 and y=x ERROR: cuvid requested, but not all dependencies are satisfied: cuda/ffnvcodec I am trying to compile FFMPEG with Nvidia Cuda support, on Debian 9.3. Parameters, what I am using:  --enable-cuda --enable-cuvid --enable-nvenc --extra-cflags=-I/usr/local/cuda/include --extra-ldflags=-L/usr/local/cuda/lib64 --enable-gpl --enable-libx264 --disable-x86asm --enable-libx265 --enable-libfdk-aac --enable-nonfree   Nvidia Cuda with drivers are installed. When I try to configure ffmpeg, it says:  ERROR: cuvid requested, but not all dependencies are satisfied: cuda   Newer ffmpeg will show a similar, re-worded message:  ERROR: cuda requested, but not all dependencies are satisfied: ffnvcodec   I absolutely don't know why I'm having this issue, because I am compiling ffmpeg on all of our trans-coding servers. Let $(B_t)_{t\geq 0}$ be a standard Brownian motion in $\mathbb{R}^d$. It is intuitive that, for fixed $s&lt;t&lt;u$  $$\mathbb{E}[B_t\mid \sigma(B_s,B_u)]=B_s+\frac{t-s}{u-s}(B_u-B_s).$$  However, I cannot think of a way to show this rigorously.   If first attempted to take $A\in\sigma(B_s,B_u)$ and show that $\mathbb{E}[1_A B_t]=\mathbb{E}[1_A(B_s+\frac{t-s}{u-s}(B_u-B_s))]$. But I cannot manage to show this equality.   I'd be very thankful for any ideas and suggestions on how to tackle this problem. Get name of caller function in PHP? Is there a PHP function to find out the name of the caller function in a given function? Install on, install in, install to When I say "programs to install on a new PC" it sounds alright to me, but I'm not sure if it's the correct usage. Which one of the following should I use?   Programs to install on a new PC Programs to install in a new PC Programs to install to a new PC 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. What is the sign of the work done on the system and by the system? What is the sign of the  done on the system and by the system?  My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.  My physics book says the opposite. It says that when work is done on the system, it is negative. When work is done by the system, it is positive.  Why do they differ? TexShop will not compile without trashing aux files after every error I have a couple of LaTeX files with the same problem. If I produce an error, fix it, and then try to compile a pdf, I get the following error.  )Runaway argument? {{ ! File ended while scanning use of \@newl@ablel. &lt;inserted text&gt;                 \par l.90 \begin{document}   If I then click on the console or trash my .aux file, it compiles fine. Any thoughts on what is going on and how to prevent this annoying extra step? How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$ How do you report percentage accuracy for glmnet logistic regression? As far as I know, humans have 23 pairs of chromosomes, each one which contains a particular amount of genes. But in the "last" pair, men have a XY pair chromosome, and women have a XX pair chromosome. Does the missing "leg" of the XY pair make men to have fewer genes than women, and if so, how many genes do each sex have? What would you see if you have 2 huge mirrors (you cant look over it or next to it)  You place them with the reflecting side to each other and you look in the mirror from behind one mirror (one way mirror = 1 side glass 1 side mirror, like in a movie when cops are questioning a suspect.)  The mirror would reflect each other endless.  The example could be preformed with a see trough mirror (1 side mirror other side glass) but I don't have one, also I don't have huge mirrors.    Would it make a diffrence if you place a light source and if you dont have a light source?  My guess is that you would always see black because there is nothing to mirror.  Edit important:   There is nothing in the room to reflect on, so it only reflects the mirror, thats what i ment. How to reinstall Ubuntu in dual boot with Windows 10? I have Ubuntu 15.10 and Windows 10 dual-booted, but I want to reinstall Ubuntu in the same partition without making any changes or causing problems in the dual boot option and without removing Windows.  Is it possible? Any guide on how to do it? Is there a way to send a file using POST from a Python script? Is there a way to determine how many digits a power of 2 will contain? Is there a direct way to determine how many digits a power of 2 will contain without actually performing the multiplication?  An estimation would help as well if there is no absolute solution.  EDIT: In both decimal and binary bases. I'm sure there is a really simple explanation to this but haven't found any pointers on this forum or elsewhere. I seem to have lost the 'processing' menu from QGIS and can't figure out how/why!? Any ideas what I might have done to make this happen?  I'm running QGIS 2.8 built against GDAL 1.10 on Ubuntu 14.04. mysqli or PDO - what are the pros and cons? In our place we're split between using mysqli and PDO for stuff like prepared statements and transaction support. Some projects use one, some the other. There is little realistic likelihood of us ever moving to another RDBMS.  I prefer PDO for the single reason that it allows named parameters for prepared statements, and as far as I am aware mysqli does not.  Are there any other pros and cons to choosing one over the other as a standard as we consolidate our projects to use just one approach?