I understand that with words that indicate portions e.g. a lot, a majority, some, all, etc, I need to look at the noun after 'of' to decide if the verb is singular or plural. If the noun after 'of' is singular, I should use a singular verb. If it is plural, I should use a plural verb. For example:  All of the pie is gone. All of the pies are gone.  But what about the following statement:  Each of the children ____ (be) given a balloon on Children's Day.  Should the answer be 'is' or 'are'? Does the same rule apply? Thanks.
Relevant:  and   The answers in the linked question don't quite help me. Specifically, what happens with this case:  My three pens are green. Each of my three pens are green. Each of my three pens is green.  Part of the confusion seems to stem from the inclusion of &quot;three&quot;:  My pens are green. Each of my pens are green. Each pen is green.  There doesn't seem to be a way to rewrite the last example with &quot;three&quot;:  Each three pen is green.  The more common application would be:  All three pens are green.  But in the event that I want to say, &quot;Each of my three pens are green&quot; which is correct? And, in the event that the correct sentence is &quot;each of my three pens is green&quot; why does prepending &quot;each of&quot; to the beginning of &quot;my three pens are green&quot; change the verb?
This question is NOT about access to USB or external drives.  WPS Witer and other just installed Ubuntu software can NOT open files saved on my /media directory. I keep getting the annoying message: « Could not read the contents of '/media': Permission denied ».   MY SIMPLE QUESTION REMAINS:  How can I access all files and folders on my user username/media/ directory?  I'm using Ubuntu 18.04.3 LTS.  Ubuntu's Nautilus can indeed access all files and folders in all locations. However, Ubuntu's software that I have downloaded (e.g. KRITA, WPS WRITER etc) can NOT access any file or folder on the /media directory. Thanks in advance. A problem from Isaacs' FGT This is problem 3B.12. from the afore mentioned book. It asks to show that, if $G$ is a solvable Frattini-free group (that is, $Φ(G)=1$) and $H$ is a subgroup of some maximal subgroup $M$ of $G$, then $G$ contains a subgroup of index $|M:H|$. It is easy to see that, if   $N \unlhd G$ and $M\cap N=1$, then $G=MN$, $M\cong G/N $ and $H\cong K/N $ for some $ K \leqslant G $, where $K$ contains $N$. Then $|G:K|=|G/N:K/N|=|M:H| $ and we are done. However, the hypothesis will not necessarily hold. But, if $N$ is minimal among normal subgroups of $G$ (in the sense of containment), then $N$ is elementary abelian, hence nilpotent, which implies that $M \cap N \lneq N_G(  M \cap N ) \cap N $. Thus, $M \lneq N_G(  M \cap N )$ and by the maximality of $M$ we deduce that $M \cap N \unlhd G$. So, for this particular $M$, if it is not true that there exists some normal subgroup of $G$ with which it intersects trivially, then $M \cap N = N$ by the minimality of $N$. Hence $M$ contains every minimal subgroup of $G$.     How should I proceed from here? Who wrote about an energy free space elevator? The other day I was trying to download something for Minecraft and it involved my bin folder. So I was looking for it and couldn't find it. I then thought that I might have accidentally deleted it, but didn't find it in the trash. I have no idea how to get the bin folder back with all the Minecraft binary files in them. show all my unanswered questions from SE Any way how to get    my all un-answered questions  from across all SE sites? Evaluating a mathematical expression in a string Ubuntu 14.04 Wireless not working: no network interface. Atheros [168c:003e] device I just installed Ubuntu 14.04.3 LTS after installing windows 10 in my new VN7-571G and the wireless is not working. It never had: even during the installation it was not recognized. I run a script to gather the data , which is . lspci -knn | grep Net -A2 output 03:00.0 Network controller [0280]: Qualcomm Atheros Device [168c:003e] (rev 20)         Subsystem: Lite-On Communications Inc Device [11ad:0804]  The OS behaves like it has no wifi card. I do not see wifi settings in network settings I'm not a linux power user, so I do not know what to do to solve the issue. What should I do to make it work? What (if any) countries are either open to or have set definitive plans to allow international tourism? What diceless tabletop RPG techniques are there? I am interested in using a diceless resolution system for my roleplaying, but am not sure what my options are in that vein. I can think of basically two categories of diceless tabletop role-playing systems - systems which eschew any randomisation, and those which randomise by some method other than dice.  Examples  Non-random tabletop systems  One option is of direct comparison of stats or other game statistics without a randomization factor. The obvious example here is Amber DRPG, but I suspect that there are other narrative driven RPGs out there that I don't know about.   Even in Amber, situation resolution it is rarely by direct comparison between stats. Narrative techniques can be used to manoeuvre two characters into a situation which narrows the gap between their ranking, widens it, or brings other stats into the picture - the classic example of course being Corwin relying on his stamina to stretch out conflicts with his siblings such that it becomes a dominant enough factor that he can escape.  Other randomisation techniques  I have seen card-based randomization system. Over the years, I've played quite a few home brew games based on the original SAGA Dragonlance system, which was similar to the SAGA Marvel superhero system.  The basic mechanics were that you had a hand size according to your experience, and for any skill check you would play a card from your hand and replace your card from the draw pile. If you had a card of the right suit as the skill check (a strength card on a strength check) you would also draw a card from the draw pile and add that to your skill check, so a small trump was often worth more than a medium value card not of the correct suit. When you were wounded, you would discard cards to the value of the damage, but those cards wouldn't be replenished - your hand size would be reduced until you were healed. One nice aspect of the system was that it simulated fatigue beautifully, you might start a scene with a spread of high, medium and low cards, but as your high cards were played they would more often than not get replaced by lower value cards, until you were left with a bunch of useless cards and feeling very vulnerable.    The only other system I've played without dice was Everway which, if I remember correctly, used a combination of these techniques, stats based resolution, card resolution and GM fiat.  What I would be interested in is what other diceless resolution techniques exist, ideally with examples of tabletop diceless resolution methods people have tried and how they found them to play. I have a table tabName with the following rows:  id(PK) .. Created(datetime)     Resolved(datetime) Status(new/resolved/open) 1          2015-05-10 00:00:00   1970-01-01 ..       open 2          2015-05-10 ..         1970-01-01 ..       new 3          2015-05-10            2015-05-12          resolved 4          2015-05-11 ..         1970-01-01 ..       open 5          2015-05-11 ..         1970-01-01 ..       new 6          2015-05-11            2015-05-11          resolved 7          2015-05-12 ..         1970-01-01 ..       open 8          2015-05-12 ..         1970-01-01 ..       new 9          2015-05-12            2015-05-12          resolved   NOTE:  1970-01-01 .. is default time for all the tickets which are still open.  I have to frame a query to get the count of tickets still open, date wise. Say like on 10 May I have 3 tickets opened. Noting that for id = 3, resolved date is not 10 but it's closed on 12 May.  I framed a query like  SELECT DATE_FORMAT(Created, '%d-%m') AS createdd, COUNT(1) FROM tabName WHERE DATE_FORMAT(Resolved, '%d-%m') &gt; DATE_FORMAT(Created, '%d-%m')       AND YEAR(Created) = '2015' GROUP BY createdd;   The above query gets all the tickets whose Resolved date is greater than the date which is considered for the count. This may count newer tickets as well. And also if the older tickets which are not resolved yet is not counted.  Is there any other way to frame the required query? I have been juggling with this query from last 3 days. Not able to find out still.  Updated: As suggested by Abhik, i have tried in sqlfiddle site.  Here is what i created:  CREATE TABLE test    (idint,createddatetime,resolveddatetime, status varchar(15), PRIMARY KEY (id));    INSERT INTO test       (id,'created','resolved',status`) VALUES       (1,'2015-05-10 00:00:00','1970-01-01 00:00:00','open'),    (2,'2015-05-10 00:00:00','1970-01-01 00:00:00','new'),    (3,'2015-05-10 00:00:00','2015-05-12 00:00:00','resolved'),    (4,'2015-05-11 00:00:00','1970-01-01 00:00:00','open'),    (5,'2015-05-11 00:00:00','1970-01-01 00:00:00','new'),    (6,'2015-05-11 00:00:00','2015-05-11 00:00:00','resolved'),    (7,'2015-05-12 00:00:00','1970-01-01 00:00:00','open'),    (8,'2015-05-12 00:00:00','1970-01-01 00:00:00','new'),    (9,'2015-05-12 00:00:00','1970-01-01 00:00:00','open')    ;   `   When i run  ` select created_date, @open:= @open+open_ticket-resolved as open from(  select   date_format(created,'%d-%m') as created_date ,  sum( case when status='open' then 1 else 0 end )+  sum( case when status='new' then 1 else 0 end )+  sum( case when status='resolved' and ( date(resolved) > date(created) or  date(resolved) = date(created)) then 1 else 0 end ) as open_ticket,  sum(case when status = 'resolved' and date(resolved) = date(created) then 1   else 0 end) as resolved  from test  where  YEAR(Created) = '2015'  group by created_date )x,  (select @open:=0)r order by created_date ; `  I got following output  created_date   open 10-05   3 11-05   5 12-05   8  Here count of still open tickets for 12-05 must be 7. The above query includes ticket id "3" , which is closed on 12-05. So is there any way to exclude this? If i am able to get this right, then i will have full fledged query. Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument I want to prove that the set of all real functions $\mathbb{R}^\mathbb{R}$ has a higher cardinality than the real numbers $\mathbb R$, by Cantor's diagonal argument.  I'm having difficulties with approaching this problem.  What I'm looking for is a hint in the right direction.  I've seen an example where it is shown that the power set $2^S$ of a countable set $S$ is uncountable, by the diagonal argument. What does '>/dev/null 2>&1' mean in this article of crontab basics? Is the neutral wire considered safe? If the neutral wire carries current, why do many people believe that it's safe? I've heard "You can touch the neutral wire/bar in the breaker box and not get shocked. Only the hot can hurt you." If the circuit is complete and current is flowing, can't you receive a shock? How to approximate the student-t CDF at a point without the hypergeometric function? Is there a way to closely approximate the CDF of a student-t distribution at a point $x$ without involving the hypergeometric function? For example, by using a series expansion, or expressing the CDF in terms of simpler functions?  The t-distribution can   $$t = \frac{X\sqrt{n}}{Y}$$  where $X$ is normally distributed with mean 0 and variance $\sigma^2$; $\frac{Y^2}{\sigma^2}$ has a chi-squared distribution. Maybe this expression can help simplify the t CDF?  I am trying to write an algorithm to compute the student-t CDF for any real number, so using the hypergeometric function will be extremely difficult. I am also trying to avoid integrating the PDF to get the CDF. What is the difference between Clamav and Clamtk? I know that both of them are antivirus. Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$? Problem:   Find the value of $$\sum_{r=0}^{44} \tan^2(2r+1)$$  Note: The angles here are in degrees.    I don't know how to solve this question because trigonometric simplifications didn't get me anywhere. I think there was a method to solve this question using complex numbers which I no longer remember. Any hint/help will be appreciated. Show discontinuity of $\frac{xy}{x^2+y^2}$ I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i &gt; -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there? Why are my textures pink? Basically, I applied my textures by taking each individual object, unwrapping it in the uv editor, then opening up an image in the uv editor and it would apply the texture in the 3D editor. However, when I render my project none of the textures appear and everything looks odd. I don't know how to set up the images properly with the bee.  For example, here's the uv layout image for the bee's Cube.001:     How do I get that applied properly to the Cube.001 in my project?  Here is   Everything appears purple if the images aren't there and I don't know how to fix that either.