A recipe calls for buttermilk but I don’t want to go to the store just for that. Can I make my own
I've got a recipe that calls for some buttermilk, but none on-hand. Is there some way I could use some common ingredient(s) as a substitute?
Can I extend a class using more than 1 class in PHP? If I have several classes with functions that I need but want to store separately for organisation, can I extend a class to have both?  i.e. class a extends b extends c  edit: I know how to extend classes one at a time, but I'm looking for a method to instantly extend a class using multiple base classes - AFAIK you can't do this in PHP but there should be ways around it without resorting to class c extends b, class b extends a I've been reading forum posts and blogs who mention "my guy" syndrome as a specific type of difficult player, but I can't seem to find a solid definition for the term. Can someone explain this particular kind of problem player to me? How do you deal with this kind of problem? Kontact in Kubuntu 16.10 will not start because the Akonadi server will not start I just proved that any finite group of order $p^2$ for $p$ a prime is abelian. The author now asks to show that there are only two such groups up to isomorphism. The first group I can think of is $G=\Bbb Z/p\Bbb Z\oplus \Bbb Z/p\Bbb Z$. This is abelian and has order $p^2$. I think the other is $\Bbb Z/p^2 \Bbb Z$.   Now, it should follow from the fact that there is only one cyclic group of order $n$ up to isomorphism that these two are unique up to isomorphism. All I need to show is these two are in fact not isomorphic. It suffices to show that $G$ as before is not cyclic. But this is easy to see, since we cannot generate any $(x,y)$ with $x\neq y$ by repeated addition of some $(z,z)$.  Now, it suffices to show that any other group of order $p^2$ is isomorphic to either one of these two groups. If the group is cyclic, we're done, so assume it is not cyclic. One can see that $G=\langle (1,0) ,(0,1)\rangle$. How can I move on? How to split numbers into columns with negative and positive values, without empty cells? Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$ Let $A,B$ be matrices $m\times n$ $(A, B \in M_{m\times n}(R))$. How can we prove that $$\operatorname{rank}(A+ B) \le \operatorname{rank}(A) + \operatorname{rank}(B)\ ?$$ Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long would it take me? Remap a key combination to another combination, e. g. Super+Ctrl+Shift+J -> Ctrl+Shift+Left For about 2 days I'm trying to configure Ubuntu so that I can send an email, but when I type in:  echo "Subject: sendmail test" | sendmail -v my@email.com   I'll get:  postdrop: warning: unable to look up public/pickup: No such file or directory Mail Delivery Status Report will be mailed to &lt;andreigbr&gt;.   Even if I change my@email with mine, the inbox will be empty. Can somebody help me, please? I watched about 5 tutorial about how to send an email fom the command line but still doesn't work. How to connect two parents to the same child, with parents not in the same tree? I'm trying to draw a specific tree, with two parents node linked to the same child. The problem is that one of the parent is outside the main tree.  Here's the code I have for the moment:  \documentclass{article} \usepackage{tikz-qtree,tikz-qtree-compat} %\usepackage{gb4e} \usepackage{forest}  \begin{document}  %\begin{exe} \begin{forest} qtree edges/.style={for tree= parent anchor=north, child anchor=south}    [A, grow=north        [C, name=C, grow'=north            [D, grow=north ]            [E, name=t5, grow=north ]        ]        [B, grow=north ]    ]    \hspace{0.8cm}    [$F$, name=F, grow=north ]    %\draw (F.north) -- (C.south); \end{forest} %\end{exe}  \end{document}   I'd like the nodes F and C to be connected. I don't know why, but if I delete the dollar signs, node F doesn't even appear on my document.  Another thing is that I want the forest environment to be embedded in an example environment, but this doesn't work either.  Thanks in advance for your help! What is needed for a game's stats to be saved? Last night I played a few games with my friend. While in the last game, I suddenly remembered something I had to do and was about to leave but my friend told me that I would lose my progress if I did so. I stayed until the end, through the scoreboard screen and quit while the next map was loading. Taking a look  now, I can't see any of yesterday's games. I don't remember how much XP I had yesterday so there is no sure way for me to check that. I had gotten a dozen ribbon and I don't see them in the feed, but there could be specific conditions to be showing them.  My questions then.   If you quit a game early, do you lose progress / XP? What if you quit on the scoreboard? Do you need to wait for the next map to load to save your progress? Any idea why the games aren't showing up? Some of them I definitely waited for the next map to load. Is there a delay for them to be shown on Battlelog?   Thanks. Rollup Summary Trigger Help I am trying to create an Apex Trigger that performs a Rollup from a custom object to Contacts.   Here is the error that I am receiving:      Didn't understand relationship 'Assignments__r' in FROM part of query   call. If you are attempting to use a custom relationship, be sure to   append the '__r' after the custom relationship name. Please reference   your WSDL or the describe call for the appropriate names.   The child relationship name is Assignments.  Below is the code:      trigger RollupActiveAssigmentLevelsToContact on pse__Assignment__c (after insert, after update, after delete) {      set&lt;Id&gt; set_id = new set&lt;Id&gt;();      List&lt;Contact&gt; con_list = new List&lt;Contact&gt;();      if(trigger.isInsert || trigger.isUpdate){         for(pse__Assignment__c myAssignment : trigger.New) {             set_id.add(myAssignment.pse__Resource__c);         }     }     else if(trigger.isDelete){         for(pse__Assignment__c myAssignment : trigger.Old){             set_id.add(myAssignment.pse__Resource__c);         }     }      if(trigger.isAfter &amp;&amp; (trigger.isInsert || trigger.isUpdate || trigger.isDelete)){         con_list = [SELECT id,Total_Levels__c, (SELECT id,name FROM Assignments__r WHERE Active_Assignment__c = TRUE) FROM Contact WHERE id IN :set_id];          for(Contact con : con_list){             if(con.Assignments__r.size()&gt;0)                 con.Total_Levels__c = con.Assignments__r.size();             else                 con.Total_Levels__c = 0;         }         if(!con_list.isEmpty())         update con_list;     } }   Below is a snap of the Child Relationship name: How do you search through flags in the manpages? Whenever I search the manpages, I'm almost always trying to find out what's going on with a specific flag. For example, when searching the man pages for  I was searching the for -f flag. I'm not sure how to say, quickly get to the flag which is here:  OPTIONS    General options        -f FORMAT, -r FORMAT, --from=FORMAT, --read=FORMAT   and filter out stuff like:  iconv -t utf-8 input.txt | pandoc | iconv -f utf-8              or  pandoc -f markdown -t latex hello.txt   I've tried searching for /-f, and I've looked at  and tried (^|\s)-f($|\s\) but it was invalid. So I'm wondering how do you quickly search less for "only the flag -f"?  Would love your thoughts or some other tool that you use to quickly go through documentation The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group An algebraic group is not necessarily a topological group, since for an algebraic group, the product map $G \times G \to G$ is continuous when $G \times G$ is given the Zariski topology, which is finer than the product topology.   So does this tell you that the additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group? The underlying variety of $\mathbb{G}_a \times \mathbb{G}_a$ is $\mathbb{A}_k^1 \times_k \mathbb{A}_k^1 = \mathbb{A}_k^2$, whose Zariski topology is the cofinite topology, where every open set is also open in the product topology (since $\mathbb{A}_k^1$ also has the Zariski topology). In my recent study of Artinian modules I have been looking at Prüfer $p$-groups (which I will denote by $\mathbb Z_{p^\infty}$ from now on).   I am attempting to prove that $\mathbb Z_{p^\infty}$ is an Artinian $\mathbb{Z}$-module which is not finitely generated.      To do this I am trying to show that every proper non-trivial submodule of $\mathbb Z_{p^\infty}$ is equal to $\left(\frac{1}{p^n}\mathbb{Z_{}}\right)/\mathbb{Z}$ for some $n$.   I am using the following definition of $\mathbb Z_{p^\infty}$: $$\mathbb Z_{p^\infty}=\left\{x\in \mathbb{Q}/\mathbb{Z}\mid \exists n:p^nx=0 \right\}$$ I have read in several places, Atiyah &amp; MacDonald Example 6.3 and Wikipedia to name a few, that the subgroups of $\mathbb Z_{p^\infty}$ are of this form. This would demonstrate that $\mathbb Z_{p^\infty}$ is Artinian. However, I can't seem to find anywhere a proof or example showing why all the subgroups are of this form. I would like to understand this further, as it is not immediate to me that this would be the case, but my attempts to figure out why have so far been futile. I may be thinking too much and missing a simple explanation. I have looked at starting with an arbitrary subgroup $H$ such that $H\neq 0$ and $H\neq\mathbb Z_{p^\infty}$ and seeing if I can deduce anything from that. I got this far, but it doesn't seem to be going anywhere. I have also looked at Sylow's theorems, but I'm not sure if they will be any use to me as $|\mathbb Z_{p^\infty}|=\infty$ (unless I'm wrong about this!).  I would be extremely grateful if anybody could offer a few hints here as I am slowly losing my sanity trying to figure it out!  Thanks,  Andy. Word to describe someone who goes to all the events in town! I'm looking for a short word that could describe people who are always going to every event in town. It doesn't need to be an existing word, feel free to create one of your own. It can also be made of words related to events and parties. (ex: club, event, guest list, etc.)  Edit  The word will serve as a new term to describ these people in a favorable way. It will probably be used for an app name so it need to be catchy and fun. ( Preferably ) Show $100+t$ is reducible in $\mathbb{Z}[[t]]$ $\mathbb{Z}[[t]]$ is the ring of formal power series with integer coefficients, and the problem asks to show that $100+t$ is reducible. This means I need to find two power series, $\sum_{i=0}^\infty a_i t^i$ and $\sum_{j=0}^\infty b_j t^j$ with $a_i,b_j\in\mathbb{Z}$, that when multiplied give $100+t$. Since the integers are an integral domain, I know that neither of these power series may be finite, but I'm having a really hard time figuring out how to come up with two series that will telescope properly. Any suggestions? Aluminum foil is said to be not absorbing light at all. It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?  If yes, then where does unreflected light go in case of less shiny aluminum foil?  Does less shiny and more shiny actually make a difference? Why?  In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too? Increasing Letterspace for words in caps or small caps Some typographers say it's a good habit to increase the letterspace when writing words in caps or small caps. So my question is, how to do it with pdflatex and/or xelatex? And while we're at it, which words would you alter this way? Acronyms like USA, NATO, IBM, GNU, etc.? How about words like PCs, UdSSR, FreeBSD or TV-Station? How to create a GUID / UUID I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how &quot;random&quot; and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around.