Is there a way to retrieve the oldMap of a trigger in a future method?
@future method: Unsupported parameter type
How do I simplify: $$\sum_{r = 0}^{\lfloor \frac{k}{2} \rfloor} \dbinom{k}{2r} \cdot \dbinom{n-k}{k-2r}?$$ Basically, the sum is: $\dbinom{k}{0} \cdot \dbinom{n-k}{k} + \dbinom{k}{2} \cdot \dbinom{n-k}{k-2} + \dbinom{k}{4} \cdot \dbinom{n-k}{k-4} \cdots.$ This seems very similar to Vandermonde's Identity but because we skip two everytime instead of one, I don't see how I can apply it to this problem. In Windows 7, How to query times, when the computer was locked? Is there a way to get a list of the following times:  whenever windows is locked (using windows+l combo)  whenever windows is unlocked in the past week?   I've tried poking in the event log, to no avail. Many thanks! Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$. Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.   How to prove? I really have no idea... Thank you a lot. how does systemd determine service is stopped? What is `$?` ? Is it a variable? The question is pretty straight forward. I can get the exit code of the previous command by using $?. But what exactly is it?  I don't think it is a variable, because you can't have any special characters in the name of variable other than _.  foo?foo=10   will result in the error: foo?foo=10: command not found  So if it is not a variable, what is it? Are there others like it? How do you read CSS rule values with JavaScript? I would like to return a string with all of the contents of a CSS rule, like the format you'd see in an inline style. I'd like to be able to do this without knowing what is contained in a particular rule, so I can't just pull them out by style name (like .style.width etc.)   The CSS:  .test {     width:80px;     height:50px;     background-color:#808080; }   The code so far:  function getStyle(className) {     var classes = document.styleSheets[0].rules || document.styleSheets[0].cssRules     for(var x=0;x&lt;classes.length;x++) {         if(classes[x].selectorText==className) {             //this is where I can collect the style information, but how?         }     } } getStyle('.test') Suppose $f$ and $g$ are Lebesgue measurable, we want to show $f+g$ is measurable. So, the hint is to consider the continuous functions $F : \mathbb{R}^2 \to \mathbb{R} $ given by $h(x) = F(f ,g ) $. If we can show $F$ Is measurable, then Taking $F = f +g $ would solve our problem.  In other words, I want to show that the set $R = \{ (f,g) : F(f,g) &gt; a $ } is lebesgue measurable.. But this set is just a rectangle in the plane. And since $F$ is continuous, then $R$ must be open, and hence a union of open rectangles which are measurable and hence $R$ must be measurable. Is this a correct approach to the problem? Can someone help me to make this formal? thanks Usage of italics in writing Check variable equality against a list of values How do I limit the running time of a BASH script I have a long running BASH script that I am running under CYGWIN on Windows.  I would like to limit the script to run for 30 seconds, and automatically terminate if it exceeds this limit. Ideally, I'd like to be able to do this to any command.  For example:  sh-3.2$ limittime -t 30 'myscript.sh'   or   sh-3.2$ limittime -t 30 'grep func *.c'   Under cygwin the ulimit command doesn't seem to work.   I am open to any ideas. Does the OP of a flagged post get comment notifications if the post is deleted by mods? Nested sequences of balls in a Banach space This seems to be a fairly easy question but I'm looking for new points of view on it and was wondering if anyone might be able to help.  (By the way- this question does come from home-work, but I've already solved and handed it, and I'm posting this out of interest, so no HW tag.)     Let $B_n=B(x_n,r_n)$ be a sequence of nested closed balls in a Banach space $X$. Prove that $\bigcap_{n=1}^\infty B_n\neq\varnothing$.   As I said before, it should be rather simple. When the radii decrease to 0, it's just a matter of selecting any sequence of points in $B_n$, and it must be Cauchy- and the limit is in the intersection.  My question is what to do when the radii do not decrease to 0? I got some tips about multiplying the balls by a sequence of decreasing scalars, or reducing the radii so that they decrease to 0, but found too many pathological cases for both methods.  Finally- I used a geometric arguemnt (which i've shown to work in any normed space) that if $B(x_1,r_1)\subset B(x_2,r_2)$ then $\| x_1-x_2\|\leq|r_1-r_2|$. This turned out to be some kind of technical catastrophe, but it worked...  Still, if anyone knows of a more elegant solution, I'd love to hear about it. Assumed True until proven False. The Curious Case of the Vacuous Truth Given two statements, $P$ and $Q$, and the logical connective, $\implies$, the truth table for $P \implies Q$ is:  $$\begin{array}{ c | c || c | }   P &amp; Q &amp; P\Rightarrow Q \\ \hline   \text T &amp; \text T &amp; \text T \\   \text T &amp; \text F &amp; \text F \\   \text F &amp; \text T &amp; \text T \\   \text F &amp; \text F &amp; \text T  \end{array}$$  Lines one and two are quite clear. What is ambiguous is lines three and four.  One explanation as to why $P \implies Q$ is true when $P$ is false, provided by Velleman goes:     Let $P(x)$ be the statement $x&gt;2$ and $Q(x)$, $x^2 &gt; 4$. When $x=3$, $P$ is true, and $Q(x) = 9$ thus $Q$ is true. If $P(x) = 1$ then $Q(x) = 1$ and they are both false. If $P(x) = -3$ then $Q(x) = 9$ and so the statement is true.   This explanation was quite unsatisfactory to me. Looking at Enderton, we have:     For example, we might translate the English sentence, ”If you're telling the truth then I'm a monkey's uncle,” by the formula ($V \implies M$). We assign this formula the value $T$ whenever you are fibbing. In assigning the value $T$, we are certainly not assigning any causal connection between your veracity and any simian features of my nephews or nieces. The sentence in question is a conditional statement. It makes an assertion about my relatives provided a certain condition — that you are telling the truth — is met. Whenever that condition fails, the statement is vacuously true.      Very roughly, we can think of a conditional formula ($p\implies q$) as expressing a promise that if a certain condition is met (viz., that $p$ is true), then q is true. If the condition $p$ turns out not to be met, then the promise stands unbroken, regardless of $q$.   Though a significant improvement over the Velleman explanation, I still feel uncomfortable with it.  Really, it seems we can conjure up as many silly counter-examples as we like, such as:     If pigs can fly, then I can walk on water.   Though following the above truth table, the implication is that my ability to walk on water is true.  After considering it, it seems to me that $\implies$ is only meaningful when $P$ is true, then we can look at it in relation to $Q$. However, if $P$ is false, then we actually know nothing about the relationship between $P$ and $Q$. This would give a truth table of:  $$\begin{array}{ c | c || c | }   P &amp; Q &amp; P\Rightarrow Q \\ \hline   \text T &amp; \text T &amp; \text T \\   \text T &amp; \text F &amp; \text F \\   \text F &amp; \text T &amp; \text ? \\   \text F &amp; \text F &amp; \text ?  \end{array}$$  where the $?$ denotes that given $P$ we actually don't know anything about $ \implies $.  Thus. one way to clear this up would be to assume that $? = T$. Thus the vacuous truth is a "definition of convenience" in a sense.  The above is my take on the matter.  Could someone provide some clarification on the conditional logical connective? Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved. How to get scroll position from GridView? Is any explanation offered for "hyper-sleep"? In Big Hero Six,      Callahan's daughter was found to be alive in the space between portals in what Baymax describes as "hyper-sleep".   I don't believe the movie offers any further explanation for this, or why Hiro isn't affected.  Are there any other sources that explain this? Negative probabilities in quantum physics This is a  about Fighting Spam.   Also related:                    There are so many techniques and so much to know about fighting SPAM. What widely used techniques and technologies are available to Administrator, Domain Owners, and End Users to help keep the junk out of our inboxes?  We're looking for an answer that covers different tech from various angles. The accepted answer should include a variety of technologies (eg SPF/SenderID, DomainKeys/DKIM, Graylisting, DNS RBLs, Reputation Services, Filtering Software [SpamAssassin, etc]); best practices (eg mail on Port 25 should never be allowed to relay, Port 587 should be used; etc), terminology (eg, Open Relay, Backscatter, MSA/MTA/MUA, Spam/Ham), and possibly other techniques. quick selection of a random row from a large table in mysql What causes a black-body radiation curve to be continuous? The  (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies.  Many objects approximate ideal blackbodies and have radiation curves very similar in shape and continuity to that of an ideal black-body (often minus some emission and absorption lines from the atoms in an object, such as radiation curves seen from stars).  I am wondering what exactly gives rise to a basically continuous black-body radiation curve in real objects? Since atomic energy states are quantized, it seems real life black-body curves would have some degree of measurable quantization to them (or perhaps the degree of quantization is so small the radiation curves look continuous).