I have been wondering why situation described in the picture below happens   Why does the water/milk or any liquid poured from the mug/bottle flow along the surface of the vessel instead of leaving it and falling.
If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess).
Failed upgrade from Ubuntu 19.10 to 20.04 "Please update the microcode" While installing the Ubuntu 20.04 updates during upgrade from 19.10 to 20.04, my screen suddenly went completely white and displayed a message saying  Please logout and try again.  But I could not locate my cursor and so I switched off my laptop. After restarting it again, it was showing an error message saying  Please update the microcode  Why did this happen? How can I solve this problem? Setup SunFire 440 Raid Configuration How can I setup Internal Hard disk RAID5 configuration? I have SunFire 440 machine with 4 internal hard disk. I have never worked on Sun systems except for now and I am exploring google for the above solution. If anyone could help me out. I want to refresh the entire service console on clicking of the save button on the visual force page. The button is an inline visual force page. Any ideas?  &lt;apex:includeScript value="/soap/ajax/26.0/connection.js"/&gt; &lt;apex:includeScript value="/support/console/26.0/integration.js"/&gt; &lt;script type="text/javascript"&gt; function focusAndSave() {     document.getElementById('focusMe').click(); }     &lt;/script&gt;     &lt;apex:form &gt;     &lt;apex:pageBlock id="pb"&gt;         &lt;apex:pageMessages id="errMsgsId"&gt;&lt;/apex:pageMessages&gt;         &lt;input type="text" id="focusMe" style="display:none" /&gt;         &lt;apex:pageBlockTable id="table" value="{!candidateMap}" var="c"&gt;             &lt;apex:column value="{!candidateMap[c].Contact__r.Name}"/&gt;             &lt;apex:column value="{!candidateMap[c].Submitted_at__c}"/&gt;             &lt;apex:column value="{!candidateMap[c].Interview_Availability__c}"/&gt;             &lt;apex:column value="{!candidateMap[c].Notice_Available__c}"/&gt;             &lt;apex:column headervalue="Stage"&gt;                 &lt;apex:outputfield value="{!candidateMap[c].Stage__c}"&gt;                     &lt;apex:inlineEditSupport event="ondblclick"/&gt;                 &lt;/apex:outputfield&gt;             &lt;/apex:column&gt;             &lt;apex:column headervalue="Ideally looking for"&gt;                 &lt;apex:outputfield value="{!candidateMap[c].Ideally_looking_for__c}"&gt;                     &lt;apex:inlineEditSupport event="ondblclick"/&gt;                 &lt;/apex:outputfield&gt;             &lt;/apex:column&gt;             &lt;apex:column headervalue="Action"&gt;                 &lt;apex:commandLink value="Save" action="{!saveCandidate}" rerender="errMsgsId,table" onclick="focusAndSave()" oncomplete="testGetFocusedPrimaryTabId()"&gt;                     &lt;apex:param name="candidateId" value="{!candidateMap[c].Id}" assignTo="{!candidateId}"/&gt;                 &lt;/apex:commandLink&gt;             &lt;/apex:column&gt;         &lt;/apex:pageBlockTable&gt;         &lt;apex:panelGrid columns="7" style="margin: 0 auto;"&gt;             &lt;apex:outputLabel value="{!noOfRecords} records found"&gt;&lt;/apex:outputLabel&gt;             &lt;apex:commandButton status="fetchStatus" reRender="pb" value="|&lt;" action="{!first}" disabled="{!!hasPrevious}" title="First Page"/&gt;             &lt;apex:commandButton status="fetchStatus" reRender="pb" value="&lt;" action="{!previous}" disabled="{!!hasPrevious}" title="Previous Page"/&gt;             &lt;apex:commandButton status="fetchStatus" reRender="pb" value="&gt;" action="{!next}" disabled="{!!hasNext}" title="Next Page"/&gt;             &lt;apex:commandButton status="fetchStatus" reRender="pb" value="&gt;|" action="{!last}" disabled="{!!hasNext}" title="Last Page"/&gt;             &lt;apex:outputLabel value="Page {!pageNumber} of {!pagecount}"&gt;&lt;/apex:outputLabel&gt;         &lt;/apex:panelGrid&gt;     &lt;/apex:pageBlock&gt; &lt;/apex:form&gt; What does the above Error mean? What is an installation candidate?  I was trying to do  sudo apt-get install munin-memcached     and I get this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Package munin-memcached is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package munin-memcached has no installation candidate   I googled for the problem and someone said to do a apt-get upgrade but it still did not solve my problem. $\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$ Let $a,b,c,x,y,z&gt;0$ and $x+ y+ z= 1$. Show that $$ax+ by+ cz\geq  a^{x}.b^{y}.c^{z}$$ I have found the generalization of this inequality: For 2 sets of numbers $\left \{ a_{i} \right \}, \left \{ b_{i} \right \}&gt; 0$ and $\sum_{1}^{n}b_{i}= 1$, we have: $$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq  \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$$ First solution Simply compare the logs: as the natural logarithm is a concave function, one has $$\ln\bigl(a^x b^y c^z)=x\ln a+y\ln b+z\ln c\le \ln(ax+by+cz)$$ for all non-negative $x,y,z$ such that $x+y+z=1$. How about another solution? I really hope to see that. Thanks! Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$ (Euclidean Norm)  Proof that $\|X\|_2\leq \sqrt{n}\|X\|_\infty$, if $x \in \mathbb{R^n}$.   With that, proof $\|X\|_\infty \to 0 \implies \|X\|_2\to 0$  I'm stuck:  $\|X\|_2= \sqrt{x^2_1+x^2_2+...+x^2_n}\leq\sqrt{n}\sqrt{x^2_1+x^2_2+...+x^2_n}$  I don't know how to use the fact: $\|X\|_\infty=\max(|x_1|,|x_2|,...,|x_n|)$ How to set shell to wrap words for long commands? Calling a method in java and returning beer cost Why don’t I have the Get Windows 10 icon? I want to get Windows 10, but I do not see this icon in the notification area (tray):    How do I get the icon to get Windows 10? Split a string by spaces -- preserving quoted substrings -- in Python I think I accidentally pressed something to make it like this:    See how the XYZ arrows are at the 3D cursor instead of those vertexes I've selected?  How do I fix that? Whenever I select on a vertex or something, those blue, red, green arrows would always be where I selected, now it just keeps going to the 3D cursor. Is there a modal command for MakeLowercase? Analog to  question I've been wondering WHAT is to \lowercase as \bfseries is to \textbf? (... and for uppercase, or \MakeLowercase and MakeUppercase, etc., which also seem to be text-block commands as explained .)  Is there a "switch"/"declaration"/"modal command" (what is the correct term here?, is there a difference between them?) that would allow one to turn something into lowercase/uppercase in the same way that one would use \scshape for example, i.e., not as text-block command with the curly braces?  Or how to create such a command?  I couldn't find any clue on the forum. Compound Adjectives and -ed A colleague asked me this question, and I couldn't come up with an answer that satisfied him, so I'm wondering if anyone can help:  Why does a man with a short temper become a short-tempered man? In other words, why do you need the -ed at the end?  Are there any special rules for this? As mentioned on :     For something that can be done so   easily by accident, there should be   the ability to undo mistakes.   I know that I have clicked several times on a comment up-vote without actually wanting to.  I would suggest being able to cancel the up-vote (maybe only for a couple of minutes or even less than a minute, no problem, as long as I can undo a miss-click). Kolmogorov's sufficient and necessary condition for SLLN - What about pairwise uncorrelated RV? Kolmogorov proved, that, as one considers independent (not necessary equally distributed) Random Variables: $\{X_n\}_{n\ge0}\subseteq \mathcal L^2$   With $\mathrm{Var} (X_n)=\sigma^2_n$ and without loss of generality $E[X_n]=0$.  If $\sum_{n=0}^\infty \frac{\sigma^2_n}{n^2} \lt \infty$ then SLLN holds, that is:  $$\frac1n\sum_{k=0}^n X_k \rightarrow 0 \,\,\,\,\,\,\,\,\,\,\,\,\,\text{a.s.}$$  Something different:  Also it is known, that if $\sup_{n\ge0}\sigma^2_n =: v \lt \infty$ pairwise uncorrelated $(X_n)_{n\ge0}$ will suffice for SLLN to hold.  My question in view of this situation: Is it possible to weaken the condition of $(X_n)_{n\ge0}$ beeing independent and instead merely consider pairwise uncorrelated $(X_n)_{n\ge0}$? How does HOTP keep in sync? MySQL: Allow both remote AND local connections Why does Type I error always occur in a NHST? Or, is NHST too weak to tell the truth? Recently I have noticed that Type I error of a test is too much persistent. Even if all the values are almost equal (variance is extremely low) and tested to that value (true mean), still there is nearly 5% Type I error of the test. I am frightened and curious to rethink, are the people who have banned (or skeptic about) NHST (null hypothesis significance testing) truly correct? Let's have a look at the following r code:       n=10000 t1err=0 set.seed(1235) for (i in 1:n){    x=rnorm(100, 10, 20)    if (((t.test(x, mu=10))$p.value)&lt;=0.05) (t1err=t1err+1)  } cat("Type I error rate in percentage is", (t1err/n)*100,"%")   It will produce roughly 5% as Type I error. Seems ok. But let's see this:      n=10000   t1err=0   set.seed(1235)   for (i in 1:n){      x=rnorm(100, 10, 0.000001)      if (((t.test(x, mu=10))$p.value)&lt;=0.05) (t1err=t1err+1)    }   cat("Type I error rate in percentage is", (t1err/n)*100,"%")   Each values are extremely close to 10. Still it produces about 5% Type I error. What conclusion we may draw from it? Or, am I missing something? Let $V=\{f : S \to \mathbb{R} \}$ be the set of all the functions $f : S \to \mathbb{R}$. Let $S=\{ 1,2,...,n$}, now my train of thought was that the basis of V must be a linearly independent set that Span V so somehow show that there is a set of functions on S that can compose as a linear combination and map to any number in $\mathbb{R}$. Any idea how to get a general answer for basis for dimension of V? "There Is"/"There are" depends on plurality of the first list element or not? It seems I put a   Bounty assigned by outside party, two lengthy, reference-citing answers, one "-1" (awarded the bounty), one "-2", two others scored "0" and "-2" respectively, the answers suggesting one or the other is correct, 73 comments and no consensus so far - and me, as the asker, lost without a clue what to think of the answers anymore -  this is no longer "Learners' Level" question, so I thought I'd bring it here and hear what the experts have to say.    Original question:  Plurality of verb depending on plurality of list elements  An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that - was my editor overzealous or am I trying to copy rules of my language that don't apply in English?    Someone linked a  for negatives, where the situation is more clear-cut ("There is no..."). Same applies to connection with "or" apparently, per accepted answer there. Still, nothing for "and".  It seems there is a consensus that in that if the verb goes after the list, it will be plural.     an orange, some grapes, two apples and a small pile of cherries were on the plate.   There doesn't seem to be clear consensus for:     On the plate { was | were } an orange, some grapes, two apples and a small pile of cherries   Adding more to the confusion is the abbreviated form: "There's"     One last note. In North America, at least, there is a widespread use of using a singular form like "there is" and "there was", without regard for the subject item or items, and this "there is" is often shortened to "there's":           There's three apples on the table!      Could you please clarify this mess?