Consider this example: \documentclass{article} \begin{document} \tableofcontents  \section*{Change log}  \section{Section1}  \section{Section2}  \end{document}  The result is:  I added * to \section to remove the section number. However, I would like this section to be included in TOC. How to fix?
If I did  \setcounter{chapter}{-1} \chapter{Introduction}   then I get Chapter 0 Introduction. I just want the word Introduction, and I want it also in the contents when I use   \tableofcontents   How can I do that?
Parameterize an SQL IN clause How do I parameterize a query containing an IN clause with a variable number of arguments, like this one?  SELECT * FROM Tags  WHERE Name IN ('ruby','rails','scruffy','rubyonrails') ORDER BY Count DESC   In this query, the number of arguments could be anywhere from 1 to 5.  I would prefer not to use a dedicated stored procedure for this (or XML), but if there is some elegant way specific to , I am open to that. still frame camera solve I've found a number of how-tos for solving video but I'm just looking to put an element in a photo and can't seem to find a how-to for that.  Is it possible in blender to do a camera solve with a still image?  Thanks. $G$ is the set of all subsets of a set $A$, under the operation of $\triangle\;$: Symmetric Difference of sets.  $A$ has at least two different elements.  I need to check if this is a group, and if it does to show if the group is abelian and/or finite.  Associativity - easy from Symmetric Difference. Identity element - empty group. Inverse element - each element is inverse to itself. Am I right?  abelian? finite? Difference between "git add -A" and "git add ." The command git add [--all|-A] appears to be identical to git add .. Is this correct? If not, how do they differ? Geocoding USA addresses that cannot be sent over internet? For a one-time project, I need to geocode a few thousand addresses.  In the past I've used various online resources for this kind of thing (e.g., Google Maps API), but the addresses I'm working with have to be kept confidential - which means no sending it over the Internet, unless there's some iron-clad guarantee of privacy.  What other options do I have? 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; Roots of polynomials in field of prime characteristic p Let $F$ be a field of characteristic $p$, and let $\alpha \in F$. Let $f \in \mathbb{Z}_p[x]$ be such that $f(\alpha) = 0$. Apparently, we have $f(\alpha^p) = 0$. This was mentioned but not proved in my lectures. Can someone explain why please?  Thanks. What does "rigorous proof" mean? I have heard several times that some mathematician has given another and more rigorous for an established theorem, but I don't know what does it really mean and what differences makes it to be more 'rigorous'. My understanding of a proof is that a proof is some explanation to convincing others that a statement is true. If some proof is not rigorous, does it mean that while the proof is acceptable for many but it is not for everybody? If so, the proof is not correct since it going to be rejected by some people and it is not a proof at all. Or, does rigorous mean it uses more advanced tools? If so, why not any alternative (but simpler) proof is also acceptable as rigorous (which is more 'valuable' as well since it's simpler!)?   Saying those limited insight of mine, my questions are:   $1-$ What does rigorous proof mean, in general definition?  $2-$ In order to understand your answers, as an example I am re-writing three of the proofs for the compactness of the torus. Which of the following proofs are most rigorous, 'normal' and least rigorous; and why so?    Theorem: The torus $T^2$ is compact.  First proof: The torus is homeomorphic to the product space $S^1 \times S^1$. The circle $S^1$ is compact. Therefore the torus is the product of two compact spaces, and thus it is compact.   Second proof: The torus $T$ is the subspace of $\mathbb{R}^3$ obtained by rotating a circle about the $z$-axis. The torus is closed since given any point in its complement, there is an open ball of sufficiently small radius centered at that point and disjoint from the torus. Also, the torus is bounded since it is contained in the ball of radius $4$ centered at the origin. Since the torus is closed and bounded in $\mathbb{R}^3$, it is compact.   Third proof: The torus is homeomorphic to a space obtained as a quotient  space of the square by identifying opposite edges. The square is a closed and  bounded subset of $\mathbb{R}^3$ and therefore is compact. Furthermore, a quotient map on the square is a continuous function, and the image of a compact space under a continuous function is compact. Therefore the torus is compact.   Thanks a lot for your guidance. MacBook Pro stuck in gray screen when booting I've got a Late-2011 15" MacBook Pro stuck in the gray screen when booting AFTER login. I've tried removing the drive (it's non-retina) and booting from a working bootable Yosemite installer, no luck. (it sees the startup USB drive, the progress bar progresses, but stuck at the gray screen again even without a drive.  Tried NVRAM reset (cmd option P R), it has reset (the login sound's volume changed) but nothing changed.  Tried holding D on startup, AHT doesn't start, instead, it tries to boot into the OS.  Tried Cmd V, it sometimes works and displays the verbose output, sometimes, it acts like I haven't even pressed. Again, stuck after login.  Tried booting again from USB, I select USB (after seeing both drives correctly), but no luck, it's also stuck.  I've stumbled upon this:    I've tried booting into single user mode with Cmd S, it worked ONCE, I've disabled the graphics extensions just as shown at that post, restarted, but again, nothing changed.  More weirdly, now the Cmd S doesn't work either. It just takes me to login screen without showing the terminal, just as I haven't pressed anything.  Why would this happen? Why would a Mac refuse to enter hardware test mode, single user mode, or refuse to boot from a working bootable Yosemite drive both with or without the main drive installed?  UPDATE: I've run the AHT and got an error:  4MEM/66/40000000: 0x84e0ec98  It looks like a memory issue, but I'm not sure.   UPDATE 2: I've tried reinserting the RAMs and the the problem is not reported anymore. However, the Mac still won't boot. When I get a third party app it says it needs to be verified before I can use it but when I go to settings to verify I tap verify and nothing happens. Is there something I can do so I don’t have to constantly reinstall my apps? Is clockwise or counter-clockwise rotated text easier to read? When rotating text with css, should it be rotated clockwise or counter-clockwise?  Is one more readable than the other?  Counter Clockwise:   &nbsp;&nbsp;&nbsp;&nbsp;&mdash;&nbsp;&nbsp;&nbsp; Clockwise: What makes the inside of a shape the inside? Scala final vs val for concurrency visibility Showing equality of sequence of holomorphic functions to limit function if converges uniformly locally I do not know how to proof following question:  Let $D$ be a domain in $C$.  ${{f}_{n}}$ be a sequence of holomorphic functions on $D$ that converges uniformly locally to a function non-constant $f$. Show that for each $z\in D$, there is a sequence ${{z}_{n}}\to z$ as ${{f}_{n}}({{z}_{n}})=f(z)$ for all sufficiently large $n$.  Actually, I know that I should use an assumption such as: ${{f}_{n}}({{z}_{n}})\ne f(z)$  Therefore, there is compact set    that  $\left\| {{f}_{{{n}_{k}}}}({{z}_{{{n}_{k}}}})-f(z) \right\|&gt;\varepsilon $  Then I think I have to use Montel theorem, but I do not know how to show the contradiction. Increase partition size on which Ubuntu is installed? I have Ubuntu installed on a drive. The problem is it is running low on disk space. This is installed on vmware. I expanded the virtual drive and booted into ubuntu. But when I opened gparted(sudo gparted), the move/resize option is unavailable. This is the partition Ubuntu is installed on, but I need to resize it. Any ideas? I am comfortable using command line Prove that $g$ is tangent to the graph of $f$ So I had these two functions and the following exercise:  $f(x)=x^3-2x^2$ $g_p(x)=px$ Prove that $g_{-1}$ is a tangent line to the graph of $f$. How many points do $g_{-1}$ and $f(x)$ have in common?  So yeah, the points in common are fairly simple to figure out:  Points in common: $x=1$ and $x=0$  So to see if it's actually tangent to the graph, I took the derivative of both functions at the points where they meet. The result:  $f'(x)=3x^2-4x$ $g'_{-1}(x)=-1$  So $f'(1)=-1$ and $f'(0)=0$ So I'm not sure why I get this answer? By the question, we are supposed to prove that its tangent to the graph of $f$ but by my calculation, it seems like only $f(1)$ is tangent with $g_{-1}(1)$. Help is appreciated! (Please avoid hint answers). How is Leibniz's rule for the derivative of a product related to the binomial formula? Possible Duplicate:          The  describes the expansion of the $n$th power of the sum $(a+b)$:  $$(a+b)^n = \sum_{k = 0}^n {n\choose k}a^kb^{n-k}$$  In calculus, there is a generalization of the product rule called , which describes the expansion of the $n$th derivative of the product of two functions $f$ and $g$:  $$(fg)^{(n)} = \sum_{k = 0}^n {n\choose k}f^{(k)}g^{(n-k)}$$  It's not difficult to prove using the product rule and induction, what I'm really trying understand here is why the formula is true. Is there a way to prove it using the binomial formula? How are these two formulas related? Is there a combinatorial proof for Leibniz's rule like there is for the ?   I understand this question is a bit vague, but I hope you'll agree that these two formulas look so similar it just feels like there should be some relation between the two. Of course this is not necessarily true, but I'm hoping it's not just a crazy coincidence. I read this story a long time ago and cannot remember either the title or the author. It was written in the 60s or 70s. The setting is sometime in the 21 century.  Here is a summary of the plot.  One of the great classical composers (maybe it was Schubert, I'm not sure) is revived with some future technology. All the guys in the lab are very happy about it, the world cheers the achievement. The composer is also quite excited to be alive. Naturally, he is asked to perform a concert. He asks for ink and music paper. Nobody knows what that is: in those days everybody writes music directly in "frequency spectrum" and similar stuff.  The composer, excited to create music again, tries to come up with something but he doesn't like anything he writes. The music is well written, but lacks something essential, it doesn't sound like his real music. Finally, the composer realizes that the lab guys recreated his mind from reviews by music critics, and his music just sounds like that. He performs the concert. The audience enjoys it, applauds and bravos. Not only to composer, but also to the lab guys.   At the end, if I remember it right, the composer gloats over the  primitive taste of the audience. The audience who writes music in frequency spectrum and applauds to lab guys at the music concert did not see the failure in the concert and ate it as it is.  Does someone recognize the story?  PS all the recent talk of advent of AI machines with Machine Learning algorithms reminded me of this story. Proof a $2^n$ by $2^n$ board can be filled using L shaped trominoes and 1 monomino Ubuntu 18.10: visual artifacts (black bar) in dock if extend-height is disabled I am using the default Ubuntu dock with bottom placement and org.gnome.shell.extensions.dash-to-dock extend-height set to false. With Ubuntu 18.10 this produces a noticeable visual glitch, note the black empty spaces at the edges of the dock:    I am getting this both on an upgraded system and on a clean install inside a VM. This was working fine in Ubuntu 18.04. Also happens if the theme is set to something else than Yaru (the default theme in Ubuntu 18.10). Reboot does not help. Dock looks OK if extend-height is enabled.  Any ideas on how to fix this?