Question:   Attempted Answer: Yes, for if $f = u + iv$ where $u$ and $v$ are real-valued functions, then we have that  $$ \int_a^b f(z)\ \overline{dz} = \overline{\int_a^b \overline{f(z)}\ dz} =\overline{ \int_a^b u(t)\ dt - i  v(t)\ dt} $$  so that  $$ \int_a^b f(z)\ \overline{dz} =\overline{ \int_a^b u(t)\ dt + i\int_a^b - v(t)\ dt} = \overline{ \int_a^b u(t)\ dt - i\int_a^b  v(t)\ dt} $$  and hence  $$ \int_a^b f(z)\ \overline{dz} = \int_a^b u(t)\ dt + i\int_a^b  v(t)\ dt = \int_a^b f(z)\ dz $$  Is my reasoning correct?  If so, wouldn't my answer extend to any line integral along a horizontal arc in the complex plane?  That is, if we lifted $[a,b]$ to the straight line from say $a+z$ to $b+z$ (for $z \in \mathbb{C}$), then wouldn't $\int_\gamma f(z)\ dz = \int_\gamma f(z)\ \overline{dz}$?
Definitionally, we have that  $$ \int_\gamma f\ \overline{dz} = \overline{\int_\gamma \overline{f}\ dz} $$  Now let $\int_\gamma f\ dz = w = x +yi$.  Question 1: Is it not the case that $\int_\gamma \overline{f}\ dz = \bar{w} = x - iy$?  Question 2:  Assuming that $\int_\gamma \overline{f}\ dz = \bar{w} = x - iy$, then is it not the case that  $$ \overline{\int_\gamma \overline{f}\ dz} = \overline{x - iy} = x+iy = \int_\gamma f\ dz? $$  Basically, I'm failing to see how $\overline{\int_\gamma \overline{f}\ dz}$ isn't just $\int_\gamma f\ dz$.
I have two large external drives with about 2.5 TB of data. About half the storage is images and videos that I want to put on a new NAS drive/device. I don’t want to carry over junk, duplicates and non photo/video files.   I am hoping Lightroom can help scour the mounds of folder structures on these drives and copy images/videos the new drive that I want to catalogue and keep clean as a working platform for all images and video. Once completed I plan to format the original drives and copy the cleaned-up content back to them as part of a backup strategy.  Can Lightroom help? If so, how? If not, is there some other application for Mac OS X that I can use for help with this? One problem I had with my original attempt is I wasn't sure how to move images and rename folders to get the new drive contents to make sense, so I formatted it and am looking to try again.  (steps for this operation would be helpful) titlesec: loss of section numbering with the new update (2016/03/15) After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15: Is it possible to skip releases during an upgrade? Possible Duplicate:          Is it possible to upgrade a 10.04 lucid installation to 11.04 Natty, without upgrading to 10.10 first? What about other versions? When reviewing Suggested Edits on Stack Overflow, I often come across "fixed formatting" suggestions that use  to place emphasis on certain keywords, but isn't actual code.  For example:     I am having a difficult time with a background task in iOS. The problem I seem to be facing is that iOS is silently terminating the App if my background task runs for too long. What can I do to increase time iOS will wait for my background task to complete?   Gets edited to:     I am having a difficult time with a background task in iOS. The problem I seem to be facing is that iOS is silently terminating the App if my background task runs for too long. What can I do to increase time iOS will wait for my background task to complete?   This seems like an invalid use of an inline code span because, well, it isn't code, and it is distracting. There are a    of these edits being made. Often enough they get approved, which reinforces the behavior.  Is this a valid use of inline code spans? If not, should it be edited and corrected? Should edits suggesting these changes be rejected? Is mass converted into energy in exothermic chemical/nuclear reactions?  My (A Level) knowledge of chemistry suggests that this isn't the case. In a simple burning reaction, e.g.   $$\mathrm{C + O_2 \to CO_2}$$  energy is released by the $\mathrm{C-O}$ bonds forming; the atoms lose potential energy when they pull themselves towards each other, in the same way that a falling object converts GPE to KE. There are the same number of protons, electrons etc. in both the reactants and products. I would have assumed that this reasoning extends to nuclear fission/fusion as well, but one physics textbook repeatedly references very small amounts of mass being converted into energy in nuclear reactions.  So I just wanted to know if I was wrong about either of these types of reactions, and if so, what mass is lost exactly? I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty principle holds for microscopic particles in motion. But what then is wrong to consider that all molecular motion ceases at absolute zero? In other words, does the uncertainty principle not hold when there is no motion?  Need some help! Does moving variable declaration outside of a loop actually increase performance? __NSArrayM insertObject:atIndex:]; object cannot be nil How to make child collide Multiple Inheritance #include&lt;iostream&gt; using namespace std;  class A  {    int a;    int b;    public:    void eat()    {       cout&lt;&lt;"A::eat()"&lt;&lt;endl;    } };  class B: public A {    public:    void eat()    {        cout&lt;&lt;"B::eat()"&lt;&lt;endl;     }  };  class C: public A {     public:    void eat()     {        cout&lt;&lt;"C::eat()"&lt;&lt;endl;     }  };  class D: public B, C {  };  int foo(A *ptr) {  ptr-&gt;eat();  } main() {  D obj; foo(&amp;(obj.B)); //error. How do i call with D's B part.  }   The above foo call is a compile time error.  I want to call foo with obj's B part without using virtual inheritance. How do i do that.   Also, in case of virtual inheritance, why the offset information need to be stored in the vtable. This can be determined at the compile time itself. In the above case, if we pass foo with D's object, at compile time only we can calculate the offset of D's A part. Probably dumb question, but I would like to ask it anyway.  I was to solve this equation:  $z^4 = -16$  At first glance, the way to solve it would be (as any other equation):  $z^2 = \sqrt{-1} * 4 \lor z^2 = -\sqrt{-1} * 4$  $z^2 = 4i \lor z^2 = -4i$  $z = 2\sqrt{i} \lor z = -2\sqrt{i} \lor z = 2i\sqrt{i} \lor z = -2i\sqrt{i}$  However, in suggested answers, there are $z_1, z_2, z_3$ and $z_4$ found using trigonometric formulas. Is there something particulary wrong in my solution and the only proper one uses trigonometric form of complex number? How do I turn on SharePoint App store in SharePoint 2013 I am getting this message when I want to add a app:     Sorry, apps are turned off. If you know who runs the server, tell them   to enable apps. How can I insert a newline in a framebox? How would one go about proving that the rationals are not the countable intersection of open sets? I'm trying to prove that the rationals are not the countable intersection of open sets, but I still can't understand why   $$\bigcap_{n \in \mathbf{N}} \left\{\left(q - \frac 1n, q + \frac 1n\right) : q \in \mathbf{Q}\right\}$$   isn't a counter-example. Any ideas? Thanks! When should a supervisor be an author? I'm loading an XML document in my C# application with the following:  XDocument xd1 = new XDocument(); xd1 = XDocument.Load(myfile);   but before that, I do test to make sure the file exists with:  File.Exists(myfile);   But... is there an (easy) way to test the file before the XDocument.Load() to make sure it's a valid XML file?  In other words, my user can accidentally click on a different file in the file browser and trying to load, say, a .php file causes an exception.    The only way I can think of is to load it into a StreamWriter and simple do a text search on the first few characters to make sure they say "  Thanks!  -Adeena Having trouble finding Plantera's Bulb I have been playing on hardmode for a while and have beaten the three  a couple of times. But I have yet to find a . It's getting really frustrating.  Does anyone have any methods to finding a Plantera Bulb? Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty$. Prove that $f$ is uniformly continuous.   Since $f(x)\to 0$ as $x\to \pm\infty$ we have $|f(x)|&lt;\epsilon $ whenever $x&lt;-K$ and $x&gt;K$ where $K&gt;0$.  Also $f$ is uniformly continuous on $[-K,K]$ as the domain is compact.  Hence $f$ is uniformly continuous in $(-\infty,-K)\cup [-K,K]\cup (K,\infty)$.  But how to conclude that $f$ is uniformly continuous on $\Bbb R$ from above as I may chose $x\in (-\infty,-K);y\in [-K,K]$ ,how to conclude that $|f(x)-f(y)|&lt;\epsilon $ from above for a given $\epsilon$?  Please suggest the edits required. shortcut key to detach a tab in firefox (move tab to new window) In FF, I can move a tab to a new window by either dragging the tab out of the browser, or right clicking the "move to New window" option from the context menu. is there a shortcut key to move the current tab to a new window without dragging or using the context menu, or a way to set one up?  Often, I like to look at 2 tabs side by side, so I drag one out, then hit WINDOWS KEY+→ to put the detached tab on the right, then ALT+TAB to tab back to the main window, then WINDOWS KEY+← to put the main window on the left. It would be great if I could do the whole process on the keyboard.  I checked  documentation and did not find any shortcut key for detaching a tab: Drawing automata for languages I'm trying to draw two automata for these two languages:   For the first one, I know that the minimum is n = 1, m = 1, but I'm having troubles drawing a NFA for it.  The second one the minimum is n = 2, m = 1, but I still don't know how to start the NFA.  I have this for q2: