SPWeb.getFile(Url) exception : value does not fall within the expected range still again
SPWeb.getFile(Url) exception : value does not fall within the expected range
I'm trying to prove : Given a simple graph $G$ with $n$ vertices, where $n$ is even, prove that if every vertex has degree $\dfrac n2 + 1$, then $G$ must contain a (simple) $3$-cycle. A (simple) $3$-cycle is a set of $3$ (distinct) vertices, $a, b, c$ such that $ab$ is an edge, $bc$ is an edge and $ac$ is an edge.  I know there are similar ones already on here, but I can't comprehend any of the answers. This is what I have so far:  Base Case: Since the graph has to have at least $3$ vertices to have a simple $3$-cycle, the lowest possible even number of vertices is $n = 4$.   $\dfrac42 + 1 = 3$ degree (edges attached to node). This means each vertex connects to each of the other $3$ vertices since $G$ is a simple graph. Thus, any combination of $3$ vertices will be a simple $3$-cycle.  Inductive Hypothesis: Assume a simple graph with $k$ vertices, where $k$ is even, contains a simple $3$-cycle if each vertex has degree $\dfrac k2 + 1$.  Inductive Step: Since only concerned about when the graph has an even number of vertices, going to show a simple graph with $k + 2$ vertices, where $k$ is even, contains a simple $3$-cycle if every vertex has degree $\dfrac{k+2}{2} + 1$   This is as far as I get and don't know how to finish the Inductive Step (Also please feel free to let me know if I messed anything up, up to this point) How to fix 'android.os.NetworkOnMainThreadException'? How to work the BibTeX? I have searched the tutorials but have not been successful in understand them. The tutorials always mensionam concepts that I do not know. I would like to understand the basics of BibTeX.  By basics I mean:   How do I install BiBTeX? How to build a file in bib? For this question assume that I already have the bibtex format each reference provided by databases like MathSciNet. See observation 1 below. What I write commands in the file format. Tex to call call the format file bib? How to exploit the format of the bibliography that comes out in PDF? The commands are made in the preamble of the file. Arquifo bib or format. Tex? What must be the BiBTeX with biblatex? Is there any tutorial (in pdf or video) that teaches step by step how to operate BiBTeX?   Observation 1 I already have the bibtex format each reference provided by databases like MathSciNet:   @article {MR2373353,  AUTHOR = {Avila, Artur and Lyubich, Mikhail},  TITLE = {Hausdorff dimension and conformal measures of {F}eigenbaum {J}ulia sets},  JOURNAL = {J. Amer. Math. Soc.},  FJOURNAL = {Journal of the American Mathematical Society},  VOLUME = {21},  YEAR = {2008}, NUMBER = {2},  PAGES = {305--363},  ISSN = {0894-0347},  MRCLASS = {37F35 (37F10 37F25)},  MRNUMBER = {2373353 (2009i:37112)},  MRREVIEWER = {Feliks Przytycki},  DOI = {10.1090/S0894-0347-07-00583-8},  URL = {http://dx.doi.org/10.1090/S0894-0347-07-00583-8}, } Labelling figures in the tikz package Consider the following piece of code, which uses the tikz-feynman package:  \usepackage{tikz-feynman, contour} \tikzfeynmanset{compat=1.1.0}  \begin{document} \begin{center}     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (c) -- [fermion] (b)                 -- [fermion] (d)                 -- [fermion] (a)                 -- (c),         };     \end{feynman}     \end{tikzpicture}     %     \feynmandiagram[baseline={(current bounding box.center)}, vertical'=a to b,] {         {   [edges={fermion}]             a -- b [label=0:\(\mu_{3}\)]             -- c [label=-180:\(\mu_{4}\)]             -- d [label=-180:\(\mu_{1}\)]             -- a [label=0:\(\mu_{2}\)],         },         {   [edges={photon}]             a -- ap [particle=\(p_{2}\)],             b -- bp [particle=\(p_{3}\)],             d -- dp [particle=\(p_{1}\)],             c -- cp [particle=\(p_{4}\)],         },     };     %     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (a) -- [anti fermion] (b)                 -- [anti fermion] (d)                 -- [anti fermion] (c)                 -- (a),         };     \end{feynman}     \end{tikzpicture}     \end{center} \end{document}   This piece of code draws the following figure:    I would like to label each figure. I do not want a caption, but just a label beneath each diagram. The label should say Diagram I, Diagram II, Diagram III.  How do I implement this into my code? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? Restart my graphics card without rebooting? Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem. Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$, with $f: (k_1,k_2)\to\Bbb R$ differentiable at $a\in (k_1,k_2)$, $\lim b_n=\lim a_n=a$, and $a_n&lt;a&lt;b_n$.   My attempt: Im trying to write the above equality as a particular case of this other equality that hold by any interior point $a$  $$f'(a)=\lim_{h\to 0}\frac{f(a+h)-f(a-h)}{2h}$$  Because $a_n&lt;a&lt;b_n$ then I can write  $$f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}=\lim_{n\to\infty}\frac{f(h_n+a)-f(a-j_n)}{h_n+j_n}$$  Where $h_n=b_n-a&gt;0$ and $j_n=a-a_n&gt;0$, where these two new sequences tends monotonically to zero.  Now my problem: my thought is that $h_n$ and $j_n$ are particular sequences then I can build a sequence $k_n$ such that $j_n$ and $h_n$ are subsequences so I can write:  $$\{h_n:n\in\Bbb N\}\subset\{k_n:n\in\Bbb N\}\text{ and }\{j_n:n\in\Bbb N\}\subset\{k_n:n\in\Bbb N\}$$  (I can build this $k_n$ by example doing $k_{2n}=h_n$ and $k_{2n-1}=j_n$) and then I have the desired expression  $$f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}=\lim_{n\to\infty}\frac{f(k_n+a)-f(a-k_n)}{2k_n}$$  My question:   Is this proof right? In particular Im unsure of the implicit statement "if the limit exist for $k_n$ then it must exist too for the particular case with $h_n$ and $j_n$". The use of two sequences, $h_n$ and $j_n$ in the limit make me unsure about the validity of this manipulation and assumption. There is a simpler/different way to prove the same?   Thank you in advance. How to remove local (untracked) files from the current Git working tree Dupehammer creates and deletes a comment, causing notifications to go out I am trying to create a 3d game in unity. I have a cube in unity and I want it to move left or right on swipe . It should move to a distance till where user swipe or take their finger off of a screen. I want it to move fast or the cube should move fast on swipe and cube should flow smooth. Like in the gif there is a circle and the user use their finger to move the circle till wherever the user swipe it and it should be instant and I want my cube to move like that at a distance till where user swipe their finger and it should be instant and fast.  I don't know how to do it. Any help is appreciated! Planet where humans fight for access to algae Set out on another planet where a human spaceship lands for a research and they observer a huge mass moving below them. On closer look this mass appears to be humans, and the density of the population increases towards the sea. The reason for this is algae,the only nutrition found on the planet. On a beach they discover tall, huge humans (developed due to the natural selection), controlling the best access to the algae. Eventually the researchers die, because humans eat them. Why can energy invested in RF radiation not be harvested fully? What are the main factors that affect this? Is there any significant research nowadays that fully describes this process? I stand on the conclusion: "Energy moves from one form to another.", but in this case why can it not be harvested in that quantity to use it for powering low-power devices or store it in significant quantities in some batteries for later use? Why is it not profitable nowadays and why is it not used today like energy from water, wind and other energy sources? I tried to install crossover and after downloading the .deb from their website, I followed the steps as indicated when opening it with Ubuntu Software Centre:     On 64-bit flavors of Debian and some Ubuntu variants, first open a   terminal and run sudo dpkg --add-architecture i386 ; sudo apt-get update   Since I have Ubuntu 16.04 LTS 64 bit I perform the command.  But when copying and pasting that command into my terminal, it stopped at Fetched 535kb in 7sec and stalled there for about 20 minutes. I ended up  closing it and tried to run both commands separately but after doing the sudo apt-get update command it also stalls again after "Fetched XXKb in XXsec."  I restarted my computer and decided to run the software updater and it stays stuck at roughly 75% for hours. Front facing camera stopped working on the iPhone 4s How can I program a simple chat bot AI? Cannot set up multiple desktops (workspaces) Unable to lock the administration directory (/var/lib/dpkg/), are you root? I get this error in Lubuntu 12.04 when I try to update in terminal:  $ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? I have 4GB RAM. When I open Firefox, IntelliJ IDEA or VS Code and some other application my memory is about used up thus my machine hangs and I can't do anything. I can't even close any applications.    Date and time are shown in the top bar so that I can view it any time without any thing typing.   If I would view memory status in this way without typing anything then I can make a decision whether to open an application or whether this application may put my machine in hanging state or not.    Is it possible in Ubuntu 18.04 LTS? How do you convert a C++ string to an int? Possible Duplicate:          How do you convert a C++ string to an int?  Assume you are expecting the string to have actual numbers in it ("1", "345", "38944", for example).  Also, let's assume you don't have boost, and you really want to do it the C++ way, not the crufty old C way.