After coming back from his duel with Voldemort, Harry was scorned at by Cornelius Fudge. There are 2 questions here:    I'm talking about Barty Crouch Jr.'s confession in point 1   Why didn't Harry, Snape, McGonagall or Dumbledore extract their memory of the event? I know memories can be tampered with, so that Fudge might have used that as an excuse if one of the 4 mentioned extracted it, but 4 separate, identical memories would be much harder to tamper with and keep identical, wouldn't they? Especially as Harry probably has no idea on how to tamper with memories. Why didn't Harry extract the memory of what happened at the Graveyard with Voldemort? It would give Dumbledore much more insight and knowledge into what happened, instead of going off of Harry's account of it? I don't think the magic to extract a memory would have been hard either, seeing all the difficult magic Harry has done previously.
Why didn't Dumbledore show his memory of Barty Crouch Jr's confession to Cornelius Fudge to confirm his point that Voldemort returned? Wouldn't that just prevent all the mumbo-jumbo happening in the 5th book?
cron job schedule Maclaurin series of $\ln(1-x+x^2)$ Is there a closed form expression for $\text{n}^{\text{th}}$ coefficient of Maclaurin series of  $$\ln(1-x+x^2)$$ Guinier regime for form factor Why is it such a good idea to plot the logarithm of the form factor vs $Q^2$ in . It seems arbitrary to me. Coordinate system for accurately calculating areas of polygons that cross UTM Zones? I have multiple polygons, all located offshore around the UK. I am trying to calculate the areas of these polygons in square kilometres, without splitting them by UTM zone.  Is it possible to do this accurately? I have been using World Mercator, but there are big distortions at this scale. If the polygons were limited to the east coast, say, I would use UTM31N. However, as they are all over the UK waters, I am unsure what to use.  Is there a coordinate system that covers this area? British National Grid does not extend far enough out to sea to be of use. $\forall$ At the beginning or at the end? I have a set of real numbers $x_1, x_2, \ldots, x_n$ and two functions $f:\mathbb{R} \rightarrow \mathbb{R}$ and $g:\mathbb{R} \rightarrow \mathbb{R}$.  What are the differences between the following statements?   $\forall v \in \{1, \ldots, n\} ~f(x_v) = 0 \vee g(x_v) = 0$ $f(x_v) = 0 \vee g(x_v) = 0 ~\forall v \in \{1, \ldots, n\} ~$ XCOPY still asking (F = file, D = directory) confirmation I tried to create a Windows 10 USB boot medium with WoeUSB. I formatted a USB drive with an NTFS partition, but WoeUSB complains with:  Installation failed! Exit code: 256 Log: WoeUSB v@@WOEUSB_VERSION@@ ============================== Mounting source filesystem... Error: File "/media/woeusb_source_1543626298_6098/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed.  You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1543626298_6098"... You may now safely detach the target device   I've also tried to start WoeUSB via command line, did not work.  sudo woeusb --partition Win10_1809Oct_English_x64.iso /dev/sdb   My iso is located in:     home/sawyer/Downloads/Win10_1809Oct_English_x64.iso  Thanks in advance! I've been trying to get windows installed for three nights now, so any help towards that goal is greatly appreciated. Triangular Numbers Modulo $k$ - Hit All Values? Any difference between "Good morning, Brian" and "Good morning to you, Brian" I often hear it on TV when they are talking to a guest.  Normally, if we want to greet Brian in morning, we would say "Good Morning Brian". But many times TV presenters say "Good morning to you Brian".  Why is that? Why do they add "to you". There seems to be no need to do it.  Regards, "strlen(s1) - strlen(s2)" is never less than zero Isomorphism $H_n(D^n, S^{n - 1};A)$ and $A$ The homomorphism $a \mapsto [[a \cdot f]]$ is supposed to be an isomorphism between $A$ and $H_n(D^n, S^{n - 1};A)$ for any homeomorphism $f: \Delta^n \to D^n$. I have proven that it is well defined and injective, but why is it surjective?  The group $H_n(D^n, S^{n - 1};A)$ is generated by elements of the form $a \cdot \sigma + b \cdot \tau + c \cdot \partial(\kappa)$ where $\sigma: \Delta^n \to D^n$, $\tau: \Delta^n \to S^{n - 1}$ and $\kappa: \Delta^{n + 1} \to D^{n + 1}$ and I do not see how an element of this form represents the same equivalence class of $[[m \cdot f]]$ for some $m \in A$. We can write $\sigma$ as $f f^{-1} \sigma$ to get $f$ in there, but I don't see that working out. Any hints? What is the best way to save values (like strings) for later use? I'm fairly new to LaTeX and I'm struggling with something apparently simple, but for which I can't find a fair solution. The problem (simplified) is as follows (please take care terms used may not have the traditional meaning in LaTeX):  I need to references to files (many) throughout a text. As example, the files:  "C:/Work/this_file1.c", "C:/MoreWork/this_file1.c" and "D:/MoreWork/another_file2.h".  So, now I would like to create an "alias" to each directory and each name file so I can reference them. A "pseudocode" could be:  % Definition \alias \c_dir = C:/Work/ \alias \d_dir = D:/MoreWork/ \alias \file1 = this_file1.c \alias \file2 = another_file2.h  % Reference in text \c_dir\file1    % For referencing C:/Work/this_file1.c \d_dir\file1    % For referencing D:/MoreWork/this_file1.c \c_dir\file2    % For referencing C:/Work/another_file2.h   My first approach was using \newcommand, but that caused numerous problems due to naming limitations. (I also tried other methods like pgfkeys, but it always gets stuck somewhere!)  Can you suggest a method? Add Virtualbox Shortcut in Unity Launcher to boot to a VM Can I create a shortcut to a virtualbox OS in the unity sidebar without it being on the desktop too.  I tried to right click in virtualbox and create shortcut on desktop then move it. but if i do it then delete the desktop shortcut it renders the unity shortcut useless.  Any ideas? Suppose $G$ is a semigroup and it holds both left and right cancellation. Suppose $G$ is a semigroup and it holds both left and right cancellation. Also for each $a,b\in G$, $xa=b$ has solution in $G$. Prove G is a group.   I know this question looks very "old" style. First I think it's easy for me too since I already practice probelems like "semigroup, $xa=b$ and $ax=b$ have solution , then group" Or "finite semigroup, both left and right cancellation hold, then group ". But I still get stuck... My try:  First of course, for $xa=a$ , there exists $e_a$ such that $e_aa=a$. Now we need to proof $e_a$ is left identity for all elements. Then left inverse exists hence $G$ is a group. But the key is to proof $e_ab=b$ for all $b\in G$. This question has an inverse:     What would be the most efficient way to translate a combination of $k$-tuple into its positions within the $\left(\!\!\binom{n}{k}\!\!\right)$ combinations? I need this to be fast for combinations of $\left(\!\!\binom{70}{7}\!\!\right)$ order of magnitude - very large, but not exceeding 2 billion (fits into int32 maximum value).  Below is an example of $\left(\!\!\binom{6}{3}\!\!\right)$, where the aim is to quickly translate (a, d, f) tuple to value 9, while in the real problem $k$ ranges between 5 and 8.  $$\begin{array} {cccccc|c} a&amp;b&amp;c&amp;d&amp;e&amp;f&amp;^{combination}/_{sort\_order}&amp; \\\hline x&amp;x&amp;x&amp; &amp; &amp; &amp;1\\ x&amp;x&amp; &amp;x&amp; &amp; &amp;2\\ x&amp;x&amp; &amp; &amp;x&amp; &amp;3\\ x&amp;x&amp; &amp; &amp; &amp;x&amp;4\\ x&amp; &amp;x&amp;x&amp; &amp; &amp;5\\ x&amp; &amp;x&amp; &amp;x&amp; &amp;6\\ x&amp; &amp;x&amp; &amp; &amp;x&amp;7\\ x&amp; &amp; &amp;x&amp;x&amp; &amp;8\\ x&amp; &amp; &amp;x&amp; &amp;x&amp;9\\ x&amp; &amp; &amp; &amp;x&amp;x&amp;10\\ .&amp;.&amp;.&amp;.&amp;.&amp;.&amp;.\\  &amp; &amp; &amp;x&amp;x&amp;x&amp;20\\ \end{array}$$  I know that I could pre-calculate all the combinations and reverse the lookup dictionary. However, such dictionary would not be efficient in terms of memory usage. Therefore I am looking for either calculation-based approach, or a more efficient data structure to perform this mapping. Is fractional scaling ( ) available in 18.04 LTS yet? I am waiting until this is available before I install. I am struggling to understand this. According to truth tables, if $P$ is false, it doesn't matter whether $Q$ is true or not: Either way, $P \implies Q$ is true.  Usually when I see examples of this people make up some crazy premise for $P$ as a way of showing that $Q$ can be true or false when $P$ is something outrageous and obviously untrue, such as "If the moon is made of bacon-wrapped apple-monkey carburetors, then I am a better wakeborder than Gauss."  $P$ is clearly false, but $P \implies Q$ is true no matter what the state of $Q$ is, and I don't understand why.  Are we saying "If $P$ is false, then all bets are off and $Q$ can be anything, either true or false, and not contradict our earlier claim, and if it isn't false, it must be true"?  Otherwise why can't we say that if $P$ is false, then we can't make any claims one way or the other on whether or not it implies anything at all? Why can't polynomials have negative exponents or division by a variable Why can't:  $$2x^{-3} - 3x$$  or  $$\frac{1}{2x}$$  be polynomials too?  Why have a definition that excludes these algebraic forms? How do I use/change Animation Extrapolation? (Can't find F-Curves / Animation Modifiers in 2.8(1)) Preventing brute force attacks against ssh? What tool or technique do you use to prevent brute force attacks against your ssh port. I noticed in my Security logs, that I have millions of attempts to login as various users through ssh.  This is on a FreeBSD box, but I imagine it would be applicable anywhere.