Dual boot Windows XP and Ubuntu 14.04
Windows installer for Ubuntu 14.04 LTS onwards
I'm trying to prove that the following set ($B$) defined by an ellipse is convex, but I am getting stuck.  $$B = \left\{(x_1,x_2):3(x_1-3)^2+2(x_2-3)^2 \leq 1 \right\} $$  My sad attempt:  $$ \textrm{Let }x,y \: \in \: B \:, \: \lambda \: \in \: [0,1]$$  $$ \lambda x+(1-\lambda)y=(\lambda x_1+(1-\lambda)y_1,\: \lambda x_2 +(1-\lambda)y_2  )$$ $$3(\lambda x_1 + (1-\lambda)y_1 -3)^2+2(\lambda x_2+(1-\lambda)y_2-3)^2=3(\lambda ^2x_1^2 +(1-\lambda)^2y_1^2+9+2\lambda x_1(1-\lambda)y_1-6\lambda x_1 -6(1-\lambda)y_1)+2(\lambda ^2x_2^2 +(1-\lambda)^2y_2^2+9+2\lambda x_2(1-\lambda)y_2-6\lambda x_2 -6(1-\lambda)y_2)$$  and this is where I have lost all confidence in proving it. I was able to factor some of the terms into the form $(\lambda x_1 -3)^2$, $((1-\lambda) y_1 -3)^2$, $(\lambda x_2 -3)^2$, and $((1-\lambda) x_2 -3)^2$, but I don't think that helps the situation any. I have a 250G disk on my Mac with around 100G in use. But the system reports only around 20G of free space. I'm using macOS 10.13.2. I have the problem at least since the upgrade to High Sierra, but probably also before.  "About This Mac" --> "Storage" reports that "System" is using around 180G. But if I check the complete disk, it looks like that:  $ sudo du -cxhd 1 /   0B    /.HFS+ Private Directory Data 1.0K    /home 4.3G    /usr 4.2G    /.Spotlight-V100 1.0K    /net  34G    /nix   0B    /.PKInstallSandboxManager   0B    /.PKInstallSandboxManager-SystemSoftware 2.6M    /bin   0B    /Network 1.1M    /sbin 3.8G    /Library   0B    /.Trashes 6.5G    /System 476K    /.fseventsd du: /private/var/db/ConfigurationProfiles/Store: Operation not permitted du: /private/var/folders/z7/[...]/0/SafariFamily: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.LaunchServices.dv: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.nsurlsessiond: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.routined: Operation not permitted du: /private/var/folders/zz/[...]/0/com.apple.nsurlsessiond: Operation not permitted 8.0G    /private 8.6M    /.DocumentRevisions-V100   0B    /.vol  32G    /Users  11G    /Applications 207M    /opt 5.0K    /dev 4.0K    /Volumes   0B    /cores 104G    / 104G    total   df also says that only 20G are available:  $ df -h / Filesystem     Size   Used  Avail Capacity iused               ifree %iused  Mounted on /dev/disk1s1  234Gi  211Gi   20Gi    92% 4019132 9223372036850756675    0%   /   Any tool I was using (Finder, Disk Inventory X, etc.) shows more or less the same numbers like df and du.  Output of mount:  $ mount /dev/disk1s1 on / (apfs, local, journaled) devfs on /dev (devfs, local, nobrowse) /dev/disk1s4 on /private/var/vm (apfs, local, noexec, journaled, noatime, nobrowse) map -hosts on /net (autofs, nosuid, automounted, nobrowse) map auto_home on /home (autofs, automounted, nobrowse)   I read and tested many, many things like:         ... but with no success. So what could consume more than 100G of disk space without showing up in any tool?  Update  Running „First Aid“ in recovery mode:   What does this error message mean?  error: btn:1: invalid key order (1) oid 440198 / oxid 114577 fsroot tree is invalid.   Update 2018-01-25  Another report of the same error:  (but no answers, yet)  I'm pretty sure this file system error is the root cause for the missing disk space. But I have no idea how to fix that. I was hoping that 10.13.3 would maybe solve it, but it didn't change anything. I guess I need to reinstall... Generate random numbers uniformly over an entire range I recently got a Windows 10 laptop. Opposite to my Macbook, I must swipe right-to-left to go to the right virtual desktop. Is there a way to reverse this, so I swipe left-to-right to go to the right virtual desktop? Cantrips seem to be the only type of spell that cares only about your class level. However, in the multiclassing section they are not mentioned, does this mean that cantrips use your character level, instead of your class level?  Does this mean a Warlock 2 / Fighter 15 can cast an Eldritch Blast with 4 beams just like a level 17 Warlock? How do you change the size of figure drawn with Matplotlib? Does a Rogue using Use Magic Device for a scroll or wand also need to emulate a class feature? I'm confused about Rogues and Use Magic Device. I've searched the core book and the Internet for the past 4 hours and can't find the answer to my simple question.   Since a Rogue doesn't have any spells, a spell list or caster level, do you have to emulate a class feature in addition to all other necessary checks to use items like scrolls and wands? I have a collection of articles written in latex, and I would like to "merge" them into a larger thesis document, in which each article will be a chapter. I have been looking at include and input, which are great if you start with the meta-document in mind. However in my articles I have sometimes a bit exotic dependencies, such as dot2texi, and using the naive approach fails rather abysmally with all kinds of broken paths.  So I was wondering, do you recommend any "best practices" for merging non-trivial documents -- which packages to look at, or to avoid at all cost, etc.  Thanks Difference between staticmethod and classmethod Can I smoothly upgrade from one LTS to next LTS release? Question is about Ubuntu release process. Are migrations from n to n+1 releases expected?  Assuming we have server with installed Ubuntu 14.04 LTS. Will it be smoothly upgradable to Ubuntu 16.04 LTS via apt-get upgrade ?  Assumptions:   scope is software therefore we assume that given hardware is supported on both releases (upgrading from and to) that's why, always before upgrade you are asked to make backup to be able to revert in case of failure Travelling as unmarried couple in Dubai Username and Password not recognized when logging into Minecraft Is there a robust command line tool for processing csv files? I work with CSV files and sometimes need to quickly check the contents of a row or column from the command line.  In many cases cut, head, tail, and friends will do the job; however, cut cannot easily deal with situations such as  "this, is the first entry", this is the second, 34.5   Here, the first comma is part of the first field, but cut -d, -f1 disagrees. Before I write a solution myself, I was wondering if anyone knew of a good tool that already exists for this job.  It would have to, at the very least, be able to handle the example above and return a column from a CSV formatted file.  Other desirable features include the ability to select columns based on the column names given in the first row, support for other quoting styles and support for tab-separated files.  If you don't know of such a tool but have suggestions regarding implementing such a program in Bash, Perl, or Python, or other common scripting languages, I wouldn't mind such suggestions. How do you use a gray card? There are already   on how to make a gray card, but unfortunately my ignorance goes deeper than that.  How do you use a gray card? How does the telepathy supernatural ability work? According to the MM books, telepathy is described as:     A creature with this ability (supernatural) can communicate telepathically with any other creature within a certain range (specified in the creature's entry, usually 100 feet) that has a language. It is possible to address multiple creatures at once telepathically, although maintaining a telepathic conversation with more than one creature at a time is just as difficult as simultaneously speaking and listening to multiple people at the same time.   Source: MM, MM3   My questions:   If a creature with telepathy knows that someone is within 100ft, can the creature communicate with that person, even if there is no line of effect or sight?  My answer would be yes, because no book says that telepathy is blocked by walls, etc. Normally, a supernatural ability is a standard action to start. If the creature wanted to communicate for more than one round using telepathy, does the creature need to use up a standard action every round they are communicating or only in the first round?  My answer is only in the first round, since the description says that maintaining telepathy is hard as speaking and listening normally. If a person the creature is communicating with moves out of the 100ft range, and then moves back into the range. Does the telepathic link need to be established again?  My answer is yes, another standard action is needed to establish the telepathy between the two creatures.   I should add the telepathy is supernatural, and a character is looking at getting it from the Mindbender class (from Complete Arcane). And also get the Mindsight feat (Lords of Madness). I couldn't find anywhere to rule whether a supernatural ability should take a standard action every round it is on. Which attacks are possible against raw/textbook RSA? What to do about a 2-year-old who won't sleep without someone else in the room? My 2-year-old son won't fall asleep without having someone in his room with him. He doesn't want to be touched or held. He just wants you to sit in the chair. And after he does go to sleep he wakes up about 4 to 5 hours later, crying and screaming and is out of his bed and by the door. I go to him and give him a hug and put him right back in his bed. If I walk out he screams and won't go back to sleep for the rest of the night. If I stay he goes right back to sleep. But he wakes right back up when I walk out of his room.   I'm at a loss as to what to do. I've tried lots of stuff and nothing seems to work. It's almost as if he is having separation anxiety. I dont know what to do. Please help. Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ Let $V$ be spherically symmetric and $W$ i.i.d. Gaussian. Then $E[V|V+W=t]=g(\|t\|)$ A random vector $V \in \mathbb{R}^n$ is said to be spherically symmetric. If for every orthogonal matrix  $A$   the distribution of $AV$ is the same as the distribution of $V$.   My question: Let $W$ be  i.i.d. zero mean Gaussian random variable.     Can we show that  for a spherically symmetric $V$ the conditional expectation  \begin{align} E[V|V+W=t]=   g(\|t\|).  \end{align}  That is the conditional expectation is only a function of the magnitude.   My attempt:  \begin{align} E[V|V+W=t]= \int  V  \frac{f_W(t-v)}{f_{V+W}(t)} dP_V(v)= \frac{\int  v  f_W(t-v) dP_V(v)}{f_{V+W}(t)}= \frac{E[ V  f_W(t-V) ]}{f_{V+W}(t)} \end{align}  Therefore, we can show that the two functions in the above ratio only depend on $\|t\|$.   Observe that we can write $t= \|t\| u_t$  where $u_t$ is a unit vector. Then, for any orthogonal matrix $A$ \begin{align} f_{V+W}(t)=f_{V+W}(\|t\|, u_t)&amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t-AV  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|tA^{-1}-V  \|^2}{2}} ]\\ &amp;= \frac{1}{(2\pi)^{n/2}} E[ e^{-\frac{\|t A^T-V  \|^2}{2}} ]\\ &amp;= f_{V+W}(tA^T)\\ &amp;= f_{V+W}(\|t\|,  u_t A^T) \end{align}  Since, $A$ was arbitrary  we have that $f_{V+W}(t)=h(\|t\|)$(i.e., only depends on the magnitute).  Now I am not sure how to show that $E[ V  f_W(t-V) ]$ only depends on $\|t\|$? Modify footer used by elsarticle.cls