Natural logarithm of -1 is 3.14159265 i
How is $\ln(-1) = i\pi$?
Newbie Question: in Blender 2.8 Adding Armature options missing? I did try searching for this but didn't find anything.   I've been following some tutorials for Rigging and have seen a lot of videos showing  Armature Templates available from the Armature sub option see attached.  On the version of blender I'm using 2.8 Beta Win 10 64 bit (23 April 19) I have no options to select anything.  Only the Armature menu heading is from the ADD option  which when selected provides a single bone.  Have these other options gone now or do I need to configure something within blender?  Thanks What is the sponsored party called? Google results for sponsee have scattered definitions in unreliable sources, so it does not appear that is a real word. I'm looking for something similar, a single word.  The specific context is a social group membership application where new members must be sponsored (as in definition 2, here - "one who assumes responsibility for some other person or thing") by existing members. I am looking for a single word to describe the target of such a sponsorship. I am about to sponsor a fraternity, but I would like to have a more general word for what I'm sponsoring. Next time, the fraternity could well be a study club, or something else.  Therefore, what is the sponsored party also called? E.g. if I sponsor somebody, that person is my __? I develop an application in which i constantly get samples of heart pulse.  I defined an interval of t seconds.  In each t seconds I have n samples.  In every interval, I want to calculate the tendency of those n samples. For example, lets say I have n = 5, and I have samples with values {70, 88, 95, 103, 115}. I want to recognize I have a growth in the heart pulse, and I want to have some measure for the rate of grows/decrease/almost no change.  I thought on two approaches for solving this problem.   I calculate the linear approximation for the n samples using linear regression by applying least squares implemented by the normal equations. (I treat each sample as two coordinates vector with x coordinate as time and y coordinate as heart pulse). I get from the normal equations a linear function of the form y = mx+b and my measure for the tendency is the slope, i.e. the m value. The second approach is to calculate the correlation (pearson's correlation) between vector x and vector y when x is the time and y is the heart pulse.   I'm asking which approach do you think is better for my problem (determining the tendency of heart pulses). Or, do you have a better algorithm for solving this problem? I seem to be having issues when I try and save the output file as a .png, or .jpeg for that matter. I've set up my user preferences, File, Render Output to my desktop as well as render output in the editor window. What am I missing here? I'm obviously very new to this program and your help would be appreciated. Thanks for your time I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized Lorentz force via a velocity-dependent potential.   I understand the generalized force   $$F_i = -\frac{\partial V}{\partial x_i} + \frac{d}{dt}\left(\frac{\partial V}{\partial v_i}\right)$$  that they derive from a Lagrangian of the form $L = \frac{1}{2}m|\vec v|^2 - V(\vec r,\vec v,t)$.  However, in the next (critical) step of the derivation, the author cites a theorem from Helmholtz saying      ...according to Helmholtz, for the existence of the Lagrangian, such a generalized force can be at most a linear function of acceleration, and it must satisfy the Helmholtz identities.   The three Helmholtz identities are then listed as:  $$\frac{\partial F_i}{\partial \dot{v_j}} = \frac{\partial F_j}{\partial \dot{v_i}},$$  $$\frac{\partial F_i}{\partial v_j} +  \frac{\partial F_j}{\partial v_i} = \frac{d}{dt}\left(\frac{\partial F_i}{\partial \dot{v_j}} +  \frac{\partial F_j}{\partial \dot{v_i}}\right),$$  $$\frac{\partial F_i}{\partial x_j} -  \frac{\partial F_j}{\partial x_i} = \frac{1}{2}\frac{d}{dt}\left(\frac{\partial F_i}{\partial v_j} - \frac{\partial F_j}{\partial v_i}\right).$$  I'm trying to understand where this theorem comes from. Razavy cited a 1887 paper by Helmholtz. I was able to find , but it is in German, so I could not verify whether or not it proved the theorem. Additionally, I could not find it in any recent literature. I searched online and in Goldstein's Classical Mechanics.   The only similar concept that I can find is in the  where we have three equations known as Helmholtz conditions. Are these two concepts one in the same? If so, how should I interpret the function $\Phi$ and the matrix $g_{ij}$ that appear in the Helmholtz conditions I found online?   If the cited theorem from Razavy does not relate from the inverse Lagrangian problem, could I have some help finding the right direction? How to store and preserve lots of data? I have many DVDs with movies and games, they are getting old and dusty, some of them are damaged. And I have more than 300 GB of general files in my PC. I want to store and preserve all of my data and keep them for a long long time.  I want to know what is the best and more reliable storage media that I should use and... I can buy. I will copy all of my DVDs to a new media and throw all of my DVDs away. It will take a very smaller physical space.  I think that everything that I need to store is currently 800 GB.  I do not like optical discs, because they are fragile and I have lost many CDs and DVDs. Hard drives would be good, but they can suddenly stop working, and it is very expensive to recover data from a broken hard drive.  Other questions: How often will I have to copy the files to a new storage media? Is it good idea to have another copy of each file stored in another storage media?  Edit: If I put all of the movies and games in a HDD, if the HDD stops working, I will lose everything. This is how valuable they are for me: If I lose 10% of them, I will not cry, because I can get new ones, but if I lose 90%, it will be a disaster.  Edit 2: I do not think that that online storage is reliable even if I pay for it, because they may be closed or may get bankrupt. They are not from my country and it would be difficult to get the files back. What is the difference between the Bash operators [[ vs [ vs ( vs ((? I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition) I installed the ubuntu 12.04 server edition for my server pc . i had installed lamp server. i need to change the var/www location to my secondary hard disk location. i was configured so many time to at gedit /etc/apache2/sites-available/default here is my code  &lt;VirtualHost *:80&gt;     ServerAdmin webmaster@localhost      #DocumentRoot /var/www     DocumentRoot /media/myserver/     &lt;Directory /&gt;         Options FollowSymLinks         AllowOverride None     &lt;/Directory&gt;     #&lt;Directory /var/www/&gt;         &lt;Directory /media/myserver/&gt;         Options Indexes FollowSymLinks MultiViews         AllowOverride None         Order allow,deny         allow from all     &lt;/Directory&gt;      ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/     &lt;Directory "/usr/lib/cgi-bin"&gt;         AllowOverride None         Options +ExecCGI -MultiViews +SymLinksIfOwnerMatch         Order allow,deny         Allow from all     &lt;/Directory&gt;      ErrorLog ${APACHE_LOG_DIR}/error.log      # Possible values include: debug, info, notice, warn, error, crit,     # alert, emerg.     LogLevel warn      CustomLog ${APACHE_LOG_DIR}/access.log combined      Alias /doc/ "/usr/share/doc/"     &lt;Directory "/usr/share/doc/"&gt;         Options Indexes MultiViews FollowSymLinks         AllowOverride None         Order deny,allow         Deny from all         Allow from 127.0.0.0/255.0.0.0 ::1/128     &lt;/Directory&gt;  &lt;/VirtualHost&gt;   and also used  sudo chown -R var/www /media/myserver/   and  chmod -R 755 /media/myserver/   still i was not able to connect my /media/myserver and my browser show the following message  Forbidden  You don't have permission to access / on this server.   Please tell anyone how to mount myserver at my var/www, thanks advance I tried to install WPS Office on my laptop (ubuntu 16.10 Gnome, 64 bit) with  Gdebi installer but it said   Dependency is not satisfiable: libpng12-0   Then I tried to open this library as follows  sudo apt-get install libpng12-0   But I encountered an error:  Reading package lists... Done Building dependency tree        Reading state information... Done Package libpng12-0 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'libpng12-0' has no installation candidate   Can anyone help? Thanks a lot Ubuntu desktop suddenly points to home folder Preventing applications from stealing focus Singularities in the punctured unit disc and square integrability I'm having trouble with the following problem:  Let $f$ be holomorphic on the punctured unit disc, $D$. If $\int_D|f(z)|dA(z)&lt;\infty$, then $z=0$ is either a removable singularity or a simple pole of $f$.  A similar problem is to prove or disprove that if $\int_D|f(z)|^2dA(z)&lt;\infty$, then $f$ has a removable singularity at $0$.  I've tried using the Mean Value Property for $f$ and taking the limit as $z\to0$, but I didn't get anywhere. Are all oscillatory motions periodic motions? For example, if a pendulum system in the real world oscillates its amplitude and period will eventually decrease. Does that still count as a periodic motion? Since the motion doesn't have the same amplitude at equal time periods. I am trying to run grep against a list of a few hundred files:  $ head -n 3 &lt;(cat files.txt) admin.php ajax/accept.php ajax/add_note.php   However, even though I am grepping for a string that I know is found in the files, the following does not search the files:  $ grep -i 'foo' &lt;(cat files.txt)  $ grep -i 'foo' admin.php The foo was found   I am familiar with the -f flag which will read the patterns from a file. But how to read the input files?  I had considered the horrible workaround of copying the files to a temporary directory as cp seems to support the &lt;(cat files.txt) format, and from there grepping the files. Shirley there is a better way. etags and other tags The  tag is a synonym of , and has the description     A program to generate tags for a large project. These tags are usable by the Emacs text editor.   This is inconsistent: tags in that sense are always plural, i.e. etags, never etag.  evidently refers to another concept, .  Should  remain a synonym of , and be about HTTP Etags, and should Emacs etags be tagged +? Or should the synonym be unmade, with HTTP Etags on  and etags on ? How to apply layer style to one object and apply it to multiple layers Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists? The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime.    The wikipedia article on , and the  "The priveleged character of $3+1$-dimensional spacetime" in particular, made me think a bit about the possibility that we might live in a non-integer amount of spatial and/or time dimensions.   The notion of attaching a non-negative real number to a metric space has at least mathematically already been described by such concepts as "" and "".   This may sound silly/ignorant/absurd to professional practicing theoretical physicists. To me (a layman), however, it doesn't sound much stranger than the idea of wrapping up six extra dimensions (which is, from what I understand, considered to be a serious possibility by those who study $10$-dimensional String Theory) into intricate shapes called "Calabi-Yau Manifolds".   Has any research on $(a +b)$-dimensional spacetime (where $a,b \in \mathbb{R}_{\geq 0} $) ever been done? If so, what where the findings? If not, why not? I have installed Ubuntu on my laptop and now I want to remove it and the Grub Loader. How I can do it without the Windows installation disk (I cannot use the Recovery Console). Inequality $(1+\frac1k)^k \leq 3$ Conditionals in English are usually formed by using if with normal word order; but for the three past (subjunctive) forms were, should, and had, it is also possible to express the conditional through subject–auxiliary inversion alone, with no if in the conditional clause.  Does forming conditionals in this manner differ semantically from if-conditionals? Is some aspect of the conditional statement or the conditionality emphasised more in one version than in the other? Or are there differences in how and when they are used? Or are they simply completely interchangeable?  For example:     If I were you, I would try it again   Were I you, I would try it again      If I had seen it, I would have told you   Had I seen it, I would have told you      If you should drink, don’t get behind the wheel   Should you drink, don’t get behind the wheel