Stay in a cold closed room, turn on a fan directed at you, it makes you feel colder instead of warmer. why? Here is the definition of heat:  Matter exists in different physical forms – solids, liquids, and gases. All matter is made of tiny particles called atoms, molecules, and ions. These tiny particles are always in motion – either bumping into each other or vibrating back and forth. It is the motion of particles that creates a form of energy called heat (or thermal) energy that is present in all matter...  so before turning on the fan, the air molecules are relatively still and not moving much. After turning on the fan, they are moving a lot faster so the motion of the particles is more and it should create heat, but why can't we feel the heat on our body and skin when standing in front of the fan? (at least in my experience)
So I was thinking... If heat I feel is just lots of particles going wild and transferring their energy to other bodies, why am I not burned by the wind?  When I thought about it more I figured out that wind usually carries some humidity, and since particles of liquid are moving same speed as the wind, they are basically static relative to each other, so no energy is transferred between them (wind and water particles). And if that water sticks to my skin and wind blows, it'll evaporate thus taking energy from my skin and make me feel cold.  Thing is, I don't think that's really the case but even if it is, if I somehow dry out the wind, will it burn me if it's strong enough? And winds can reach some pretty high velocities (though I must admit I'm not sure if they are comparable to movement of atoms in warm bodies etc...).  So. Bottom line. Can I be burned by wind in some perfect scenario?
Ubuntu/Kubuntu 16.04.1 installation in VirtualBox I'm trying to install Kubuntu 16.04.1 on a virtual machine (I'm using VirtualBox). When I boot from the disk image Ubuntu begins to load and then I get this screen:   It looks like it's loading but the display is not working properly (the pink blob is my mouse pointer, only very large and pink).  I also tried installing Ubuntu 16.04.1 and I get a very similar result:   Am I missing something in VirtualBox? Thanks! CSS3's attr() doesn't work in major browsers I'm trying to solve a question where I need to write $\frac {1}{1+z^2} $ as a power series centered at $z_0=1$  I'm not allowed to use taylor expansion. So my first thought was to rewrite the function in a form where I can apply the basic identity:  $$ \frac{1}{1-x} = \sum_{n=0}^\infty x^n $$  So let's rewrite the original function $f(z) = \frac {1}{1+z^2} $ and use above identity:  $$\frac {1}{1+z^2} = \frac {1}{1-(-z^2)} $$ But observe that I need to center it at $z_0=1$ so I rewrote it to:  $$\frac {1}{1-(-z^2)}=\frac {1}{2z-(-(z-1)^2)} $$  I can factor out $\frac {1}{2z}$ and use the basic identity to get : $$\frac {1}{2z}\frac {1}{1-\frac{(z-1)^2}{2z}} = \frac {1}{2z}\sum_{n=0}^\infty \left(\frac{-(z-1)^2}{2z}\right)^n =\frac {1}{2z}\sum_{n=0}^\infty \frac{(-1)^n(z-1)^{2n}}{(2z)^n} = \sum_{n=0}^\infty \frac{(-1)^n(z-1)^{2n}}{(2z)^{n+1}}$$  The problem is if I ask wolfram alpha: power series$ \frac{1}{1+z^2} $centered at z = 1 it will give me a different answer that doesn't match the sum I found.  Can anyone help me figure this one out? What am I doing wrong? What is the relationship between regression and linear discriminant analysis (LDA)? Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two classes? I have a many-to many relationship between three objects. LGFProducts, PartsinProducts, and Parts. PartsinProducts is the junction object. I want to be able to get data like the names of the parts that are related to the selected LGFProduct.   I understand that parent-child relationship can only traverse one level down while grandchild-grandpa can travel 5 levels at most. What is the parent-child or child-parent in a many-to-many relationship?  I assumed that I should be traversing upwards from Parts to the junction object partsinproduct and then LGFProducts? But my friend who is not a Salesforce expert but has knowledge in CS said that I should do a parent-child query (of LGFProducts to partsinproduct) to child-parent relationship query (PartsinProduct to Parts). Or perhaps both of these options are wrong and another is appropriate.   Also, I am having a little trouble traversing for custom objects. I understand that I need to append the letter r instead of c but get confused. For example, this is my attempt at a three level upward traversal that fails.   SELECT Id, Name, Parts__r.PartsinProducts__r,LGFProducts__r.Name FROM Parts__c   Also if three levels of upward traversal are needed, could one provide an example with custom relationships? As seen above, I am having difficulty successfully querying a three level upward traversal statement for custom objects.  This is my attempt at the parent-child relationship query of LGFProduct to PartsinProducts:  SELECT Name,   (     SELECT Name     FROM PartsinProduct__r   ) FROM LGFProduct__c    I am then given this error: What does capital letter I mean in this formulas? Hello I don't understand meaning of the symbol represented by a capital letter "I" in the formulas below. There is  to the paper with the formulas.    At the beginning I thought it mean "where c is not equal to the result of classifier T(m)", however in step (d) there is a multiplication symbol before it, so it probably mean that "I" should "return" a value. Could we please be a bit nicer to new users? There is a distinct decline in the level of civility on all the sites here.  Some of this is due to new users coming in and posting spam and other nonsense, but the off-topic and downvote buttons are doing a pretty good job of keeping this under control. Unfortunately, a lot of this is coming from more experienced users, and the site's built-in moderation system does not (and probably cannot) handle this very well.  Folks are rushing to pound new users down with &quot;this belongs on meta!&quot;, &quot;this is off topic&quot;, &quot;this is a duplicate!&quot; and &quot;read the Help!&quot;. (Which is correct, but should be done nicer) All this, of course, is accompanied by a flurry of downvotes.  This is not very welcoming to new users who don't know about meta, the Help, or what counts as off-topic. Now I am not proposing that we just allow off-topic, meta, or duplicate questions.  However, I think we could be gentler in the way we express these sorts of things.  Explain what meta and the FAQ are and provide useful links.  Just using please and thank-you when asking folks to read the FAQ or post something on meta would be an improvement.  I also think we could rein in the downvoting a bit.  Not that we shouldn't vote stuff down, but unless a new user's post is clearly spam, voting it down to -1 or -2 should be sufficient to send a message without piling on. I like Stack Exchange and I want it to become a resource for everyone, not just an elitist site for high-rep users on the sites. Is there a maximum number of devices allowed on a Google Play Account? Is this a valid partial fraction decomposition? Write $\dfrac{4x+1}{x^2 - x - 2}$ using partial fractions. $$ \frac{4x+1}{x^2 - x - 2} = \frac{4x+1}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x-2} = \frac{A(x-2)+B(x+1)}{(x+1)(x-2)}$$ $$4x+1 = A(x-2)+B(x+1)$$ $$x=2 \Rightarrow 4 \cdot2 + 1 = A(0) + B(3) \Rightarrow B = 3$$ $$x = -1 \Rightarrow 4(-1) +1 = A(-3)+ B(0) \Rightarrow A = 1$$ Thus, $$\frac{4x+1}{x^2-x-2} = \frac{1}{x+1} + \frac{3}{x-2}\textrm{.}$$  The substitution of $x$ ($x = 2, -1$) is a common method to find out the coefficient of the partial fractions. However, the equation on the third line is obtained by multiplying $(x+1)(x-2)$, which is assumed to be nonzero. Here we have a contradiction. Furthermore, the original function is not defined at $x=-1,2$. How can we substitute these value for $x$? So is this method valid and rigorous? How to modify it so that it is rigorous? I'm transitioning a Drupal 6 site to Drupal 8.1 so following the official instructions, I set up a new install in its own directory. Since this is only one site, I followed the instructions to put my database credentials in sites/default/default.settings.php after the declaration of the $databases array.  Running drush --status returns the following.  Drush version          :  8.1-dev                                           Drush temp directory   :  /tmp                                              Drush configuration    :                                                    Drush alias files      :                                                    Drupal root            :  /media/psf/Home/apps/newp                         Drupal Settings File   :  MISSING   Since this Drupal is 8.1-dev that must mean I need to upgrade it. Since this is a global install using Composer, I run composer global update.     Your requirements could not be resolved to an installable set of   packages drush/drush dev-master requires codegyre/robo ~1.0.0-beta1   Checking the drush-ops page on github doesn't show any anomalies like this nor my Google search.   What am I overlooking? There are many times when I curse the autocorrection mechanism for changing what I typed, but overall, much of the corrections are welcome so I don't really want to disable it. I do want to have it do it's work but alert me when it makes each change so I don't have to proofread everything or focus with perfect attention to the screen to see the momentary red and/or blue underlining that alerts me to the machine override.  I would love a way to turn on an audible beep (customizable of course) so that I also get a warning each time my typing gets corrected (and only when autocorrection occurs). How to use Stokes theorem in the presence of holes? I drew a parallelepiped that is spanned by three vectors, and we know the volume is given by the absolute value of the determinant of the matrix - with the three vectors arranged in rows (or columns, since $detA = detA^T$).  How can I draw the tetrahedron from this parallelepiped to convince myself it is indeed 1/6th of the volume, i.e., 1/6 * |detA|?  Thanks, Ubuntu 16.10 Wifi Trouble - RT2561/RT61 Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A I ran across this problem in my Analysis class and can't seem to come up with a good solution. Here's the question: Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals $A$. $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$.  I tried applying the Mean Value theorem like this: There exists a $c \in (a, x)$ st $f(x)-f(a)=f'(c)(x-a) \implies \frac{f(x)-f(a)}{x-a}=f'(c) \implies f'(a)=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}=\lim_{c\to a}f'(c)=A$  However, I think this is wrong. I am pretty sure the Mean Value theorem is needed, but my application of it seems to be incorrect. Would somebody be able to point me in the right direction? Let $R$ be a commutative ring with identity, and $S$ a multiplicative subset of $R$ not containing $0$. Which step in my reasoning is wrong?   Every element of $S$ is a unit in $S^{-1}R$. Every element of $S$ that's a zero divisor in $R$ is a zero divisor in $S^{-1}R$. But zero divisors can't be units. Therefore it's not possible to localize $R$ at $S$. koma-script/scrlayer-scrpage: How to get rid of the rulers at the page edge when enabling the draft class option? Is it possible to get rid of these rulers when enabling draft class option?  \RequirePackage{luatex85} \documentclass[draft]{scrreprt}  \usepackage{scrlayer-scrpage}  \usepackage[tuenc]{fontspec} \usepackage{graphicx,mwe}  \begin{document}  \begin{figure}[h]     \centering     \includegraphics[width=\textwidth]{example-image} \end{figure}  \end{document} How can I get LaTeX to warn about unreferenced figures and unused labels in general? When writing documents, I consider it to be necessary that all figures and tables are referenced (\ref) in the text, whether or not I've remembered to \label them. LaTeX does not currently warn if a figure or table is not referenced. Is there a way to ensure that this is flagged up as a warning?  Note that I am specifically concerned about figures and tables, not chapter or section headings; it will be no good looking just at \labels that don't have an associated \ref.  In other words, it should report boo and not report bla in the following MWE:  \documentclass{article} \begin{document} \section{BLA}\label{bla} \section{BOO}\label{boo} In Section~\ref{bla} we do something. \end{document} Suppose a book consists of three sections:     The book is/was divided into three sections.   I am thinking the past tense option "was" should be used, because the act of dividing the book into three sections happened at the time of writing. Is my analysis good? How to remove "onclick" with JQuery?