Lenovo Laptop Ubuntu 18.04.2 LTS 16 GB RAM Intel® Core™ i5-5200U CPU @ 2.20GHz × 4 GNOME 3.28.2 64-bit   Swap File Partition:    If I have enough memory all the time (16gb) does that mean it just doesn't need the swap file?  Does 18.04.2 even need the swap?
I read many places that the rule of thumb for swap space is to double the amount of physical RAM. However, 32 GB does seem a LOT. Do I need that much? Do I need it at all with this high amount of physical RAM?
Integer solutions to the equation $a^3+b^3+c^3=30$ I am using two books for my calculus refresher.   Thomas' Calculus  Higher Math for Beginners by Ya. B. Zeldovich   My question is : When applying Integral Calculus for calculation of volumes of solids, generated by curves revolved around an axis, we use slices of 'cylinders' to approximate the volume of the resulting solid and then integrate the sum of those infinitesimal cylinders. However, when we are using the same techniques to calculate the surface area of the surfaces generated by revolving curves around an axis, we consider the 'slope' of the differential length of curve 'dx', calculate the total length of the curve and derive the required surface area.  Are we not supposed to use the same 'slope' for calculating the volumes of the infinitesimal 'cylinders' for calculation of volumes? Shouldn't we use 'sliced portions of 'cones' as the infinitesimal volumes?? When it come to calculation of volumes of solids of revolution, why are we neglecting the slope of the curve for the differential length and simply assume that it is an infinitesimal cylinder??  Ex: Let us say we want to calculate the surface area and the volume of the solid generated when the parabola y = 10 . x^2 is revolved about the y-axis, with limits of x from 0 to 5.  In such cases, when calculating the volume of the solid, we consider infinitesimal 'cylinders', ignoring the 'slope' of the curve for the differential element 'dx', but when calculating the surface area, we consider the 'slope' of the differential element 'dx'. As of late, and without my deliberately doing anything to make it happen, my Bash prompt has an  (i.e. @) prepended to it. This did not previously happen. Nor can I see anything in my ~/.bashrc that seems as though it ought to be making this happen.  This is on Debian Jessie GNU/Linux, using GNU Bash.  For example, my current Bash sessions look like this:  @sampablokuper@debianbox:~$ python3 Python 3.4.2 (default, Oct  8 2014, 13:14:40)  [GCC 4.9.1] on linux Type "help", "copyright", "credits" or "license" for more information. @&gt;&gt;&gt; 1+2 3 @&gt;&gt;&gt; exit() @sampablokuper@debianbox:~$    whereas originally, they would have looked like this:  sampablokuper@debianbox:~$ python3 Python 3.4.2 (default, Oct  8 2014, 13:14:40)  [GCC 4.9.1] on linux Type "help", "copyright", "credits" or "license" for more information. &gt;&gt;&gt; 1+2 3 &gt;&gt;&gt; exit() sampablokuper@debianbox:~$    Here are all the lines from my ~/.bashrc that appear to in any way relate to the Bash prompt:  # set variable identifying the chroot you work in (used in the prompt below) if [ -z "${debian_chroot:-}" ] &amp;&amp; [ -r /etc/debian_chroot ]; then     debian_chroot=$(cat /etc/debian_chroot) fi  # set a fancy prompt (non-color, unless we know we "want" color) case "$TERM" in     xterm-color) color_prompt=yes;; esac  # uncomment for a colored prompt, if the terminal has the capability; turned # off by default to not distract the user: the focus in a terminal window # should be on the output of commands, not on the prompt #force_color_prompt=yes  if [ -n "$force_color_prompt" ]; then     if [ -x /usr/bin/tput ] &amp;&amp; tput setaf 1 &gt;&amp;/dev/null; then         # We have color support; assume it's compliant with Ecma-48         # (ISO/IEC-6429). (Lack of such support is extremely rare, and such         # a case would tend to support setf rather than setaf.)         color_prompt=yes     else         color_prompt=     fi fi  if [ "$color_prompt" = yes ]; then     PS1='${debian_chroot:+($debian_chroot)}\[\033[01;32m\]\u@\h\[\033[00m\]:\[\033[01;34m\]\w\[\033[00m\]\$ ' else     PS1='${debian_chroot:+($debian_chroot)}\u@\h:\w\$ ' fi unset color_prompt force_color_prompt  # If this is an xterm set the title to user@host:dir case "$TERM" in xterm*|rxvt*)     PS1="\[\e]0;${debian_chroot:+($debian_chroot)}\u@\h: \w\a\]$PS1"     ;; *)     ;; esac   How can I get my Bash prompt to appear as it did originally? Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $ I would like to prove that the equation $ 3^x+4^x=5^x $ has only one real solution ($x=2$)  I tried to study the function $ f(x)=5^x-4^x-3^x $ (in order to use the intermediate value theorem) but I am not able to find the sign of $ f&#39;(x)= \ln(5)\times5^x-\ln(4)\times4^x-\ln(3)\times3^x $ and I can't see any other method to solve this exercise... When I visit the reputation tab of my profile, I see a lot of stuff. I can make out some of it, but not all.   What do all the event types mean? Why do some events show an odd reputation gain or not show any reputation change at all? Why are some events sometimes highlighted in yellow? My reputation suddenly dropped, but I don't see anything. What happened? Why do some events disappear from my reputation history? Beautiful table samples I'm interested in learning about some nice-looking table samples. Colors can make a huge difference, and just providing some color to headers, background, or borders can dramatically change presentation. Any samples you're proud to share?  (BTW here's a sample I like, but unfortunately, not TeX...) PHP variable variables Update a field without changing the node I need to change a field in a node without altering the 'changed' timestamp. I know this was possible in Drupal 7 using field_attach_update(), but that has been removed since then.  I could use an update query and change the field directly in the database, but I was wondering if there is a better way (or a replacement for field_attach_update()). Why does $x$ divided by zero not equal $x$? After all, $x$ is not being divided by anything. The Stack Imgur service is no longer resizing images correctly Another "can't use Alt. Series Conv. test" (How do I determine if it converges or diverges?) Is changing your passport a good strategy for removing a negative immigration history in Schengen? When certain nationalities of people want to travel in the Schengen zone, they are required to apply for a Schengen visa. This is a straight-forward process for most, but when an applicant has had problems with removals or refusals they may be reluctant to apply because they want to avoid the complexities of serial visa refusals. This reluctance may lead some into wondering how their history can be expunged, and this line of thought inevitably leads to the idea of getting their passport replaced with a new one.  This sounds like a great formula for people who have had prior refusals or removals.  In essence they can become 'reincarnated' as a first-time traveller and hence avoid the unpleasantness of revealing their prior interactions with the Schengen authorities.  The relevant parts of the application form are shown here...    Nothing asks about a prior removal or refusal, and the applicant is left with simple denials for 3 questions in order to present themselves as a first-time traveller.  Assuming the person is happy to set aside the moral issues associated with denying their history, are there any holes to this strategy?  This question is scoped to Schengen visa applications so that it will not be unmanageably broad, but answers from other regimes (particularly the affluent Commonwealth and the USA) are acceptable as long as the main points are relatively consistent with Schengen. I've read many years ago in books, that the brain has no nerves on it, and if someone was touching your brain, you couldn't feel a thing.  Just two days before now, I had a very bad migraine, due to a cold. It's become better now, but when I had it I felt my head was going to literally split in half, as the pain was literally coming from my brain.  So it lead me to the question: How come people can get headaches if the brain has no nerves? I was wondering how one can construct a Borel set that doesn't have full measure on any interval of the real line but does have positive measure everywhere.   To be precise, if $\mu$ denotes Lebesgue measure, how would one construct a Borel set $A \subset \mathbb{R}$ such that $$0 &lt; \mu(A \cap I) &lt; \mu(I)$$ for every interval $I$ in $\mathbb{R}$?   Moreover, would such a set necessarily have to contain infinite measure? I'm having trouble opening jar files because there is no java runtime in open with listed. Even I have installed it via Software Center(i also try to reinstall it via synaptic and i do a --purge via terminal). How does the speed of electrons change around a circuit? I have been thinking about ways of teaching electronics and I'm wondering if the following is true...  For starters, when we talk about voltage as energy per unit charge, is this energy manifest simply as the kinetic energy of the electron?  So, all other things being equal, will the electrons coming out of a 4 volt battery will have twice the velocity of electrons coming out of a 1 volt battery because of ${1 \over 2}mv^2$?  This would seem to imply that the voltage drop across different parts of the circuit is essentially a comparison of the electron speeds at those points.  Furthermore doesn't this imply that the electrons are nearly halted by the time they reach the positive terminal of the battery? This makes intuitive sense to me, it seems pedagogically sound, and it provides an explanation for how electrons "know" to give up their energy across the circuit -- electrostatic repulsion communicates later resistances to earlier parts of the circuit.  How much of the above is correct? The one things that makes me suspicious is that, in this picture, electron density at the positive terminal of the battery is very high, and repulsive forces would prohibit this. On the other hand, if the Joules per Coulomb are not coming from kinetic energy, then what? The field? But wouldn't that just dissipate as light?  Something is wrong but I don't know what. I keep reading in economics journals about a particular result used in random utility models. One version of the result is: if $\epsilon_i \sim_{iid}, $ Gumbel($\mu, 1), \forall i$, then:   $$E[\max_i(\delta_i + \epsilon_i)] = \mu + \gamma + \ln\left(\sum_i \exp\left\{\delta_i \right\} \right),  $$  where $\gamma \approx 0.52277$ is the Euler-Mascheroni constant.  I've checked that this makes sense using R, and it does.  The CDF for the Gumbel$(\mu, 1)$ distribution is:  $$G(\epsilon_i) = \exp(-\exp(-(\epsilon_i - \mu)))$$  I'm trying to find a proof of this and I've had no success.  I've tried to prove it myself but I can't get past a particular step.   Can anyone point me to a proof of this?  If not, maybe I can post my attempted proof up to where I get stuck. Nested cross validation for model selection How can one use nested cross validation for model selection?   From what I read online, nested CV works as follows:   There is the inner CV loop, where we may conduct a grid search (e.g. running K-fold for every available model, e.g. combination of hyperparameters/features) There is the outer CV loop, where we measure the performance of the model that won in the inner fold, on a separate external fold.    At the end of this process we end up with $K$ models ($K$ being the number of folds in the outer loop). These models are the ones that won in the grid search within the inner CV, and they are likely different (e.g. SVMs with different kernels, trained with possibly different features, depending on the grid search).  How do I choose a model from this output? It looks to me that selecting the best model out of those $K$ winning models would not be a fair comparison since each model was trained and tested on different parts of the dataset.  So how can I use nested  CV for model selection?   Also I have read threads discussing how nested model selection is useful for analyzing the learning procedure. What types of analysis /checks can I do with the scores that I get from the outer K folds? Dell Vostro 5490 no WIFI in Ubuntu 18.04 This was the question of a test. My question is if my attempt to solve it is correct, and if it is, why is it correct.  $$\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $$  My attempt:   Let $\xi = -x-y $. Then $\xi \to 0$ whenever $(x,y) \to (0,0)$ and $x+y \neq 0 \iff \xi \neq 0$. (Is it then correct to say that the previous limit exists and is equal to the following iff the following exists? And why?):  $$\lim_{\xi \to 0, \xi \neq 0}{\frac{\ln(1+\xi )}{-\xi}}$$   If it is correct, then the limit exists and is $-1$. If it is correct, why is it correct?