If a ribosome is made of protein, yet is used in protein sysnthesis, what created the first ribosome?  What created the ribosomal RNA?
Proteins are synthesized on ribosomes from mRNA copies of regions of the DNA. But ribosomes themselves are made up of proteins (and RNA). So how could the first ribosomes have arisen? Was there previously some other way of making proteins other than by ribosomes and mRNA?
tikz declare function and babel french option Photons travel at the fastest speed in our universe, the speed of light.  Do photons have acceleration? 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. Date(time) ranges using `datetime2` Where can I rent a decent mountain bike in Zürich? I am going for a 4 day trip in Zürich and I would like to bike quite a lot. Though biking is quite advertised, I failed to find a decent bike rental shop in the city. Would highly appreciate some tips! Do objects rotate around the torque vector or its center? If a sphere has a torque vector coming out of it at point A, would the sphere rotate about its center or the axis of the torque vector? This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post.  This problem is from assignment $5$.     Prove directly that distinct cosets do not overlap.   Let $H$ be a subgroup of $G$ and let $a$, $b$, and $c$ be elements of $G$ such that $b\not\in aH$ and $c$ is in both $aH$ and $bH$.  Then there are elements $h$ and $h^\prime$ in $H$ such that $c=ah$ and $c=bh^\prime$.  So $ah=bh^\prime$ and $b=ahh^{\prime -1}$.  But $hh^{\prime -1}\in H$ so $b\in aH$.  This contradicts our original assumption. Therefore, there can be no element in more than one distinct coset.  Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem.  Thanks. No surname on passport and applying for Japanese Visa Finding the distribution of the sum of three independent uniform random variables When to use a GAM vs GLM I realize this may be a potentially broad question, but I was wondering whether there are assumptions that indicate the use of a GAM (Generalized additive model) over a GLM (Generalized linear model)? Someone recently told me that GAMs should only be used when I assume the data structure to be &quot;additive&quot;, i.e. I expect additions of x to predict y. Another person pointed out that a GAM does a different type of regression analysis than a GLM, and that a GLM is preferred when linearity can be assumed. In the past I have been using a GAM for ecological data, e.g.:  continuous time-series when the data did not have a linear shape I had multiple x to predict my y that I thought to have some nonlinear interaction that I could visualize using &quot;surface plots&quot; together with a statistical test  I obviously don't have a great understanding of what a GAM does different than a GLM. I believe it's a valid statistical test, (and I see an increase in the use GAMs, at least in ecological journals), but I need to know better when its use is indicated over other regression analyses. How to Set Firefox 4 to only store History for a set period of time, i.e. one day? How do I set up an account with multiple users? I have two raster images, Boolean classified (1 or 2).  They overlap in given areas.   I need a raster that is only the overlapping sections.  Using Arcinfo 10.  Answer can only use raster methods, no converting to polygons, points, etc... Present Perfect vs. Present Perfect Continuous how are you?  Well, my biggest doubt at the moment is the difference between these two tenses. Actually, the more I study the more I have doubts with these tenses.      /         These similar threads helped me to clarify and reiterate my previous understanding.   I'm not posting in these threads because the site suggests avoiding asking for clarification (I don't know why because it would avoid new threads with the same content).  My main doubt is as follows:     I've lived in New York for two years.   In my understanding, the sentence above implies (1) that I lived in NY for two years and now I live in another place; or (2) I'm moving to another city after two years living in NY; or (3) I lived in NY for two years, then I moved to another place for some period and, finally, I'm returning. Is that correct?     I've been living in New York for two years.   Whereas the sentence above, in my understanding, implies that I lived in NY for two years and I still living there.  Anyway, many sources that I've already read say that these two sentences have the same meaning and are interchangeable. Therein lies my question. Is that correct? Because if these two sentences are interchangeable, it destroys all my understanding.  Thanks in advance. I have lecture notes with the claim $(C_b(X), \|\cdot\|_\infty)$, the space of bounded continuous functions with the sup norm is complete.  The lecturer then proved two things, (i) that $f(x) = \lim f_n (x)$ is bounded and (ii) that $\lim f_n \in \mathbb{R}$.  I don't understand why it's not enough that $f$ is bounded. I think the limit of a sequence of continuous functions is continuous and then if $f$ is bounded, it's in $C_b(X)$. So what is this $\lim f_n \in \mathbb{R}$ about? Many thanks for your help. Product of two cyclic groups is cyclic iff their orders are co-prime Say you have two groups $G = \langle g \rangle$ with order $n$ and $H = \langle h \rangle$ with order $m$. Then the product $G \times H$ is a cyclic group if and only if $\gcd(n,m)=1$.  I can't seem to figure out how to start proving this. I have tried with some examples, where I pick $(g,h)$ as a candidate generator of $G \times H$. I see that what we want is for the cycles of $g$ and $h$, as we take powers of $(g,h)$, to interleave such that we do not get $(1,1)$ until the $(mn)$-th power. However, I am having a hard time formalizing this and relating it to the greatest common divisor.  Any hints are much appreciated! Theorem 3.2 Rudin -- How is 0 concluded? I'm having trouble understanding why the arbitrariness of $\epsilon$ allows us to conclude that $d(p,p')&lt;0$. It seems we could likely conclude a value such as $\frac {\epsilon}{100}$ couldn't we?? The other idea that would normally work is the limit (as $n$ approaches $\infty$, $p$ approaches $p'$) but that would mean we are further in another sequence which would have same problem Thanks in advance   $\ $  $\ $  $\ $   Definition of Convergence     A sequence $\{ p_n \}$ in a metric space $X$ is said to converge if there us a point $p \in X$ with the following property: For every $ \epsilon&gt;0$ there is an integer $N$ such that $n \ge N$ implies distance function $d(p_n, p) &lt; \epsilon.$ Why do fantasy writers depict pointy hats as the headgear of choice for Witches and Wizards? They don't always wear a hat, but when they do, it's pointy.   Why do fantasy writers depict pointy hats as the headgear of choice for Witches and Wizards? how to install the DDE to the ubuntu 20.04? I have installed the Ubuntu 20.04, and want now I want to install Deepin Desktop Environment (dde)  My steps are:   add the ppa and install using apt  sudo add-apt-repository ppa:leaeasy/dde sudo apt-get update sudo apt install dde    But during the command sudo add-apt-repository ppa:leaeasy/dde I get the following error:  $ sudo add-apt-repository ppa:leaeasy/dde  You can install deepin desktop environment by run  sudo add-apt-repository ppa:leaeasy/dde sudo apt-get update apt-get install dde ------ Ubuntu Bionic: https://drive.google.com/file/d/1xkQPb4tWocknuYeY-t41W--kz-9SSL0V/view?usp=sharing ------ Important Issue: Q: Can dde on Ubuntu 16.04? A: Sorry, the dde depends on qt version above than 5.6.      If you want to install dde, please upgrade to 17.04 or above.  More info: https://launchpad.net/~leaeasy/+archive/ubuntu/dde Press [ENTER] to continue or Ctrl-c to cancel adding it.  Hit:1 http://in.archive.ubuntu.com/ubuntu focal InRelease Hit:2 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease                                      Hit:3 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease                                    Ign:4 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal InRelease                                      Hit:5 http://security.ubuntu.com/ubuntu focal-security InRelease            Err:6 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release             404  Not Found [IP: 91.189.95.83 80] Reading package lists... Done E: The repository 'http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   I get the similar error with sudo apt-get update :  $ sudo apt-get update Hit:1 http://in.archive.ubuntu.com/ubuntu focal InRelease Hit:2 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease                                       Hit:3 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease                                     Ign:4 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal InRelease            Hit:5 http://security.ubuntu.com/ubuntu focal-security InRelease Err:6 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release   404  Not Found [IP: 91.189.95.83 80] Reading package lists... Done E: The repository 'http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   How can I install dde ? combine 2 fields in 1 to use it in the "group by" section of the reports is it possible to combine two fields in one and use that field to group by in reports? for example, i would like to combine ee id and ee name fields in 1 and show as 1 field in the "group by" section on reports.