“COVID-19 changed / has changed / has been changing the everyday life of people”
How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er?
Why would I want to use Interfaces? I understand that they force you to implement methods and such but what I cant understand is why you would want to use them. Can anybody give me a good example or explanation on why I would want to implement this. What is object serialization? What is meant by "object serialization"? Can you please explain it with some examples? What IDE to use for Python? Fill the area under minimum of two functions using tikz and pgfplots Standard and/or common directories on Unix/Linux OSes How Do I Compute the Eigenvalues of a Small Matrix? Is there a way to show that $\sqrt{p_{n}} < n$? Is there a way to show that $\sqrt{p_{n}} &lt; n$?  In , I show that $f_{2}(x)=\frac{x}{ln(x)} - \sqrt{x}$ is ascending, for $\forall x\geq e^{2}$. As a result, $\forall n \geq 3$ $$\frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}}\leq \frac{p_{n+1}}{ln(p_{n+1})} - \sqrt{p_{n+1}}$$ Also (and as a result), $\forall n \geq 3$ $$ \frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}} &gt; 0$$ Or $$ \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$  According to  $$\displaystyle\smash{\lim_{n \to \infty }}\frac{\pi (p_{n})}{p_{n}/ln(p_{n})}=1$$ Or, $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; 1+ \varepsilon$$ Or $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$ As a result $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$(1 - \varepsilon ) \cdot  \sqrt{p_{n}} &lt; \pi (p_{n}) = n$$  But this is not enough.  Interestingly,  is true iff function $f_{4}(x)=\pi (x) - \sqrt{x}$ is strictly ascending ($x &lt; y \Rightarrow f(x) &lt; f(y)$) for prime arguments.  If $f_{4}(p_{n}) &lt; f_{4}(p_{n+1})$ then $$\pi (p_{n}) - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \sqrt{p_{n+1}}$$ Or $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \pi (p_{n}) =1$$  And vice-versa, if $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; 1$$ Then $$-\sqrt{p_{n}} &lt; -\sqrt{p_{n+1}} + 1$$ Or $$\pi (p_{n})-\sqrt{p_{n}} &lt; \pi (p_{n}) + 1 -\sqrt{p_{n+1}} = \pi (p_{n+1}) -\sqrt{p_{n+1}}$$  So, if Andrica's conjecture is true then $\forall n \geq 3$ $$\pi (p_{n})-\sqrt{p_{n}} &gt; 0$$ Or $$\sqrt{p_{n}} &lt; \pi (p_{n})= n$$ Explanation of method for showing that $\frac{0}{0}$ is undefined One server with multiple desktops "heads" with VNC I am managing a system of kiosks.  Each kiosk currently is running a web browser with the application for the kiosk running in the browser.  Each kiosk needs to be able to display separate content.  At times, the application running in the web browser freezes.  Thus, I have to go out to the site to refresh the page.  I want to see if there is a way to have one central server that has multiple browser heads.  Then each kiosk would run a program like VNC to display one of the heads.  This way when the program freezes, I just have to login to the central server and refresh the page.  Getting VNC or another remote desktop software installed on the clients is no problem.  What I am looking for is a way to have VNC remote into a specific head of a head of a web browser.  Does such a thing exist?  Or do I have to run a VM for each kiosk to remote into?  Any advice, pointers, or solutions would be helpful. Because of past conflicts, I don't believe my advisor will write me a good LOR for postdoc positions. What should I do? How do I reset my Unity configuration? I've been messing around with Unity and broke something, how do I "start over"? Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$ If $x.y.z=1$ show that $\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}=1$  My attempt - L.H.S$=\dfrac 1{1+x+y^{-1}}+\dfrac1{1+y+z^{-1}}+\dfrac1{1+z+x^{-1}}$  $=\dfrac y{y+xy+1}+\dfrac z{z+yz+1}+\dfrac x{x+zx+1}$  $=\dfrac{yz}{yz+xyz+z}+\dfrac z{z+yz+1}+\dfrac x{x+zx+1}$  What to do next? Rendered image doesn't show what Rendered Viewport shows... (pictures below) this is my first question on PhysicsSE (I'm already an user of MathSE).   I'm a mathematics students trying to understand Faraday's law, that is   $$\varepsilon= -\frac{d \Phi_B}{dt}$$  where $\varepsilon$ means electromotive force and   $$\Phi_B=\iint \mathbf{B}\cdot d\mathbf{S}$$   means flux of magnetic field. As my textbook points out, there is an interpretation problem here: if the change in magnetic flux is due to movement of the conductor, then free charges in it are subject to Lorentz force, which then causes a current. On the contrary, if the conductor holds steady in a changing magnetic field, the induced current must be explained in terms of an electric field $\mathbf{E}$, described by the equations   $$\begin{cases} \nabla \cdot \mathbf{E}=\frac{\rho}{\varepsilon_0} \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}\end{cases}.$$  Question Do those equations hold if we have a moving conductor in a stationary magnetic field? I guess not: this would mean $\mathbf{E}=\mathbf{0}$. How to solve this? Is the universe fundamentally deterministic? I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you think that this is a duplicate or inappropriate for this forum. Anyway, I'm an electrical engineer and I have some basic knowledge of quantum mechanics. I know that Schrödinger's equation is deterministic. However, quantum mechanics is much deeper than that and I would like to learn more. If this question is not clearly answerable at this point than can anyone point out some recognized sources that try to answer this question. I would appreciate it if the source is scientific and more specifically, is related to quantum theory. I have unistalled and reinstalled the Ubuntu Software Center as per info I found in a similar thread and I got the same response about line 91 or something like that.  I just tried to upload a screen shot but since I'm new it won't allow me to.  I also can not figure out how to cut and paste anything so I have to hand type what the error screen says, both when I attempt to open the software center and nothing happens, when I try to enter commands into the terminal to uninstall, reinstall, whatever I get the same following:  COULD NOT INTITIALIZE THE PACKAGE INFORMATION An unresolvable problem occured while initializing the package information Please report t:his bug against the 'update-manager' package and include the following error message: 'E: Malformed line 91 in source list/etc/apt/sources.list (dist parse)  E: The list of sources could not be read.,  E: The package list of status file could not be parsed or opened.   How do I report bugs?  What can be done about this.  I have searched and everything everyone says to do leads me back to the same line error message.  So, I don't know how to get to line 91 in the source list; to tell you what it says. Sorry, I'm really new to this. That is what I need is to find out how to get there and fix what it says. I would really like to NOT have to re partition my hard drive and start from scratch, so I'm really looking forward to getting this problem solved. I need to be able to install new software. nodejs vs node on ubuntu 12.04 Ubuntu Server 18.04 LVM out of space with improper default partitioning Interpreting the 'metric' column in routing table I'm a little confused about the output I'm seeing in my routing table, particularly the 'metric' column:  $ route -n Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface 0.0.0.0         192.168.0.1     0.0.0.0         UG    0      0        0 wlan0 172.16.35.0     0.0.0.0         255.255.255.0   U     0      0        0 vmnet1 192.168.0.0     0.0.0.0         255.255.255.0   U     9      0        0 wlan0 192.168.82.0    0.0.0.0         255.255.255.0   U     0      0        0 vmnet8   According to the man page, metric indicates the 'distance' to the target. I was a little confused about what exactly "target" was. I assumed it was my router (it goes to gateway 0.0.0.0, which then goes to my router at 192.168.0.1). Thus, I expected the metric to be a single hop to my router. However, it's 9! Why is this so number high? I use Gedit a lot and thus tend to have a lot of tabs open at any one time. In Gedit 2.* I could switch between tabs using my mouse wheel but since Oneiric I can't. I assume this is because of various GTK "upgrades".  Does anybody know of a plugin (or workable fix -- that doesn't require me to recompile everything and its brother) that will see me back to mousewheeling my day away?