Is sum of two square summable sequences is again square summable?
$\sum x_n^2$ and $\sum y_n^2$ converge, what does $\sum (x_n + y_n)^2$ do?
Restored iOS 10 with broken Home button I restarted my iPhone 6 running iOS 10 and the home button is broken, so I was using Assistive Touch. But at the first launch, Assistive Touch is disabled. On iOS 10, we have to "Press home button to unlock".  What can I do? How to minimize residual sum of squares of an exponential fit? I have the following data and would like to fit a negative exponential growth model to it:  Days &lt;- c( 1,5,12,16,22,27,36,43) Emissions &lt;- c( 936.76, 1458.68, 1787.23, 1840.04, 1928.97, 1963.63, 1965.37, 1985.71) plot(Days, Emissions) fit &lt;- nls(Emissions ~ a* (1-exp(-b*Days)), start = list(a = 2000, b = 0.55)) curve((y = 1882 * (1 - exp(-0.5108*x))), from = 0, to =45, add = T, col = "green", lwd = 4)   The code is working and a fitting line is plotted. However, the fit is visually not ideal, and the residual sum of squares seems to be quite huge (147073).   How can we improve our fit? Does the data allow a better fit at all?  We could not find a solution to this challenge on the net. Any direct help or linkage to other websites/posts is greatly appreciated. What are the benefits of modeling in one piece, or as separate parts? Is there any benefit of creating model in one piece or I can create separate pieces and just overlap them to create a visually joint part.  For example, the below image were made from two parts 1. Blade 2. Spinner  Is there any benefit to model them (e.g. extrude from the spinner) or it is actually ok to have them separated since visually I can achieve the same effect (See picture 2) MySQL not using indexes with WHERE IN clause? Where was this picture taken (screensaver on LG Oled TV)? Can someone please tell me where this picture was taken? What is this yellow and white mass inside my red cabbage? Schengen Visa four years- 90 days stay I have been granted multiple entry Schengen Visa valid for 4 years with the duration of stay of 90 days. Does it mean only 90 days of stay in total during a 4 years period?  I'll be travelling to Schengen Area in September for 25 days, then after 2 month or so I will travel again for 30 days. Similarly, I'll be traveling to the Schengen Area in the future depending on the business meetings.  How will I know, that how many days are left? On what basis the calculations are done?  Also, please explain the "90/180" rule. Can we have an option to disable notifications on community wiki posts? Mortarboard badges being awarded as a result of bounties after recalc What is this icon depicting a phone and Wi-Fi together? How to install Gnome 3 without breaking Unity? I tried installing gnome 3 , but it broke Unity and I had to reinstall Natty from scratch.  Does anyone know if there is a way to install Gnome 3 without breaking Unity? In a simple battery + resistor circuit, what form of energy is lost from the electrons upon exiting the resistor? I will give this question a little context. Firstly, as I understand it, as soon as I "close the switch" on a circuit, electric current pretty quickly establishes a steady state where, at any given cross section along a wire, the average kinetic energy of that slice is both constant and equal anywhere along the wire. (Please correct me if I am misunderstanding).   If the average kinetic energy is constant anywhere throughout the wire in the circuit (which confuses me, as I would think that the electrons should all accelerate after exiting the resistor since they are no longer being impeded as much), that means that the average velocity is constant. So, in the example of a simple circuit with a battery of v Volts and a resistor of o Ohms, my question is the following:  Because a 'voltage drop' is known to occur across the resistor, what type energy is being "traded" to generate the heat that radiates from the resistor? I would think that the reflexive answer is "electrical energy"...hence the VOLTAGE drop (the sacrificed energy is clearly not kinetic, as the velocity is constant everywhere). However, I find this confusing. Does this mean that if I had a positive test charge, it would be easier for me to bring it to the beginning of the resistor as compared to bringing it to the end of the resister?     Further, if the correct answer IS "electrical energy", why exactly DOES electrical energy get "dissipated" as the electrons pass through the resistor? I always here the comment Oh! It's because all the electrons are running into densely packed crap which impedes their flow but that to me sounds like a reason for their KINETIC energy to be reduced. However, clearly that's not the case. So, ultimately, I guess the real question is:  **What goes on in the resistor that is literally removing electrical energy **. I am sure that this is a quantum mechanics question, but my quantum mechanics knowledge is not terribly strong. If I could get an answer that is devoid of crazy wave function equations, I would greatly appreciate it. Thanks! Let's assume there's this random company (XYZ)--that few are aware of--is selling stocks and they're doing really well. If their stock price is at $50 and no one is buying, will it still go up?  Do stock prices only go up when people are buying? Error when installing: "unable to find a medium containing a live file system" Error message:  (initramfs) unable to find a live medium containing a live file system   I got this error while trying to install Ubuntu 10.10 from a bootable USB stick on to Asus X64J series laptop. After getting this error the installation fails to start.  I have used the same USB stick on some other laptops and the installation started as usual. Any help will be appreciated. Why does the base of this slinky not fall immediately to gravity? My guess is tension in the springs is a force > mass*gravity but even then it is dumbfounding. How can I mass rename files? I've got a bunch of files named with a the pattern 99 - DescriptiveName.txt and I'd like to remove the number from the front so I just have DescriptiveName.txt.  How can I do this? Can I do it from the command line or is there a utility that can do this? Why are the shebang parts of the following elementary scripts not working:  $ cat hello.sh #! /bin/sh echo Hello $ ./hello.sh bash: ./hello.sh: /bin/sh^M: bad interpreter: No such file or directory  $ cat hello.py #! /usr/bin/env python3 print("Hello") $ ./hello.py : No such file or directory   whereas calling the interpreter manually is working:  $ sh hello.sh Hello $ python3 hello.py Hello Prove there's a simple path of length $k$ in a simple graph $G$ where all the vertices have degree of at least $k$.   Relevant definitions:  $G$ is a simple graph that consists of a vertex set $V(G) = \{v_1, v_2, ..., v_n\}$ and an edge set $E(G) = \{e_1, e_2, ..., e_m\}$ where each edge is an ordered pair of vertices. The edge $\{u,v\}$ is denoted $uv$.  A walk of length $k$ is a sequence $v_0,e_1,v_1,e_2,...,e_k,v_k$ of vertices and edges such that $e_i=v_{i-1}v_i$ for all $i$. A path is a walk with no repeated vertex.   My attempt:  Induction, for $k=1$ it's obvious.  Suppose for $k-1$ and we'll prove for $k$.  Let $G$ be a simple graph such that $\forall v \in V : d(v)\ge k$.  We can assume that there are at least $k+1$ vertices since there are $k$ neighbours to every vertex.  Let $v_0$ be some vertex, it has $k$ neighbours, we'll move to one of its neighbours say $v_1$ and remove $v_0$. So now there are $k$ vertices with a degree of at least $k-1$ and from the induction hypothesis we'll have a path of length $k$.  Is using only $k$ vertices from $n$ right? Does it keep the generality when using only all the neighbours of $v_0$? Many sysv init scripts used a corresponding file in /etc/default to allow the administrator to configure it. Upstart jobs can be modified using .override files. How do I override or configure systemd units, now that systemd is the default in Ubuntu? I have a weird port forwarding problem. I tried to open my port 22 to the outside network. I was able to access it as long as I am not inside the LAN. I can access it from my office for example. But from within the LAN, I can access the port using the local ip, but I can't access the port using the external IP. It's as if the router is blocking the loopback. I've check all my router settings, turned off anything firewall/filtering related. Any ideas?