Unexpected inconsistency, root filesystem requires manual fsck, boots to (initramfs) This shows up on my screen when I boot my laptop on Ubuntu.
fsck error on boot: /dev/sda6: UNEXPECTED INCONSISTENCY; RUN fsck MANUALLY I dual boot Ubuntu and Windows 7. I was browsing on FireFox in Ubuntu and all of a sudden I get some error message, so I rebooted.  Now when I try to boot into Ubuntu I get this message:  fsck from util-linux 2.26.2 /dev/sda6 contains a file system with errors, check forced. /dev/sda6: Inodes that were part of a corrupted orphan linked list found.  /dev/sda6: UNEXPECTED INCONSISTENCY; RUN fsck MANUALLY.         (i.e., without -a or -p options) fsck exited with status code 4 The root filesystem on /dev/sda6 requires a manual fsck  Busybox v1.22.1 (Ubuntu 1:1.22.0-15ubuntu1) built in shell (ash) Enter 'help' for a list of built-in commands.  (initramfs) _   How can I fix this?
Square root of Positive Definite Matrix Prove that a set in $\mathbb R^3$ is not an algebraic set I want to prove that the set $\{(\cos(t),\sin(t),t)\in A^3(\mathbb R); t\in \mathbb R \}$ is not an algebraic set.   I already proved that the set $\{(\sin(t),t)\in A^2(\mathbb R);t\in \mathbb R \}$ is not algebraic but the method that I used doesn't seems to be general. Sigma algebra and algebra difference Connectivity, Path Connectivity and Differentiability I have two questions which pertain to differentiability, connectivity and path connectivity. Ocasionally, I will encounter an author who defines connectivity in the following way:   An open subset $U$ of $\mathbb{R}^n$ is said to be connected if and only if given two points $a$ and $b$ of $U$ there exists a differentiable mapping $\phi: \mathbb{R} \rightarrow U$ such that $\phi(0) = a$ and $\phi(1) = b$.   This particular example is from Edward's Advanced Calculus of Several Variables p 84. Now, this is obviously not the standard definition we learn from topology which has nothing to do with differentiability but rather whether there exists two nonempty open subsets that comprise a separation. It also seems to me that what the author is really defining what it means for a space to be "smoothly path connected", which of course implies connectivity and, it seems to me, considerably more.  My first question is: Is "smoothly path connected", as defined above actually equivalent to "connected", in the topological sense, in $\mathbb{R}^n$?  Next, in Vector Calculus by Baxandall and Liebeck on p 150 the authors state the existence of a continuous path $\alpha$ from the closed interval $[0,1]$ to an open subset $D$ of $\mathbb{R}^n$ where $\alpha (0) = a \in D$ and $\alpha(1) = b \in D$ guarantees the existence of a differentiable path with the same properties. This claim is stated without proof.   My second question is: Can someone provide a reference to a proof of the above claim or explain why it is so? Prove or disprove an inequality involving complex numbers Consider following inequality:     $|z_1 + z_2|\ge|z_1| - |z_2|  \  \ \ \ \ \  z_1,z_2 \in \mathbb{C}$   Is that true always? I tried many examples and it was correct but I don't know how to prove that if it's right. For some or other reason, typing @ᔕᖺᘎᕊ in a chat room pings everyone who's been in that chat room for the last 7 days...    Seems to work in all chat rooms (I only tested 2 as I don't want to upset too many people...)  How should we proceed? Explanation behind Second Derivative of a Parametric Equation Formula Is it possible to cancel or clear a notification created by using notify-send? So I wrote a little script that makes sure a certain user plugs in a laptop when he logs on (it disables if he doesn't). The script uses notify-send to tell him to plug it in. If he plugs it in, the script quits. Is it possible to clear the notification automatically when he plugs it in? I'm thinking it might require somehow getting the process id spawned by notify-send and killing that PID, but I don't know how to do this.  Here's the current script:  #!/bin/bash   cat /sys/class/power_supply/BAT0/status OUTPUT="$(cat /sys/class/power_supply/BAT0/status)" echo "${OUTPUT}" if [ "${OUTPUT}" = "Charging" ] || [ "${OUTPUT}" = "Unknown" ]; then     echo charging or full elif [ "${OUTPUT}" = "Discharging" ]; then     notify-send -i /home/evamvid/Documents/Programming/OokiNoUse/power25.png "Hey there brother" "plug it in"     COUNTER=0 while [ "$COUNTER" -le 12 ] do     cat /sys/class/power_supply/BAT0/status     OUTPUT="$(cat /sys/class/power_supply/BAT0/status)"     echo "${OUTPUT}"     if [ "${OUTPUT}" = "Charging" ] || [ "${OUTPUT}" = "Unknown" ]; then         exit     elif [ "${OUTPUT}" = "Discharging" ]; then         COUNTER=$(($COUNTER+1))         echo $COUNTER         sleep 1     fi done fi What is appropriate to use here, who or which?       There are around 50 companies who/which deliver scanning services to private and business consumers. Solving $a \sin\theta + b \cos\theta = c$ Could someone help me with the steps for solving the below equation $$a \sin\theta + b \cos\theta = c$$ I know that the solution is $$\theta = \tan^{-1} \frac{c}{^+_-\sqrt{a^2 + b^2 - c^2}} - \tan^{-1} \frac{a}{b} $$ I just can't figure out the right steps to arrive at this solution. I am having a problem understanding displacement maps. I'm starting to think that I don't understand them at all.  Clarifying My Understanding  My understanding (which might be completely wrong), is that a displacement map is a gray-scale image whereby a value of 0.5 produces no displacement, >0.5 produces displacement in the positive direction, and &lt;0.5 produces displacement in the negative direction. This, however, does not seem to match my actual observations in Blender.  I am using a displacement map within Cycles, plugging it into the Displacement socket on the Material Output node (I am also using the new experimental adaptive subdivision and micro-vertex displacement). I note that a value of 0.5 actually produces a displacement in the positive direction, causing the whole mesh to jump up slightly, as well as creating the peaks and valleys that you would expect for >0.5 and &lt;0.5 values respectively.  This affects my entire understanding of displacement maps. Why is this happening? Why is a value of exactly 0.5 creating displacement? Further, how are you supposed to arrange and line up objects in your scene when, in rendered view, the displacement maps will push them out of position, even if those maps are only supposed to create displacement in specific areas.  The Problem in Practice  This is the problem I am having at the moment. I have a plane which is supposed to be a snowy field, and I am using a displacement map to give some depth to the snow. In rendered view, my plane jumps up significantly. This is what lead me to investigate my understanding of displacement maps, and to this question.  Additionally, what is the correct way to increase and decrease the strength of a displacement map? At the moment, I will run them through a Math node set to multiply, however, as you might imagine, this exaggerates the issue that I am complaining about above.  To be clear, however, I am not using a math node when experiencing the "jump up" for 0.5 values. This is not the source of my problem, but another aspect to it. Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$. The title of  of  is, "Is it posible [sic]?"  This doesn't provide any information at all. It should be mandatory for everyone asking questions on the Internet to read , which says:     Help your community learn from the question. When you field a good question, ask yourself "How would the relevant documentation or FAQ have to change so that nobody has to answer this again?" Automatic field should take the required entry Is this correct for Rudin exercise 3.7? Prove the series is convergent This is Baby Rudin exercise 7 of Chapter 3. Prove that the convergence of $\sum{a_n}$ implies the convergence of $\sum{\sqrt {a_k} \over k}$ if $a_n \ge 0$.  Proof:  I will attempt to show that the cauchy criterion is met so $${\sum_{k=n}^m {\sqrt {a_k} \over k}} \le \epsilon $$ for all $n,m \le N_1$. Im disregarding the absolute value since its all positive terms.   Since $\sum{a_n}$ converges, we know that the $\lim \limits_{n \to \infty} a_n =0$ So there exists some $N_2$ such that for all $n \ge N_2$, $$   a_n \lt \ {{(m-n)}^2k^2(\epsilon)^2} $$ I am again disregarding the absolute values because its always positive Let N=max{$N_1,N_2$} then for all $n,m \ge N$ $$\sum_{k=n}^m {\sqrt {a_k} \over k} \le \sum_{k=n}^m {\sqrt {{(m-n)}^2k^2(\epsilon)^2} \over k} \le \sum_{k=n}^m{(m-n)(\epsilon)} = \epsilon $$  Maybe this is just crazy, should I just use Cauchy-Schwarz inequality and forget about this or could I possibly make this method work? How many non congruent trapeziums are possible with the side lengths from {1,3,4,5,6} I need to find number of mutually non  congruent trapeziums with side lengths from {1,3,4,5,6}.   I know for a trapezium with a,c as non parallel sides the condition for my question is that  $$|a-c|&lt;b+d&lt;a+c$$  But i cant apply it to count the cases. Can someone help in how to get the number of cases? Can't save batch file shortly after running it on Windows 7 My laptop's cable broke and sadly it seems like I need to buy a new power supply.  What I wonder is, I've found that universal power supplies are much cheaper than the official HP ones. Are they really worth it?  Another question: the original supply has these specs: 65W, 18.5V, 3.5A. However the universal supplies are more powerful (90W, 100W) and come in integer voltages (17V, 18V, 19V, etc). Are they compatible? Should I set them to 18V or 19V? I'm using Chrome 32 on an Android tablet (not phone) and just can't figure out how to close all open tabs in one go. How do I find (or exclude) all directories and sub-directories matching a certain pattern (in Linux)?