The windows 10 task manager suddenly shows two curves for CPU utilization, one light colored and one darker blue colored:   As far as I remember, it always used to show just one curve for current CPU utilization. What do the two curves mean? Which one should I trust to be correctly describing the resources spent on the current task?
I was looking at the task manager in Windows 10 and for the first time noticed a secondary dashed line below the solid? What does this line indicate?
How to start/stop/restart a thread in Java? How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$ Emmy Noether's theorem in simpler terms I'd like to understand  and its contents as to what it implies in a bit simpler terms. I am familiar with mathematics unto Calculus 1,2,3 and some linear algebra and group theory. I am familiar with that for each symmetry there is a conservation law.    Now is there a one-one correspondence between these two always? What about laws like conservation of charge?  And conservation of energy?  And conservation of mass?  Considering our view of nature was changed as Special Relativity was introduced and thus, what earlier the theorem would have asserted as mass and energy to be originating from different symmetries then how did we reconcile these two as just one symmetry? From the  on the dual of a norm:  $X$ and $Y$ are normed spaces, and we associate with each $f\in L(X,Y)$ (the space of bounded linear operators from $X$ to $Y$) the number $$\|f\| = \sup\{|f(x)|:x\in X, \|x\| \leq 1\}.$$  At some point in the proof that $L(X,Y)$ is bounded, it seems like they use the inequality $$\|fx\| \leq \|f\|\cdot\|x\|,$$ where $\|x\|\leq 1$.  I can't see why this should holds.   $\|f|\|$ is the supremum of what $|f(x)|$ can be, given that $\|x\|\leq 1$. So, given that $\|x\| \leq 1$, $|fx|$ should be bounded by $\|f\|$. But why should it be bounded by $\|f\|\cdot\|x\|$? Prove $\int_{a}^{b}{f(x)dx}>0$. Let $f\ge0$ be integrable on $[a,b]$. Let $f$ be continuous on $x_0\in (a,b)$ and let $f(x_0)&gt;0$.   Prove $$\int_{a}^{b}{f(x)dx}&gt;0$$  It is easy to see it, graphically, because $$f\ge 0 \Rightarrow\int_{a}^{b}{f(x)dx}\ge0$$  and if $f&gt;0$ somewhere between $a$ and $b$, then the zone of $F$ between those point is "real" (positive) and $\ne 0$.  My problem is, how do I show it formally?  I would appreciate your help. Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal. Prove: Let $R$ a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.     I got stuck on this. I understand that every ideal is generated by finitely many elements. Here is my approach:  It's enough to prove the following implication: $$ R/I \ \text{is a domain} \quad \Rightarrow \quad R/I \ \text{is a field}$$ Then only finding an inverse is left. So let $x \in R$ in arbitrary. We have to find an inverse element of $x+I \in R/I$, that as an element y so that $x \cdot y \in I+1$. We denote $I = (x_1, x_2, \cdots, x_n)$.  Now I have to find y so that $xy -1 = r_1 x_1+ r_2 x_2 + \cdots + r_n x_n$. This is where I no more knew what to do.   Your advise will be appreciated. Cardinality of the set of bijective functions on $\mathbb{N}$? Expectation of truncated normal Teenagers find an ancient lizard creature in stasis and accompany him on adventures to an undersea city When I was a kid, I read a book (likely from the '60s) about a pair of kids who find an ancient lizard/fish man inside a cave. The cave has been recently exposed by an earthquake and the creature is inside a super technologically advanced stasis chamber. I think this creature's name is something like "Sslaa". He takes the kids on a quest to find his lost underwater city.  They end up finding the city, which is still populated by creatures like himself and protected from the ocean above by an immense diamond dome. Eventually, Sslaa has to drive an advanced mining vehicle deep into the crust of the earth, presumably to prevent his city's destruction by an impeding magma flow or other seismic event.  For extra obscurity bonus points, I could swear I managed to find this book on Google several years ago, and was shocked to learn that it had originally been written in German, and then translated to English.  Does anyone out there recognize this one? Question:  Let ${a_n}$ be a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$  Prove that  $\lim_{n\to\infty}a_n^2=a^2$  Attempt: Without using any properties of limits (this is a question in a section of the book that came before any list of any limit theorems)  By definition:  $|a_n^2-a^2|&lt;\epsilon$   $|a_n^2-a^2|$ $\leq$ $|(a_n+a)(a_n-a)|$ $\leq$ $|(a_n+a)| |(a_n-a)|$ $\leq$   $(|a_n | + |a|)(|a_n -a|)$ $&lt;$ $\epsilon$  And since I know that $\lim_{n\to\infty}a_n=a$, I'll subsitute that in for $|a_n|^2$ as $a^2$   $\therefore$ $a^2-|a|^2 &lt; \epsilon$ which is true since $a^2-|a|^2$ in my case.  I wonder if this is a possible solution? Often I see code blocks pasted into questions with no formatting, or terrible formatting.  It's sometimes quite a chore to fix these: you have to either manually space out each line, or paste the code into an IDE, format it there, and paste it back.  Could we have a button/function where you could highlight a code block, and it would turn this:  foreach (var i in stuff) { if (i==1) { Whatever(); } }   into this:  foreach (var i in stuff) {   if (i==1) {     Whatever();   } }   I realise the function would have to work differently based on the language in the code block. Perhaps  it could use the same rules as the prettify code.  Also, it wouldn't be a big deal if it gets the language wrong and breaks the code, since you can always just ctrl+z. Ugly "Next Privilege" text on user activity page Install CentOS 7 on HP dl120 gen9 server with b140i raid controller I'm trying to install CentOS 7 on a HP DL120 gen 9 server with a b140i controller. I have 4 1TB HDD setup in a raid 1+0 and the CentOS installer doesn't seem to recognize the logical drive created from the storage utility.  From my understanding i need some drivers for CentOS 7 to recognize the B140i controller. Also, the driver seems to be closed source by HP.  What is my approach here? Is there any other free linux OS that i can use on this server and that would recognize the raid controller?  Thank you. VSE isn't multi-threading Whenever I render a video using the blender video editor only one core is ever used at any time. I have an 8 core CPU(FX-9590) yet regardless of whether blender is set to auto detect or a fixed 8 threads only one core ever sits at 100% at any given time. The rest of the cores sit and really low usage as if blender is completely ignoring them. I'm running blender 2.77a on Linux. I'm using Theora as the codec with an ogg container and Vorbis audio. How do I get blender to use all my cores? This should be a very easy question but it might just be that I'm confusing myself. So we have the definition of a function $f$ on $S$ being continuous at $x_0$:     For any $\epsilon$>0, there exists $\delta&gt;0$ such that: whenever $|x-x_0|&lt;\delta$, we have $|f(x)-f(x_0)|&lt;\epsilon$   And I assume the negation is     There exists $\epsilon$>0 such that for all $\delta&gt;0$, $|x-x_0|&lt;\delta$ yet $|f(x)-f(x_0)|\ge \epsilon$.   Now I want to show that the function $f(x)=\sin(\frac{1}{x})$ together with $f(0)=0$ cannot be made into a continuous function at $x=0$. So I need to show that there exists $\epsilon&gt;0$ such that for all $\delta&gt;0$, $|x|&lt;\delta$ yet $|f(x)|\ge\epsilon$.  Let $\epsilon = \frac{1}{2}$. Then no matter what $\delta$ we choose, let $|x|&lt;\frac{1}{2}$. It is certainly possible that $|f(x)|\ge \frac{1}{2}$, because, well, $\frac{1}{x}$ can really take on arbitrarily large value as $x$ is small.  Now, what confuses me is that, as $x$ gets small, $f(x)$ can certainly be greater than $\frac{1}{2}$ for infinitely many times, but it will be less than that infinitely many times, too. But I suppose it doesn't really matter. So I think there's something wrong with my negation but I couldn't figure out where.  Update: The correct version can be found . Watch for Lemma 4.6 Equivalent Resistance? How do you find the equivalent resistance here? (I realized it's a Wheatstone bridge, but it's unbalanced, so that doesn't help.) I tried using Kirchhoff's laws, but there is no cell given. Differentiation - simple case In the book calculus made easy, page 22 the case of the negative power for   $y=x^{-2}$    $$\begin{align}  y+dy &amp; =(x+dx)^{-2}\tag{1}\\ \\ &amp; = x^{-2}\left(1+\frac{dx}{x}\right)^{-2}\tag{2} \end{align}$$  How do they get from $(1)$ to $(2)$?  And why isn't the binomial function applied to the second line but applied on the third line (the line that comes after line $(2))$? How can I determine if someone's SSH key contains an empty passphrase? Some of my Linux &amp; FreeBSD systems have dozens of users. Staff will use these "ssh gateway" nodes to SSH into other internal servers.  We're concerned that some of these people use an unencrypted private SSH key (A key without a . , because if a cracker ever gained access to their account on this machine, they could steal the private key and now have access to any machine which uses this same key. For security reasons, we require all users to encrypt their private SSH keys with a passphrase.  How can I tell if a private key is not-encrypted (e.g. Does not contain a passphrase)? Is there a different method to do this on an ASCII-armored key vs. a non-ASCII-armored key?  Update:  To clarify, assume I have superuser access on the machine and I can read everybody's private keys. Combinatorics Distribution - Number of integer solutions Concept Explanation I reading my textbook and I don't understand the concept of distributions or number of solutions to an equation.  It's explained that this problem is 1/4 types of sampling/distributions problems.  An example is provided to illustrate:     In how many ways can 4 identical jobs (indistinguishable balls) be distributed among 26 members (urns) without exclusion (since one member can do multiple jobs)?      A sample outcome might be:   $\text{_____________}$   |  A  |  B  |  C  |...|  Z  |    $\text{--------------------}$      $\text{_____________}$   |  o  | oo|    |   |    ||| o  |    $\text{_____________}$   |  A  |  B  |  C  |...  |  Z  |    $\text{--------------------}$      Thus, the question is reduced to, "How many $(26-1+4)$ letter words are there consisting of four circles and $(26-1)$ vertical lines?"  Therefore, the solution is:  $\binom{26-1+4}{4}$   I really don't understand why its $(26-1+4)$.  There's only 26 different spots or "urns" to place the 4 jobs.  Can someone please explain?    I looked through another text to try and understand and I found it explained as such:       There are $\binom{n+r-1}{r-1}$ distinct nonnegative integer valued vectors $(x_1,...,x_r$ satisfying the equation $(x_1 + ... + x_r = x_n$ for $x\ge0$. $\spadesuit$   How in the world are they deriving this?  For distinct positive integers I understand:  Assume I have 8 balls (n=8) and I have 3 urns (r=3): o^o^o^o^o^o^o^o, where o represents  a ball and ^ represents a place holder where an urn could be placed.  For this scenario:     There are $\binom{n-1}{r-1}$ distinct positive integer valued vectors $(x_1,...,x_n)$ satisfying the equation:  $x_1 + ... + x_n = n, x_i&gt;0, i=1,..,r$ $\clubsuit$   It's clear that I could have this specific case ooo|ooo|oo.  Here the bar represents a divide for the urn and you see I have 3 sections.  So that case is clear.  Can anyone please explain this problem to me?  I don't understand the nonnegative integer case.   Also, people who post tend to be crazy smart and explain things very in a complicated manner.  I'd appreciate it if it could be explained in layman's terms as much as possible.   Thank you!!! Is a continuous function on a bounded set bounded itself? If $f\colon A\to\mathbb R$ is continuous and $A$ is a bounded set, does it necessarily follow that $f$ is bounded?