Lipschitz continuity power type function Is the function $f(x)=x^{\gamma+1}$, where  $x&gt;0 $ and $\gamma&lt;0$ Lipschitz continuous ? I am a bit confused !
Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous? Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous near $0$? If yes, find a constant for some interval containing $0$.   I think the answer is yes since I can find $L=1$ that satisfies Lipschitz continuity criteria in a interval close to $0$, am I right?
Any way to send a personal message to another user? One hour Lufthansa transit time in Frankfurt from Bangalore to Dublin Basic voltage divider issue in my amateur circuit XBee Once again I need your help in my project. I have a 4,5v powered circuit. I put a voltage divider with 2 resistors in series to reduce my initial voltage of 4.5 V to 3.4 V (to feed an XBee module).  The issue is that if I do not connect the xbee, the voltage divider reduces the input voltage to the desired voltage(3.4 V), but when I connect the XBee module, the resulting voltage divider voltage drops to a value very low (0.85 V), making the XBee malfunction. Surely it is a basic mistake, I am asking something that is very clear, but I'm newbies.   Basic Circuit:  Vin(4.5 V)-----R2(10 kΩ)---------R1(33 kΩ)--------GROUND                        |                        |                  Vout desired (3.4 V)                        |                        |                       XBee Fundamental question about dimensional analysis Checking out  and  (and some papers) was a bit difficult for understanding Group Action. The closest to understanding was this part:    I understand the definition of homomorphism (a structure-preserving map between two algebraic structures of the same type). And from what I understand the symmetric group is a group of functions (bijective functions) mapping elements of a set $X$ onto itself.  However I get confused at this line:     ...an action of $G$ on $X$ may be formally defined as a group homomorphism $\phi$ from $G$ to the symmetric group of $X$.   That seems to be the definition of group action, but I am having trouble understanding how to apply that.  What that says to me is it is a homomorphism (function) $f \colon X \rightarrow S$ where $S$ is a set of bijective functions on $X$. That itself seems weird, I thought a group action would result in a number or something related to $\{1, 2, 3\}$ (defined next).  Continuing, if we have a set $X = \{1, 2, 3\}$ and a group $(*,\{4, 5, 6\})$, then the symmetric group of $X$ would be something like $S = \{1 \rightarrow 2, 2 \rightarrow 3, \dots \}$, and $\phi$ would be something like $f : \{4, 5, 6\} \rightarrow S$. That doesn't make sense to me and I feel like I'm interpreting something wrong. I don't see how mapping to a set of functions $S$ will result in an action on the set. Did Obi-Wan Kenobi ever become more powerful? In Star wars: IV A New Hope, Obi-Wan says to Darth Vader:     You can't win, Darth. If you strike me down, I shall become more powerful than you could possibly imagine.    What did he mean by this? Was he bluffing? Was he alluding to him being able to help Luke as a Force Ghost? Or was he talking on behalf of The Force? USB sticks and multiple partitions How does electricity propagate in a conductor? More than a decade ago, I read a short story about a small group of people at the end of the world. The story was premised on some sort of mass-produced device which took ambient heat and turned it into power. The devices had been overused, and now the world was freezing.   I think the people were essentially bandits; the main character may have been a woman who lured men to her house and killed them for their body heat? There was also a strong implication that one person she had done this to was an alien who had come to warn that the devices were destroying the world.  I think the story was in a hardbound collection, and I think the collection was from the late 70's or very early 80's.  (Calling it a "short story" is just meant to distinguish it from a full novel — it may have actually been a novella or similar.) Currently in my last year of high school, and I have always been told that  does not exist by my physics teachers. Today my girlfriend in the year below asked me what centrifugal force was, I told her it didn't exist, and then she told me her textbook said it did, and defined it as "The apparent force experienced towards the outside of a circle is the centrifugal force and is due to the mass of the object resisting the inward centripetal acceleration that the object is experiencing". I was pretty shocked to hear this after a few years of being told that it does not exist.  I did some reading and found out all sorts of things about pseudo forces and reference frames. I was wondering if someone could please explain to me what is going on? Is it wrong to say that centrifugal force does not exist?   This has always nagged me a bit as I often wonder that if every force has a reaction force then a centripetal force must have a reaction centrifugal force, but when I asked my teachers about this they told me that centrifugal force does not exist. I have a doubt on something. I have a theorem that says that if $R$ is a ring, then $R/I$ is a domain iff $I$ is prime. Since $X^2-1$ is note prime, $\mathbb Z[X]/(X^2-1)$ is not a domain. But, $X^2-1=(X-1)(X+1)$, and since $X-1$ and $X+1$ are prime in $\mathbb Z[X]$, there are coprime, and thus, by the chinese remainder $$\mathbb Z[X]/(X^2-1)\cong \mathbb Z[X]/(X-1)\times \mathbb Z[X]/(X+1),$$ since $\mathbb Z[X]/(X-1)\times \mathbb Z[X]/(X+1)$ is a domain, then so is $\mathbb Z[X/(X^2-1)$. What is the mistakes here ? Add parenthesis as an accepted Markdown ordered list delimiter The Markdown editor knows that an empty line, followed by a number, followed by a period, followed by a space, is a list item.  This works great It's almost magic  The problem is that I almost always use a close parenthesis for my lists. I think it's a pretty common practice, but the problem is that the editor / Markdown parser doesn't accept parenthesis as an acceptable list delimiter:  This fails horribly This is on the next line I swear I stupidly ran sudo rm /* followed by sudo rm -R /*  My sites still run, although the vast majority of commands like ls are now broken.  Is there a simple way to get data off the server or reverse some of damage? Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$ As we all know, air consists of many gases including oxygen and carbon dioxide. I found that carbon dioxide is heavier than O2. Does the volume difference neglect the mass difference? Is it same for all other gases in air or is there another force that keeps all of these gases together?  If I take a breath of a fresh air, will the exhaled air be heavier because of its higher CO2 content? Will it fall on the floor? Adding hyperlinks to pop-up data in qgis2web? Does anyone know if it is possible to add hyperlinks to image fields etc. in the pop-up windows of Qgis2web?  I've had a look in the layers javascript file, but the image source path isn't rendered using html, so I can't simply append &lt;a href" to it.  The image is coming in via the usual method of having a field that contains the path of the image file.  I'd like to achieve linking of the image, like in the example below. Alternatively, I could just populate the 'more info' field with the URL, but if I did that I'd like to avoid just doing it by having a field that contains the entire URL, as some may be quite long (these will only be internal links). Is it a good idea to take a break from studying a mathematics PhD and revisit academia at a later stage? Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact? History of changes to a particular line of code in Subversion Is it possible to see the history of changes to a particular line of code in a Subversion repository?  I'd like, for instance, to be able to see when a particular statement was added or when that statement was changed, even if its line number is not the same any more. If $a^2$ divides $b^2$, then $a$ divides $b$