Participles in sentences
"...would have trouble imagining...": Is this present participle or gerund?
A simple regex search and replacement in php for minifying/compressing javascript? Can I visit the US for tourism on a previously unused B1/B2 visa? Note: This is NOT a duplicate of  Difference: In both other questions, the posters traveled once to the US for the original purpose for which the B1 visa was obtained. Their question is about visiting again using the same visa. However, I've not traveled to the US yet, and I'm planning my visit. What I want to understand whether I can use this visa for a visit whose purpose is not the same as what was submitted along with the application.  Can I use a B1/B2 visa for tourism that was originally obtained for business purposes BEFORE I actually visit the US even once? I had applied for a business visitor visa for a valid business reason but by the time I got it stamped, my plan changed. So I've not visited the US even once. Can I now use this visa to visit as a tourist without having used that visa for its original intended purpose? PS: I live in India. Find the representing matrix with the respect to the standard basis Let $\Bbb R^2$ be a finite-dimensional vector space and $T:\mathbb{R}^2\to \mathbb{R}^2$ a linear operator. Let $[T]_B =  \begin {bmatrix}0 &amp; 0 \\-1 &amp; 1 \end{bmatrix} $ be a matrix representation of $T$ in the basis $B= (1,1),(-1,0)$.   How can I find the matrix $[T]_E$ where $E$ is the standard basis $(1,0),(0,1)$ if the transformation isn't given in the question?  Thanks,  Alan Proving that $f(x)$ is less than or equal to $1+\pi/4$ Suppose $f$ is a real valued differentiable function defined on $[1,\infty)$ with $f(1)=1$. Suppose also that $f$ satisfies $$f'(x)=\frac{1}{x^2+f^2(x)}.$$ The question is to prove that $f(x) \leq 1+\pi/4$ for every $x \geq 1$    I tried to solve the differential equation but could not bring it in some known form. I examined the derivative of $\tan^{-1}x$ which looks similar to that  in the question. However I could not get any idea with that. Any help shall be highly appreciated. Thanks. Residence has changed - Must I re-apply for ESTA? I have an old, but still valid ESTA, with the country of residence showing my home country. However, I have recently moved for education in the UK. Do I have to apply for a new one?  Nothing else has changed - country of citizenship, passport, names etc Solution for PHP / MySQL website loading fast in multiple regions How far do you go with const?  Do you just make functions const when necessary or do you go the whole hog and use it everywhere?  For example, imagine a simple mutator that takes a single boolean parameter:  void SetValue(const bool b) { my_val_ = b; }   Is that const actually useful?  Personally I opt to use it extensively, including parameters, but in this case I wonder if it's worthwhile?  I was also surprised to learn that you can omit const from parameters in a function declaration but can include it in the function definition, e.g.:  .h file  void func(int n, long l);   .cpp file  void func(const int n, const long l)   Is there a reason for this? It seems a little unusual to me. Windows losing IPv6 address after ~10 minutes When I initially connect to my home network my windows PC is assigned an IPv6 address - however after a few minutes it loses this address! I seem to have similar behaviour on multiple hosts using both wireless and wired connections.  My router is an Asus RT-AC87U.  How could it be losing the IPv6 address? How can I mintor / diagnose this issue?  Update:  Based on @grawity's suggestion below I ran wireshark on this. Sure enough I see a Router Solicitation message and a Router Advertisment message with a Router lifetime of 600 seconds. After 600 seconds my computer drops its Ipv6 address.  What is supposed to happen? Should my host send another Router Solicitation message? Or should the router periodically resend the Router Advertisment message?  Update 2:    says that Router Adverticement messages should be sent periodically. Show $\frac{a_{1}+...+a_{n}}{b_{1}+...+b_{n}}$ is between the smallest and largest fraction $\frac{a_{i}}{b_{i}}$, where $b_{i}&gt;0$.  Attempt  Assume the largest is $\frac{a_{n}}{b_{n}}\Rightarrow$  $\frac{a_{n}}{b_{n}}-\frac{a_{1}+...+a_{n}}{b_{1}+...+b_{n}}\Rightarrow $  $\frac{b_{1}+...+b_{n-1}}{{b_{1}+...+b_{n}}}[\frac{a_{n}}{b_{n}}-\frac{a_{1}}{b_{1}+...+b_{n-1}}-...-\frac{a_{n-1}}{b_{1}+...+b_{n-1}}]\Rightarrow $  if $a_{1}&lt;0$, $w=\frac{a_{n}}{b_{n}}-\frac{a_{1}}{b_{1}+...+b_{n-1}}-...-\frac{a_{n-1}}{b_{1}+...+b_{n-1}}&gt;\frac{a_{n}}{b_{n}}-\frac{a_{2}}{b_{1}+...+b_{n-1}}-...-\frac{a_{n-1}}{b_{1}+...+b_{n-1}}$  any hints or solutions? What does a linear transformation do to a vector in $\mathbb{R}^2$ $\newcommand{\Reals}{\mathbb{R}}$Doing some linear algebra. This question has me intrigued. I imagine it causes the vector to rotates the $x$ axis. But I mean, is there more to it?  $$ T_{A(\theta)}: \Reals^2 \to \Reals^2,\qquad A(\theta) =  \left[\begin{array} {rr}\cos \theta &amp; -\sin \theta \\   \sin \theta &amp; \cos \theta \\ \end{array}\right]. $$ What, geometrically, does the linear transformation $T_{A(\theta)}$ do to a vector in $\Reals^2$? Seeking documentation for {z}/{x}/{y} syntax in tilesource urls? Speaking of tilesource urls such as   http://{s}.tile.stamen.com/watercolor/{z}/{x}/{y}.png  is there any technical documentation or canonical reference for the curly braces syntax?  I'd specifically like to know what other things can be used in curly braces, and in which places, and how they work. When is a MOSFET more appropriate as a switch than a BJT? Does a family of a distribution have a different definition for statistics than in other disciplines?  In general, a  is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is varied. Such families are used, for example, to .  For statistics, a family according to  is the result of varying the shape parameter. How then can we understand that the gamma distribution has a shape and scale parameter and only the generalized gamma distribution has, in addition, a location parameter? Does that make the family the result of varying the location parameter? According to @whuber the meaning of a family is implicitly A "parameterization" of a family is a continuous map from a subset of ℝ$^n$, with its usual topology, into the space of distributions, whose image is that family.  What, in simple language, is a family for statistical distributions?  A question about relations among of the statistical properties of distributions from the same family has already generated considerable controversy for a  so it seems worthwhile to explore the meaning.  That this is not necessarily a simple question is born out by its use in the phrase , which has nothing to do with a family of curves, but is related to changing the form of the PDF of a distribution by reparameterization not only of parameters, but also substitution of functions of independent random variables. Variance of a linear combination of vectors Let $A$ and $B$ be two constant matrices and let $x$ and $ y$ be two random vectors, what is the general formula for $Var(Ax+By)$? I know the formula for when $x$ and $y$ are scalar random variables and $A$ and $B$ are constants, but what about the matrix case? Sometimes a suggested edit is  because of a concurrent direct edit that takes precedence.  Since this is no fault of the edit suggestor, such rejections should not count against the suggestor when counting .  Here are some examples where it happened: UFW Allows 22 for IPv4 and IPv6 but SSH Disconnects When Enabling sudo ufw disable followed by sudo ufw enable kicks me out of SSH  DMESG reports  [UFW BLOCK] IN=eth0 OUT= MAC=30:........ SRC=192.168.1.me DST=192.168.1.server LEN=52 TOS=0x00 PREC=0x00 TTL=128 ID=15776 DF PROTO=TCP SPT=55640 DPT=22 WINDOW=253 RES=0x00 ACK URGP=0  I can log back in without having to change rules via the console (UFW still enabled).  This started after upgrading Xenial (16.04) from kernel 4.4 to 4.15 (HWE). Upgrading to 18.04.1 did not solve the issue.  Versions:   iptables v1.6.1 ufw 0.35 4.15.0-29-generic #31-Ubuntu Ubuntu 18.04.1 LTS   UFW status verbose is (some rules were omitted, but they are all ALLOW)  Logging: on (low) Default: deny (incoming), allow (outgoing), disabled (routed) New profiles: skip  To                         Action      From --                         ------      ---- 22                         ALLOW IN    Anywhere 22 (v6)                    ALLOW IN    Anywhere (v6)   Why is this happening, or at least, how to revert to the expected behavior?  I looked at , and I am not sure it applies, but here's /etc/ufw/before.rules  # # rules.before # # Rules that should be run before the ufw command line added rules. Custom # rules should be added to one of these chains: #   ufw-before-input #   ufw-before-output #   ufw-before-forward #  # Don't delete these required lines, otherwise there will be errors *filter :ufw-before-input - [0:0] :ufw-before-output - [0:0] :ufw-before-forward - [0:0] :ufw-not-local - [0:0] # End required lines   # allow all on loopback -A ufw-before-input -i lo -j ACCEPT -A ufw-before-output -o lo -j ACCEPT  # quickly process packets for which we already have a connection -A ufw-before-input -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT -A ufw-before-output -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT -A ufw-before-forward -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT  # drop INVALID packets (logs these in loglevel medium and higher) -A ufw-before-input -m conntrack --ctstate INVALID -j ufw-logging-deny -A ufw-before-input -m conntrack --ctstate INVALID -j DROP  # ok icmp codes for INPUT -A ufw-before-input -p icmp --icmp-type destination-unreachable -j ACCEPT -A ufw-before-input -p icmp --icmp-type source-quench -j ACCEPT -A ufw-before-input -p icmp --icmp-type time-exceeded -j ACCEPT -A ufw-before-input -p icmp --icmp-type parameter-problem -j ACCEPT -A ufw-before-input -p icmp --icmp-type echo-request -j ACCEPT  # ok icmp code for FORWARD -A ufw-before-forward -p icmp --icmp-type destination-unreachable -j ACCEPT -A ufw-before-forward -p icmp --icmp-type source-quench -j ACCEPT -A ufw-before-forward -p icmp --icmp-type time-exceeded -j ACCEPT -A ufw-before-forward -p icmp --icmp-type parameter-problem -j ACCEPT -A ufw-before-forward -p icmp --icmp-type echo-request -j ACCEPT  # allow dhcp client to work -A ufw-before-input -p udp --sport 67 --dport 68 -j ACCEPT  # # ufw-not-local # -A ufw-before-input -j ufw-not-local  # if LOCAL, RETURN -A ufw-not-local -m addrtype --dst-type LOCAL -j RETURN  # if MULTICAST, RETURN -A ufw-not-local -m addrtype --dst-type MULTICAST -j RETURN  # if BROADCAST, RETURN -A ufw-not-local -m addrtype --dst-type BROADCAST -j RETURN  # all other non-local packets are dropped -A ufw-not-local -m limit --limit 3/min --limit-burst 10 -j ufw-logging-deny -A ufw-not-local -j DROP  # allow MULTICAST mDNS for service discovery (be sure the MULTICAST line above # is uncommented) -A ufw-before-input -p udp -d 224.0.0.251 --dport 5353 -j ACCEPT  # allow MULTICAST UPnP for service discovery (be sure the MULTICAST line above # is uncommented) -A ufw-before-input -p udp -d 239.255.255.250 --dport 1900 -j ACCEPT  # don't delete the 'COMMIT' line or these rules won't be processed COMMIT   PS: I didn't expect this to "fix" the issue but just for reference I changed the port SSHD listens on (and the corresponding rule) and the problem persists. How to get the type of T from a member of a generic class or method Can I have two Schengen visas in one passport? Drawing users' attention to unrecoverable actions? Quantum Hall effect for dummies In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned.  First, here are some random points that I've been able to gather   I(nteger)QHE occurs due to the presence of Landau levels IQHE is an embodiment of topological order and the states are characterized by the Chern number that tells us about topologically inequivalent Hamiltonians defined on the Brillouin zone IQHE requires negligible electron-electron interations and so is dependent on the presence of impurities that shield from Coulomb force F(ractional)QHE occurs because of formation of anyons. In this case Coulomb interaction can't be neglected but it turns out an effective non-interacting description emerges with particles obeying parastatistics and having fractional charge FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff FQHE has something to do with hierarchy states   So, here are the questions        Most importantly, do these points make sense? Please correct any mistakes I made and/or fill in other important observations   How do explanations 1. and 2. of IQHE come together? Landau quantization only talks about electron states while topological picture doesn't mention them at all (they should be replaced by global topological states that are stable w.r.t. perturbations)   How do explanations 4., 5. and 6. relate together   Is there any accessible introductory literature into these matters?   Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. IQHE can be treated as a special case? My understanding (based on 3.) is that this is not the case but several points hint into opposite direction. That's also why I ask about both QHE in a single question