Align horizontally side by side equations
Numbering a set of horizontally distributed equations
Transforming the dummy values to be able to take logs I have a panel data model with double-log functional form. I have 4 variables, one of which is a dummy. What is the best way to transform the values of 0 for my dummy to be able to take natural logs (since you can't take logs from zero)? I have found 2 options so far, but I dont know which is the best (or perhaps there is a 3rd option).  1) Transform all the values of 0 into a very small value (0.00000000001) and then take the logs. I'm not sure this wouldn't still change the outcome of my model quite a bit. 2) Change the values of 0 into 1 and the dummy values of 1 into e (the base of natural logarithm). The log of this newly defined dummy then takes on the values of zero and one and the interpretation of my betas would remain the same. If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$ Suppose that a function $f:[a,b]\to\mathbb{R}$ is continuous and nonnegative. Prove that if $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$.   I've been trying to prove it using the extreme value theorem, continuity and the upper and lower sums but can't come up with something tight enough. More specifically, I've been trying to relate $|f(x)-f(t)|&lt;\epsilon$ to the sum of $M_k-m_k(x_k-x_{k-1})$ How to get the last date of a particular month with JodaTime? Got French Schengen visa but no "VIS" after giving fingerprints I had my French Schengen visa interview 3 days ago (got the stamped visa and passport within two days, super efficient!). However there's no "VIS" written on the visa, even though I gave my fingerprints during the interview in US. I had presumed VIS would be written on the visa since I gave my fingerprints, or is it for something else? I do remember it took a while to take the fingerprints because the machine looked old and was taking a long time to read my fingerprints.  The next time I want to apply for a visa, do I need to go for an interview again just because the visa has no VIS on it? Prevent ligatures in Safari (Mavericks/iOS7) via CSS Windows does not mount USB NTFS superfloppy I have a Transcend Storejet external USB hard disk. This is not an SSD, but a mechanical disk with rotating plates. I have formatted the whole disk, without partitioning, as NTFS. I have used mkntfs tool under Linux.  When plugged into a Linux machine, the system sees a drive with two partitions (/dev/sdc /dev/sdc1 /dev/sdc2). However, as I know it is a partitionless disk, I can mount the whole device (mount -t ntfs /dev/sdc /mnt) and it works without any problems.  When plugged into a MS Windows XP machine, the systems sees a disk with two unformatted partitions, and it does not assign a drive letter to either the whole disk, nor to any of the partitions.  Would anyone know how to get MS Windows to mount my disk as a NTFS superfloppy?  I have already tried removing old USB mounting points and residual devices using 'DriveCleanup'. It did not help.  By the way, I also have an external Kingston USB SSD, also formatted as NTFS superfloppy, without partitioning. However, this one is recognized and mounted normally by MS Windows. 1) How do I prove the following:   Let A = {6a + 4b ∈ Z : a, b ∈ Z} and B = {2a ∈ Z : a ∈ Z}. Show that A = B.  Thank you all for the help! i'm surprised there is so little documentation on this issue. But i'm trying to duck the audio on all the mix buses in Unity so that you can clearly hear the VO of the game.  Now it works great except that I have some reverb zones in the game and any sound that plays in these reverb zones, the actual reverb itself is NOT DUCKED.  So the VO is accompanied with a huge wall of wishy washy muddy noise.  Anyone deal with this before? How can we deal with this? Mesh imported to Unity is inside out Is this group solvable? Let $G=H\times K$ (a direct product of $H , K$) where $H$ is an abelian 2-group and $K$ is a non-abelian simple group. Is $G$ solvable? why?  These three answers are true, and I thought so. But in a book I found a remark that made me confused: T.M. Gagen, Topics in Finite Groups, London Math. Soc. Lecture Note Ser., vol. 16, Cambridge Univ. Press, Cambridge, 1976, Remark, Theorem A on p. $40 $ and Definition $11.3$ on p. $39$. Please see it and say me your ideas. Splitting a semicolon-separated string to a dictionary, in Python How can I create documents in LaTeX using a calligraphic first letter for chapters? Hopefully I'm using the right terminology. I'd basically like to know how specific of a location I can make a Pokemon Lure. An Address will not cut it, would need to be like 5ft of my phone or something for it to be useful.  I do not currently play the game and am only interested in this to attract new customers similar to,  but I wouldn't be in a storefront with an address. Hello [Comma?] John, Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares What is the explanation of the non-existence of magnetic monopoles? Server only reachable over VPN I have an Apache server running on a Raspberry P and it works just fine in the local network. And after forwarding port 80 and trying to connect using the public IP, Chrome says ERR_CONNECTION_REFUSED. But the strange thing is that I CAN reach the server when using VPN and using the same IP. What can I do?     -telnet 80.***.***.78 80      Trying 80.***.***.78...     telnet: connect to address 80.***.***.78: Connection refused     telnet: Unable to connect to remote host     -route -n      Destination     Gateway         Genmask         Flags Metric Ref    Use Iface     0.0.0.0         192.168.0.1     0.0.0.0         UG    0      0        0 eth0     192.168.0.0     0.0.0.0         255.255.255.0   U     0      0        0 eth0      -sudo netstat -lapute:              Active Internet connections (servers and established)     Proto Recv-Q Send-Q Local Address           Foreign Address         State       User       Inode       PID/Program name     tcp        0      0 *:http                  *:*                     LISTEN      root       6137        2051/apache2     tcp        0      0 *:ssh                   *:*                     LISTEN      root       6367        2249/sshd     tcp        0      0 pi.local:ssh            nmb.local:65535         ESTABLISHED root       8669        2565/sshd: pi [priv     udp        0      0 *:9949                  *:*                                 root       5918        1809/dhclient     udp        0      0 *:mdns                  *:*                                 avahi      6293        2184/avahi-daemon:     udp        0      0 *:54070                 *:*                                 avahi      6295        2184/avahi-daemon:     udp        0      0 *:bootpc                *:*                                 root       5946        1809/dhclient     udp        0      0 pi.local:ntp            *:*                                 root       6310        2200/ntpd     udp        0      0 localhost:ntp           *:*                                 root       6309        2200/ntpd     udp        0      0 *:ntp                   *:*                                 root       6304        2200/ntpd Just noticed the "meta user" link under the picture and reputation on the Stack Exchange user's page. It doesn't seem to work for all users. Error is "Page Not Found".   Not working:  /  Working:  /    My guess is this is because they've never logged into the meta site. "Compared with" vs "Compared to"—which is used when? Is only one of them correct? Are they used in different situations? Or are they interchangeable? Validationengine jquery not working properly for localization