I did use to live in London. I did used to live in London.  Which one is correct? According to the usage of emphatic do with past tense (eg &quot;I lived in London/I did live in London&quot;), did should change ‘used to’ to ‘use to,’ but I didn't find anything about it except in English Grammar Today by Cambridge. However, Cambridge used did with ‘used to.’ Shouldn't emphatic did change ‘used to’ to ‘use to’?  used to From  Emphatic did We can use the emphatic auxiliary did with used to:  We never used to mix very much with the neighbours, but we did used to say hello to them in the street. (Don't use this form in written exams.)  —
Which is the correct sentence, if there is a correct one?     I use to be a hitman.        I used to be a hitman.   I've read the second sentence recently in a book, but I was sure it should be I use to be a hitman.
How to stop kernel messages from flooding my console? I'm using Centos 6, rsyslog logging. Console is flooded with kernel messages.  Klogd is not running (I'm using rsyslog) Rsyslog config does not direct anything to the console Even tried stopping rsyslog altogether  Still something is flooding my console with kernel log messages. What it is and how do I make it stop? Update: These are the messages generated by the kernel (hardware, iptables, etc.), stuff that goes out of /proc/kmsg, like this:  Shorewall:pub2loc:DROP:IN=br0 OUT= MAC=xxx SRC=xxx DST=xxx LEN=60 TOS=0x00 PREC=0x00 TTL=128 ID=15731 DF PROTO=TCP SPT=63767 DPT=3493 WINDOW=8192 RES=0x00 SYN URGP=0 Can you upgrade the RAM of an Android device? I'm sure many people like me are aware and annoyed by the extremely limited amount of RAM in Nexus S (512MB but only 300+ is usable), I have searched all over google for a solution to increase the amount of RAM available and came up empty (I tried swap file applications but they just broke my system's SD card partitions causing a complete reset).  I wonder if there is any hardware solution to this problem. Is it possible to swap the chip out for a bigger capacity one? I realize that it is not as simple as swapping out PC RAM from a dimm but I haven't seen any schematics for the chip layout on the ARM boards in the smartphones so I really hope that it is somewhat possible to increase the amount of RAM on the board. Let $f(z)=\sum\limits_{n=0}^{\infty}a_n z^n$ be an analytic function in $|z|\leq R$ such that $|f(z)|\leq M$. Prove an inequality about $f$'s zero ASP.NET Call Code Behind Function From Javascript Geometric series and big theta Consider the following function:  $$S(n)=1+ c + c^2 + ··· + c^n,$$  where c is a positive real number.  (A) This function is the sum of a geometric series. Give a precise closed-form formula for $S(n)$, interms of $c$ and $n$, in the case where $c \neq 1$.  (B) Show that $S(n)$  is:  $\theta(1)$ if $c&lt;1$  $ \theta(n)$ if $c=1$  $\theta(c^n)$ if $c&gt;1$    can someone please explain how i can go about finding the solutions for these problems, i have never encountered these and am stuck, i know that big theta means that the function is bond on both sides but how do i got about finding the answer?  (edit) im still having trouble understanding part B. can someone please explain? (can someone walk me through the second one) so far i have $n \leq c^{n+1} \leq ???$  (edit #2) i tried doing the first one can someone verify if i did it right  $S(n)$ is $\Theta(1)$ if c&lt;1  (1)$S(n)$ is $O(1)$ if c&lt;1  (2)$S(n)$ is $\Omega(1)$ if c&lt;1  (1) $$\frac{C^{n+1}-1}{C-1} \lt (C_1)(1)$$ $$\frac{C^{n+1}-1}{C-1} \lt (C_1)$$ $$C^{n+1} \lt C_1(C-1)$$ $$C^nC-1 \lt C_2C-1$$ $$C^n \lt C_2$$ $$C^n \lt 1$$ since c&lt;1 this means that any number that will be $C^n$ will be less then 1 for all positive n  i did the omega part pretty much the same way and got $$C^n \gt C_2$$ $$C^n \gt 0$$ since c&lt;1, $C^n$ can potentially become very very small so the only thing bounding it is 0 for all positive n Isomorphism $f$ preserves the order of an element? Let's say $f$ is an isomorphism $f:G  \rightarrow G'$, where $G$ and $G'$ are multiplicative groups.  Then for $x\in G$, if $f(x) = x' \in G'$. Do we have always have $\text{ord}(x) = \text{ord}(x')$? Why? Match-3 algorithm to fill empty space left from removing matches I am currently creating a match 3 game.   I am at the point where I have objects dropping down in the column when only one item is removed. So if an item is removed, the above item moves into its old position etc.  The problem I am having now is that when more than one item is removed from a column, the items in that column only drop down to the first item that was removed. Instead of filling in both items that were removed it just drops down to fill in the first one.   So basically, if two(or more) items are removed from a column the second, third, fourth, etc positions are left blank.  The way I am designing my game is I am using units of 1. So each item takes up 1 unit by x and 1 unit by y. This means that I can position the items like in a grid, at 0x1, 0x2, etc.   What kind of algorithm could I use to move multiple items down to fill the empty space? Mounting /cow on root failed: Invalid argument overlay mount failed I am using an xps 13 9365, which was data wiped from bios by a friend who then gave it to me thinking it was dead. I tried booting with a USB (current LTS distro (18.04 or similar)) boot disk and got into the language selection / setup menu. By using the F6 option I selected noapic. In bios sata is set to raid and legacy the secure boot option is off.   But when I try to install I get kicked into a tiny font window with the following message  (initramfs) mount: Mounting /cow on root failed: Invalid argument overlay mount failed  Any ideas? The parmesan cheese in pasta recipe is quite expensive.....do we have cheaper alternative??  Are there are cheddar cheese which can replace parmesan cheese? Count the items from a IEnumerable without iterating? private IEnumerable&lt;string&gt; Tables {     get     {         yield return "Foo";         yield return "Bar";     } }   Let's say I want iterate on those and write something like processing #n of #m.   Is there a way I can find out the value of m without iterating before my main iteration?  I hope I made myself clear. Can houseplants actually improve air quality? Inline elements shifting when made bold on hover I created a horizontal menu using a HTML lists and CSS. Everything works as it should except when you hover over the links. You see, I created a bold hover state for the links, and now the menu links shift because of the bold size difference.  I encounter the same problem as . However, the post does not have proper solution. I've searched everywhere for a solution and can't find one. Surely I can't be the only one trying to do this.  Does anyone have any ideas?  P.S: I don't know the width of the text in menu items so I cannot just set the width of the li items.    .nav { margin: 0; padding: 0; } .nav li {      list-style: none;      display: inline;      border-left: #ffffff 1px solid;  } .nav li a:link, .nav li a:visited {      text-decoration: none;      color: #000;      margin-left: 8px;      margin-right: 5px;  } .nav li a:hover{      text-decoration: none;      font-weight: bold;  } .nav li.first { border: none; } &lt;ul class="nav"&gt;     &lt;li class="first"&gt;&lt;a href="#"&gt;item 0&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 1&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 2&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 3&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 4&lt;/a&gt;&lt;/li&gt; &lt;/ul&gt; $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible? Hungerford's book of algebra has exercise $6$ chapter $3$ section $6$ [Probably impossible with the tools at hand.]:     Let $p \in \mathbb{Z}$ be a prime; let $F$ be a field  and let $c \in  F$. Then $x^p - c$ is irreducible in $F[x]$ if and only if $x^p - c$   has no root  in $F$. [Hint: consider two cases: char$(F) = p$ and   char$(F)$ different of $p$.]   I have attempted this a lot. Anyone has an answer? In first.bat, I use  var5=C:\Program Files (x86)\Microsoft Visual Studio 10.0\VC\bin\x86_amd64\ CALL scripts\vc64.bat %var5%   And in scripts\vc64.bat, I use  SET var6=%1vcvarsx86_amd64.bat CALL %var6%   But I get : 'C:\Programvcvarsx86_amd64.bat' is not internal or external command..... error.  If the path assigned to var5 has no space, then it is fine.  I tried several combination of quotations and %1vcvarsx86_amd64.bat, but no change.  How do I make it works with path with spaces?    To be more precise, suppose it is C:\a b c\  In first.bat:       SET var6=C:\a b c\  =====&gt;  '"C:\avcvarsx86_amd64.bat"' is not.....`      SET var6="C:\a b c\" ====&gt;   There should not be a b      SET var6=C:\a\ b\ c\ ====&gt;    Can't find the specified path      SET var6=C:\a b c\ + Using "%var6" ====&gt; There should not be a b     Update: Here is an example. Change a b to ab works.  call.bat in C:\  @ECHO OFF  SET var5=C:\a b\ CALL C:\1.bat "%var5%"  pause   1.bat in C:\  @ECHO OFF  SET var6=%~1Test.bat CALL %var6%  RMDIR /S C:\NoWorry   Test.bat in C:\a b Test.bat in C:\ab  @ECHO OFF  RMDIR /S C:\ThereIsNoSuchFolder Number of subrings of a Field What is the difference between a teaching assistant and an instructor? It seems to me that the terms "Teaching Assistant" and "Instructor" refer to a variety of positions. At some places, a teaching assistant is responsible for things like helping the actual lecturer by handing out papers, grading homework, etc., and instructors hold recitation sessions.  At other places, I saw the term "instructor" referring to the lecturer giving the course, while a teaching assistant is the person doing anything else (recitations, grading etc.).  Is there some widely accepted definition of the two positions?  For context: The question arose because I wasn't sure whether I'm using the correct terms in my CV -- I am a math graduate student, and I would like to make a distinction between jobs in which I only graded course assignments/final exams, and courses in which I held recitation classes* (and also participated in grading the final exams). Is it OK to use "Instructor" for the latter? What should the former be referred to as?  *In the course I'm currently teaching, the recitations are planned and written by the ones giving them (without the professors' supervision). Also, the people giving the recitations are not necessarily grad students (some already hold a PhD). I'm elaborating on that because from what I've seen, some of it could be relevant for the definition of the job. What is a good way to transform Cyclic Ordinal attributes? So,  Each of my polygons is a separate object. Their default normals point like this:   But their orientation or local axes are like so:   How can I make their local axes to be like so, but automatically?   I guess particles might be one solution for this exact case (if you emit new objects on top of the existing ones) but let's say the original objects are triangles and I wouldn't want to change their shape and pointing direction at all, only their local orientation axes, would that be possible?  Cheers! Thermistor control of peltier voltage with Arduino (for DSLR chill box project) I am mildly familiar with electronics, mostly from playing around with electronics kits as a kid. That was a long time ago, though, maybe as much as 20 years ago. I am currently working on a cold or "chill" box for my Canon 5D III, so I can keep it's temperature very low, and very consistent, for doing low noise astrophotography.  I have a general design for the box, and I'm using a single 12v 5.8amp peltier (TEC) attached directly to a copper box for cooling. The box is currently insulated with extruded foam board, and the hot plate of the peltier will be cooled with a water cooler from an old computer kit.   I'm getting more ambitious with my project, however. I want thermal regulation, to maintain a consistent temperature, and I'd eventually like to get into two-stage cooling to achieve a Delta-T of closer to -55-60°C relative to ambient (the chill box will be cooling the camera, so the sensor will be warmer, probably by as much as 10°C, than the temperature of the copper plating in the box itself.) I want to have two primary modes:   Rapid cooling mode, operating the peltier at 12v or higher (max voltage is 15.4v) to quickly cool the box down to the target temperature. Regulated maintenance mode, operating the peltier at lower voltages to maintain a consistent temperature, above the maximum potential cooling the peltier can supply (for headroom as the voltage is adjusted in response to small temperature fluctuations).   I'd like to maintain temperature within 2-3°C if possible. I've looked into Arduino (and I've messed with similar things in the past), and it seems perfectly ideal for the task, with one exception: It doesn't seem to handle the kind of current I need top power a single peltier, and certainly not two.   I've done some research on how I might achieve this, but I'm falling up short on my understanding of the electronics involved. I've found a two-relay "shield" for Arduino Uno that can power two devices with up to 8amps each, and up to 30v each. That can be controlled from the Arduino itself. It seems the design of a relay uses a magnetic coil to actuate a switch that allows an independent power source to be used to power components like a motor, solenoid, or in my case a peltier. I haven't found any way of actually regulating the voltage of the relay with the Arduino, however.  So I kept investigating, and I came across some schematics that showed how to use transistors, specific mosfets to be exact, where the base was connected to an Arduino output, and the collector/emitter were connected to the power loop of whatever needed to be powered at a higher voltage (not sure about current here), and this still allowed control of the voltage.   It's been so long since I messed with any of these components, my memory is extremely rough, and I'm not quite connecting how it all works. I'd be happy with some references to complete examples of powering, and controlling the voltage of, high powered devices via an Arduino, but if anyone here can explain how all this works and why, that would be most ideal. I'd rather understand the concepts, so I can reapply them later, than just have a pattern to follow. given that $f$ is an analytic function with real part $u$ is a polynomial in the variable of $x,y$, $z=x+iy$, we need to show $f$ is a polynomial in $z$, I am kind of puzzled to see the problem, first I would like to say:any hint please