We are offering our product to you at the price of $20 (twenty dollars) per pound.   Wouldn't it be better to write     We are offering our product to you at a price of $20 (twenty dollars) per pound.   When googling, I seem to find both variants, and can't make out the difference.   The Google Ngram for "at the price of" vs. "at a price of" is puzzling too:
According to preliminary estimates, the project should be completed by 2020 at a cost of about RUB 40 bn.    or      According to preliminary estimates, the project should be completed by 2020 at the cost of about RUB 40 bn.    Are both options okay, or is the first better?   We are introducing the sum to the reader, so logically it should be the first option. But there's a lot of google-hits for "at the cost of" too.
Can I mention professors' names in the statement of purpose? For PhD applications, I have mentioned that I am interested in some research areas. Besides, I am thinking about mentioning some professors' names, so that it shows I have read their websites and I am not just sending out generic statements applicable to many schools.  But is it good to mention some professors' names in the statement of purpose, if I don't know them personally? In what cases is it good, and in what cases it isn't?  For example, is it good to only mention    those whose research directions are aligned with my research interests, or/and those whose books or notes I have heard of, or better, might have read some parts of, or/and those who are already established and famous (such as having certain titles), or/and those that are directing the PhD graduate programs, or/and those that are heads of the departments?    What will other professors who are not mentioned think? How will you do, if it were you? Will yearly moderation statistics be published on all sites this year, and future years? How to set an image as a background for Frame in Swing GUI of java? How did Montague Apparate into the Hogwarts bathroom? In year 5, Fred and George jam Montague into the Vanishing Cabinet. He's found weeks later in a toilet.      ‘He never managed to get all the words out,’ said Fred, ‘due to   the fact that we forced him head-first into that Vanishing Cabinet   on the first floor.’      […]      ‘They’ve found Montague, sir, he’s turned up jammed inside a toilet   on the fourth floor.’   ‘How did he get in there?’ demanded Snape.   ‘I don’t know, sir, he’s a bit confused.’   In year 6 Malfoy expands on that.      ‘I had to mend that broken Vanishing Cabinet that no one’s used for years. The one Montague got lost in last year.’      […]      ‘The other’s in Borgin and Burkes,’ said Malfoy, ‘and they make a kind of passage between them. Montague told me that when he was stuck in the Hogwarts one, he was trapped in limbo but sometimes he could hear what was going on at school, and sometimes what was going on in the shop, as if the Cabinet was travelling between them, but he couldn't make anyone hear him ... in the end he managed to Apparate out, even though he’d never passed his test. He nearly died doing it.   What happened here? Did he Apparate out into Hogwarts, Apparate into Borgin and Burkes and somehow wander back to Hogwarts and get stuck into a toilet? How do I know if I am flagging correctly? Is there any way to know how useful are the flags of a user? I read that flagging - weights used to exist (were visible) before, which would indicate this. However, what indicator is there now?  Is percentage of accepted flags a good measure of useful flagging, so to say? If yes, then what percentage would indicate that a user is flagging correctly or in a useful way?  I am asking about interpreting the numbers in terms of how useful you are. Is a 80% good or a 90% good? Or does the percentage even matter?     contains some explanation regarding the issue. Free way to clone HDD to SSD? Is there a free way to clone a full Windows 7 installation from HDD to SSD? (The free part is important, I know I can pay for Acronis True Image.)      SSDs are usually much smaller than HDDs which complicates matters. For instance, I have about 50GB data, my new SSD is 80GB but I still can't use Windows clone/restore system if my HDD is something like 300GB.  Therefore, I'm looking for a third party tool that will be able to:   Create a clone of my C: partition Store it onto an external USB drive Boot from some rescue / restore CD Load the image onto the new SSD   Acronis True Image seems like a tool that should support this but it's a paid-for software and the trial version cannot create clones. Acronis Migrate Easy is a fully functional tria for 15 days but need both the HDD and SSD connected at the same time which is a bit of a problem for me as a laptop user.  P.S. I almost got there combining Windows image backup combined with Acronis True Image restore CD (which can load .vhd's) but was not able to boot as some boot information were probably lost and could not be repaired using the Win7 installation DVD. Changing default width of blocks in beamer I use a custom Beamer theme for my presentations. In my presentations I'd like to use blocks (\begin{block}…\end{block}). These blocks are rendered slightly too wide to fit into my theme. Is there a way how I can set the default width of blocks, e.g. to .9\textwidth? Stripped out bottom bracket The bottom bracket of my bike was completely stripped to the point that when you push the left side crank arm, the right crank moves and you can see the bottom bracket lock move out the frame. The bike shop tried putting Teflon tape but it's temporary. It's a 26' xc hard tail. For all I know both sides of the bottom bracket(square tapered) are stripped clean hence the Teflon tape put by the previous owner. Can I fix the problem by changing into a hallow tech cranks because it works like a thread less bb, or should I just buy a thread less square tapered bb? Any suggestion on what to do? Conditional expectation in AR(1) process Suppose we have a stationary AR(1) process: $Y_{t+1}=a+ \rho Y_{t} + \epsilon_{t+1}$ where $\epsilon_{t+1}$ is white noise with probability density function $\phi(.)$.   Now say we have a equation $P_{t+1}=u\cdot (A_{m}-Y_{t+1})^{+}$ where $(Y_{m}-Y_{t+1})^{+}$ = $ \max \{(A_{m}-Y_{t+1}),0\}$ and $u$ is a constant.  So $P_{t+1}=u\cdot(A_{m}-a-\rho Y_{t}-\epsilon_{t+1})^{+}$.   Can we write $E[P_{t+1} \mid Y_{t}]= u\cdot \int_{-\infty}^{(A_{m}-a - \rho Y_{t})}(A_{m}-a-\rho Y_{t}-\epsilon_{t+1})\phi(\epsilon_{t+1})d\epsilon_{t+1}$ ? What should I do if I want to be able to run a given program regardless of my current directory? Should I create a symbolic link to the program in the /bin folder? The table cards were A,K,K,8,3. All four suits were on the board. Player one had A,8. Player two had A,3.   Is this a split pot? How do I get from Terminal 1 to Terminal 5 in Fiumicino Airport? The official site mentions a shuttle bus service, I also googled but the infos are not clear, so I hope to find some firsthand experience.  I have a flight with a stop in Fiumicino, I will arrive in Terminal 1 and the next departure is from Terminal 5, the transfer time is around 5 hours.  Is it correct that I should go to Terminal 3 first (using the internal transfer area) and after exit from Terminal 3 and take the shuttle to Terminal 5?  The terminal 5 has a waiting area with some shops or is just a terminal for departure? In your opinion is better to wait some hours inside Terminal 3 before going out to take the shuttle bus? Does a run scored on a tag out on a forced runner? The situation:   Runners at third and first, ball is hit to the second basemen, 2nd basemen goes to tag the runner out. Runner stops, runner on third scores and then 2nd basement tags the runner, does not step on base.Does the run count? How can I check the actual size used in an NTFS directory with many hardlinks? On a Win7 NTFS volume, I'm using cwrsync which supports --link-dest correctly to create "snapshot" type backups. So I have:  z:\backups\2010-11-28\cygdrive\c\Users\... z:\backups\2010-12-02\cygdrive\c\Users\...   The content of 2010-12-02 is mostly hardlinks back to files in the 2010-11-28 directory, but there are a few new or changed files only in 2010-12-02. On linux, the 'du' utility will tell me the actual size taken by each incremental snapshot. On Windows, explorer and du under cygwin are both fooled by hardlinks and shows 2010-12-02 taking up a little more space than 2010-11-28.   Is there a Windows utility that will show the correct space acutally used? What do \makeatletter and \makeatother do? Many LaTeX “hacks” begin with \makeatletter and end with \makeatother. What do these commands do? I live in Hong Kong, and the Play Store displays everything in the local Cantonese language. I have set everything I can (Android language, Account language, even the app locale via Xposed Module "App Settings") to English, but I still see all the categories in the store in Chinese. Can someone help me change those to English?  (Click image to enlarge) Why can't I import a SVG file from Adobe Illustrator or Inkscape? I've tried multiple times to  import a SVG file from illustrator CS5.5 to Blender 2.71 and 2.73. However, I do not see a mesh, curve, or anything pop up in my "Outliner" window. So I know its not so small I can't see it. I even made sure under user preferences that the "import and export of SVG 1.1 format" is "checked." I've tried even just importing text from illustrator and I'm still getting no where. What can I do to resolve this problem? If this is common error with this version of Blender, then what can I do to transform an image into a 3D object in Blender? Join lines from two files How to populate UIList with all material slot in scene? 2.8 The set of integers $n$ expressible as $n=x^2+xy+y^2$