Compiler error C4430: missing type specifier - int assumed
Resolve build errors due to circular dependency amongst classes
How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? I've found in Wikipedia the formula for calculating an individual row in Pascal's Triangle: $$v_c = v_{c-1}\left(\frac{r-c}{c}\right).$$ where $r = \mathrm{row}+1$, $c$ is the column starting from $0$ on left and $v_0 = 1$.  Now, I've tried to do by hand and it works,  but I don't understand how to find this magic formula when I don't have access to Wikipedia...:) From Berkeley Problems in Mathematics, Spring 1999, .  Let $f(x)\in \mathbb{Q}[x]$ be an irreducible polynomial of degree $n\ge 3$. Let $L$ be the splitting field of $f$, and let $\alpha\in L$ be a zero of $f$. Give that $[L:\mathbb{Q}]=n!$, prove that $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$.   (BELOW IS NONSENSE, SHOULD BE IGNORED)  Following Gerry Myerson's advice, since $L$ is the splitting field of $f$, $L$ must be Galois over $\mathbb{Q}$. Thus the Galois group for $[L:\mathbb{Q}]=S_{n}$. Gerry now asserts that either $\mathbb{Q}(\alpha^{4})$ is of degree 2 over rationals or it must be $\mathbb{Q}$. But assuming this one can rule out the case $\mathbb{Q}$, since this would imply $\alpha$ is the root of a 4th or 2nd degree polynomial over $\mathbb{Q}$. But we know $n\ge 3$. So $\alpha$ must be the root of a 4th degree polynomial. We know $S_{n}$ has normal subgroups $A_{n}$ when $n\not=4$ and $V,A_{4}$ when $n=4$. I do not know how to proceed any further.   Now assuming $\mathbb{Q}(\alpha^{4})$ is a degree 2 abelian extension over $\mathbb{Q}$. We should have a chain of normal extensions $\mathbb{Q}(\alpha)\supset \mathbb{Q}(\alpha^{2})\supset \mathbb{Q}$. This would imply $S_{n}$ has a normal subgroup which has a normal subgroup. But we know $A_{n}$ for $n\ge 5$ are simple. So the only possibility is $\mathbb{Q}(\alpha)$ has a Galois group isomorphic to $V$. In this case $n=4$ as well. I can only proceed to here. Is there a way to easily turn on/off showing the boot messages (loading the services) when Ubuntu starts? Is it something in Grub2?  I am running 10.04. I am learning Linux and I was trying the gzip command. I tried it on a folder which has a hierarchy like  Personal/Folder1/file1.amr Personal/Folder2/file2.amr Personal/Folder3/file3.amr Personal/Folder4/file4.amr   I ran     "gzip -r Personal" and now its like  Personal/Folder1/file1.amr.gz Personal/Folder2/file2.amr.gz Personal/Folder3/file3.amr.gz Personal/Folder4/file4.amr.gz   How do I go back? What's the most efficient way to select the last n rows in a table without changing the table's structure? What's the most efficient way to select the last n number of rows in a table using mySQL? The table contains millions of rows, and at any given time I don't know how large the table is (it is constantly growing). The table does have a column that is automatically incremented and used as a unique identifier for each row. How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$ Why is the second order perturbative correction to the ground state energy always down? Over time, I've noticed an increasing practice among moderators of the smaller sites (i.e. not in the Trilogy) to move extended comment chains to chat, just because they're too long. Is this a good idea? In the past, I've taken the position on many occasions that I believe that comments serve two purposes only: clarification, and asking for clarification.  I take this position because as a mod I want the freedom to purge a comment trail that is clearly running off the rails without having to argue with anyone about politeness definitions. But that's not the same thing as two pedantic C++ language lawyers debating the finer points of &quot;undefined behavior.&quot;  I give wide latitude to such discussions, as long as the participants don't start throwing spears, because I believe they are instructive. The SE software even has accommodations for this.  Long comment chains are automatically collapsed, so as not to disrupt the Q&amp;A format of the post.  And moving a comment chain to chat is not even a move, really; to do an actual move, you have to perform the conversion, and then delete all of the copied comments from the post. Here is a recent example:  and it's accompanying . What I find amusing is that the OP's detailed POV about the term, where he floats a theory about why everyone thinks that &quot;bugged&quot; is not a thing (that conversation took place in the comments, and is now safely sequestered in the chat room) gets to stay prominently featured in his question, at the very top of the post. Now you could argue that the chat room is a better environment to have these discussions anyway, and you'd be right.  I could argue that if we're going to do that, then why not just automatically convert long discussions to chat rooms? The problem is not so much where the comments reside.  I don't understand why mods are taking it on themselves to fix something that isn't hurting the site (at least in my opinion).  In addition, every time I see this happen, the participants in the conversation immediately lose interest in it.  The only comment that was posted in that room after all the comments were moved is most likely this one:  It wouldn't surprise me if the folks using &quot;bugged&quot; to refer to a certain software quality are the same folks who refer to their programs as &quot;codes&quot; and who believe textspeak is the pinnacle of modern English.  Which nobody will ever see. :) Some mods are really aggressive about this.  I discussed this with a mod on Physics, and he told me that they routinely move discussions when they think they might run off the rails. Find all natural numbers $n &gt; 1$ and $m &gt; 1$ such that $1!3!5!\cdots(2n - 1)! = m!$   I have been thinking about coming up with some inequalities which would narrow the possible range of pairs $(n, m)$, however the best I have been able to find so far are $m \ge 2n - 1$ and $m \lt n^2$, which is clearly not enough.  Update. The question has tag combinatorics as it is from a book about combinatorics, so there must be at least partly combinatorial solution. I'm asked to used induction to prove Bernoulli's Inequality: If $1+x&gt;0$, then $(1+x)^n\geq 1+nx$ for all $n\in\mathbb{N}$. This what I have so far:  Let $n=1$. Then $1+x\geq 1+x$. This is true. Now assume that the proposed inequality holds for some arbitrary $k$, namely that $$1+x&gt;0\implies (1+x)^k\geq 1+kx,~\forall~k\in\mathbb{N}\setminus\{1\}$$ is true. We want to show that the proposed inequality holds for $k+1$. Thus multiplication of $(1+x)$ on each side of the above inequality produces the following result: $$(1+x)(1+x)^k\geq (1+kx)(1+x)\implies (1+x)^{k+1}\geq 1+x+kx+kx^2\cdots\cdots\cdots$$  I'm not sure where to go from here. I'm looking to implement a phase lock in an FPGA without using any external components (other than the ADC). For simplicity locking to a simple binary pulse is adequate. The frequency of the signals is ~0.1-1% of the clock. I can't use the onboard clock PLL's because they are typically:   Not configurable (set during synthesis). Jittery. Don't support the frequency I need.   I've been sorting through the literature and found a few binary phase locked loops. Most notable a "pulse steal" design that I can post a link to if desired. I have implemented and synthesized with some success, but its jitter and lock range was not as good as advertised. I've also had success using a external DVCO, but I would prefer if I can implement everything on chip.  A digital circuit design or even a hint in the right direction would be helpful (I've been banging my head against this for a while), a proven FPGA implementation would be wonderful but not expected.   ADDED 10-27-2010   The actual DPLL design that I used has a "Random Walk Filter" as the loop filter (not the "pulse steal" described earlier, going through my notes that didn't work to well), which then drives the clock pulses to the DCO. The lock-in range is set via divider in the DCO. The sensitivity of the loop is established by varying the length of the random walk.   The paper in which this is found is cited at the end of this post. After implementing parts of it myself, I found that it was actually already implemented on OpenCores, however it turns out that in the last few months the project was deleted but I have the Verilog files saved if anyone wants them.  Yamamoto, H.; Mori, S.; , "Performance of Binary Quantized All Digital Phase-Locked Loop with a New Class of Sequential Filter," Communications, IEEE Transactions on , vol.26, no.1, pp. 35- 45, Jan 1978  doi: 10.1109/TCOM.1978.1093972  URL: In our network the name of the network domain is also the domain of the organization's website (say, example.com). Externally, people can enter example.com to visit our website, but internally, this points to one of the several domain controllers, we have for Active Directory, some of which do not even run a webserver.   As a result of this, links to http://example.com don't work internally (only www.example.com does work internally).  How do we point http requests transparently to the web server, and what side effects does this have? Looking for the title of a gold heist movie involving the telekinetic son of an extraterrestrial/alien? Some 30 years back, I saw a film about the son of an extraterrestrial who gets involved in a gold heist.  The main character does not initially know that he is the son of an extraterrestrial and that has special telekinetic powers. The film opens, I think, with him being in some train yard, his foot getting stuck in a switch with a locomotive approaching. He stops it using his powers intuitively, possibly passing out (not realizing what he actually did). I think his mother subsequently reveals his heritage to him.  He somehow gets hired as a bodyguard for someone planning a gold heist. I think they know his abilities and use him to steal a million US dollars. Actually, that is just a distraction, covering that they steal 30 million dollars from the same location (through the air, not sure on that part).  The last part I remember is some underground tunnels where the thieves set up to melt the gold. The main character is locked in there.  Does anyone know the title of this movie? Searching for things like "sci-fi gold heist extraterrestrial etc." did not reveal anything to me. I also had a hard time picking proper tags (sorry). How to address a professor in person at US universities? At US universities, how should one address a professor while talking to him or her? In my home country, we usually address the professors as either "sir" or "madam" while talking about our queries in person.   What's the norm at US universities? Can I get UAC prompt for user from batch file? Can I get UAC prompt for user from batch file?  For example I need put some keys to registry under CurrentControlSet from batch file by     reg import path\to\my.reg   PS. runas is not a solution as my customers uses different Windows localisation and I can not guess which name used for Administrator account (this can be Администратор)...  And script don't know administrator password.  And UAC dialog box does not require password entering... "On/at/for/over the weekend" in American English Some sources say that "at the weekend" is wrong, while other ones say it's correct. Which form is acceptable in American English?        On Saturdays her sister Ann usually comes to stay with Mary on/at/for/over the weekend/s.   What are you going to do at/on/for/over the weekend/s?    We are going to Paris on/at/for/over the weekend/s.   Are you going to stay here for/at/on/over the weekend/s?      Which preposition do American English speakers use — at, on, for, over? If $\lambda$ is an eigenvalue of $A^2$, then either $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A$ $A$ is an $n\times n$ matrix of complex numbers. Prove that if $\lambda$ is an eigenvalue of $A^2,$ then $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A.$    If $\lambda$ is an eigenvalue of $A^2,$ we have $\lambda\alpha=A^2\alpha$ for some $\alpha.$ Then how can we find a $\beta$ s.t. $\sqrt{\lambda}\beta=A\beta?$ Turning a cipher into a hashing function How to sail downwind faster than the wind? Recently a  set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a  talking about it, but it doesn't explain exactly how it works.  I can imagine some configurations, but I don't get how a system could be set up to push forward with a tailwind (when the cart is moving slower than the wind) and push forward with a head wind (when the cart is moving faster than the wind).  Could someone help explain how this is possible? Typeset the shrug ¯\_(ツ)_/¯ emoji I'm completing a problem set, one problem for which I literally have no idea what to do on. The graders would prefer to have a physical copy of the problem so I thought it best to include the ¯\_(ツ)_/¯ emoji as my answer, instead of something like "Dunno" or "No idea."  Option #1 is to include an image.  Beyond that I actually don't understand how this emoji works. The middle character is Japanese kana "tsu" and proves problematic - TeX wants it in math mode then renders "?" when it is.