Is the Sigma 18-200 F3.5-6.3 DC Macro compatible with full-frame Nikon DSLRs?
What do all those cryptic number and letter codes in a lens name mean?
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ if $m &lt; 0$. This statement came up in an algebraic geometry text with no explanation provided, and I'm trying to understand why it's true.   Thoughts so far:   Since $H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m))$ is the vector space of regular sections of $\mathcal{O}_{\mathbb{P}^n}(m)$ over $\mathbb{P}^n$, we can try to find a basis. Since the regular sections are the degree $m$ polynomials in $x_0, \dots, x_n$, it seems like the collection of degree $m$ monomials in $x_0, \dots, x_n$ should work. But I don't see how there are ${n + m \choose n}$ of these. Is it just a basic counting argument that I'm struggling with?  On a side note, I think I understand what global sections of $\mathcal{O}_{\mathbb{P}^n}(m)$ look like, but how can we describe the regular sections over a distinguished open set $D(f)$? Is it something like degree $m$ polynomials with denominator $f$? I'm from Western Pennsylvania. Until I moved away, I never realized that when I omitted the to be from phrases like needs to be cleaned, my usage was different than what most English speakers are accustomed to. Is it wrong? How do I clone a single branch in Git? What is the danger of running untrusted software as a normal user Sometimes I have to use some propriety softwares which I don't trust or even pre-compiled open source ones which I don't know if they've been compiled as their source are.   Lets say we installed a propriety application in /opt/software, then we run it as a normal user (without sudo, gksudo, etc).   I know when we run a program it is able to connect to the Internet, monitor X, keystrokes, collect user data and so on. It can't change anything important in the system or infect the system, (because of the Linux permissions system). It is possible for program to add some plug-in/extension to a user's browser (Because browser profiles are available in user home directory). After closing the program and rebooting it can't do anything anymore. Wrong because:   Program can add itself to a shell/file/directory which does the autostart process, so it will run at any login.  If we consider the autostart process clean, without rebooting there is a chance that a process of the program is still active. Programs can delete or modify any file in the user home directory (or any other file which a user has write permission to).   So what should we do?   I think the only safe way to run a propriety program is running it as another user. If running the program as another user somehow is not possible then we should change the autostart files permission so only root can change them. then after closing the program a reboot will do the job.   Am I right? Is there anything that I'm missing? Maximum power of $2$ which divides $3^{1024}-1$ What is the maximum power of $2$ which completely divides $3^{1024}-1$?  I proceeded thus: $\phi(2^n)=2^{n-1}$ for all $n\ge1$ $$3^{1024}=3^{2^{10}}\equiv1\pmod {2^{11}}$$ $$3^{1024}-1\equiv0\pmod {2^{11}}$$ Since $\phi(2^{11})=2^{10}$.  So, maximum power of $2$ must be $11$. But the answer says it is $12$. Where am I wrong and how to solve it correctly? This is a  about DNS server administration.   I have one hundred or so domains. All of these domains need to be configured identically, but it seems like a huge waste of time to have to configure a new zone and/or zonefile for every one of these domains. There has to be a better way to automate this!  I think I'm on to something...if I create a zone called ., or use some other feature in my DNS software to always return a specific IP when an A record is requested, this seems to get me pretty close to my desired end result. My server is responding authoritatively to the requests and it's so much easier to manage!  This was working great until nameserver validation software started checking these domains. I figured out that I can make most of the errors go away by adding NS records, but my software won't let me put more than one SOA record in the same zone file.  How do I work around this multiple SOA record problem? Use of a semicolon before and comma after "however" Several years ago, a previous boss told me to use a semicolon and comma with the word "however".  I've always questioned this and would like to know if the following random sentences are using the correct method.        Our plane was delayed overnight; however, the airlines reimbursed us for lodging.   It looks as though he's upset; however, she told me he always has that look on his face.   I want to find him a nice gift; however, I am a broke until payday.      Normally I would use a less "wordy" sentence in casual writing, but hopefully the example will suffice.  For example, on number 3 I would usually type:      I want to get him a nice gift, but I'm broke until payday. A. These kinds of problem are to be avoided. B. These kind of problems are to be avoided.  Are both A and B grammatical? If not, why not? If so, after having noticed the parallelism between A and C, and between B and D, could we say that C and D are &quot;standard&quot; English, too?  C. These kinds of problem are ones to avoid. D. These kind of problems are ones to avoid. Smooth reload of uitableview data when rows are deleted Are there any synonyms for the noun 'crush'? I must clarify, when I say 'crush', I mean the subject of an unrealistic, one-sided infatuation. For example, it can be used in this sentence: 'My celebrity crush is David Beckham.'  Could that word be interchanged for another? Preferably, can it be a word which is not necessarily too formal/complex? I've searched online for a while but can't find any synonyms for this form of 'crush.'  I want the word for a novel which is set in an old-ish fantasy period so I don't think 'crush' would feel in-place.  The main character is a lower-class worker. I'm planning a trip to recover a motorcycle from a distant city. The ideal trip would be flying to that location and coming back riding the bike, but that would require me to transport my riding gear with me in the plane: Leathers, boots, gloves, back protector and crash helmet.  All this is bulky and expensive stuff, and a crash helmet may be damaged if dropped or hit hard.   I don't expect any airline to allow me a crash helmet as hand luggage; and wearing it all the time is out of the question :-)   To complicate things, I would be coming back riding the bike, so any hard suitcase would have to be left behind.   How do people normally transport that kind of stuff? Are aerosol cans allowed and safe, in checked luggage? Is it fair to buy a return ticket I know I will never use just because it's cheaper? I am planning a trip to Asia and then back to Rio. The thing is that I am traveling on flexible dates, so I am thinking of buying a one way ticket to Hong Kong, and I was planning to do the same when I want to come back.  But what I noticed is that, for example, a one way ticket from Melbourne to Rio costs no less than $2700 dollars for the month of May.  When I do a search for a round-trip from Melbourne to Rio and back, I can find flights for $2200.  I know I will not be using that return to Melbourne, but I'd still prefer to save those $500.   Can there be any issue with buying a round-trip with a return that I will never use? Is it a good practice to refer to countries, ships etc using the feminine form? While talking about ships and countries, is it a good practice to use the feminine form?  For example:  "Her economy" - while referring to a country's economy "Her flag (or deck etc)" - while referring to a ship  Is this practice common? Is it used today? change environment of a running process How might it be possible to alter some variable in the env of an already running process, for example through /proc/PID/environ? That "file" is read-only.  Need to change or unset the DISPLAY variable of a long-running batch job without killing it. Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere? I wanna prove that   "if $f: \mathbb{R}^n \to \mathbb{R}$ is continuous and satisfies $f=0$ almost everywhere (in the sense of Lebesgue measure), then, $f=0$ everywhere."  I am confident that the statement is true, but stuck with the proof. Also, is the statement true if the domain $\mathbb{R}^n$ is restricted to $\Omega \subseteq \mathbb{R}^n$ that contains a neighborhood of the origin "$0$"? Inverse of $f(x)=\sin(x)+x$ What is the inverse of   $$f(x)=\sin(x)+x.$$  I thought about it for a while but I couldn't figure it out and I couldn't find the answer on the internet.  What about  $$f(x)=\sin(a \cdot x)+x$$  where $a$ is a known real constant.  Thank you for taking the time to read this question! Sorry if this has been asked before... Synaptics driver doesn't load sometimes Say I have a Python function that returns multiple values in a tuple:  def func():     return 1, 2   Is there a nice way to ignore one of the results rather than just assigning to a temporary variable? Say if I was only interested in the first value, is there a better way than this:  x, temp = func() What is the emergency phone number in different countries?