What does "America" mean?
Why are the United States often referred to as America?
What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why? What is the result of the next limit:   $$ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $$  Why (theorem)? Programmatical Setting of 'Store Relative Pathways' for multiple MXDs ArcGIS 10.1 I am looking to move large number of mxds to a different location on the same drive. Many mxds haven't got 'Store relative pathways' option checked therefore this operation will result in broken links to data. I've only started using ArcGIS 10.1 and it is now possible to programmatically update relative pathways for all mxds by using arcPy and setting relativePaths to be "True". I had a go at writing Python script which (in theory) loops through a top folder and searches for all mxds and then updates "Store relative pathways" setting to be on. When I run this script in PyScripter, it fails to complete, I get the following error:  "exceptions.NameError: name 'mxd' is not defined  Can anyone help ?!? Thanks in advance, Magda      import arcpy, os  folderPath = r"C:\My Folder Path\...\...\..."  for filename in os.listdir(folderPath):     fullpath = os.path.join(folderPath, filename)     if os.path.isfile(fullpath):         basename, extension = os.path.splitext(fullpath)         if extension.lower() == ".mxd":             mxd = arcpy.mapping.MapDocument(fullpath)             mxd.relativePaths = 'True'         mxd.save() del mxd Creating compressed GeoTIFF with QGIS Clipper tool? I have a geo-tiff created by Pix4D which is about 375 Mb in file size.   I have clipped it to a smaller area using Qgis 2.8(using Raster ‣ Extraction ‣ Clipper), and the output file is about 900 MB in size.  Why did the clipping process generate such a large file, when the source file was smaller?   How do I run the clipper tool so that it produces a smaller size? How do I stop Illustrator from snapping to pixel increments? I am working in Illustrator (15.0.2 (CS5) or 16.0.0 (CS6)) and when I try to move objects small distances, they snap to the nearest two pixels on some invisible grid. I can't find anything in the preferences. Here are some screen shots: Why did the snake wink at Harry at the zoo? This is mostly a memory question - I'm having a hard time remembering this and I can't read the book right now.  On the first book, a snake at the zoo winks at Harry. For the sake of the question, we'll assume that snakes can in fact wink.  I have a fuzzy memory here - I think that it winked before Harry had any kind of interaction with the snake (was this before or after Harry broke the glass?)  So, why did the snake wink at Harry? Given that they had not met ever before.  I suppose that the only reason it would wink at Harry would be because it knows Harry can communicate with it. But this would imply that snakes are capable of sensing such ability on wizards - is there (other) evidence that this is true? What defines a PC's consciousness of self, memories and knowledge? I am trying to determine what issues could be caused by using the following serialization surrogate to enable serialization of anonymous functions/delegate/lambdas.   // see http://msdn.microsoft.com/msdnmag/issues/02/09/net/#S3 class NonSerializableSurrogate : ISerializationSurrogate {     public void GetObjectData(object obj, SerializationInfo info, StreamingContext context)     {         foreach (FieldInfo f in obj.GetType().GetFields(BindingFlags.Instance | BindingFlags.Public | BindingFlags.NonPublic))             info.AddValue(f.Name, f.GetValue(obj));     }      public object SetObjectData(object obj, SerializationInfo info, StreamingContext context,                                 ISurrogateSelector selector)     {         foreach (FieldInfo f in obj.GetType().GetFields(BindingFlags.Instance | BindingFlags.Public | BindingFlags.NonPublic))             f.SetValue(obj, info.GetValue(f.Name, f.FieldType));         return obj;     } }     Listing 1 adapted from   The main issue I can think of that might be a problem is that the anonymous class is an internal compiler detail and it's structure is not guaranteed to remain constant between revisions to the .NET Framework. I'm fairly certain this is the case based on my research into the similar problem with iterators.  Background  I am investigating the serialization of anonymous functions. I was expecting this not to work, but found it did for some cases. As long as the lambda did *not&amp; force the compiler to generate an anonymous class everything works fine.   A SerializationException is thrown if the compiler requires a generated class to implement the anonymous function. This is because the compiler generated class is not marked as serializable.  Example  namespace Example {     [Serializable]     class Other     {         public int Value;     }      [Serializable]     class Program     {         static void Main(string[] args)         {             MemoryStream m = new MemoryStream();             BinaryFormatter f = new BinaryFormatter();              // Example 1             Func&lt;int&gt; succeeds = () =&gt; 5;             f.Serialize(m, succeeds);              // Example 2             Other o = new Other();             Func&lt;int&gt; fails = () =&gt; o.Value;             f.Serialize(m, fails); // throws SerializationException - Type 'Example.Program+&lt;&gt;c__DisplayClass3' in Assembly 'Example, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null' is not marked as serializable.         }     }   Listing 2  This is similar to the issue of trying to serialize iterators and I had found the following code in a previous search (see ) Using the code from Listing 1 and an ISurrogateSelector I was able to successfully serialize and deserialize the second failing example.  Objective  I have a system that is exposed via a web service. The system has a complex but small state (many objects, not a lot of properties per object). The state is saved in the ASP.NET Cache, but is also serialized to a BLOB in SQL in case of cache expiration. Some objects need to execute arbitrary "events" upon reaching some condition. Hence they have properties accepting Action/Func objects. Contrived example:      class Command     {         public Command(Action action, Func&lt;bool&gt; condition);     }   Somewhere else      void DoSomethingWithThing(Thing thing)     {         state = Store.GetCurrentState();          Command cmd = new Command(() =&gt; thing.Foo(), () =&gt; thing.IsReady())         state.Add(cmd);          Store.Save(state);     } In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"? I was reading  on Category Theory and it said (paraphrased to add context):     Exercise 4: Explain why in $\textbf{Set}$ (the Category of Sets), the product of an empty set of sets is a one-element set.   which I think is incorrect. The product of two empty sets (or any number) is empty because we are considering:  $$ \emptyset \times \emptyset = \{ (a,b) : a \in \emptyset, b \in \emptyset \} = \emptyset$$  where $a \in \emptyset , b \in \emptyset$ are false, so the above is the $\emptyset$ which is NOT a one element set (its a zero element set).   This should be trivial so I am assuming I am somewhere mis reading the natural language of the exercise. Someone help me catch where is it and what the answer should be? i.e. whats being asked and the answer? Finding $\frac {d(\tan \theta)}{d\theta}$ As I understand it, anything created with an alloc, new, or copy needs to be manually released. For example:  int main(void) {     NSString *string;     string = [[NSString alloc] init];     /* use the string */     [string release]; }   My question, though, is wouldn't this be just as valid?:  int main(void) {     NSAutoreleasePool *pool;     pool = [[NSAutoreleasePool alloc] init];     NSString *string;     string = [[[NSString alloc] init] autorelease];     /* use the string */     [pool drain]; } Check whether an array is a subset of another Any idea on how to check whether that list is a subset of another?  Specifically, I have  List&lt;double&gt; t1 = new List&lt;double&gt; { 1, 3, 5 }; List&lt;double&gt; t2 = new List&lt;double&gt; { 1, 5 };   How to check that t2 is a subset of t1, using LINQ? Does a bad grade in one course (with otherwise OK record) affect graduate admissions? I'm currently an M. Phil student in Math and I failed a course last semester because I was not able to hand in a home work assignment (which was worth 40% of my grade) on time (I was 30 minutes late).   Apart from that I'd say I'm a fairly decent student, I got an upper second class honours bachelors degree, I have a B+ and A's for all my other courses in my current programme and I'm almost finished with my first paper to be published.   I've however been deeply worried about this failure as it would reflect poorly on my transcript if I were to apply to a Ph.D or another Master's programme.   Will my failing grade affect my chances of getting into a competitive programme or greatly lower my chances of getting a scholarship? Do I have to pay taxes in the US if my online store sells to US customers even though I don't live in the US? I  own a website and I sell digital content. I'm a nonresident alien with the US. Most of my customers are US based so I was wondering will I have to pay any taxes to the US?  I have read that      For nonresidents, taxable income is separated into two categories:         Income that is effectively connected with a U.S. trade or business, after the deductions that are allowed, is subject to U.S. income tax   at graduated rates - the same rates that apply to U.S. citizens and   residents - or lower rates if the provisions of a tax treaty apply.   Income that is subject to U.S. income tax, for being U.S. source income, but that is not effectively connected with a U.S. trade or   business, is subject to a flat 30% tax      Is this true and do I belong to any of these categories?  If I form an LLC or C corp am I liable for this withholding tax?  My customers are based in the US and I believe all income is considered FDAP income according to the IRS:     Fixed, Determinable, Annual, or Periodical (FDAP) income is all   income, except:         Gains derived from the sale of real or personal property (including market discount and option premiums, but not including original issue   discount)   Items of income excluded from gross income, without regard to the U.S. or foreign status of the owner of the income, such as tax-exempt   municipal bond interest and qualified scholarship income      The thing is the IRS also says:     Effectively Connected Income, after allowable deductions, is taxed at   graduated rates. These are the same rates that apply to U.S. citizens   and residents. FDAP income generally consists of passive investment   income; however, in theory, it could consist of almost any sort of   income. FDAP income is taxed at a flat 30 percent (or lower treaty   rate) and no deductions are allowed against such income. Effectively   Connected Income should be reported on page one of Form 1040NR. FDAP   income should be reported on page four of Form 1040NR.   In the last quote, it’s like they say it only applies to passive income but if they feel like it, they can apply this to all income?? How do I create a file and mount it as a filesystem? How do I create a file of size 10M, format it with ext3 filesystem and then mount it in /media/fuse?  I tried with  mkfs -t ext3 file   then to mount it  mount -t ext3 file /media/fuse   It didn't work because it said that file wasn't a block device. Can anybody help me? Enumerate paragraphs and subparagraphs like sections but with letters I am having difficulty with this proof. I have previously proved that for an automorphism on the extension field $K$ of $F$ that when restricted to $F$ is the identity automorphism must take roots of $f(x)\in F[x]$ in $E$ to roots of $f(x)$ in $E$. I was thinking of using the minimal polynomial $x^{3}-2\in\mathbb{Q}[x]$ and the result of previous problem I solved, but I suspect there are automorphisms that don't fix the subfield, so the result can't be used or I need to prove that any automorphism of an extension field must fix the subfield that is being extended or always sends roots in $E$ to roots in $E$.  I am not asking for a solution to this, but maybe a hint or pointer in the right direction. This problem is introduced in the text prior to Galois theory, so please keep that in consideration. Let $P$ be a probability measure on $(\Omega, \mathscr{F})$, If $a,b,\in\mathscr{F}$ and $A\subset B$, then $P(B)-P(A)=P(B\setminus A)\ge 0$.  So far I have:  $A\subset B \implies B\setminus A = B\cap A^c = \emptyset$ as $A$ and $B^c$ are disjoint. Since $A\cup (B\setminus A)=A\cup (B\cap A^c)=(A\cup B)\cap (A\cup A^c)=B\cap\Omega = B$  Then for $A,B\in \mathscr{F}\implies P(A\cup (B\setminus A))=P(A)+P(B\setminus A) = P(B)$ by countable additivity.  Rearranging, $P(B)-P(A)=P(B\setminus A) \ge 0$. What does 1x1 convolution mean in a neural network? I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what is a 1x1 convolution.  I have also seen  by Yann Lecun.  Could someone kindly explain this to me? Is it OK to leave "What have you tried?" comments? Give $a, b. c$ be the lengths of a triangle and $a+ b+ c= 3$. Prove that: $$\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq  \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$$ My try  We have England MO inequality: $$\left ( \frac{a}{b}+ \frac{b}{c}+ \frac{c}{a} \right )^{2}\geq  \left ( a+ b+ c \right )\left ( \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c} \right )$$  and $$\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a} \geq  3=  a+ b+ c$$  But it cannot be used to prove the above inequality and how to use triangle inequality in this inequality. I need the help. Thanks!