This is a question from a textbook: If G is a group and $|Aut(G)|=1$then prove G’=(e) I’m completely stuck (for about a whole day ), A proper hint or an answer would be so appreciated.
Well, this is an exercise problem from Herstein which sounds difficult:   How does one prove that if $|G|&gt;2$, then $G$ has non-trivial automorphism?   The only thing I know which connects a group with its automorphism is the theorem, $$G/Z(G) \cong \mathcal{I}(G)$$ where $\mathcal{I}(G)$ denotes the Inner- Automorphism group of $G$. So for a group with $Z(G)=(e)$, we can conclude that it has a non-trivial automorphism, but what about groups with center?
Style every four posts differently Possible Duplicate:          Is it possible to style every four posts differently? I mean something like this:  &lt;div class="row"&gt; &lt;div&gt;1st post&lt;/div&gt; &lt;div&gt;2nd post&lt;/div&gt; &lt;div&gt;3rd post&lt;/div&gt; &lt;/div&gt; &lt;div class="row&gt; &lt;div&gt;4th post&lt;/div&gt; &lt;/div&gt; ...Repeat   I'm using , so it would be great if I could experiment more with that.. :) Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc.  I went ahead and gave them a proof by contradiction like so:  Assume $(-x) \cdot (-y) = -xy$  Then divide both sides by $(-x)$ and you get $(-y) = y$  Since we have a contradiction, then our first assumption must be incorrect.  I'm guessing I did something wrong here. Since the conclusion of $(-x) \cdot (-y) = (xy)$ is hard to derive from what I wrote.  Is there a better way to explain this?  Is my proof incorrect?  Also, what would be an intuitive way to explain the negation concept, if there is one? Possible point location algorithm Alert on edit after a downvote How to show TCP listenings and filter them by local IP on Windows? Server has numerous IP addresses, set up on it's network interface.  How to find, who is listening to specific IP port 80?  netstat shows very long list. Are there any builtin means?  UPDATE  Also can't use findstr with also wishing to know process name because brocess name is displayed on separate line. R : Format the text file output How do I rename all folders and files to lowercase on Linux? Can't save my render as an image I seem to be having issues when I try and save the output file as a .png, or .jpeg for that matter. I've set up my user preferences, File, Render Output to my desktop as well as render output in the editor window. What am I missing here? I'm obviously very new to this program and your help would be appreciated. Thanks for your time Tourist to F1 change of status within 60 days I have a PhD place at a US university starting Aug 21 but want to visit a different university for casual research for 6 weeks from July 1. This is longer than the 30 day grace period for the F1. Can I arrive on the visa waiver program or tourist visa in July and then just stay on for the PhD? I guess I might need to change status. Will this work?  Please don’t suggest exiting and reentering, that’s too expensive.  (British masters student in UK) I will give this question a little context. Firstly, as I understand it, as soon as I "close the switch" on a circuit, electric current pretty quickly establishes a steady state where, at any given cross section along a wire, the average kinetic energy of that slice is both constant and equal anywhere along the wire. (Please correct me if I am misunderstanding).   If the average kinetic energy is constant anywhere throughout the wire in the circuit (which confuses me, as I would think that the electrons should all accelerate after exiting the resistor since they are no longer being impeded as much), that means that the average velocity is constant. So, in the example of a simple circuit with a battery of v Volts and a resistor of o Ohms, my question is the following:  Because a 'voltage drop' is known to occur across the resistor, what type energy is being "traded" to generate the heat that radiates from the resistor? I would think that the reflexive answer is "electrical energy"...hence the VOLTAGE drop (the sacrificed energy is clearly not kinetic, as the velocity is constant everywhere). However, I find this confusing. Does this mean that if I had a positive test charge, it would be easier for me to bring it to the beginning of the resistor as compared to bringing it to the end of the resister?     Further, if the correct answer IS "electrical energy", why exactly DOES electrical energy get "dissipated" as the electrons pass through the resistor? I always here the comment Oh! It's because all the electrons are running into densely packed crap which impedes their flow but that to me sounds like a reason for their KINETIC energy to be reduced. However, clearly that's not the case. So, ultimately, I guess the real question is:  **What goes on in the resistor that is literally removing electrical energy **. I am sure that this is a quantum mechanics question, but my quantum mechanics knowledge is not terribly strong. If I could get an answer that is devoid of crazy wave function equations, I would greatly appreciate it. Thanks! What is the sum of the 'second half' of the harmonic series?  $$\lim_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} =~ ?$$  More precisely, what is the limit of the above sequence of partial sums? Visualization for Euclidean Algorithm Finding Elevation Change, any method So, I think it'd be cool - for goal setting for example - if I could keep track of my elevation change.  The problem is, the local cyclocomputers I looked at seem to use barometric pressure to determine the change.  This is fine, unless some weather is moving in, which happens not infrequently in the Midwestern United States.  Or do some of them try to use an inclinometer, your speed, and some math you learn in Calculus II to keep track of your change?  That would seem more accurate!  I could try to use a GPS meter, but those things are expensive -  and based on back when I had service to my smart phone, not guaranteed to match my car's odometer for distance even - I've read from some other riders that the distance varies at least slightly from local measurement on a bike as well.   Alternatively, let's say that I ride along a known route.  Is there any good way of plotting that route for elevation change?  Thanks! Create Task in loop but all tasks take the same parameter Using ST_Union in PostGIS I have a spatial table (polygons,polylines) in a database. These are digitized by multiple people. For example, a state is divided into multiple Grids and given to multiple people to digitize using QGIS; which is connected to a postgres database. Now, I have to merge all those polygons and polylines. I don't know how to do this via ST_Union. I Used the following snippet to merge the polygons and polylines CREATE TABLE schema_name.polygon_un2 AS SELECT upg.un_geom,npg.Column1,npg.Column2,npg.Column3,npg.Column4,npg.Column5  FROM (  SELECT st_union(the_geom) As un_geom,(   SELECT oid FROM schema_name.polygon    WHERE oid = 100748191   ) FROM schema_name.polygon WHERE oid IN (100748191,100763519)  ) upg  INNER JOIN schema_name.polygon npg ON npg.oid = upg.oid;   DELETE FROM schema_name.polygon WHERE oid IN (100748191,100763519);  I have the interesecting polygon oid in a Seperate Table, I want to do this process in an update query and that should be a dynamic plpgsql function.  Green : Grid , Other : Polygon But This snippet did not work !! The snippet which i expect is  It should create a new row for the merged polygons and polylines (eg oid - 1 and 2 merged to oid 3).  The polygons which are not merged (eg 1 and 2 should be deleted) How old should you be when you begin Jedi training? Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? My final goal is to generate Impulse Response Functions in R.  I have variables that are non stationary when I set k = 5 in a Unit Root test, and they are cointegrated which to my understanding prompts the use of the VECM, from which the Vec2Var argument is used to then generate IRFs. However, my response functions from this methodology do not decay over time and mostly do not revert to the zero line.  Furthermore, I noticed that when I input first differenced variables into the VECM as opposed to level data above, response function do revert to the zero line. Therefore my first question is: 1) is it appropriate to use differenced variables in a VECM model?  Secondly, as an alternative I am considering restricting the number of lags used in the Unit Root tests so that the variables are not all non-stationary; in this case 2) would the use of VECM be void and the VAR with first differences be a more appropriate model? Again, using differenced data is giving me better response functions that revert to zero in the long run. However, 3) is it ok to use the VAR for stationary/non-stationary data in levels where these variables are still cointegrated?  Also, I am using growth rate variables, 4) should I still long transform all variables and use logs in all tests?  Thank you for the help! Why a backslash displays as "W"+strikethrough in Netbeans? I'm facing a strange problem with Netbeans. In the editor, when I type a backslash(), I see a W with a strikethrough (as shown in the attached image).  So the c:\\abc is displaying as:    But, when I copy and paste that string into notepad, it gets pasted normally (i.e. c:\\abc).  Has anyone faced this problem before? How to fix it? Traveling to the US with new passport, visa on the old one I have a valid B1/B2 US visa expiring about a year from now. The passport it's in expired a few years ago, and I recently got a new one.   The passport number does not match, but the national ID number, mentioned in both, does (it used to be the same as your national ID, but not anymore)  Can I travel to the US carrying both passports? Or is it asking for trouble? (I read a few years ago that it was possible, but that might have changed)  Should I just get a new visa to avoid potential complications? What is the name for these type of images? I love these kind of graphics and it's so flat which totally matches my current product development.      Do we have a name for it? A name will make it easier to search for examples and how to's.