Image of homomorphism from ideal is ideal
Must an ideal contain the kernel for its image to be an ideal?
Splitting all lines in layer at vertices using QGIS MongoDB could not connect local server I had mongdb installed and evrything was working fine. I wanted to delete the mongodb lock. By mistake the directory /var/lib/mongodb/ got deleted.  So, I uninstalled mongo db and installed again. But now i always keep getting this error:  Error: couldn't connect to server 127.0.0.1:27017 at src/mongo/shell/mongo.js:145 exception: connect fail   The error remains same even if I try to login from terminal or rockmongo or my application. I am using ubuntu12.04 and have latest version of mongo. Is it possible to overload the null-coalescing operator for a class in C#?    Say for example I want to return a default value if an instance is null and return the instance if it's not. The code would look like something like this:     return instance ?? new MyClass("Default");     But what if I would like to use the null-coalescing operator to also check if the MyClass.MyValue is set? According to the definition on , a multiple  is a root with  $n\geq 2$. For example, in the equation $(x-1)^2 = 0$, $1$ it the multiple (double) root.  Question: Why is $x = 1$ the multiple root of $(x-1)^2 = 0$?  What does multiplicity mean in this case? According to Wolfram multiplicity is the number of values for which a condition holds, or the number of times for which a polynomial equation has a root at a given point. In what way does the polynomial $x^2 - 2x + 1 = 0$ have multiple roots? I have read about copying files with terminal but these examples will help me a lot. So here is what I want to do:  Examples:   I have a file in /home/levan/kdenlive untitelds.mpg and I want to copy this file to /media/sda3/SkyDrive and do not want to delete any thing in SkyDrive directory. I have a file in /media/sda3/SkyDrive untitelds.mpg and I want to copy this file to /home/levan/kdenlive  and do not want to delete any thing in kdenlive directory  I want to copy a folder from home directory to sda3 and do not want to delete any thing on sda3 directory and opposite I want to cut a folder/file and copy to other place without deleting files in that directory I cut it into. Change System Language Solaris 8 I have Solaris 8 OS installed in French.  Is it possible to switch from French to English without reinstalling the OS ? If yes how ?  When locale -a i have this :  POSIX common en_US.UTF-8 C iso_8859_1 en_CA en_CA.ISO8859-1 en_US en_US.ISO8859-1 en_US.ISO8859-15 en_US.ISO8859-15@euro fr_CA fr_CA.ISO8859-1 iso_8859_15 th th_TH th_TH.TIS620   Even when I try to edit /etc/default/init with :  LANG=en_US.ISO8859-15 LC_COLLATE=en_US.ISO8859-15 LC_CTYPE=en_US.ISO8859-15 LC_MESSAGES=en_US.ISO8859-15 LC_MONETARY=en_US.ISO8859-15 LC_NUMERIC=en_US.ISO8859-15 LC_TIME=en_US.ISO8859-15 LC_ALL=en_US.ISO8859-15   and reboot : nothing happens.  To verify the result i always use date and when i reboot : i also have the date in french.  P.S : I have to do this configuration in a computer which isn't here in my office, so i have to this manipulation in a an another computer here in my office and if it works, i'll do it to the other computer.  So the computer here is configured in English and i have to switch it to French. Here is the content of my ~./dt :  C                     errorlog              sessionlogs Desktop               errorlog.old          sessions Trash                 errorlog.older        simulateur.dtwmrc appconfig             help                  startlog appmanager            icons                 startlog.old asr.dtwmrc            outils.dtwmrc         startlog.older bin                   palettes              tmp bookmarks             sdtfonts              types dtwmrc                sdtpcaction.conf      wsmenu en_US.ISO8859-15      sdtpcaction.conf.bak   Thanks Device not detected in Eclipse when connected with USB cable Export multiple objects to .obj Is it possible to use the startup.blend UI layout in older files? I have Blender 2.79 on my Windows 7 system.    I want to install 2.8, but I'm completing some courses which use 2.79.  If I install 2.8, will it automatically replace 2.79?  Will they interfere with one another?  Thanks. How do the radian have a unit? Is there a way to opt out of Alexa rankings or prevent them from gathering data about my site? My competitor is using Alexa to see what I am doing. I need to get stop Alexa from including my sites in their rankings. How can I do so?   Is it possible to deny access to any visitor with the Alexa toolbar and deny access to Alexa bot requests? Reverse / invert a dictionary mapping Unknown site on Android app When I select the unknown site (i.e. the meta sites) the app crashes.   I have a Samsung Note 5 and version 1.0.89 of the app. Why are our planets in the solar system all on the same disc/plane/layer? I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why? I understand that a black hole bends the fabric of space time to a point that no object can escape.   I understand that light travels in a straight line along spacetime unless distorted by gravity. If spacetime is being curved by gravity then light should follow that bend in spacetime.  In Newton's Law of Universal Gravitation, the mass of both objects must be entered, but photon has no mass, why should a massless photon  be affected by gravity in by Newton's equations?  What am I missing? I went to the doctor's I have run across such a sentence:     Yesterday I was ill, so I went to the doctor's.   What is the function of possessive here, that is doctor's? Why does default auto.arima stop at (5,2,5)? The function auto.arima in the forecast package of R is a powerful tool to identify the best ARIMA(p,d,q) model for a given data series. In the   of the function, they report the following:  auto.arima(y, d=NA, max.p=5, max.q=5, max.order=5, max.d=2, start.p=2, start.q=2, ...)   According to the above function it seems that, by default, auto.arima tries to find the best model among all the combination having:   p equal or lower than 5 q equal or lower than 5 d equal or lower than 2 order equal or lower to 5, i.e. p + q + d  ≤ 5.   However, why does the default code stops at these conditions? Is there any particular reason why p, q and d should be equal or lower than 5, 5 and 2 and their sum lower than 5? I want to install the latest version of Eclipse but the Ubuntu Software Centre contains an older version.  Is there a PPA or some other way to install latest Eclipse? Please describe the steps for full installation. If I have random variables $X_1,X_2,\ldots,X_n$ that are Poisson distributed with parameters $\lambda_1, \lambda_2,\ldots, \lambda_n$, what is the distribution of $Y=\left\lfloor\frac{\sum_{i=1}^n X_i}{n}\right\rfloor$ (i.e. the integer floor of the average)?  A sum of Poissons is also Poisson, but I am not confident enough in statistics to determine if it is the same for the case above.