I need to create a buffer around a polygon.   I know how to do this, but my problem is I need the buffer to be 250 feet to the south, east, and west, but 500 feet to the north.   Is there any way to specify the distance of a buffer in a certain direction from a feature?
I want to create buffer polygon(with curved edges) from  points like this using ArcGIS for Desktop.   distance toward North from a point 5, toward South 1.5, toward west 1, toward East 2.   all this distance is attached as attribute in point in different fields.
How can friction do no work in case of pure rolling? I have read various answers , on PSE and elsewhere , and most of them explain that the point of contact of the rolling object undergoes 0 instantaneous displacement in the direction of friction, I agree , but then there is a feeling that the friction does provide a torque , so how can it do 0 work . ( The pure rolling here is under a constant external force on the object so friction does act ). General Relativity Equivalence Is Einsteins Equivalence theorem in General Relativity correct? It seems to me that it neglects the fact that gravitational acceleration depends upon separation distance squared, thus neglecting the effect of tidal forces.   For example, as I sit on earth, I experience the affect of earth's gravity; Although the acceleration on my head is slightly less than the acceleration acting on my feet. If I make the claim that my frame is equivalent to me being in a space ship traveling at g, doesn't that mean my whole body is accelerating at g uniformly? This is contrary to the previous statement though. How to redirect output to a file and stdout New 16GB of RAM installed yet I see 15.3 on my system. Why? Just switched 4GBs to 16GBs of RAM. However, when I look at how much memory I have, it says 15.3. I'm just wondering why did my memory drop down when I just installed 16 GBs of RAM. What does accepting an answer actually convey (2015 edition)? Showing that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$ Show that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$.   My reasoning is as follows:  Since the only ways $X^2$ and $X^3$ can be factored in $K[X^2,X^3]$ are $X^2 = X^2 * 1$ and $X^3=X^3*1$ it follows that $X^2$ and $X^3$ are irreducible.  To show that they are not prime in $K[X^2,X^3]$ I argue that $X^2\mid X^3*X^3$ but $X^2\nmid X^3$ and $X^3\mid X^4*X^2$ but $X^3\nmid X^4$ or $X^3\nmid X^2$.  Is that correct? See permissions for new files on a given directory I don't understand how my Linux machine is operating on new files.   I have an Amazon Linux AMI (RHEL based distro) and when I execute umask I get 0002, so I get whenever I create new stuff other users won't get write access.  But then I go to my home directory and I type:  $ mkdir myDir $ touch myDir/myFile $ ls -l | grep myDir   and I get  drwxrwxr-x 2 myself myself 4096 May 11 22:37 myDir   and for the folder:  $ ls -l myDir -rw-rw-r-- 1 myself myself 0 May 11 22:37 myFile   So apparently there's more going on there then my umask, since myFile permissions are more restrictive than just write protection.  Digging deeper, if I try:  $ sudo touch /var/run/myPidFile.pid $ ls -l /var/run/ | grep myPidFile.pid -rw-r--r-- 1 root    root       0 May 11 22:42 myPidFile.pid   So myPidFile.pid gets a much more restrictive default permission, under /var/run then myFile gets under my home folder.  We could blame the root umask but if I run umask under root I get 0022 which is indeed more restrictive then my user's 0002 umask but still doesn't explain how the execution bit permission isn't set.  So how can I understand a folder's default permission on Linux? Is having a skills bar chart on a resume a good idea? Why is there an "electric" potential drop across the resistor? An electric potential difference is created when two charges are separated. In a capacitor, there is a clear accumulation of opposite charges on the two separated plates, therefore work has to be done in moving an unit charge from one plate to another, against the electric field.   But, , a potential difference is created in a resistor due to the heat produced by the collision and increased lattice vibrations. So there is an energy loss across the resistor, yes, but how does this energy loss due to heat create an electric potential difference. In other words, do electrons accumulate on one or both sides of the resistor? If not, why should we do electric work in moving from one end of the resistor to another. If the difference in energy is not due to electric work, then that's not electric potential, is it? I was reading about the equipartition theorem and I got the following quotations from my books:  A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis down the length of the molecule doesn't count. - Daniel V. Schröder's Thermal Physics. A diatomic molecule can rotate like a top only about axes perpendicular to the line connecting the atoms but not about that line itself. - Resnick, Halliday, Walker s' Fundamentals of Physics.  Why is it so? Doesn't the rotation take place that way? Isomorphism of quotient modules implies isomorphism of submodules? Let $A$ be a commutative ring, $M$ an $A$-module and $N_1, N_2$ two submodules of $M$.  If we have $M/N_1 \cong M/N_2$, does this imply $N_1 \cong N_2$?  This seems so trivial, but I just don't see a proof... Thanks! Finding an angle within an 80-80-20 isosceles triangle The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it.  So here is the puzzle:    The triangle $ABC$ is known to be isosceles, that is, $AC=BC$. The labelled angles are known to be $\alpha=\gamma=20°$, $\beta=30°$. The task is to find the angle labelled "?".  The only solution that I know of is to use the sine formula and cosine formula several times. From this one can obtain a numerical solution. Moreover this number can be algebraically shown to be correct (all sines and cosines are contained in the real subfield of the 36th cyclotomic field). So in this sense I solved the problem, but the solution is kind of a brute force attack (for example, some of the polynomials that show up in the computation have coefficients > 1000000). Since the puzzle originates from a book that deals only with elemetary geometry (and not even trigonometry if I remember correctly) there has to be a more elegant solution. I have this directory /foo/bar/. Inside, I have a python file named myfile.py. I made it executable by adding (at the top):  #!/usr/bin/env python   Then, I made it executable by issuing   chmod +x myfile.py   I edited my path by issuing  sudo nano /etc/paths   I added /foo/bar/ to it.  The problem is that although I can run myfile.py by typing ./myfile.py while I am inside /foo/bar/, it doesn't work from any other location. What am I doing wrong?  Thank you. Can I travel to Dublin, Republic of Ireland with UK Tier 2/Schengen visas with Indian Passport Occasionally I see constructs like this in English sentences:        Not only is this true in this case, but ...      What puzzles me is the "is this" part of it. The sentence is not a question, yet it seems to have a question-like order. Isn't this correct/preferred:        Not only this is true in this case, but ...      Are there other cases where non-question sentences contain question-like parts (so to speak)? How can you find and replace text in a file using the Windows command-line environment? I am writing a batch file script using Windows command-line environment and want to change each occurrence of some text in a file (ex. "FOO") with another (ex. "BAR"). What is the simplest way to do that? Any built in functions? Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$ Fatal Error: Allowed Memory Size of 134217728 Bytes Exhausted (CodeIgniter + XML-RPC) I have a bunch of client point of sale (POS) systems that periodically send new sales data to one centralized database, which stores the data into one big database for report generation.  The client POS is based on PHPPOS, and I have implemented a module that uses the standard XML-RPC library to send sales data to the service. The server system is built on CodeIgniter, and uses the XML-RPC and XML-RPCS libraries for the webservice component. Whenever I send a lot of sales data (as little as 50 rows from the sales table, and individual rows from sales_items pertaining to each item within the sale) I get the following error:  Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 54 bytes)   128M is the default value in php.ini, but I assume that is a huge number to break. In fact, I have even tried setting this value to 1024M, and all it does is take a longer time to error out.  As for steps I've taken, I've tried disabling all processing on the server-side, and have rigged it to return a canned response regardless of the input. However, I believe the problem lies in the actual sending of the data. I've even tried disabling the maximum script execution time for PHP, and it still errors out. Should I be worried that yum update suddenly wants to update well over 100 packages on my CentOS 6 system? This is a trivial problem, but it annoys me that I can't get to the bottom of it:  I'm running Windows 8, Powershell version 3.0. By right-clicking on the title bar I can go into the Properties and change the font, size, background colour etc without any problems.  After closing and restarting Powershell, all of the changes I've made stick except that if I've set the font to Lucida Console then on reopening I get the Raster font.  (Note that all of the above applies to when I run Powershell as Administrator.)  So:   If I set the font to Lucida, then it switches to Lucida for the remainder of the session. If I set the font to anything other than Lucida, then it stays as that after closing and reopening. If I alter the window sizes or text colours or anything else, the changes persist after reopening. The only thing that goes wrong is that if I set the font to Lucida, it switches to 'Raster fonts' when I reopen. But cmd and powershell ISE don't have this problem - only the powershell console.   Can anyone suggest what might be going wrong?  (One observation I've made is that upon re-opening Powershell after setting the font to Lucida, at first the width of the window is what it would be if the font were Lucida, but then after a second, it widens slightly to accommodate the raster font.)