Property of a continuous function with $f(0)=f(2)$
Universal Chord Theorem
From the :   -exec command ;     There are unavoidable security problems     surrounding use of the -exec action; you should use the     -execdir option instead.  -execdir command {} +     Like -exec, but the specified command is run from the     subdirectory containing the matched file, which is not     normally the directory in which you started find.  This a much     more secure method for invoking commands, as it avoids race     conditions during resolution of the paths to the matched     files.    What does this mean? Why are there race conditions with running it from the starting directory? And how are these security risks? Since there are  complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions").   Yet no one uses these. Why is this? Here are my configurations: DB type: postgresql (9.3 if that's necessary) Table name: product_sections Column names: section_id (integer) &amp; section_path (ltree)    Detail: I have one reference value: section_id: 15 &amp; section_path: Automation_Solutionz. So, when I want to rename Automation_Solutionz to, say Chrome, I want all references of Automation_Solutionz to be updated.      FROM:  Automation_Solutionz Automation_Solutionz.Test_Case_Creation Automation_Solutionz.Test_Case_Creation.Automation Automation_Solutionz.Test_Case_Creation.Manual   TO:  Chrome Chrome.Test_Case_Creation Chrome.Test_Case_Creation.Automation Chrome.Test_Case_Creation.Manual     Similarly, when I update a value which is in the middle, it should rename those too. In the case above, Test_Case_Creation should be renamed to something like TestCase or anything else. The same goes for any item which is either in the middle, end or at the start.  Hope, I explained things correctly. Thanks in advance :) Quantify Difference/Distance between Lognormal distributions I am trying to determine a metric that quantifies the distance between two continuous lognormal distributions. The data is actually a mixture of two lognormal distributions (I am not sure if this can be called bimodal). The individual distributions have different means but the same standard deviations. I have 20 data sets that can be divided into 4 groups, with each group having a constant standard deviation, but the 5 data sets in each group are made up of two distributions with different means. Some examples:      I am in search of a metric that accounts for the contrast (difference in means) and the standard deviation. I have tried out some parameters like coefficient of variation (of the mixture), Ashman's D etc. I have also tried percentage of overlap. However the problem always is that, at the end when plotted against the results I end up with 4 trend-lines again, corresponding to the 4 different standard deviations. Is there some other way I can quantify this?  Just to make myself clear, I want to quantify the difference between two distributions in a single case (between the red and green PDFs in the above image). Can we have a list of all the Stack Exchange domains somewhere, for firewall purposes? Importing single symbol from MnSymbol What does a two overlapping circles symbol mean in an electrical schematic/diagram? In the datasheet for a A3503 Hall Effect Sensor, I saw a circuit diagram labeled 'Functional Block Diagram', and it shows a symbol I have not seen before. It's shown here between 3 - Output and 2 - Ground.  What is this supposed to represent?    The full datasheet is available Switching between one and two monitors When running my MBP, I attach an external monitor, a keyboard and trackpad to it so I have two separate desktops which are contiguous; like it's a "fancy" desktop.   Back in the day on Mavericks, it behaved properly: when I unplugged the external monitor to, say, take the laptop into a meeting, it would just put all of the desktops separately on the built in display, roughly preserving which window stayed on which desktop so all you'd have to use was a run a restore tool like Display Maid to restore your window positions when you plug your external monitor back in. This was handy because you didn't have to manually clean up your desktop when done.   Now, with El Cap, it would seem that when you unplug the external monitor, it used the monitor count of whichever screen had the most desktops and merges the windows from the two "combined desktops" into one desktop in a way that seemed to be random, which is clumsy.   Worse, setting back Display Maid to restore the original configuration automatic doesn't work like it used to - previously it saved positions on all desktops in one action, but now it does it one screen at a time and forcing you restore eech desktop separately, which is tedious. It would seem that Display Maid is not great software anymore.  Is there some other utility out there that must work better so you can restore how your windows and desktop setup was as it was before you unplugged the external monitor. Any ideas? 2D random walk within a bounded area How can I turn on the Intel HD manually? For some weeks my MacBook 6.2 does not switch to the integrated graphics adapter (Intel HD). This is especially crucial when I work on battery (which happens quite often). I guess the runtime could be enhanced when it would take the HD adapter for display.  I checked that it automatically changes the graphics mode. I am running Snow Leopard 10.6.8.  I recently installed 8GiB RAM (not from Apple). Could this probably related to this issue? Actually I do not want to downgrade or use the expensive Apple RAM.  So, how can I manually turn on the internal graphics adapter? Finding the 1st three derivatives of a function and plotting all four curves Get current URL with jQuery? I am using jQuery. How do I get the path of the current URL and assign it to a variable?  Example URL:  http://localhost/menuname.de?foo=bar&amp;amp;number=0 Adding shapefile or feature class as layer in ArcMap using ArcPy I am trying to automate various tasks in ArcGIS Desktop (using ArcMap generally) with Python, and I keep needing a way to add a shapefile to the current map. (And then do stuff to it, but that's another story).  The best I can do so far is to add a layer file to the current map, using the following ("addLayer" is a layer file object):  def AddLayerFromLayerFile(addLayer):  import arcpy  mxd = arcpy.mapping.MapDocument("CURRENT")  df = arcpy.mapping.ListDataFrames(mxd, "Layers")[0]  arcpy.mapping.AddLayer(df, addLayer, "AUTO_ARRANGE")  arcpy.RefreshActiveView()  arcpy.RefreshTOC()  del mxd, df, addLayer   However, my raw data is always going be shapefiles, so I need to be able to open them. (Equivalently: convert a shapefile to a layer file without opening it, but I'd prefer not to do that). "Goose"–"geese" vs. "moose"–"moose" Why is it that the plural of goose is geese but the plural of moose is moose? The same goes for mouse and house. Mouse becomes mice, yet house becomes houses. Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? CSS two divs next to each other Spurious @ symbol at start of bash prompt in Debian Jessie How does an accelerating charge radiate electromagnetic waves? Beamer Bibliography Icon I want to list my references in a beamer presentation using thebibliography environment, with the nice little    book icon (\beamertemplatebookbibitems) and  article icon (\beamertemplatearticlebibitems)   in front of each source.  Is there an icon for websites too? something like \beamertemplatewebsitebibitems? If not, is there a way to implement this easily ? Examples and further results about the order of the product of two elements in a group