Trying to String.split on new line after matched substring
Catch Regex too complicated when splitting a string in salesforce
Proving the cross product matrix tranformation identity with an alternative solution I'm solving a problem from the book, Mathematics for 3D Game Programming and Computer Graphics, Third Edition, by Eric Lengley. The problem goes:  Let $N$ be the normal vector to a surface at a point $P$, and let $S$ and $T$ be tangent vectors at the point $P$ such that $S \times T = N$. Given an invertible 3 $\times$ 3 matrix $M$, show that $(MS) \times (MT) = (\text{det}M(M^{-1})^{T}(S \times T)$, supporting the fact that normals are correctly transformed by the inverse transpose of the matrix $M$.  The author provided a hint stating we can represent $(MS) \times (MT)$ as $$ (MS) \times (MT) = \begin{bmatrix} 0 &amp; -(MS)_{z} &amp; (MS)_{y} \\  (MS)_{z} &amp; 0 &amp; -(MS)_{x} \\  -(MS)_{y} &amp; (MS)_{x} &amp; 0  \end{bmatrix} MT $$ We then find a matrix $G$ such that $$ GU = \begin{bmatrix} 0 &amp; -(MS)_{z} &amp; (MS)_{y} \\  (MS)_{z} &amp; 0 &amp; -(MS)_{x} \\  -(MS)_{y} &amp; (MS)_{x} &amp; 0  \end{bmatrix} M $$ where $$ U = \begin{bmatrix} 0 &amp; -S_{z} &amp; S_{y} \\  S_{z} &amp; 0 &amp; -S_{x} \\  -S_{y} &amp; S_{x} &amp; 0  \end{bmatrix} $$ and show that $G = (\text{det}M)(M^{-1})^{T}$ to solve the problem. I am aware that there is an  to this problem, but I would like to solve it through the hints provided. Unfortunately, I am only able to go as far doing: $$ G = \begin{bmatrix} 0 &amp; -(MS)_{z} &amp; (MS)_{y} \\  (MS)_{z} &amp; 0 &amp; -(MS)_{x} \\  -(MS)_{y} &amp; (MS)_{x} &amp; 0  \end{bmatrix} M U^{-1} $$ At this point, I do not know how to proceed with showing that $G = (\text{det}M)(M^{-1})^{T}$. How would you proceed? I'd like to ask for hints on solving the problem. The Half-Elven and their choices Earendil and Elwing were given the choice of kindreds after their journey to Valinor, This choice was extended to their sons (specifically sons, not daughters or grandchildren)  Elrond chose the race of the Eldar and his brother Elros chose to be counted amongst the Edain. Thus far Manwë's proclamation has been fulfilled.  There are some inconsistencies here:   Arwen was given the choice, but Elladan and Elrohir remained as Eldar in Imladris Tar-Vardamir was not given the choice The offspring of Imrazor and Mithrelas in Dol Amroth dont seem to have been given a choice   I can think of only one explanation, that the Mannish blood is dominant over the blood of the Eldar, thus, As Vardamir was the offspring of two mortals he did not fall under Manwë's proclamation despite being the son of a half elven.  However this does not seem to explain the other inconsistencies, Is it possible that Elladan and Elrohir and also the princes of Dol Amroth weren't considered important enough by Manwë or Eru to give them the choice.  Also as a side note Tolkien states there were only three unions between man and elf, but this seems to ignore Turin/Finduilas and Imrazor/Mithrelas  My question is, Why was Arwen given the choice and not the sons of Elros? Why are home networks prefixed with 192.168? Why are home networks prefixed with 192.168 ?  Why those numbers?  For some historical reasons? How does "proof of effort" make a question better? It seems like many questions by new users are downvoted immediately.  Sometimes there is a comment to the tune of "lacks research", "we're not here to do your homework", or "show us some effort".  Now I wonder, what does it matter how much work someone has done before posting?  If someone can ask a good question in 5 seconds, more power to them.  To illustrate this point, look at how you could "improve" a question to include proof of effort.  You could put in 5 failed code snippets and their in- and output.  This would make for very long questions with a high noise ratio.  Another suggestion is to add "research".  By "research", I suppose most programmers mean "Google".  So this is basically a suggestion to add a list of fruitless Google queries.  That doesn't sound interesting either.  How can "proof of effort" turn a bad question into a good one? How do I set focus follows mouse? Is there a way to set up "focus follows mouse" behavior in Unity? Can [sic] be used to highlight a punctuational error?    In the sentence below, the bracketed sic would obviously denote that the punctuation preceding it was an error &mdash; that is, a semicolon should supplant the comma. Has anybody ever seen this usage, and would you support it?     The sun is high, [sic] put on some sunblock. How do I iterate over a range of numbers in Bash when the range is given by a variable?  I know I can do this (called "sequence expression" in the Bash ):   for i in {1..5}; do echo $i; done   Which gives:     1    2    3    4    5   Yet, how can I replace either of the range endpoints with a variable? This doesn't work:  END=5 for i in {1..$END}; do echo $i; done   Which prints:     {1..5} Should you use "who" or "that" when talking about multiple people doing something? Which of the following is correct?        There were 10 people that went to the store.   There were 10 people who went to the store.      Edit:  Which of the following is correct?        There were 10 people that had brown hair.   There were 10 people who had brown hair. How to generate a random number between 1 and 10 with a six-sided die? Maximum table size for a MySQL database What is the maximum size for a MySQL table? Is it 2 million at 50GB? 5 million at 80GB?  At the higher end of the size scale, do I need to think about compressing the data? Or perhaps splitting the table if it grew too big? How to make an ext4 formatted usb drive with full RW permissions for any linux machine? I want to format my USB stick to ext4 and just use as I would any other typical non-linux format drive (FAT32, exFAT, NTFS).   That is to say, I want to be able to plug the usb stick into any of my linux machines, and read/write to it without needing to adjust permissions, like doing chmod or chown stuff.  I would prefer to use GUI partition software like GParted, rather than command-line commands, though I welcome any solution!  I'm sure a post like this is duplicate flag heaven for some, but after browsing 6~10 SO and forum posts from google, I didn't find a simple solution to my question. Seemed like everything was about adjusting permissions on a per-user basis. Maybe you just cannot use ext4 drives with the same brainless convenience as NTFS. I have a DEM that I would like to smooth or generalize to remove topographic extremes (chop off peaks and fill-in valleys). Ideally, I would also like to have control over the radius or level of "blurriness". In the end, I will need a set of rasters that range from slightly blurry to really blurry. (Theoretically, the blurriest would be a constant raster of the arithmetic mean of all values).  Are there any tools or methods I can use (based on Esri, GDAL, GRASS)?   Do I need to home bake my own  routine?   Could I use a low-pass filter (e.g. ArcGIS's ), and if so, would I need to run it a bunch of times to get the effect of a large radius? I have a python script that checks file path names for corresponding files in a drive location. All of the inputs were originally hard coded, and it works well enough:      import arcpy     import os     shp = r"C:\Users\dotwell\Desktop\Locations.shp"     fields = ["ZdriveLoc"]     f = open (r"C:\Users\dotwell\Desktop\ValMapsTest.txt", "w")     cursor = arcpy.da.SearchCursor (shp, fields)         for row in cursor:             Roll=str(row[0])             if not os.path.exists(Roll):             f.write(Roll + os.linesep)       f.close()   I'm trying to create an ArcGIS script tool from this, and I've only had partial success. I can use   shp = arcpy.GetParameterAsText(0)   to allow the user to select the shapefile. I'd like to then have a drop down list of the fields in that shapefile for the user to select the field that contains the path names, but I can't get it to work. Can someone show me how to generate the drop down? Here's my latest try. It works, but requires the user to type in the field name. It would also be nice for the user to designate the output text file name and location.   import arcpy import os shapefile = arcpy.GetParameterAsText(0) field = arcpy.GetParameterAsText(1) f = open (r"C:\Users\dotwell\Desktop\ValMapsTemp.txt", "w") cursor = arcpy.da.SearchCursor (shapefile, field) for row in cursor:     Roll=str(row[0])     if not os.path.exists(Roll):         f.write(Roll + os.linesep)   f.close()   Here are the parameters in my ArcGIS script tool: increasing impedance of headphones I have headphones with differential input and impedance of 8 ohms. I need to drive this headphone with some DAC with built in headphone driver (Currently I have chosen ADAU1772). DAC's datasheet mentions that the minimum impedance of headphones it supports is 16 ohms. Can I increase impedance of my headphones so that I can drive them through this chip? What will happen if I drive this 8 ohm headphone through a chip supporting minimum impedance of 16 Ohms? I have a table similar to this:  CREATE TABLE example (   id integer primary key,   name char(200),   parentid integer,   value integer);   I can use the parentid field to arrange data into a tree structure.  Now here's the bit I can't work out. Given a parentid, is it possible to write an SQL statement to add up all the value fields under that parentid and recurse down the branch of the tree ?  UPDATE: I'm using posgreSQL so the fancy MS-SQL features are not available to me. In any case, I'd like this to be treated as a generic SQL question.  BTW, I'm very impressed to have 6 answers within 15 minutes of asking the question! Go stack overflow! A commutative ring is a field iff the only ideals are $(0)$ and $(1)$ How to prove that we are living in a 3+1D world? Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions?  Thank you all who helped in the improvement of this question (which was not clear at first).   EDIT:  I know that this can be a little philosophical, but it is also a scientific question.  Let's consider the scenario where the mankind was not ever able to see.  Let's also consider that this limitation could be surpassed thus not limiting us to reach a scientific and technological knowledge "similar" to what we have today.  Would this civilization of blind people reach the conclusion that they are living in a 3D spatial world?  Is the sense of touch enough to reach that conclusion? Is there any scientific experiment that can lead us to that conclusion without the premise of the conception of limited dimensions?  Would it be easier, harder, or just different to reach a conclusion predicted by the M-Theory? (please do not focus only on this last question) Can I just fit a cassette with more gears with the same derailleur? I've got a Boardman Road Sport which I use for commuting and doing reasonable length rides during the week etc. I have Shimano Claris as my rear derailleur and so is some of my groupset. I would like to upgrade my cassette to an either 9 or 10 speed to give me a greater variety of gears. To do this do I need to change my rear derailleur from 8 speed to Shimano 105 or something similar? Or can I just change my cassette? Do I also need to change my shifters as well? Can I use my Windows 7 license in a dual-boot configuration? Possible Duplicate:          I've purchased a retail license of Windows 7 Ultimate for my machine at home.  I'm thinking of creating a dual-boot install:   64-bit install for work apps (need the RAM for virtual machines and RAMDisk) 32-bit install for entertainment apps (Media Centre, games, etc)   How does retail licensing work in such situations? Can I activate the same license on both installations?  Edit:  I would like to add that I want to have separate partitions for work and play. No hair theorem for black holes and the baryon number