How to calculate statistics for several sub-catchments (polygons) in the same time?
How can the pixel values of a raster image be extracted under a polygon fishnet?
Is there an (easy) way to create or personalize .bst files? Is "do something by date X" inclusive? Possible Duplicate:          For example, if John says:      Return it to me by March 24th.    Does it mean that I need to return it to him before 23:59 p.m. March 24th, or before 23:59&nbsp;p.m. March&nbsp;23rd? How to find the determinant of this $3 \times 3$ Hankel matrix? Today, at my linear algebra exam, there was this question that I couldn't solve.   Prove that $$\det \begin{bmatrix}  n^{2} &amp; (n+1)^{2} &amp;(n+2)^{2} \\  (n+1)^{2} &amp;(n+2)^{2}  &amp; (n+3)^{2}\\  (n+2)^{2} &amp; (n+3)^{2} &amp; (n+4)^{2} \end{bmatrix} = -8$$   Clearly, calculating the determinant, with the matrix as it is, wasn't the right way. The calculations went on and on. But I couldn't think of any other way to solve it. Is there any way to simplify $A$, so as to calculate the determinant? for a $3 \times 3$ matrix A ,value of $ A^{50} $ is I f $$A= \begin{pmatrix}1&amp; 0 &amp; 0 \\  1 &amp; 0 &amp; 1\\ 0 &amp; 1 &amp; 0 \end{pmatrix}$$  then $ A^{50} $  is   $$ \begin{pmatrix}1&amp; 0 &amp; 0 \\  50 &amp; 1 &amp; 0\\ 50 &amp; 0 &amp; 1 \end{pmatrix}$$ $$\begin{pmatrix}1&amp; 0 &amp; 0 \\  48 &amp; 1 &amp; 0\\ 48 &amp; 0 &amp; 1 \end{pmatrix}$$ $$\begin{pmatrix}1&amp; 0 &amp; 0 \\  25 &amp; 1 &amp; 0\\ 25 &amp; 0 &amp; 1 \end{pmatrix}$$ $$\begin{pmatrix}1&amp; 0 &amp; 0 \\  24 &amp; 1 &amp; 0\\ 24 &amp; 0 &amp; 1\end{pmatrix}$$   I am stuck on this problem. Can anyone help me please............... Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane. I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines represented by the equations : $$a_1x+b_1y+c_1=0$$ $$a_2x+b_2y+c_2=0$$ $$a_3x+b_3y+c_3=0$$ Then the area of the triangle that these lines will enclose is given by the magnitude of : $$\frac{det\begin{bmatrix}a_1 &amp; b_1 &amp; c_1\\a_2 &amp; b_2 &amp; c_2\\a_3 &amp; b_3 &amp; c_3\end{bmatrix}^2}{2C_1C_2C_3}$$ Where $C_1,C_2,C_3$ are the co-factors of $c_1,c_2,c_3$ respectively in the above matrix.  What I'm wondering is, where did this come from? And why isn't it famous? Earlier we had to calculate areas by finding the vertices and all but this does it in a minute or so and thus deserves more familiarity. Multiplication in Permutation Groups Written in Cyclic Notation Are there any examples of $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$? I am writing a short discussion of Farey numbers and was wondering if there are any examples of when the mediant function is ever actually equal to the sum of the two fractions in the usual sense? (Not to produce Farey numbers, I just thought it might be an amusing way to introduce Farey addition).   Explicitly: Are there any examples of fractions $\frac{a}{b}$ and $\frac{c}{d}$ where  $$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$$ for positive integers?   Currently I have found the example  $$\frac{1}{1}+\frac{1}{i} =\frac{1+1}{1+i}$$ if we remove the integers requirement but it would be nice to find a case that didn't involve complex numbers though! In Harry Potter, we know ghosts became ghosts when they are too afraid of death to go on - I thought about it and I'm quite certain they all go to their own version of Harry's King's Cross and become ghosts when they return as Harry did.  So can they return there? Once they've been a ghost long enough that they no longer fear death, can they move on? I have a question on my assignment asking me to prove that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$. What I did so far is:  We know that $A\cdot A^t = I$ (since it is orthogonal), and that would mean that if $A$ is a matrix with elements $a,b,c,d$ then :  \begin{cases}a^2 + b^2 = 1\\ ac + bd = 0\\ c^2 + d^2 = 1\end{cases}  which implies that \begin{align}\det(A)&amp;= ad - bc\\ &amp;= -\frac{bd^2}{c} - cb\\ &amp;= -\frac{bd^2}{c} - \frac{c^2b}{c}\\ &amp;= -\frac{bd^2 + bc^2}{c}\\ &amp;= -\frac{b(d^2 + c^2)}{c}\\ &amp;= -\frac{b(1)}{c}\\ &amp;= -b/c\end{align}  I might be doing something wrong here, could someone please help me out understand this? Update Manager doesn't ask for a password Oneiric update manager no longer asks for a password to update already installed software.  This is a change in behavior from previous versions.  Is there a way to revert this behavior and get the Update Manager in Oneiric to ask for a password again?  Thanks! Which novel involves vampires, burning satellites, space travel, and body modification? About a decade ago, I encountered a novel or a novella that I cannot locate.   The setting was Earth, about one century into the future.  I remember vampires and a mesh of satellites around the Earth that were burning up in the atmosphere.  This motivated a mission to deep space to find the intelligence responsible for the satellites.  Most of the novel focused on the crew of the mission &mdash; I recall that they were not "standard" humans.  They had modifications to their minds and bodies, possibly for the mission.  At the time, I had gone on a binge, reading many short stories, novellas, and novels in quick succession.  I fear that I might be combining several stories into one, especially the vampires and the deep-space first-contact mission, and so I am fully prepared for an answer of the form, "No such story exists."  Any assistance would be greatly appreciated. Truncated 200GB table but disk space not released Regression - How do I know if my residuals are normally distributed? Performing a regression and need to find out if my residuals are normally distributed. I have looked everywhere for lava or obsidian in 0.7.1. I've looked all the way from top to bottom and all around, in about a 100 block diameter, but I can't find any. Where can I get some? How to skip validation when a specific button is clicked? How to solve "permission denied" when using sudo with redirection in Bash? Can $3p^4-3p^2+1$ be square number? Permanently mounting loop device I created a file   touch /datastore/virtual/pseudoblock   created a loop device with it  sudo losetup /dev/loop0 /datastore/virtual/pseudoblock   (although I got a warning about its size)  and then initialized it with random data  dd if=/dev/urandom of=/dev/loop0 bs=1M count=100   My questions are  a) why is it not displayed yet in my block devices' list?  NAME                     MAJ:MIN RM   SIZE RO TYPE  MOUNTPOINT sdb                        8:16   0 489.1G  0 disk   ├─sdb2                     8:18   0   488M  0 part  /boot ├─sdb3                     8:19   0 488.1G  0 part   │ └─sdb3_crypt           253:0    0 488.1G  0 crypt  │   ├─ubuntu--vg-root    253:1    0 472.2G  0 lvm   / │   └─ubuntu--vg-swap_1  253:2    0  15.9G  0 lvm   [SWAP] └─sdb1                     8:17   0   512M  0 part  /boot/efi sda                        8:0    0 931.5G  0 disk   └─sda1                     8:1    0 931.5G  0 part     └─sda1_crypt           253:3    0 931.5G  0 crypt      └─store--vg-store1tb 253:4    0 931.5G  0 lvm   /datastore   b) how can I permanently mount it via /etc/fstab since I cannot get its UUID?  $ blkid /dev/mapper/sdb3_crypt: UUID="fSHjbj-51K2-QfhI-G0Wb-o3lN-4pE1-BB4wCP" TYPE="LVM2_member" /dev/mapper/ubuntu--vg-root: UUID="9e452886-4d8g-fj54-854c-80bc171826e8" TYPE="ext4"   working on   $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 16.04.5 LTS Release:    16.04 Codename:   xenial   with  $ uname -a Linux pkara-pc01 4.15.0-42-generic #45~16.04.1-Ubuntu SMP Mon Nov 19 13:02:27 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux Let $C[0,1]$ denote the ring of continuous functions on $[0,1]$. Consider the maximal ideal $M_a =\{ f\in C[0,1] | f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated?   Note: It may seem that $M_a = \langle x-a\rangle$ which is certainly not true because $ \vert x-a \vert $ is in $M_a$ but not in $\langle x-a\rangle$. Any ideas for solving this question? Zooming to selection in arcpy.mapping and only seeing selected features? I selected data by using select layer by attribute, then I need to only select these selection and zoom in to the selection.  my code is this, it can zoom in base on the scale I set, but I see other adjacent polygon that has other Code_No, why?  Layer = arcpy.mapping.ListLayers(mxd, "lyr", df)        arcpy.SelectLayerByAttribute_management(lyr, "NEW_SELECTION", "Code_NO = '%s'"%mycodeNo)            df.extent = lyrLayer1.getSelectedExtent() df.scale *= 2