Dissolve shapefile and summarize text fields
Summary table with a field that shows components of each summarized record
Print total free memory from `free -m` Reading Chapter 2 of Koblitz's Introduction to Elliptic Curves and Modular Forms, I got stuck on the following question. I would like to proceed my reading, so I would appreciate any hint to this. I have no background in Algebraic Number Theory, but if someone explains in that language, I would like to see it and learn it as much as I can at this moment. References will also be appreciated!  Let $q$ be a power of prime $p$ such that $q \equiv 1 \mod 4$ and $p \nmid 2n$.  Question. Let $\chi_{4} : \mathbb{F}_{q}^{*} \rightarrow S^{1}$ be the character of order $4$, show that $\chi_{4}(-4) = 1$.  The hint in the book says we may show that $\chi_{4}(4) = \chi_{4}(-1) = 1$ for $q \equiv 1 \mod 8$ and $\chi_{4}(4) = \chi_{4}(-1) = -1$ for $q \equiv 5 \mod 8$.  If $q \equiv 1 \mod 8$, then $\chi_{4}(4) = \chi_{4}(2)^{2} = \chi_{2}(2) = \pm 1$, where $\chi_{j}$ denotes the character of order $j$. So I think $2$ must be quadratic residue in this case, but I cannot figure out why. I've completed 20 suggested edits reviews today. Then, I came across a  and I approved it.   Then, I had a doubt that whether the review count has incremented or not, oh! it's not incrementing. System works fine.  But, take a look at review page,     The edit was already reviewed by one reviewer and then I reviewed it. As I'm the Owner of the post it's enough to approve the edit. But, the review history doesn't show the detail that I had approved it. It's misleading that only one vote of a reviewer who is neither the community user nor the OP nor the moderator, is enough.  So, what should we do in this type of situation?  Is it correct to make OP to review the suggested edit after completing daily limit?  Should we need to display/hide the OP has approved the edit in the review history? In Chiswell's Mathematical Logic, there is the following problem is posed using the language of propositions (LP):     In some systems of logic (mostly constructive systems where 'true' is taken to mean 'provable') there is a rule      if $(\Gamma\vdash(\phi\,\lor\psi))$ is a correct sequent then at least   one of $(\Gamma\vdash\phi)$ and $(\Gamma\vdash\psi)$ is also correct.      By giving a counterexample to a particular instance, show that this is   unacceptable as a rule for LP. [Start by giving counterexamples for   both the sequents $(\vdash p_0)$ and $(\vdash(\neg p_0))$.]   In my , it was answered that one can let $\Gamma = \{p_0\,\lor\,(\neg p_0)\}$.  From there, one can deduce neither $(\Gamma\vdash p_0)$ nor $(\Gamma\vdash (\neg p_0))$.  But this does not proceed by the counterexample route that the author suggests.  Namely, he seems to imply that we should (1) take an interpretation of propositional variables $p_0,\,p_1,\,\ldots$ (setting each one equal to T or F), and (2) write $\phi$ and $\psi$ as functions of these propositional variables, and (3) pick sentences for $\Gamma$ which are all T, all with the conditions that (A) $(\phi\,\lor\psi)$ is evaluated as T, yet (B) both $\phi$ and $\psi$ are evaluated as F.  This, of course, seems impossible.  What, then, am I missing?  It seems that taking a concrete interpretation of the propositional symbols makes the constructivist's rule irrefutable.  (Note: this is supposed to be a very simple problem set, and I am an elementary logician). Text in an equation This is best explained by example. Suppose I have the following:  \[     \begin{align*}     C_3 \rightarrow 6 automorphisms\\     C_4 \rightarrow 8 automorphisms\\     C_5 \rightarrow 10 automorphisms     \end{align*} \]   How can I get the word "automorphisms" to display as if it were not enclosed by the brackets? What effect does the Barr body have, in relation to female Turner syndrome? Why do persons with  have  developmental abnormalities, when normal XX-females do not, even though they only have 1 active X chromosome? From what I know, one X-chromosome is inactivated into a Barr body in normal XX-females, but these obviously don't show the symptoms of Turner syndrome. What function does the inactive chromosome have? As I'm learning about iptables I've made a couple of mistakes and locked myself out.  What method(s) do you use to test rules without locking yourself out?  I'm using ubuntu server 12.04 LTS    All the answers below were helpful.  In the end I used a combination of options.  It also helps to have IPMI access to your remote server just in case!  But ideally test the rules locally on a replicated environment and test that first.  Vagrant helps in this regard to get test setups working quickly. Run 32bit applications on Windows 10 64 Bit I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme Placement of varistor with respect to fuse My design includes a pretty standard AC/DC converter powered by mains for intended use at home. For overvoltage and overcurrent protection, I am planning to use a combination of varistor and fuse placed before the power converter.  I understand it is good practice to put the fuse before the varistor - in an overvoltage event, the varistor will draw a large current that may blow the fuse, protecting the rest of the circuit and even the upstream circuitry.  However, due to extremely tight layout, it is very hard to put the fuse before the varistor.  What risk am I running if I put the varistor before the fuse?  What if I put a second fuse in series with the varistor? Does it negate the varistor's protection of the downstream circuit? Is there a way to absolutely force a Log Out, Shut Down, or Restart with open tabs and unsaved documents? I could not find any relatively simple way to log out of a public use Mac quickly with many tabs open and unsaved document in the background without resorting to sudo shutdown -h now.  The reason I ask is that sometimes a user will have his/her account logged into the iMacs here at school and they would try to log off and then leave, thinking it has completed but the process is interrupted by Safari and Office apps, leaving their account, mounts, and websites still accessible to the next person who sits down.  Obviously a shortcut string would be nice instead of posting a note telling the person to type arcane things in a terminal. For example, just having them try to find Terminal.app is going to be a chore.  This doesn't seem to make sense because the user can just quit each app and click a few dialog boxes but unlike you and I to whom repeatedly pounding Command-Q while hitting the spacebar and D keys are probably second nature. Taking a screenshot (within X) How can I take a screenshot in X.org?  I am unsure if the Print Screen button will "just work" and I don't know how I would go about testing it. Proposition II.7.5 of Hungerford's Algebra goes     Proposition 7.5. A finite group is nilpotent if and only if it is the direct product of its Sylow subgroups.   Let $G = (\mathbb{Z}_6, +)$. $G$ is abelian, so it is nilpotent and thus by the proposition is the direct product of its Sylow subgroups.  The Sylow subgroups of $G$ are $H = (\mathbb{Z}_3, +)$ and $K = (\mathbb{Z}_2, +)$, so the proposition says $G = H \times K$. In particular, $0 \in H$ and $0 \in K$, so $(0,0) \in H \times K = G$... but that's not true, since $G = \{0,1,2,3,4,5\}$.  Where is/are my misunderstanding(s)? I have a long running BASH script that I am running under CYGWIN on Windows.  I would like to limit the script to run for 30 seconds, and automatically terminate if it exceeds this limit. Ideally, I'd like to be able to do this to any command.  For example:  sh-3.2$ limittime -t 30 'myscript.sh'   or   sh-3.2$ limittime -t 30 'grep func *.c'   Under cygwin the ulimit command doesn't seem to work.   I am open to any ideas. Proof of property of abelian group I want to show that $\forall x$,$y\in G$, $(xy)^2=x^2y^2 \iff G $ is an abelian group.  Proof of the backward direction seems easy enough:  Assume $G$ is an abelian group. Then consider $(xy)^2=(xy)(xy)$. By associativity, $(xy)(xy)=xyxy$. Since $G$ is abelian, $xyxy=xxyy=x^2y^2$.   Proof of the forward direction I attempt by contrapositive:  That is, assume $G$ is not an abelian group. Then, consider $(xy)^2=xyxy$ as above. Yet, $xyxy\neq xxyy=x^2y^2$ since we no longer have commutativity.  Is this proof by contrapositive completely correct? This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the observation $Y$ is first regressed against its previous values $Y_{t-1}, ..., Y_{t-n}$ and then one or more $Y - \hat{Y}$ values are used as the error terms for the MA model.  But how are the error terms calculated in an ARIMA(0, 0, 2) model? If the MA model is used without an autoregressive part and thus no estimated value, how can I possibly have an error term? ctrl + a doesn't work in browsers The combination for select all (Ctrl+A) doesn't work in a browser (either if we speak about firefox or chromium). It doesn't work if I try to clik in to the adress bar nor if I try to use it to select what I've written in google search bar at google.com. When I press Ctrl+A it simply takes the cursor before the first letter.  This doesn't happen when I use a text editor software like Libre Office. There the shortcut does what's supposed to do, selecting all the text.  What could be the problem? Problem: James has a pile of n stones for some positive integer n ≥ 2. At each step, he   chooses one pile of stones and splits it into two smaller piles and writes the product   of the new pile sizes on the board. He repeats this process until every pile is exactly   one stone.      For example, if James has n = 12 stones, he could split that pile into a pile of size   4 and another pile of size 8. James would then write the number 4 · 8 = 32 on the   board. He then decides to split the pile of 4 stones into a pile with 1 stone and a   pile with 3 stones and writes 1 · 3 = 3 on the board. He continues this way until he   has 12 piles with one stone each.      Prove that no matter how James splits the piles (starting with a single pile of n   stones), the sum of the numbers on the blackboard at the end of the procedure is   always the same.   Hint: First figure out what the formula for the final sum will be. Then prove it using strong induction.  The formula I came up with is $n(n-1) / $2. It could be totally wrong...  My (Partial) Solution:  1) Base Case: (n=2) James has one pile of 2 stones. Suppose he takes the top-most stone and puts in one pile A, which now has size 1. He takes the remaining stone and places it into another pile B, which now has size 1. Then the product of the sizes is 1. The sum of all the products on his board is 1. Now, if he were to start again, and take the bottom stone first and put it in pile A, he has a pile of size 1, and then takes the top stone and puts it in pile B, he has a pile of size 1, and the product is 1, with sum of all products on the board is 1.   2) Inductive Hypothesis (Strong Induction): Suppose for some $k \geq 2$, $n$ stones can be split in $ 2 \leq n \leq k $ stones and $k-n$ stones.  3) Inductive Step:  Consider $n=k+1$. What do I do now? I use netstat to check my port status.  I was wondering what's the difference between port status LISTENING, TIME_WAIT, CLOSE_WAIT, FIN_WAIT1 and ESTABLISHED? Light "diode" and 2nd law of thermodynamics If I had a light "diode" - an object that only allowed light (at least for a range of frequencies) to travel through it in one direction, would this necessarily allow violations of the 2nd Law of Thermodynamics?  Or would it be possible to restrict other properties of the device such that it could be okay.  Why I think it should violate 2nd law:   I can place such devices at temperature T in a bath of thermal radiation at temperature T, such that it forms a box which only lets the light in or out.  This would appear to always allow one to create a thermal gradient.  Once a thermal gradient is formed, useful energy can be extracted.  This seems to allow useful energy to always be extracted from a thermal bath and thus give perpetual motion. Release one such device at temperature T in a bath of thermal radiation at temperature T.  Since the photons are absorbed or reflected in one direction, and undisturbed in the other, the device will start moving.  It can use a thermal bath to directly generate useful motion.   Why I think I'm missing something and such a device could potentially co-exist with the 2nd Law:   The above arguments seem valid if the diode was only 'partially' rectifying as well.  However there exist sunglasses which largely reflect on one side, but not from the other side. Researchers have succeeded in using meta-materials to create a "blackhole" for microwaves.   Can anyone help sort this out? This is a canonical question that will hopefully encompass all of the questions we get asking us to determine what year a bicycle was manufactured (how old is my bike, how old is my frame, etc.). Each "answer" should address a different way to determine the manufacturing year of a bicycle. To some extent, these will also help you narrow down the model as well as it will tell you what distinguishing features to look at.  The span of answers would include things such as:      Skiptooth cranks Cartridge bottom brackets (BB30/90 etc) Elliptical chainring Quick releases versus contemporary through-axles How the steerer attaches to the fork (quill vs. threadless)  Braking system (especially with mountain bikes: v-brake, direct pull, etc.)   Shifting ramps and pins on cassettes/sprockets and chainrings (versus flat sprockets) Frame material (e.g., shift from tubular steel to use of CF and hydroformed aluminium)  Frame tubing type (e.g. Reynolds 531 tubing introduced around 1934, still used today; Reynolds 501 tubing introduced around 1983). So a frame with an original 501 decal can't be from the 70', 531 decal doesn't help as much because of the range of years produced. Also, see Decals.   *Decals: style/design, amount, placement, color, etc. can help not only determine models, but also year of manufacture. Many changed decal design for the same model bike often yearly, with special/limited editions even more specific. This applies only if decals are original or have been replaced with the identical design. Tubing decals (Reynolds, Columbus, etc.) also changed designs for same tubing made in different years, although the changes aren't made as often, and manufacturers didn't always put tubing Brand decals on every model. Earlier bikes tended to have less fancy, less colorful, less quantity of decals.   Headbadges: most early bikes had actual "badges", often quite detailed and fancy, made of metal, then plastic, and finally just using decals on the headtube. Most bikes lost their metal badges in the 60's and early 70's, although some brands still have actual badges to this day, but in general a real badge indicates an earlier model bike. Dropout style (including the later inclusion of lawyers lips) Presence or absence of CPSC reflectors (USA only) Manufacturing method (shift from lugs to TIG welding, for example)  Number of gears (shift from 2x5 ten-speed to 3x8, 2x9, 1x11, etc.)  Inspection of lug design: pantographs, cut-out, stampings, custom brazing/filing, chrome, fork crow n sweep, etc. Frame/Fork Braze-ons. Race bikes tended have less braze-ons the earlier the year of manufacture. Most 60's racers and earlier had few or none with cable guides/stops, shifters, bidons, etc. being clamp-on. By the 80's if it was clamp-on, it was a sign of very cheap models and most frames had braze-ons for all cables, with multiple bottle and accessory bosses depending on style and use.   and so forth. Please edit this question if you have an answer that isn't in the index above.   A couple of caveats:   A previous owner could have replaced or upgraded components on a bicycle, so this guide only applies to original equipment There is a delay between the introduction of a technology (such as indexed shifting) and when manufacturers start selling products that use it. Low-end manufacturers may continue using technology that is severely outdated (such as one-piece cranks, freewheels, or quill stems) because it is cheaper to do so. A number of bikes are built in a Retro style, but with modern components.  Dutch bikes, trendy coffee cruisers, and beach cruisers may be modern but appear to be 1950s styling.  These tend to have modern rims and brakes as a giveaway.     Note that bicycles.stackexchange does not do valuations of bicycles. How much your bicycle is worth depends on the location of the buyer and seller, how much the buyer wants the bike, etc. etc. etc.