edit: ^^ the answer to that question talks about the lens being the same and but not how or why this is the case, and does not answer the question about resultant image,   First of all, to let you know what I understand:   I am aware that focal length is focal length, and that doesn't change* (that's usually the first line of every answer I've read), the difference between full frame and smaller sensors and the effect that the same lens will have on different bodies (with different frame sizes), the difference between focal length, crop factor and field of view angle, what some are calling "effective" focal length as compared to FOV, cropping and multiplication factor.   (* see second question)  I know this question sounds the same as  and   (and a whole heap of others **) but they all seem to go off in slightly different tangents, namely what I will see on different bodies (I don't care about this, I have only one body type), they also cover things such as the effect of (say) an EF-S lens on a FF body (I'm not doing that either).   Put very specifically, here is my question broken into (now) four parts:   Does mounting an EF vs an EF-S lens produce the same results on a camera body that has an APS-C frame size? (my thinking is NO because of the design of the lens and "short back focus" of the EF-S, and the fact that the EF lens produces a picture for a FF sensor and the fact it is further away—when directly comparing 50mm EF and 50mm EF-S—do they have the same field of view, which then leads onto the next question), (this is probably where my confusion lies, but) aren't the EF-S range of lenses physically closer to the sensor whereby the focal length IS actually shorter?   If EF-S lenses (as a whole unit) are shorter and have a shorter back focus plane, wouldn't that make the FOV wider (ergo not producing the same image)?   edit:   is it the case that Canon have labelled their EF-S 50mm lens as 50mm to the focal plane AS IF the focal plane was a FF 35mm plate at 50mm? Or is the focal distance 50mm to the actual smaller frame? (I think my confusion here is that a 50mm EF lens sits further forward than a 50mm EF-S lens, which to me seems to indicate that one of them isn't 50mm :)   (** others):

I have a Canon 550D with the standard 18-55mm kit lens. The 550D has a 1.6× crop factor.  My question is very simple but whenever I've asked before (Yahoo Answers) I always got overly-complicated answers which confused me even more. So here goes.  If I get the EF 50mm f/1.4 USM lens, will it be the same as setting my EF-S zoom lens to 50mm when attached to the 550D? Or will it be the equivalent of an 80mm EF-S lens?


I was debugging my Android Studio project and I found where it crashes:  try {             if (mLocationPermissionGranted) {                 Task<Location> locationResult = mFusedLocationProviderClient.getLastLocation(); // HERE!  // so the code below is not executed                  locationResult.addOnCompleteListener(this, new OnCompleteListener<Location>() { ... ...   The message on the Debug Terminal is "mFusedLocationProviderClient = null" Where am I going wrong?  Thank you all.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Can you find the Duke 'o' Death in GTA 5 on xbox 360 when you start the game with no updates?

I was watching some videos on YouTube showing how to get the Duke O' Death in GTA 5, however what I have seen is sort of unclear.  Some people say you must be a returning player on GTA 5 to get it (what does this mean too BTW?), some people don't say that. Some people say you have to be Trevor, some people don't. Some say the time of day matters, some don't. And apparently you can buy it from Warstock website (I can't).   Can someone please tell me how to get it?! GTA 5 came with my PS4 (I didn't play it on PS3) if that helps.


According to General Relativity, space and time are aspects / dimensions of a unified whole. If the speed at which wave energy travels through spacetime is constant, $c$, then as distance expands, should not time expand by corresponding amount? If so, then would 1 Plank time from Plank Epoch, be something like ~1 picosecond in today's space-time?

Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and because of the difficulty (impossibility?) of defining a coordinate system where things have well defined coordinates while also moving away from each other without changing the metric on the space, we interpret this to mean that space itself is expanding.   Because space and time are so directly intertwined is it possible that time too is expanding? Or perhaps it could be contracting?


I have the following data :  Yield   Rain    PH  EC  OC  N   P   K   S   Zn  Fe  Cu  Mn  Hydro 7778.1  103.03  3   1   2   1   1   2   1   1   2   3   2   1 5929.4  91.23   3   1   2   1   1   2   3   2   2   3   3   1 2872.3  109.47  3   1   2   1   1   2   2   1   2   3   3   2 4332.7  92.58   3   1   2   1   1   2   3   1   2   3   3   2 5236    100.37  3   1   2   1   1   2   1   1   2   3   3   2 3086.5  103.68  3   1   2   1   1   1   1   1   2   3   3   2 4526.1  83.38   3   1   1   1   1   2   2   2   2   3   3   1   Where Yield is my dependent variable. and Rain , PH, EC ... are independent.  I have to use regression analysis for predicting the Yield.  But, I notice that accept Rain variables all others are ordinal levels. (Like High=3, Medium=2, Low=1) where PH, EC , N, P, Fe, Cu are same values for each observation  Which regression model is the best to predict the yield? I am using python with scikit-learn.

I am using a logit model. My dependent variable is binary. However I have an independent variable which is categorical and contains the responses: 1.very good, 2.good, 3.average, 4.poor and 5.very poor. So, it is ordinal ("quantitative categorical"). I am not sure how to handle this in the model. I am using gretl.  [Note from @ttnphns: Although the question says the model is logit (because the dependent is categorical), the crucial issue - ordinal independent variables - is basically alike, be the dependent categorical or quantitative. Therefore the question is equally relevant to, say, linear regression too - as it is to logistic regression or other logit model.]


I have 40 close votes per day, which I can go through in 15-20 minutes on reviews (or much less if I filter to opinion-based/too-broad).  The current close vote queue size is 90.7k. At 4 remaining normal user votes per close that's about 362,800 total votes needed.  This means every day, I can contribute 40/362,800 = 0.011% of the total work required to take care of that queue.  That seems... low. Is there some way I can make a bigger dent?  Also, are there statistics available that show, for a given day (or on average per day), the number of new items added to the close review queue, the number of votes on questions in that queue, and the number of users who typically participate in reviews (I know there's the stats site I just don't know how to make this query)?

Today, the size of the close-votes queue is 55k questions and growing. Is that a problem?   Which action could be taken to clean it up? It seems to be growing faster than Stack Overflow members are capable to handle it.


I have a basic CRUD system setup, however the system fails when special characters are used. For example, here is my route for a delete request: // DELETE OPERATIONS router.route('/delete/:id').delete((req, res) => {   const title = req.params.id;   // console.log('DEBUG: aricles.js: server receiving title: ', title)   DBM.deleteArticle(title).then(() => {     console.log('DEBUG: article deleted: ', title);   }).catch((err)=>{     console.log('articles/delete error', err);   });   res.end(); });  My unique ID for an entry is a string which is the title of the article.  However if the string ends with a ? which is a special character it disappears by the time it gets to the server. The client sends the delete request as follows: const options = {    headers: {'Content-Type': 'application/json'},    method: 'DELETE',    body: JSON.stringify(this.props.data) };  this.debug && console.log('cleint sending title: ', title);  fetch("/articles/delete/" + title, options )   .then((response) => {     console.log('response', response);   })   .catch((error) => {     console.log('delete clicked error', error);   });     I imagine other special characters in the URL would cause issues as well such as # and :, etc.

When encoding a query string to be sent to a web server - when do you use escape() and when do you use encodeURI() or encodeURIComponent():  Use escape:  escape("% +&=");   OR  use encodeURI() / encodeURIComponent()  encodeURI("http://www.google.com?var1=value1&var2=value2");  encodeURIComponent("var1=value1&var2=value2");


class A {     int a; public:     A()     {     }     virtual void f1()     {         cout<<"A "<<endl;     }     virtual void f2()     {         f1();     } };  class B: public A {     int b; public:     B()     {     }     void f1()     {         cout<<"B "<<endl;     } };  int main(void) {     B obj;     obj.f2(); }   o/p - B  I am running this code on visual stdio 2010. Please explain Why class B's function f1() is called? and why not class A's function f1().

Here is an example of polymorphism from  (edited for readability):  // abstract base class #include <iostream> using namespace std;  class Polygon {     protected:         int width;         int height;     public:         void set_values(int a, int b) { width = a; height = b; }         virtual int area(void) =0; };  class Rectangle: public Polygon {     public:         int area(void) { return width * height; } };  class Triangle: public Polygon {     public:         int area(void) { return width * height / 2; } };  int main () {     Rectangle rect;     Triangle trgl;     Polygon * ppoly1 = &rect;     Polygon * ppoly2 = &trgl;     ppoly1->set_values (4,5);     ppoly2->set_values (4,5);     cout << ppoly1->area() << endl; // outputs 20     cout << ppoly2->area() << endl; // outputs 10     return 0; }   My question is how does the compiler know that ppoly1 is a Rectangle and that ppoly2 is a Triangle, so that it can call the correct area() function? It could find that out by looking at the "Polygon * ppoly1 = ▭" line and knowing that rect is a Rectangle, but that wouldn't work in all cases, would it? What if you did something like this?  cout << ((Polygon *)0x12345678)->area() << endl;   Assuming that you're allowed to access that random area of memory.  I would test this out but I can't on the computer I'm on at the moment.  (I hope I'm not missing something obvious...)


I have 2 partitions on my hard drive, one with windows 7 and the other with ubuntu 16.04.1. I went to windows 7 and deleted the volume that has ubuntu on it, and now I installed linux mint 18 on it, is there any chance to recover some files that were stored on ubuntu ?

Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file.


Find the units in $\mathbb Z_4[x]$.  I saw something online about this possibly having an infinite amount of units, but am not sure.  Any help someone can give would be greatly appreciated. Thank you.

Q: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.  I know (2x+1) is a unit. Is there any other units in $Z_4[X]$ if there are infinite units, could you generalize it in a certain from such as (2nx+1) s.t n is an integer?


I am developing a set of plug-ins for QGis (2.14). Every time I need to try it out I must quit and relaunch QGis. Is there any way to force QGis to reload the plug-ins without restarting it?

I am rewritting a custom QGIS application as a plugin for QGIS. I am testing it by writing some new code, then deactivate/activate the plugin in the plugin manager, which seems to me a bit cumbersome. Is there a way to reload the plugin faster?


I have noticed that we write 'USA' not 'U.S.A'. But why? It is the contracted form of "United States of America" so there must be dots but there are not. Same for MLA, AD and BC. But when it comes to a.m. or p.m. we use them . Why so?

Okay, when I see acronyms I usually see stuff like NYOB, OMG, PM, stuff like that. I also see some of them with periods on them like N.A.S.A. Do you put the dots in them, or not?


look at these two conditions in the code and output respectively: #include <iostream> using namespace std;  int main() {     int i=1;     i=i++;  // first condition      i++; //2nd condition      cout << i << endl; //it will print 2 in second condition **but why print 1 in first condition?**       return 0; }

In C, what is the difference between using ++i and i++, and which should be used in the incrementation block of a for loop?


If there was a huge rod the length of a light-year in space and someone pulled one end of it, when would the other end move?

Is it possible for information (like 1 and 0s) to be transmitted faster than light?   For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.   The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.  Would this actually work?


My understanding is that a larger focal length corresponds to a larger working aperture diameter, since the numerator is larger.  Why doesn't a larger working diameter correspond to a brighter image? Shouldn't there be more light coming into the lens?  Wouldn't a subject framed with 42.5/1.2 lens be brighter than a 35/1.2 if the subject is framed the same?

Cheaper zoom lenses usually are faster at the wide end and slower at the long end (for example, the $150 Canon EF-S 18-55mm f/3.5-5.6). More expensive constant-aperture zoom lenses have the same aperture regardless (for example, $800 Canon EF 17-40mm f/4.0 L).  My question is: are these good lenses  at the wider settings, or do they have a different optic system that allows them to maintain the same aperture throughout the zoom range?


I am attempting to make a command that triggers when someone dies on my server. When someone dies, a /title command should run.   All the other answers I've found are for version 1.12, and I need an answer for 1.15

Is there any way to run a command automatically when a player joins the server? I need to do this without the use of a Bukkit plugin. I think it's possible with MCP but I want to know how!


It would be nice to have possibility to access favourite questions for each community site from Android app.

I haven't been able to find my favorite questions in the official Stack Exchange Android app.  Looking at my accounts page gives nothing on them.


I'm using Python to process a text file, line by line, using RegEx. The first line includes the pattern to be matched, but for some reason Python isn't matching it. If I add a blank line—and make no other changes—it matches that line.  Any thoughts on why this might be happening?  Here's the relevant code:  infile = open(filename, 'r') fulltext = infile.readlines()  pattern = r'{LO[^{]*}(.)\s(.*)' regex = re.compile(pattern)  for line in fulltext:   match = re.match(regex,line)   Here's that first line. Again, it matches when it's not the first line, so I don't see what the issue is.  {LO 1.1a}m Plain text here.

What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it.


I am trying to install Ubuntu alongside windows and it won't work. I go through the installation process and it says to remove installation media and close tray. Then press enter. When I do this the computer restarts like normal and then boots to windows!

I installed Windows 7, which ate Ubuntu's boot file. When starting up the computer, it now goes straight to Windows, without giving me the option of booting Ubuntu.   How can I get Ubuntu back?


Let $X:=S^1 \times S^1$ be the torus.   Is the zero and second singular cohomology group $\mathbb{Z}$, the first $\mathbb{Z}^2$ and otherwise vanishing?   To show this: One first computes singular homology which gives that the zero and second homology group equals $\mathbb{Z}$ and first homology group equals $\mathbb{Z}^2$. Using universal coefficient theorem and that homology groups are free over $\mathbb{Z}$, we get the desired.  I was just wondering, because I wanted to compute cohomology groups of the sheaf of locally constant function with values in $\mathbb{Z}$, which should coincide with the singular cohomology group, but in this case I get that the first cohomology group equals $\mathbb{Z}^4$.

I computed the homology groups of the torus, can someone tell me if this is correct? The calculation, not the result that is. Thanks!  The cells of $T^2$ are $e^0, e^1_a, e^1_b, e^2$  The chain groups are  $$ C_0(T^2) = \{ k e^0 | k \in \mathbb{Z} \} = \mathbb{Z}$$  $$ C_1(T^2) = \{ k_1 e^1_a + k_2 e^1_b | k_1 , k_2 \in \mathbb{Z} \} = \mathbb{Z} \oplus \mathbb{Z}$$  $$ C_2(T^2) = \mathbb{Z}$$  $$ C_k(T^2) = \{ 0 \} , k > 2$$  Now the homology groups:  $$ H_0(T^2) = \ker \partial_0 / im \partial_1 = \mathbb{Z} / 0 = \mathbb{Z}$$  where $im \partial_1 = 0$ because there is no chain in $C_1(T^2)$ whose boundary is a zero-chain in $C_0(T^2)$. (Is this reasoning correct?)  $$ H_1(T^2) = \ker \partial_1 / im \partial_2 = \mathbb{Z} \oplus \mathbb{Z}$$  where $\ker \partial_1 =  \mathbb{Z} \oplus \mathbb{Z} $, i.e. again everything maps to zero because there is no element in $C_1$ whose boundary maps to an element in $C_0$.  $im \partial_2 = 0$ again because there is no element in $C_2$ whose boundary is an element of $C_1$.  I don't want to use Hurewicz to do $H_1$.  $$ H_2(T^2) = \mathbb{Z}$$ using similar arguments as above.  Thanks for your help.  Edit  I posted the computations as an answer below. I got two up votes but I don't know by who so I'm not yet sure I can trust them...


I installed Ubuntu 12.04 and I chose to install 'alongside windows 7'.  After installation and restart, Windows 7 loaded but there is no sign that Ubuntu is actually installed.    Windows 7 is installed in hdd0, boots in legacy mode (only 1 HD in machine), UEFI secure boot is disabled.  I don't see anything on UEFI boot.    Partitions on my 1TB HDD:    100MB ntfs (win 7 installation made it automatically) 200GB NTFS (Win 7 partition) 4 GB Partition (I don't know what fs type) rest all unallocated   Edit: Yesterday I deleted the unused 4 gb partition current OS is running on live usb fat 32  The result of fdisk -l    Result of sudo parted -l


So i cant install katoolin on my ubuntu  lienux@JPC:~$ su Password: root@JPC:/# git clone https://github.com/LionSec/katoolin.git Cloning into 'katoolin'... remote: Enumerating objects: 253, done. remote: Total 253 (delta 0), reused 0 (delta 0), pack-reused 253 Receiving objects: 100% (253/253), 95.77 KiB | 554.00 KiB/s, done. Resolving deltas: 100% (145/145), done. root@JPC:/# cp katoolin/katoolin.py /usr/bin/katoolin root@JPC:/# chmod +x /usr/bin/katoolin root@JPC:/# chmod +x /usr/bin/katoolin root@JPC:/# chmod +x /usr/bin/katoolin/katoolin.py root@JPC:/# katoolin katoolin: command not found root@JPC:/#   Im running ubuntu 18.10 64-bit

I have followed the , but this happens:  # sudo katoolin sudo: katoolin: command not found   I have searched hard on the net with no joy. What am I doing wrong? I have a Macbook Pro Early 2011 i7 processor.


I have a question regarding HTML tags. I'm still not clear totally when to use <strong> instead of <b>, and <em> instead of <i>. My question is: The HTML Strong Importance Element (<strong>) indicates that its contents have strong importance, seriousness, or urgency and The HTML Bring Attention To element (<b>) is used to draw the reader's attention to the element's contents, which are not otherwise granted special importance (as per MDN). Both are used to bold out the letters. Then what's the use of <strong>, as the front-end user won't know the difference between the <b> and <strong>. Similarly, both <em> and <i> italicize the words enclosed between that tag. Then how can we identify which tag has been used? In short, I want to know when to use these tags and what are practical applications of developers using these tags. PS: I am a bit unsure about the cite tag. I understand that it's used in the titles of creative works but I'm still unclear on its usage. Please help me with this as well.

What's the difference between <b> and <strong>, <i> and <em> in HTML/XHTML? When should you use each?


How do I disable portrait/landscape mode after the app is started? Say, if I start the app in landscape mode, it stays in landscape mode. If I start it in portrait mode, it stays in portrait mode?  Thank you

How can I disable landscape mode for some of the views in my Android app?


I'm trying to learn more about prototypal inheritance and I'm a little confused about the difference between adding methods to the prototype and adding them to the instance. Why would I do one over the other?  Prototype method:  function Foo() {} Foo.prototype.doBar = console.log.bind(console, 'Did bar!'); var foo = new Foo(); foo.doBar(); // prints "Did bar!"   Instance method:  function Foo() {   this.doBar = console.log.bind(console, 'Did bar!'); } var foo = new Foo(); foo.doBar(); // prints "Did bar!"   What is the advantage of putting my methods on the prototype? Is there ever a time when it makes more sense to declare the method on the instance via the constructor?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


I have a list of stations in rivers. I want Earth Engine to return me a list of stations whose upstream area overlaps with at least one other country in addition to the country the station is in. This is more or less the code for one station in Brazil using the hydro package by gena. The station should be in the list because its upstream area crosses into Colombia and Venzuela. How can I run a code over all stations and return a list with the property 'GEMS_Stati' for stations with an international upstream area?  var stations = ee.FeatureCollection('users/basins/stations'); var countries = ee.FeatureCollection('USDOS/LSIB_SIMPLE/2017'); var hydro = require('users/gena/packages:hydro');  var filter = ee.Filter.inList('GEMS_Stati', ['BRA00020']); var FilteredStation = stations.filter(filter);  var catchmentsSelected = hydro.getCatchments({outlet: FilteredStation, level: 6})  var union = catchmentsSelected.union(); Map.addLayer(union);  var spatial_filter = ee.Filter.intersects({   leftField: '.geo',   rightField: '.geo',   maxError: 10 });  var saveAllJoin = ee.Join.saveAll({   matchesKey: 'scenes', });  var join_output = saveAllJoin.apply(union, countries, spatial_filter); print(join_output);

I want to calculate the sum of the population living in the upstream area of stations using the hydro package by gena. I think I will have to loop over the stations (using the identifier "GEMS_Stati"). This is my (not very elegant) code to get the population for a single station:   var stations = ee.FeatureCollection('users/basins/stations');  //select only one station var filter = ee.Filter.inList('GEMS_Stati', ['EGY00002']); var FilteredStation = stations.filter(filter);  var PopCount2000= ee.Image('CIESIN/GPWv411/GPW_UNWPP-Adjusted_Population_Count/gpw_v4_population_count_adjusted_to_2015_unwpp_country_totals_rev11_2000_30_sec');  var hydro = require('users/gena/packages:hydro');  var catchments = hydro.getCatchments({level: 6}); var catchmentsSelected = hydro.getCatchments({outlet: FilteredStation, level: 6}) ;  var catchment_Pop2000 = PopCount2000.reduceRegions({   collection: catchmentsSelected,   reducer: ee.Reducer.sum(), });  var sum_pop_upstream = catchment_Pop2000.reduceColumns({   reducer: ee.Reducer.sum(),   selectors: ['sum'] });   How can get a table that contains the station ID, "GEMS_Stati", and the respective value of "sum_pop_upstream" for each station?


Recently I read about Denial of Service attack on Amazon & PayPal. I am curious that how this is performed. These big companies must have huge servers, so DOS would require billions of bots to access it.   So my questions are   How DDOS attack performed at this level? How to know beforehand that this is attack is happening? How to prevent this (how to distinguish from bot vs user, apart from common captcha way that is done)

This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it?


Problem:Find all primes $p$ such that $p^3-4p+9=x^2$, where $x$ is a positive integer.  My Attempt: I have made the following observations while trying tot solve this problem:    $p=2$ yields $x=3$. For $p>2$ the following is true: $x^2\equiv 0\pmod 4$ and $p\equiv 3\pmod 4.$  It seems that $p=2,7$ and $11$ are the only primme numbers that satisfy the conditions of this problem. Below are the values of $p^3-4p+9$ evaluated for $1\leq p\leq 100.$   9  24  114  324  1296  2154  4854  6792  12084  24282  29676  50514  68766  79344  103644  148674  205152  226746  300504  357636  388734  492732  571464  704622  912294  I would like to know how one can prove that $p=2,7$ and $11$ are the only solutions to the above-mentioned equation.

Find all primes $p$ such that  $ p^3-4p+9 $ is a perfect square.   I tried a few different values for $p$, namely $2,3,5,7,$ and $11$. The prime $p =2,7,11$ all worked but $p =13$ didn't so it makes me wonder. How can I find all primes such that it is a perfect square?  EDIT: it turns out this is problem P25 in post number #63 at


Today we've designed Unforgettable Day campaign. or Today we've designed the Unforgettable Day campaign.

I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know.


How can I write the following symbol? I tried but I couldn't find any source...I am looking for cursive i

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


Let $\sigma_n = \frac{1}{n}(s_1 + \ldots + s_n)$. Assuming that $\lim_{n \rightarrow \infty} s_n = s$, prove that $\lim_{n \rightarrow \infty} \sigma_n = s$.  How do I start with this proof? It makes intuitive sense, but I don't know how to do it formally. I've tried writing down the definition of the limit but have not gotten very far, so some hints would help. Thanks!

Prove that if $\lim_{n \to \infty}z_{n}=A$ then:  $$\lim_{n \to \infty}\frac{z_{1}+z_{2}+\cdots + z_{n}}{n}=A$$ I was thinking spliting it in: $$(z_{1}+z_{2}+\cdots+z_{N-1})+(z_{N}+z_{N+1}+\cdots+z_{n})$$ where $N$ is value of $n$ for which $|A-z_{n}|<\epsilon$ then taking the limit of this sum devided by $n$ , and noting that the second sum is as close as you wish to $nA$ while the first is as close as you wish to $0$. Not sure if this helps....


Essential Question: Which Peltier is the most Efficient for reaching coolest temperature, and is the 6V 2A peltier inefficient?  I was looking into more efficient Peltiers for my project and tried to test the amperages of certain Peltiers on a 5V power supply.   Here are the results I have up with:   Using a 5V power supply,    TEC-12704 (12V 4A standard draw) drew 5V 1.4A. Peltier TEC-12705 (12V 5A standard draw) drew 5V 1.36A.    I don't understand how a Peltier rated higher than the previously mentioned runs at a lower power, and furthermore, when converting 12V -> 5V current output using ratios, (12V/5A = 5V/XA, where a 12V 5A Peltier should draw 5V 2.083 Amps? Why is this happening!    Lastly, I tested a 6V 2A Peltier which ran at 5V 2.2 Amps, more amperage at a lower voltage? - so does that mean this is inefficient compared to the last 2 Peltiers?   Currently I am using the 6V 2A Peltier, trying to find a more efficient Peltier and need to figure out: are these weird numbers due to one Peltier being more efficient than the other (critical to my project) or something else?

I am trying to achieve the strongest cooling effect using a TEC Peltier element.    Currently, my set up is two small, 20mm x 20mm peltier TES1-4902 run with a 5V 2.4A USB Battery Pack per peltier.   I need a way to reduce my costs while keeping the same cooling power.   Right now, it is expensive for me to run this set up due to the fact I need two batteries, and I am also looking to improve my efficiency while cutting out an entire battery and/or Peltier. The reason I have two separate battery packs is that I can not find a cheap, small, and thin battery pack that will output 4.8 Amps: however, putting two battery packs in a series may help eliminate one peltier.     So, I have a few branching question that center around a theme:  1) Would a larger Peltier allow for a stronger cooling effect as a result of a larger surface area, say like a 50MM x 50MM peltier, despite the fact (presumably) that it may be more difficult to cool one single peltier than 2 smaller, seperate ones?   2) Is there a Peltier size that would allow me to reduce my power consumption while maintaining a similar cooling effect?   3) Is there a way that I can output 5V 4.8A that is not in two separate USB battery packs that is small and relatively cheap, as battery price:output ability for small scale consumer is quite high and USB battery packs have been the cheapest source of sustainable power for me.    My problem stems from the fact that I am trying to pump as much power and achieve as much cooling power as possible without having to have, say, two battery packs and make the project too expensive. I need a way to reduce my costs while keeping the same cooling power.


For example searching for file does right thing:  file:.git  However searching for directory returns nothing:  directory:.git

I've had some issues with the new search function in Windows 7. The Search in Windows XP was packed with so many more options. The only option I can access now are Date Modified and Size.  Any pointers to how to get more options in the Windows 7 Search, or links to external programs that can make my life easier?


I am using MiKTeX 2.9 for compiling my TeX documents. I am getting an error with contains the line $\mathscript{F}$ showing that it is undefined control sequence. How should I rectify it?


The question tells me to find the volume of a spherical cap with height $h$ and radius $r$ (by radius I mean radius of the cap, not the whole sphere).  Well I attempted to solve it, as $R$ is the radius of the sphere, $r =\sqrt{R^2-y^2}$ via Pythagorean theorem. Now $A$ is the cross-section of the sphere, which is $\pi\big(\sqrt{R^2-y^2}\big)^2$. That can be simplified as $\pi(R^2-y^2)$.  Then I integrated it in terms of $R$ and $R-h$ (the height of the spherical cap), and got $\pi(h^2R-h^3/3)$. But how do I express it in terms of $h$ and $r$, where $h < r$?

A solid spherical cap of radius $R$ is the solid delimited by a sphere    of radius $R$ and a plane that intersects the sphere.   The height $h$ of the solid spherical cap is the largest distance from a point of the solid to the plane intersecting the sphere.   Show that the volume of a solid spherical cap is given by:  $$V = \frac{\pi h^2(3R-h)}{3}$$   It is enough to consider the solid spherical cap delimited by the sphere $x^2 + y^2 + z^2 = R^2$ and the plane $z = R-h$  use triple integrals by spherical or cylindrical coordinates. Give me a few min to try it out.


Find all $h:\mathbb{N}\rightarrow \mathbb{N}$ such that   $$h(h(n)) + h(n+1) = n+2$$   I tried this, but wasn't able to make any progress after a while. So, in vain, I looked at the solution. The solution basically obtained $h(1)=1$ and $h(2)=2$ after some casework, and then claimed that $$h(n) = \lfloor n\alpha \rfloor -n + 1$$ (where $\alpha$ denotes the golden ratio) without explaining at all why one would come at such a conclusion. How did they jump to this conclusion?  (Source: Functional Equations: A Problem Solving Approach, Venkatachala.)

Find all functions $f$ such that $f:\mathbb{N}\rightarrow\  \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$   Let us plug in $n=1$  $f(f(1))+f(2)=3$  Since the function is from $\mathbb{N}$ to $\mathbb{N}$, $f(2)$ can only take the values $1,2$. Now we divide the problem into cases.  Case-1: $f(f(1))=2,f(2)=1$  We can assume that $f(1)=c$ for the time being. Then plugging in $n=3$ and using $f(2)=1$ gives $$f(3)=4-c$$ and again since the range of the function is positive integers,then $4-c$ has to be positive and hence $c$ belongs to  {$1,2,3$}. Now, $$f(1)=c$$$$\implies f(f(1))=f(c)$$$$\implies 2=f(c)$$ by the assumption that $f(f(1))=2$ . Now,since $c$ can only take the values $1,2,3$,we start treating cases. If $c=1$,$$f(c)=2$$$$\implies f(1)=2$$ but we know from the deinition of $c$ that $f(1)=c=1$,a contradiction.If $c=2$,then $2=f(c)=f(2)$ but $f(2)=1$ by assumption. Finally,if $c=3$ $$2=f(c)=f(3)$$ but $$f(3)=4-c=4-3=1$$ which is once again a contradiction. Therefore there are no such functions in this case.  Case-2: $f(f(1))=1,f(2)=2$  Again assuming $f(1)=c$ and using $f(n)\le n$ along with plugging $n=c-1$ will give us that $f(1)=1$ and then it is easy to prove that such a function exists by recursion. I can only give a "sort of recursive" way to define the function. Here it goes $$f:\mathbb{N}\rightarrow \mathbb{N}$$$$f(1)=1$$$$f(n)=n+1-f(f(n-1))$$  But this case is harder to deal with.Some help will be appreciated.


I'm not familiar with algebra theory, but I'm interested to know if there is an ensemble in mathematics for which the power of ensemble could be a real number, we take for example $\mathbb{R^{\frac{1}{2}}}$, Does this meant the space dimension is $\frac{1}{2} $?  Note:I want $\mathbb{R^{\frac{1}{2}}}$ have a metric space structure   Thanks for any comments

Can the notion of vector space or algebra over a field be meaningfully extended to fractional dimensions, so that for example $\mathbb{R}^{-2/3}$ makes sense? Has this been explored somewhere?  I know that super vector spaces can be thought of as one way of generalizing vector spaces to negative integer dimensions. Is there a similar concept for dimensions that are rational numbers? I'm not talking about Hausdorff dimension, because it doesn't allow for negative rationals, and I'm rather looking for extensions from a more algebraic point of view (dimension as the trace of the identity map), without recurring to a given metric.


I am having a problem at a Java program. Exception in thread "main" java.lang.NullPointerException  Exception in thread "main" java.lang.NullPointerException     at DBOperation.DBOperation.checkLogin(DBOperation.java:30)     at DBOperation.DBOperation.main(DBOperation.java:82)   who can help me find error? how to fix them? (Please note that the code is still complete and I have entered some print statements for checking)  My code:   package DBOperation;  import java.sql.Connection; import java.sql.DriverManager; import java.sql.ResultSet; import java.sql.SQLException; import java.sql.Statement; import java.util.*; public class DBOperation {     private String url;     private String serverName;     private String dbName;     private String usr;     private String pwd;     private Connection cnn;          public boolean checkLogin(String user, String pass) {         boolean tmp = false;         Statement stm = null;         ResultSet rs = null;          try {             stm = cnn.createStatement();             rs = stm.executeQuery("Select *from ListUser where username = '"+user+"' and password = '"+pass+"'");             if(rs.next())                 return tmp = true;         } catch (SQLException e) {             // TODO Auto-generated catch block             e.printStackTrace();         }finally{             try {                 rs.close();                 stm.close();             } catch (SQLException e) {                 // TODO Auto-generated catch block                 e.printStackTrace();             }          }         return tmp;     }      public DBOperation() {          this.url = "jdbc:sqlserver://";         this.serverName = "localhost";         this.dbName = "sharefile";         this.usr = "sa";         this.pwd = "123456";     }     @SuppressWarnings("finally")     public Connection getMyCon()     {         Connection cn = null;         try {             Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");             try {                 cn = DriverManager.getConnection(getMyUrl(),usr,pwd);                 if(cn!=null)                 {                     System.out.println("Ket noi thanh cong");                 }                 else{                     System.out.println("Ket noi khong thanh cong");                 }             } catch (SQLException e) {                 // TODO Auto-generated catch block                 e.printStackTrace();             }         } catch (ClassNotFoundException e) {             // TODO Auto-generated catch block             e.printStackTrace();         }finally{         return cn;         }     }     private String getMyUrl() {         // TODO Auto-generated method stub         return url+serverName+"; databaseName="+dbName;     }     public static void main(String[] args) {         DBOperation objDB = new DBOperation();         objDB.getMyCon();         objDB.checkLogin("teri", "123456");      }   }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Hello is this someone has worries under Ubuntu 18.04.1 LTS with GitKraken to connect with GitHub?, Because on 2 PC freshly installed and updated can not authorize the connection.  I get this error by launching Gitkraken in a terminal    So I search on Google and enter his orders, but it does not solve my problem I always have the same error  sudo apt install libcanberra-gtk-module libcanberra-gtk3-module sudo apt-get install libcanberra-gtk-module:i386 sudo apt-get install --reinstall libcanberra-gtk-module

Gtk-Message: Failed to load module "canberra-gtk-module"   but I already have the libcanberra-gtk-module  and libcanberra-gtk3-module installed. (i.e. I tried , but it is already installed.)  This happens for instance, when I run ipython --pylab  I'm running Ubuntu 13.04 - raring.


I am 20 years old. I live currently in Mexico and have been living here for 9 years. My parents took me to the USA when I was a minor (1 year and a half) and stayed until I was about 12 years old. I lived with my mom and sister. We asked to leave the US and exited voluntary. I have graduated from middle school and high school. I have an internship in accounting. I have my own small business and a family with 2 kids. I have never had any issues with the law in Mexico or in the USA. Is there a way that they will deny me automatically a visa for having been to the USA illegally? I want to go to the USA for a 4-day vacation fishing.

I was born in Brazil and came to the United States at the age of 7, in 2007. I no longer need to live in the United States because I have found success in investing and no longer depend on having a job. I am going to buy property in my home country soon, but I have just turned 18.   Will I ever be able to return to the United States to see my friends and other family members? Even if it is a 30-day visa? And, if so, in the future, am I still eligible for the EB-5 visa? Will I be barred from entry?


I have a domain name on DNSimple, with email forwarding to my Gmail account.  It's working well, except I would like to be able to send emails from Gmail using my DNSimple's email.  But when I go on Gmail settings, and click the Add another email address you own link and set my DNSimple email and Next step button, Gmail ask me for an SMTP password. And I have no idea about it.  If I correctly remember, at the beginning of Gmail it was automatic.  Any solutions?

I used to be able to go to Accounts and Import → Add another email address you own and add an email account that's only a forwarding address. That is, it's not a mailbox and I don't have SMTP access to it.  Gmail would send me a confirmation email to that address, I'd confirm it's mine, and done. Now it only gives me the option to add SMTP credentials.  Did they stop supporting the previous method? Is there any other way I can get that option back?


The code below just keeps giving the else error message I don't know what's wrong..     Boolean loop2 = true; userInput = scan.next();  while (loop2) {     userInput = scan.next();     if(userInput.toLowerCase() == "") {         out.println(             "Please pick a option! it's in the 'Commands' <= type this in!"         );         loop2 = true;     } else if(userInput.toLowerCase() == "fight") {          Fights(); loop2 =   false;     } else if(userInput.toLowerCase() == "train") {          Training(); loop2 = false;      } else if(userInput.toLowerCase() == "bosses") {          Bossing(); loop2 =  false;      } else if(userInput.toLowerCase() == "shops") {          ShopsAll(); loop2 = false;      } else if(userInput.toLowerCase() == "commands") {          Menu(); loop2 = false;      } else {         out.println("ERROR MESSAGE!!.");     } }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Does anyone know of a tool that can resize a batch of images to the largest size that keeps each one under a specified file size (preserving aspect ratio)?  This would be very useful when uploading to sites with different file size limits  Edit: only needs to run on Windows

I have a bunch of photos of jewelry that I need to upload to a website. Unfortunately there is a 2MB file size limit. Most of the photos are JPEGs over 3MB.  I want to keep the aspect ratio, meta data, and highest quality possible at under 2MB. Adobe Bridge will allow me to set an image size limit when I export, but not the file size.  Does anyone know of a way to render the images with a max filesize limit?


Yesterday I received the Razer Core X with an AMD RX5700 XT Graphics card to use with Blender 2.92. Unfortunately, Cycles will not recognize this eGPU in the Blender System Cycles render device Preferences. Whenever I instruct Cycles to render with my GPU Compute device, my Mac's fans start whirring, indicating that my integrated GPU is rendering, and not my eGPU. Does anyone know how to render with an eGPU? Thanks! -Jake MacBook Pro Mid 2020, 13.3 Inch MacBookPro16,2 Quad-Core Intel Core i7 2.3 GHz Number of Processors: 1 Total Number of Cores: 4 eGPU: Razer Core X eGPU Chasis 8GB AMD RX5700xt

Hello I just got the AMD Radeon RX Vega 56 (blackmagic eGPU Pro) yesterday  plugged it in to my brand new Mac mini (Mojave), it shows up in the menubar and as an alternative as a render engine,. My question is, can I use this eGPU for cycles renders? (Blender 2.80)  Very grateful for your responses.


I'm not suggesting to apply this on main sites (-3 score), as wrong answers or with bad advice/bad code (etc) are beneficial being less visible (greyed out).    However, Metas are different beasts to their main sites, and there's some leniency towards Meta answers.   Meta Answers:     Don't need to strictly answer the question Are often discussion points, adding alternative or additional suggestions or ideas Are often not "right or wrong", they're opinions, and votes on them are just X people agree or disagree   So on Meta sites (maybe not all of them), the answers with a negative score being greyed is not necessarily a good thing, as they're still potentially viable discussion points, showing what people think.      Example:     I'm happy to leave it as the question is about usage of a specific tag, and the downvotes show a general consensus that people disagree with a certain side of the argument. However, it's almost pointless me doing so when it's barely visible.    We can see it's (currently) -8 and most people "disagree", and it's at the bottom of all other answers.    An example showing we're losing visibility on a good discussion point:     While that answer has a -38 score it also has +44 votes - on Meta specifically I don't think it's logical/useful having that answer less visible.      There may be some Meta sites where this wouldn't be preferred - but on MSO and MSE (at least) I think it would be worthwhile.    Do you think it would be welcomed to not grey out -8 negatively voted answers on at least some Meta sites, to allow them to be seen as part of the discussions?

Since  from other SE sites and is not thought to point out a lack of quality or helpfulness, but only to express agreement or disagreement, I'm wondering why downvoted answers here on meta are shown semi-transparent.  Shouldn't they be non-transparent then (like upvoted answers)?  Or am I missing something?


I have a Dell Precision M2800, which comes with the usual Intel 4600 as well as an AMD FirePro W4170M GPUs. The OS is Win 8.1 with the latest drivers for everything. Bios is fully updated (A06).  Dell has a "feature" called Dell Intelligent Display, which dims the screen according to the brightness of the displayed data. Not to be confused with the Adaptive Brightness feature of Windows.  This feature is annoying as hell. Everytime I switch tabs on my browser, or switch an IDE, The screen dims or brightness.   The way to turn this off . But alas, the Precision line comes with an app called "Dell Command | Power Manager", and this feature is not present there. The Battery Meter app is not compatible with my laptop.  I see a lot of woe around this feature expressed over the Interwebs, but no official answer from Dell.  Anyone has any experience with this?  P.S. One of Dell's laptops strongest sell points is their "Pro support". Well - it's a joke. The 24hrz immediate response is ofcourse ignored, and both the Morocan and Greece call centers are not staffed by knowledgable, or even caring people. Beware!  EDIT 1: @BreakThrough suggested . Well, my Intel control panel looks like this:

I am not talking about adjusting screen brightness through power management (this is a laptop), I'm not talking about how the screen brightness setting may be different between 'plugged in' and 'battery powered', and unplugging the laptop will suddenly change the brightness. I'm talking about:  I have a Dell XPS 15 (L502X), and with intell hd graphics driver installed (from a vanilla win7 64 bit install), I start to see a brightness change. (This is also before the nvidia driver install).  I set my desktop to black, and open notepad, fullscreen. Now the entire screen is a bright white. I then alt-tab back to desktop, all black.  This is the interesting part:  I alt-tab back to notepad (all white, fullscreen), and the brightness of the white slowly, every so slightly, incrementally steps up (less than even one brightness adjust as you would do via the power settings). Then you swith back to the black desktop, and barely you can tell it steps back down (the backlight on the black grows a bit darker). It is a small change, but noticeable in a dark room. Again back to white, and a step up to a brighter white.  It. drives. me. crazy. :)  It is very annoying googling for info (everyone has something about power management). I can't find any setting in the intel hd graphics properties that affects this. Oddly enough, I have an older install of windows on this same machine which doesn't do it, I fixed it once about a year ago and I can't remember how I did it (I work on quite a few pc's, I THOUGHT I tweeked something in the intel hd graphics properties, but nothing seems to stick this time).   What is this feature called? How do I disable it?   EDIT  This does behave a lot like the automatic brightness adjustment that my smart phone exhibits. Ironically, that annoyed me as well (fixed with root and app)  I have tried to disable this feature, but here is a screenshot of my "Power" tab:    // The brightness feature is missing  I'm going to check what this tab looks like on my other disc (where I believe i once 'fixed' this)  EDIT 2  Turns out it was in the same view, but you have switch to change the power source to 'on battery' and disable "DIsplay Power Saving Technology"    Thank you.


How can a black hole grow in mass, if it takes an infinite time to cross the event horizon,  for matter approaching the black hole (as seen from an outside observer far from the black hole)?  To make a black hole, one must concentrate mass or energy sufficiently that the escape velocity from the region in which it is concentrated exceeds the speed of light.  So , as seen from an outside observer, we have redshift and time dilation (all the GR effects in action ) for matter approaching the event horizon of a black hole.   Eventually (in finite time ),  the outside observer sees sufficient matter (energy ) accumulating in a small neighborhood of the event horizon of the original  black hole that other  black holes must emerge (in the neighborhood of the event horizon of the original black hole ). So the outside observer sees a continuous merging of black holes , those formed in the neighborhood of the event horizon of the original black hole, and the original black hole itself. That could explain how a black hole can grow, even as seen from an outside observer.   Question.  Is this explanation correct?

The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through?


Determine the Galois group of $X^4 - 2X^2 +2$ over $\Bbb Q$   EDIT : I want to address the particular polynomial and not the full general case. In order to solve this problem, I want to have a self-contained proof/answer and am not willing to reproduce the general argument when even it might not be required. If you can provide help overcoming this simple obstacle then please help, instead of just lazily labeling the question as duplicate !  The result that is being linked\suggested, it boils down to the same problem whether $\sqrt 2$ is in the field $\Bbb Q(\alpha)$ or not, so it's pointless to refer the link just by merely looking at the form of the polynomial!  Mt attempt :  Obtained roots of $X^4 - 2X^2 +2$ to be : $\pm \frac{1}{\sqrt 2}(\sqrt{1+\sqrt 2} \pm i \sqrt{\sqrt 2 -1})$ . Then considered $\Bbb Q(\alpha)$ where $\alpha=\frac{1}{\sqrt 2}(\sqrt{1+\sqrt 2} + i \sqrt{\sqrt 2 -1})$ .  So I need to show whether $\frac{1}{\sqrt 2}(\sqrt{1+\sqrt 2} - i \sqrt{\sqrt 2 -1}) \in \Bbb Q(\alpha)$  or not (then the Galois group will be of order 4 or 8 respectively) .   I have observed that $\sqrt 2 \in \Bbb Q(\alpha) \implies $ $\frac{1}{\sqrt 2}(\sqrt{1+\sqrt 2} - i \sqrt{\sqrt 2 -1}) \in \Bbb Q(\alpha)$  So, (1) How to show (if it is true) $\sqrt 2 \in \Bbb Q(\alpha)$ ?  (2) How to obtain the Galois group ? If (1) is true I was tempting to use computational tricks like the ones exhibited in    Thanks in Advance for help!   has been asked on this polynomial before, but the OP was confused himself , I could not follow his arguments and most importantly the question did not had any answer.

I want to compute the Galois group of some polynomials, but I want to see some examples first. For example this proposition could be helpful. I don't know how to prove it <.<  Let's consider a polynomial $f(x)= x^4+ax^2+b \in \mathbb{Z} $. Let $ \pm\alpha , \pm\beta$ denote the roots of $f(x)$. Note that $f$ is irreducible iff $\alpha^2, \alpha\pm\beta \notin \mathbb{Q}$. So let's suppose that $f(x)$ is irreducible. Let's denote $G$ the galois group of $f$ (the Galois group of the splitting field $\mathbb{Q}(\alpha,\beta)/\mathbb{Q}$)  $i)$ $G\cong V$ the Klein 4-group iff $\alpha\beta \in \mathbb{Q}$  $ii)$ $G\cong \mathbb{Z}_4$ iff $\mathbb{Q}(\alpha\beta)=\mathbb{Q}(\alpha^2)$  $iii)$ $G\cong D_8$ the dihedral group of order 8, iff $\alpha\beta \notin \mathbb{Q}(\alpha^2)$  I need help with the proofs of this propositions... Well I'm very lost with the computation of Galois group, some care must be exercised, I don't have it. For example I know that Galois group acts transitively, in the sense that $u\in K/F$ a galois extension, the other roots of the minimal polynomial of $m_u(x)\in F[x]$ are precisely the elements $ \sigma(u)$ , where $\sigma \in Gal(K/F)$. And clearly any automorphism, is determined by only the value of a basis. In this case we are working on $\mathbb{Q}(\alpha,\beta)$, so I have to know the values of both. But I have to respect the algebraic relations involving $\alpha , \beta$ I proved that in $i),ii)$ $\mathbb{Q}(\alpha,\beta) = \mathbb{Q}(\alpha) $ So I have to know the values on $\alpha$.   My first question is: If in both cases $i),ii)$, I have an extension of degree 4 (so $|G|=4$) I have to map $\alpha$ to determine the automorphism, but I have also to map $\alpha$ to all of it's four roots. Why the galois group in this case are different?  My second question is about $iii)$ I have no idea How to attack it.


I'm quite new to Ubuntu and lately I've been struggling with software updater.  It lists the software to update but when I try to update gives the message  Requires installation of untrusted packages This requires installing packages from unauthenticated sources.     I tried to execute sudo apt-get update && sudo apt-get upgrade but the software updater continues listing software outdated.  Any help would be welcomed.

Any install that I'm trying through the Software Center is telling me:  Requires installation of untrusted packages: The action would require the installation of packages from not authenticated sources.  I did an apt-get update from the command line, then removed the software sources that the keys were bad from (PPAs I added myself), and unchecked them in the software sources for software center, but to no avail.  I can't install anything from software center anymore - only> from the command line with apt-get. Is uninstalling/installing the only option?  I don't want to break other PPAs that I have. Additional information: Here's a paste from apt-get update: Reading package lists... Done W: GPG error: http://ppa.launchpad.net oneiric Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY B725097B3ACC3965 W: GPG error: http://us.archive.ubuntu.com oneiric Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>  I've tried apt-key update, and there was no effect (two keys unchanged). The output of apt-get update and apt-get upgrade, and the contents of /etc/apt/sources.list, can be found in .


I should add a header row: 1 2 3 4  to a matrix and a column (as before: 1 2 3 4 ) on the left of the same matrix. But the style should be different like below:    this is my MWE:  \documentclass{beamer} \usepackage{tikz} \usetikzlibrary{matrix} \begin{document} \begin{tikzpicture}  \tikzset{square matrix/.style={     matrix of nodes,     column sep=-\pgflinewidth, row sep=-\pgflinewidth,     nodes={draw,       minimum height=#1,       anchor=center,       text width=#1,       align=center,       inner sep=0pt     },   },   square matrix/.default=0.5cm }  \matrix[square matrix] { 16 & 3 & 2 & 13 \\ 5 & 10 & 11 & 8 \\ 9 & 6  & 7 & 12 \\ 4 & 15 & 14 & 1 \\ };  \end{tikzpicture} \end{document}   Thank you so much!

I'm trying to write the following matrices.    I used the following code (given by )  \documentclass{article} % Load TikZ \usepackage{tikz} \usetikzlibrary{matrix,decorations.pathreplacing,calc} % Set various styles for the matrices and braces. It might pay off to fiddle around     with the values a little bit  \pgfkeys{tikz/mymatrixenv/.style={decoration=brace,every left delimiter/.style=    {xshift=3pt},every right delimiter/.style={xshift=-3pt}}}  \pgfkeys{tikz/mymatrix/.style={matrix of math nodes,left delimiter=[,right delimiter=    {]},inner sep=2pt,column sep=1em,row sep=0.5em,nodes={inner sep=0pt}}}  \pgfkeys{tikz/mymatrixbrace/.style={decorate,thick}}  \newcommand\mymatrixbraceoffseth{0.5em}  \newcommand\mymatrixbraceoffsetv{0.2em}  % Now the commands to produce the braces. (I'll explain below how to use them.) \newcommand*\mymatrixbraceright[4][m]{ \draw[mymatrixbrace] ($(#1.north west)!(#1-#3-1.south west)!(#1.south west)-    (\mymatrixbraceoffseth,0)$)     -- node[left=2pt] {#4}      ($(#1.north west)!(#1-#2-1.north west)!(#1.south west)-(\mymatrixbraceoffseth,0)$); }  \newcommand*\mymatrixbraceleft[4][m]{  \draw[mymatrixbrace] ($(#1.north east)!(#1-#2-1.north east)!(#1.south east)+    (\mymatrixbraceoffseth,0)$)     -- node[right=2pt] {#4}       ($(#1.north east)!(#1-#3-1.south east)!(#1.south east)+    (\mymatrixbraceoffseth,0)$); } \newcommand*\mymatrixbracetop[4][m]{ \draw[mymatrixbrace] ($(#1.north west)!(#1-1-#2.north west)!(#1.north east)+(0,\mymatrixbraceoffsetv)$)     -- node[above=2pt] {#4}      ($(#1.north west)!(#1-1-#3.north east)!(#1.north east)+(0,\mymatrixbraceoffsetv)$); } \newcommand*\mymatrixbracebottom[4][m]{ \draw[mymatrixbrace] ($(#1.south west)!(#1-1-#3.south east)!(#1.south east)-(0,\mymatrixbraceoffsetv)$)     -- node[below=2pt] {#4}      ($(#1.south west)!(#1-1-#2.south west)!(#1.south east)-(0,\mymatrixbraceoffsetv)$); }  \usepackage{tikz} \usetikzlibrary{matrix,decorations.pathreplacing}  \begin{document}    \[  \begin{tikzpicture}[mymatrixenv]  \matrix[mymatrix] (m)  {     a & b & c & d & e & f \\     g & h & i & j & k & l\\     l & m & n & o & p & o \\     \hline \\     q & r & s & t & u & v \\     w & x & y & z & a & b \\     c & d & e & f & g & h \\   };   \mymatrixbraceright{1}{3}{$E_1$}   \mymatrixbraceright{5}{7}{$E_2$}   \mymatrixbracetop{1}{3}{$E_1$}   \mymatrixbracetop{4}{6}{$E_2$} \end{tikzpicture} \]  \end{document}     It's really nice but still it doesn't serve my purpose. Any help in this regard will be highly appreciated. Thanks


If you were at the door and found out that you had forgotten your keys you might say: "I have forgotten my keys" ..  but what would it mean if you said I forgot my keys instead?

Non-native speakers often get confused about what the various tenses  and aspects mean in English. With input from some of the folk here I've put together a diagram that I hope will provide some clarity on the matter.  I offer it as the first answer to this question. Consider it a living document. Input is welcome, and good suggestions will be  incorporated into the diagram.    Nota bene: What this is not is a discussion of whether there are  more than two tenses in English. , to which this question is not intended to supply arguments one way or the other.  Here, the aim is to provide an overview of what constructions English-speaking people use for conveying information about actions referring to past, present, and future, and to provide it first and foremost to precisely the people who are likely to use "tense" as a catch-all term in their search, rather than to linguists who know better.  Breaking News There is now an excellent ELU blog article titled  . It is highly recommended reading.


I look up the dictionary that it means It doesn't matter to me for couldn't care less . However, I can't get *couldn't have cared less* Thanks.  A: How long have you been divorced?   B: Two years since it's been final, but it hadn't been good for years. Honestly, we stuck it out for the kids, who couldn't have cared less.

What's the deal with the phrase "could care less"?  Whilst growing up, I've always known people (parents etc) to use the phrase "couldn't care less", but I've also come across people who use the phrase "could care less" to mean the same thing (that is, "I do not care at all about that").  To me "couldn't care less" seems a lot more logical. If I couldn't care less about something, that implies I do not care about it at all. In contrast to this, to my mind the phrase "could care less" seems to indicate "I do care about this to some degree at least", but that's definitely not the meaning intended.  What's going on here? Is my (logical) analysis correct or in error?


Iterating over an array or a list that has no element, foreach seems very slow compared to for. Running below code, the result I got is:  3ms  143ms  7ms  Is foreach really slow or am I doing something wrong?   var l = new List<int>(); var watch = new Stopwatch(); var test = 0;  watch.Start(); for (int i = 0; i < 10000000; i++)      if (l.Count > 0)          test = 1; watch.Stop(); Debug.Log(watch.ElapsedMilliseconds);  watch.Reset(); watch.Start(); for (int i = 0; i < 10000000; i++)      foreach (var item in l)          test = 1; watch.Stop(); Debug.Log(watch.ElapsedMilliseconds);  watch.Reset(); watch.Start(); for (int i = 0; i < 10000000; i++)      for (int j = 0; j < l.Count; j++)          test = 1; watch.Stop(); Debug.Log(watch.ElapsedMilliseconds);

In C#/VB.NET/.NET, which loop runs faster, for or foreach?  Ever since I read that a for loop works faster than a foreach loop a  I assumed it stood true for all collections, generic collections, all arrays, etc.  I scoured Google and found a few articles, but most of them are inconclusive (read comments on the articles) and open ended.  What would be ideal is to have each scenario listed and the best solution for the same.  For example (just an example of how it should be):   for iterating an array of 1000+ strings - for is better than foreach for iterating over IList (non generic) strings - foreach is better than for   A few references found on the web for the same:               [Edit]  Apart from the readability aspect of it, I am really interested in facts and figures. There are applications where the last mile of performance optimization squeezed do matter.


Hi guys I have a laptop dual-booted with Ubuntu 16.10 and Windows 7. So I was wondering if I could downgrade back to 16.04 LTS and btw I installed 16.04 then upgraded to 16.10. I really want to go back to 16.04 because a lot of software I want hasn't been released for 16.10 "Yakkety"

I just installed a new version of Ubuntu and I want to roll it back to the previous version.  How can I do that? Is that even possible?


Is there a way to find a missing cubic root if a maximum turning point and a turning point on the x axis is known? The maximum turning point is at (50,30) while the turning point root is (100,0)  So in this equation   F(x) = (x+a)(x-100)(x-100)  I need to find knowing that the given points are stat points with a gradient of zero.   Thank you

How can I find a cubic function from two known points $\left(50,30\right)$ and $\left(100,0\right)$ which are turning points, hence the gradient at these points is zero. My final function must be in the form  $\,\mathrm{F}\left(x\right) = A\left(x + a\right)\left(x + b\right)\left(x + c\right)$.  I already know that  (X+b)= (x-100) (X+c)=(x-100)  So I'm missing A and a  The graph will then be set with a domain so it flows smoothly in this graph   I need very clear steps on finding a graph that flows smoothly and ends up in this form :)   Thank you!


I am not a javascript expert but thought this was a slam dunk to code until I saw the results. I am looking for help to make this MUCH more efficient. I have a simple for-loop going over a list of data rows. Typically there are 10 or so but sometimes there might be up to a couple of thousand. With 10 its no problem. With 1200 it takes 34 seconds!! The code -            for(let i = 0; i < selectedRows.length; i++) {                 selectedRows[i].checked = event.target.checked;             }  I am setting the "checked" variable in all rows to true or false. i.e. someone selected the "Check all boxes" checkbox. As mentioned above, with 1200 rows it takes 34 seconds. When I add timers in like the following -             for(let i = 0; i < selectedRows.length; i++) {                 console.time('handle checking of box - ' + i);                 selectedRows[i].checked = event.target.checked;                 console.timeEnd('handle checking of box - ' + i);             }  what is interesting is that the loop starts out fast. It does a row in about 1ms which is what I would expect.  But, as the loop progresses it gets much slower until at the end each row takes 20ms.  Can anyone help me understand why the loop gets slower and slower as well as perhaps a better way of doing this?

I have an LWC template like this: <input list="counties"> <datalist id="counties">   <template for:each={counties} for:item="county">     <option key={county.Id}>{county.Name}</option>   </template> </datalist>  I load the county records from the server. There are about 3,000 of them. When the counties are loaded and the template updates, it hangs the entire page for 10-20 seconds. This is a fairly small amount of elements to insert into the DOM.  Why are LWCs so slow when updating the DOM? What about them under the hood makes this such an inefficient operation? How can I speed this up, so that my autocomplete input can be populated by accurate information without hanging the entire page for 20 seconds?


Also, Prove that every edge-coloring of $K_6$ with $2$ colors contains at least two monochromatic copies of $K_3.$ I have no idea how to start these problems. What should I do?

Let $K_n$ be a complete $n$ graph with a color set $c$ with $c=\{\text{Red}, \text{Blue}\}$. Every edge of the complete $n$ graph is colored either $\text{Red}$ or $\text{Blue}$. Since $R(3, 3)=6$, the $K_6$ graph must contain at least one monochromatic $K_3$ graph. How can I prove that this graph must contain another (different) monochromatic $K_3$ graph. I saw proofs which uses the fact that there are at most $18$ non-monochromatic $K_3$ graphs. Since there are $20$ $K_3$ graphs (how can you calculate this) there are at least 2 monochromatic $K_3$ graphs. Are there other proofs?


I would like to know why my unmarshalling process cause some troubles:   I save my java object in a xml file. I load my java object from the xml file   Once that's done, strange behaviour occurs in the method of my java object (ClassMain.java).  Indeed the method isLogin() returns false just before it returns true (ClassMain.java. Any ideas?  MainClass  public static void main(String[] args) {     Player p1 = new Player();     p1.setLogin("p1");     p1.setMdp("mdp1");           try {          //Test : verify that player's login is 'p1' (return true)         System.out.println(p1.isLogin("p1"));          marshaling(p1);          Player pfinal =unMarshaling();          //Test : verify that player's login is 'p1' (return False ?why?)         System.out.println(pfinal.isLogin("p1"));      } catch (JAXBException e) {         e.printStackTrace();     } } private static Player unMarshaling() throws JAXBException {     JAXBContext jaxbContext = JAXBContext.newInstance(Player.class);     Unmarshaller jaxbUnmarshaller = jaxbContext.createUnmarshaller();     Player player = (Player) jaxbUnmarshaller.unmarshal( new File("C:/Users/Public/player.xml") );     return player; }    private static void marshaling(Object o) throws JAXBException {     JAXBContext jaxbContext = JAXBContext.newInstance(Player.class);     Marshaller jaxbMarshaller = jaxbContext.createMarshaller();     jaxbMarshaller.setProperty(Marshaller.JAXB_FORMATTED_OUTPUT, true);     jaxbMarshaller.marshal(o, new File("C:/Users/Public/player.xml")); }}   Player Class  @XmlRootElement(name = "joueur") @XmlAccessorType (XmlAccessType.FIELD) public class Player{  @XmlAttribute private String login;  public Player() { } public String getLogin() {     return this.login; } public void setLogin(String login) {     this.login = login; }  public boolean isLogin(String n){     if(this.login == n)         return true;     else          return false; } }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I believe df is reporting incorrect disk usage, as I have the following problem:  I deleted a few files to free up space, then run the following:     $ df -H   reports 7.7GB on Volume and 400MB available, however, running:     $ du -sh /   reports 3.8GB usage, on this volume. There is a loss of roughly 3.9GB.  I have ensured there are no opens files using $ lsof and also rebooted the server after deletion.  FYI - OS Version: Centos 6.5  I would appreciate it if you would be able to guide me or point me in the right direction. Thank you.

I have a fileserver where df reports 94% of / full. But according to du, much less is used:  # df -h / Filesystem            Size  Used Avail Use% Mounted on /dev/sda3             270G  240G   17G  94% / # du -hxs / 124G    /   I read that open but deleted files could be responsible for it but a reboot did not fix this.  This is Linux, ext3.  regards


My laptop is Toshiba satellite l350-15k. My processorIntel R Core i3, Ram is 4 Gb, OS is 64 bit, display card is AMD Radeon HD 7600M series. I'm just a beginner about Linux and I couldn't decide which Linux version, I should install to my laptop.  Could someone help me, please?

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


First Statement :   Select GroupMember FROM Group    Result:                          Los Angeles,San Diego                          (it is a string)  Second Statement :    SELECT *  FROM Store_Information   WHERE Store_Name IN ('Los Angeles', 'San Diego');   How to turn Los Angeles,San Diego(one data) to IN ('Los Angeles', 'San Diego')?

How do I parameterize a query containing an IN clause with a variable number of arguments, like this one?  SELECT * FROM Tags  WHERE Name IN ('ruby','rails','scruffy','rubyonrails') ORDER BY Count DESC   In this query, the number of arguments could be anywhere from 1 to 5.  I would prefer not to use a dedicated stored procedure for this (or XML), but if there is some elegant way specific to , I am open to that.


So I have a clients server that is infected with malware. Basically any index.php file on the server was infected as well as header.php, function.php. The infection seems to be primarily wordpress sites although other types of sites reside on the account as well.  The hack seems to generate some type of a "key" in a file called ".." That file, even though it gets deleted, returns within in a few minutes. (probably 10 or 15 minutes). I've gone ahead and cleaned all the infected files I've found with some scripting.  Here's my question, I am presuming that if I can find the file(s) that are respawning the ".." file(s) back on the server, I am thinking it will lead me to the source of the infection as well. But what I'd like to know is, how can I actually track that down?  I was thinking maybe tailing the logs in SSH or something to see if that would show me something, but I am not quite sure. I know I'd like to find the infection point and get it removed before I have to do a complete reclean of the server. Right now - I'm just baby sitting respawned ".." files.  Any thoughts on how I can dig this out?

This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault.


How can I remove the spacing after a table that appears on top of page 2, when I have a paragraph that starts from page 1 and continues on to page 2? I can't use \vspace since that just moves the whole paragraph on page 1.

\documentclass{mwrep}  \usepackage[draft]{graphicx} \usepackage{hyperref} \usepackage[all]{hypcap}  \makeatletter \g@addto@macro\@floatboxreset\centering \makeatother I use figures with captions.  \begin{document}  \listoffigures  \chapter{foo}  First paragraph (previous).  \begin{figure}[h]   \includegraphics{a.jpg}   \caption{Opis} \end{figure}  Second paragraph (following).  \end{document}   How can I change vertical space (padding?) between caption and following paragraph? Also, I want to change (increase a little) space between previous paragraph and top of image.


I'm trying to basically find the width and height of someone's face I know the following:  distance from face to camera in mm the sensor height in mm the focal distance in mm distance in pixels distance between my points Height/Width of image in pixels  How can I accurately get the width and hight measurements in MMs. I took a look at this. Could I use it for width measurements as well? Is there a more accurate way to go about doing it?

first post so please be nice. I am doing an image processing project and my problem is now that I would like to know how big my digital image is in the real world.  I have: digital image: 336x256 pixel  camera focal length: 9mm  camara aperture: f/1,25  camera distance: 40m  pixel pitch: 17 micro m  FOV: 35° x 27°1.889 mr  Is there a way to calculate the real width and height of the image?


The frontpage looks like the following screenshot for me as I have a zoom level of 110% set:    It looks perfectly fine if I set the zoom to 100%, but then the text is a bit too small for me. I'm using the latest Chrome on Windows 7.

The individual questions take up a lot more vertical space in the question listing compared to any other site.  As you can see in the screenshot below, SO can fit about 5 and 1/2 questions in the same space that Meta.SE fits 3 questions.    Is this on purpose or because the site is still being worked on?


So, I can't really get my head around what is going on here. I started by allowing a command line input. I then select the values I want and pass them via instantiation (i think I used that correctly), to be received in the constructor of my second class (MyDate).  They are received and I use:      this.day = day; etc.  To set them to my class variables to be used across all methods of the class.  I then have my get methods for day, week, month. They return day, week, month.  So, then I call on my print method, and that was tricky because from what I understand, I had to instantiate the MyCalendarOne class in order to reference a non static method from a static context. So, that done, I referenced the method.  Within that method, I have some print statements and they call upon the methods in the MyDate class via the following code:  System.out.println(myDate.getDay()); System.out.println(myDate.getMonth()); System.out.println(myDate.getYear());   I just don't understand why the values haven't been passed and I am getting the nullpointer error. Which from what I understand is that I'm trying to print 'null'.  Pretty stumped on this one.  I firstly made sure my command line input and parsing was correct. It was.   I actually don't really know what else to try. I had worked through all the other errors but ugh. I'm stumped.  class MyCalendarOne { private MyDate myDate; private enum Day {MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY,  SATURDAY, SUNDAY};  public static void main(String[] args) {     String dateInput = args[0];      int day = Integer.parseInt(dateInput.substring(0,2));      int month = Integer.parseInt(dateInput.substring(3,5));      int year = Integer.parseInt(dateInput.substring(6,10));      MyDate myDate = new MyDate(day, month, year);      MyCalendarOne calendar = new MyCalendarOne();      calendar.printCalendar();   }  /*public MyDate myDate() {     return; }  public Day dayOfWeek() {      return; }  public int weekOfMonth() {     return; } */  public void printCalendar() {     System.out.println(myDate.getDay());     System.out.println(myDate.getMonth());     System.out.println(myDate.getYear());  } }  class MyDate { private int day; private int month; private int year;  public MyDate(int day, int month, int year) {     this.day = day;     this.month = month;     this.year = year; }  public int getDay() {      return day; }  public int getMonth() {     return month; }  public int getYear() {     return year; }  public boolean isDateValid() {     return true; } }   I simply expected it to print out the day, month, and year. However, I got this error back:  java MyCalendarOne 01/01/2011 Exception in thread "main" java.lang.NullPointerException     at MyCalendarOne.printCalendar(MyCalendarOne.java:45)     at MyCalendarOne.main(MyCalendarOne.java:22)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


So I've gone through this , and in my primitive understanding I assume we do log transformation when we 'care' about relative changes and also to even out the positive skweness from our data. So for example let's imagine having a dataset as follows:    Quantity  Area  TotalSF  Year  Price     7     1710   856     2003  321510     6     1262   1262    1976  183190     7     1786   920     2001  228410     7     1717   756     1915  171230     8     2198   1145    2000  201000   After log transforming 'Area', 'Price' and 'TotalSF' the respective plots shows nice normal distribution. The log transformed data looks something like this:     Quantity  Area     TotalSF     Year  Price     7    7.444249   6.752270    2003  18.34     6    7.140453   7.140453    1976  17.75     7    7.487734   6.824374    2001  17.92     7    7.448334   6.628041    1915  17.43     8    7.695303   7.043160    2000  18.12   My questions are:     Are we going to train our model on this log transformed data ? If yes, then do we need to log transform our test data as well ? How do we get back the normal/actual values, say for the variable 'Price', after log transforming it ?   Edit: This question specifically asks for suggestions whether to train a model based on log transformed data or not, and how to get the actual values back - more of a beginner-friendly question. The  that's used to flag this question as a duplicate on the other hand asks whether it is valid to back transform or not. That's a completely different premise, I believe.

I'm fitting a regression on the $\log(y)$.  Is it valid to back transform point estimates (and confidence/prediction intervals) by exponentiation?  I don't believe so, since $E[f(X)] \ne f(E[X])$ but wanted other's opinions.  My example below shows conflicts with back transforming (.239 vs .219).  set.seed(123)  a=-5 b=2  x=runif(100,0,1) y=exp(a*x+b+rnorm(100,0,.2)) # plot(x,y)  ### NLS Fit f <- function(x,a,b) {exp(a*x+b)}  fit <- nls(y ~ exp(a*x+b),  start = c(a=-10, b=15))  co=coef(fit) # curve(f(x=x, a=co[1], b=co[2]), add = TRUE,col=2,lwd=1.2)  predict(fit,newdata=data.frame(x=.7)) [1] 0.2393773  ### LM Fit # plot(x,log(y)) # abline(lm(log(y)~x),col=2) fit=lm(log(y)~x) temp=predict(fit,newdata=data.frame(x=.7),interval='prediction') exp(temp)         fit       lwr       upr 1 0.2199471 0.1492762 0.3240752


I used the Windows install for Ubuntu today, it all installed easily and automatically but I could not go on the Internet. Please tell me how to solve this problem.   I think it was "Ubuntu Desktop 12.04 LTS" but I'm not sure, I did it today, 8th of June 2012. I am using the HP Mini 110 1199EA.  It says 'firmware not found' or something like that. What is firmware and why isn't it found?  My wireless device seems to be called "Broadcom 802.11b/g WLAN" does that make any sense?

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


I am going through POI Excel tutorial on you tube. when I executed following code I get NullPointer exception. Plz suggest the ans.  Thanku.  package main;  import entities.*; import dao.*; import java.util.*; import org.apache.poi.hssf.usermodel.*; import org.apache.poi.hssf.util.*; import org.apache.poi.ss.usermodel.*; import org.apache.poi.ss.util.*; import java.io.*;   public class Main {      public static void main(String[] args) {         // TODO Auto-generated method stub         try{             ProductModel pmodel = new ProductModel();             HSSFWorkbook workbook= new HSSFWorkbook();             HSSFSheet sheet=workbook.createSheet("List Products");             //create heading             Row rowHeading = sheet.createRow(0);             rowHeading.createCell(1).setCellValue("Id");             rowHeading.createCell(2).setCellValue("Name");             rowHeading.createCell(3).setCellValue("Creation Date");             rowHeading.createCell(4).setCellValue("Price");             rowHeading.createCell(5).setCellValue("Sub Total");              for(int i=0;i<6;i++)             {                 CellStyle stylerowHeading= workbook.createCellStyle();                 Font font = workbook.createFont();                 font.setBold(true);                 font.setFontName(HSSFFont.FONT_ARIAL);                 font.setFontHeightInPoints((short)11);                 stylerowHeading.setFont(font);                 stylerowHeading.setVerticalAlignment(CellStyle.ALIGN_CENTER);                 rowHeading.getCell(i).setCellStyle(stylerowHeading);              }              //save to excel             FileOutputStream out =                       new FileOutputStream("D:\\AVIATE\\excel\\listproducts.xls");             workbook.write(out);             out.close();             System.out.println("Excel written successfully........");          }catch(Exception e){             System.out.println("exception");             e.printStackTrace();         }     }  }


I use rsync for backing up the data from servers to a backup machine. For that purpose I start bash scripts via cronjobs but one of them is not working. I searched through the web to see if there is a solution but I couldn't find one, so I thought it'd be a good idea to post it here.  #!/bin/bash  KDIR=/usr/cron LOCKDIR=$KDIR/lockdir LOCKFILE=$LOCKDIR/filename.lock if [ -f $LOCKFILE ] then     exit 0; fi touch $LOCKFILE RSYNC_PASSWORD=<passwd> rsync -vvv --delete -aW --old-compress \   --compress-level=4 \   rsync://rsyncod@XXX.XXX.XXX.XXX/Directory1/Subdirectory1 \   /STORAGEDIRECTORY/storagesubdirectory  rm -rf $LOCKFILE   and the error i got:  @ERROR: Unknown module 'home' rsync error: error starting client-server protocol (code 5) at main.c(1635) [Receiver=3.1.1]   oh, the dir I want to backup is a subdirectory to /home/

Is it possible to name the full path to source directory in rsync command instead of the name of the module?  For example:  rsync -av rsync://10.171.73.23/home/user/work/tests .   instead of:  rsync -av rsync://10.171.73.23/ftp/work/tests .   (ftp is a module from /etc/rsyncd.conf)   When trying the first version I get @ERROR: Unknown module 'home'


Everyone has been so nice but never answered my questioned. Can I have a double gfci coming from a panel to a double gang box in a laundry room using line side only nec approved? Why? Because I want both to be independent in case one shuts down and doesn't affect the other.

Cam I have two GFCIs connected to one double gang box in my laundry room and if so can I do a single line connection so that they both can work independently?  I have a 12/2 going from the panel through conduit (copper wire) to the double gang box. I want to have each GFCI to run independently without using the load. Why, in case one shuts off the other isn't affected. the double gang box is standard. the device is a Leviton 20 amps. I was told that you can run 12/2 from the panel to the first GFCI black and white. Then connect the second GFCI using a jumper and attaching it to he second GFCI. Is this acceptable by code. we use a washer,dryer in the laundry and the garage heavy machinery. so why should this be a problem running two independent?


when I run command dd if=/dev/random count=1 bs=32 I get some random junk binary data but after receiving them, there is still some characters (as I see always 1;2c) after termination of dd process. [amirreza@localhost ~]$ dd if=/dev/random count=1 bs=32 ¾¿܄ÌYLÔAëEÔr/f&-È<>ýø1+0 records in 1+0 records out 32 bytes copied, 3.5878e-05 s, 892 kB/s ^[[?1;2c[amirreza@localhost ~]$ 1;2c  what is this character and why it's thrown after the termination of dd ?

This appears to be an easy concept, but I'm having difficulty finding out what is going on via Google:  I have a binary file generated by a C program, example_binary.   After using cat example_binary, the output looks like a typical output after running cat on a compressed file.   However, after cat has finished, letters and numbers remain on the command line. In this case, I see 1;2c.   $ cat example_binary ... $ 1;2c   Why would there be leftover numbers and letters remaining on the command line? What does 1;2c mean?


There are times where I want, say, a superscript $t$ to the left of another letter to denote, say, the transpose of a matrix. Or, I might want to decorate a letter on the left with a prime, $'$, because the right side is busy being decorated by another letter. Right now I use, $\left.^t M\right.$ and $\left.'E^r\right.$ which is inadequate because it introduces white spaces. How do I deal with this?

I know how to write a usual index with the help of the underscore, but I seem to be unable to find out how to write an (upper/lower) index in front of a letter/text.  These kind of indices are common in chemistry.


Okay so someone put a bounty of $201336200 on me. If I never get killed what will happen with the money? Will I get the money or will the bounty stay on me?

Is it possible to shake off a bounty in GTA Online?   If so, how?


I've got an 16GB SD card with Raspbian on it.  $ lsb_release -a No LSB modules are available. Distributor ID: Raspbian Description:    Raspbian GNU/Linux 8.0 (jessie) Release:    8.0 Codename:   jessie   There are (as usual) two partitions on the device. The boot partition and the root partition. The root partition uses almost all the space.  $ sudo fdisk -l /dev/mmcblk0   Disk /dev/mmcblk0: 14.6 GiB, 15640559616 bytes, 30547968 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x4ae87cfb  Device         Boot  Start      End  Sectors  Size Id Type /dev/mmcblk0p1      204800   729087   524288  256M  c W95 FAT32 (LBA) /dev/mmcblk0p2      729088 30547967 29818880 14.2G 83 Linux   But the filesystem only uses something around 7GB of this partition:  $ df -T / Filesystem     Type 1K-blocks    Used Available Use% Mounted on /dev/root      ext4   7155064 5881840    893372  87% / $  df -Th /    Filesystem     Type  Size  Used Avail Use% Mounted on /dev/root      ext4  6.9G  5.7G  873M  87% /   The Problem  For some reason resize2fs denies to resize the filesystem on-line to the partitions size:  $ sudo resize2fs /dev/mmcblk0p2  resize2fs 1.43.3 (04-Sep-2016) Filesystem at /dev/mmcblk0p2 is mounted on /; on-line resizing required old_desc_blocks = 1, new_desc_blocks = 1 resize2fs: Permission denied to resize filesystem   Any ideas, what the reason could be?

Im attempting to resize a filesystem on a mulipathed volume that I've grown, rescanned all the disks, and resized the multipath map.  # resize2fs /dev/mapper/my_vol  resize2fs 1.43-WIP (20-Jun-2013) Filesystem at /dev/mapper/my_vol is mounted on /var/lib/myvol; on-line resizing required old_desc_blocks = 6, new_desc_blocks = 12 resize2fs: Permission denied to resize filesystem    # strace -f resize2fs /dev/mapper/my_vol (finishes with) ....snip....  write(1, "Filesystem at /dev/mapper/my_vol"..., 101Filesystem at /dev/mapper/my_vol is mounted on /var/lib/myvol; on-line resizing required ) = 101 write(1, "old_desc_blocks = 6, new_desc_bl"..., 42old_desc_blocks = 6, new_desc_blocks = 12 ) = 42 access("/sys/fs/ext4/features/meta_bg_resize", R_OK) = 0 open("/var/lib/my_vol", O_RDONLY) = 4 ioctl(4, 0x40086610, 0x7fffb729c2e8)    = -1 EPERM (Operation not permitted) write(2, "resize2fs", 9resize2fs)                = 9 write(2, ": ", 2: )                       = 2 write(2, "Permission denied to resize file"..., 38Permission denied to resize filesystem) = 38 ioctl(2, SNDCTL_TMR_TIMEBASE or TCGETS, {B38400 opost isig icanon echo ...}) = 0 ioctl(2, SNDCTL_TMR_TIMEBASE or TCGETS, {B38400 opost isig icanon echo ...}) = 0  write(2, "\n", 1 )                       = 1 exit_group(1)                           = ?   I would like to keep this server up as it hosts many virtual machines, and I've not experienced permission denied when running a resizefs as root before, what could be denying root a simple resize? Any help greatly appreciated.   The server has selinux disabled, and the multipath -ll shows the volume in a read-write state. (wp=rw)  myvol (3600c0ff00013d24d8c20725301000000) dm-12 HP,P2000 G3 iSCSI size=186G features='1 queue_if_no_path' hwhandler='0' wp=rw   I have noticed that ls -ld on the mount point shows  drwxr-xr-x  5 root root 4096 Jan 27 12:49 myvol   and not  drwxr-xr-x. 5 root root 4096 Jan 27 12:49 myvol  #ls -Zd myvol drwxr-xr-x root root ?                                myvol   Related?


String [] P = K.split(" "); //NB: the value of K is "malaria zika AIDS"   for (int x=0;x< P.length; x++)     {        if (P[x]=="zika")            {              System.out.println( "This is zika virus P[x]="+ P[x]);                 }else{            System.out.println( "This is NOT zika virus P[x]="+P[x]);            }    }   Expecting  This is NOT zika virus P[x]=Malaria This is zika virus P[x]=zika This is NOT zika virus P[x]=AIDS   But Getting  This is NOT zika virus P[x]=Malaria This is NOT zika virus P[x]=zika This is NOT zika virus P[x]=AIDS   What am I missing? I believe that this is the part with the problem. if (P[x]=="zika")

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Company Director with a MacBook Air and she's having problems attaching pages files and PDF's to her e-mails. Mail keep embedding them into the message window so she cannot type, or see what she's typed in the window. Many times recipients of her messages say they are missing some of the attachments she thinks she has attached.  How can I turn off the embedding of any attachments into the message body and just displaying them as a 'file' icon somewhere rather than the contents?

Is it possible to turn off automatic preview of attachments when composing an e-mail?  NOTE: Yes I know that I can manually ctr+select the attachment and disable preview, but I want this done automatically