I am new in Ubuntu`s world.  I wrote lspci and the output I received was;  06:00.0 Network controller: Broadcom Corporation BCM43142 802.11b/g/n (rev 01)  07:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI Express Fast Ethernet controller (rev 07)   I have also wrote sudo rfkill list and the output was;  0: phy0: Wireless LAN  Soft blocked: no  Hard blocked: no  1: brcmwl-0: Wireless LAN  Soft blocked: no  Hard blocked: no  2: hci0: Bluetooth  Soft blocked: no  Hard blocked: no

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.


Can someone please explain wave particle duality for large bodies? Why don't large bodies exhibit wave like nature for example if I am walking with some momentum, the wavelength associated with me is $h/p$ what does this mean?

Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc.  For instance, this example, taken from a textbook:     Calculate the de Broglie wavelength for      (a) a proton of kinetic energy 70 MeV      (b) a 100 g bullet moving at 900 m/s   The pedagogical motivation behind these questions is obvious: when the de Broglie wavelength is small compared to the size of an object, the wave behaviour of the object is undetectable.  But what is the validity of the actual approach of applying the formula naively? Of course, a 100g bullet is not a fundamental object of 100g but a lattice of some $10^{23}$ atoms bound by the electromagnetic force. But is the naive answer close to the actual one (i.e. within an order of magnitude or two)? How does one even calculate the de Broglie wavelength for a many body system accurately?


Sorry for the poorly written question, but I'm panicking right now.  I accidentally mv prefix* instead of mv prefix* target_dir/  Now, there's only one prefix file left. Have I killed them? If so how/why? Is it possible to recover the files?

I did this on the command line (Ubuntu 12.04 , ext4)  mv some_arbit_file required_file   Is there any way I can recover required_file? I had put so much work into this. I usually backup files but I forgot this time.


I am attempting to write out the basic process for finding the absolute value of some number.  In ASCII, this is what I am attempting to write.  |X| = {         x  if x > 0         0  if x = 0         -x if x < 0       }   This is what I have so far.  \begin{equation} \left|x\right| = \biggl\{ x\ if\ x > 0 \biggr\} \end{equation}   I cannot figure out how to add the vertical spacing to allow the other two lines.

I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex?


Why does RSA use semiprime numbers? Why not just use any big number ??  What is the advantage of the two original numbers being  prime?  Because factoring any big number will be difficult

I am just learning about the RSA algorithm. Looking at the first two steps:   Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$.    I have some probably stupid questions:   Why do $p$ and $q$ have to be prime numbers? Why couldn't they be any integers or odd integers? Or does that break the whole algorithm? Because prime numbers are rare in comparison to regular integers, does restricting the algorithm to only prime numbers reduce security? It would seem easier to find the private key if an attacker knows it's only going to be some prime number?


I want to be able to do this only with the keyboard.

I want to not have to use the mouse to create Spaces. I want to use the keyboard for that.


When I hover the arrow near my name in stackoverflow, used to open the points bar(not the correct word to refer).  But now it is not getting loaded(around 30 mins).    I guess, since they are working on SQL server issues.  Just to let you know.  EDIT: I got back my "reputation summary popup" But there are some alignment issues within it. See this screenshot

For some reason, the profile-hover view thingy is not loading at all(on Stackoverflow). I initially thought that it might be because of , but its been closed with the status, no-repro. Also, this is now persisting for the past 1 hour for me.  I tried to clear the cache and stuffs but nothing seems to be working, as the hover view is still not loading. Is this some sort of  or an issue with the browser? I'm using Firefox 25.0.1 on Win7 Pro(x86) machine. Here is a snapshot of it.


We have a house from the 1960s with armored cable and metal boxes.  I was trying to replace the outlets and a switch in the kitchen so they weren't almond/painted but the new outlets and switch keep causing the breaker to pop. I put the old one back and everything works fine again.  Is there something I am missing on old vs new outlets

I purchased a Hubbell "USB Dual Port Charger with 15A Duplex Receptacle" from Lowes to replace the duplex receptacle on my kitchen island.  I first opened the circuit labelled for the island.  The breaker takes two slots.  I removed the existing receptacle and noticed that the brass screws had a black and red wire.  The bridge between the screws was not broken.  I connected the new USB charging receptacle as: white wire to silver screw, bare to green screw, and the black and red wires to the brass screw.  I put everything back together.  When I closed the circuit the fuse blew as well as tripping the mains to the house.  I took the receptacle out of the metal gang box to ensure that it wasn't touching.  I verified the connections as stated above.  With the receptacle hanging outside of the gang box I closed the breaker only to have it and the mains trip.  I reconnected the old simple receptacle and closed the breaker with no problems.  I tried with just the black wire in the new receptacle and it worked!  But now I can't connect the new receptacle with this new red wire.  I researched the uses of the red wire however none of them seem to apply to my kitchen.  The fuse box lists the island as the only part to control and nothing else in the kitchen turned off when I opened the circuit.  There is only one receptacle on the island and no other electrical items including lights.  Why would the kitchen island of only one receptacle require both black and red? why would this USB charger receptacle be so sensitive to two hot wires? why would this single outlet require such a large breaker switch?  And finally... is there anything I can do so that I can install this receptacle?  Thanks!


The title conveys my true question, but for the sake of clarity I will now rephrase it in a more mathematical flavor using the Hamiltonian formalism of classical mechanics and the terminology of differential geometry, including  and the  $d$.  Consider a physical system with configuration space $M$, a manifold. Its phase space is the cotangent bundle $T^*M$, consisting of (position, momenta) pairs. There is a  $\theta$ on $T^*M$ turning it into a symplectic manifold $(T^*M,-d\theta)$. Any function $H\colon T^*M\to \mathbb R$ may be regarded as a Hamiltonian. From $H$, the dynamics are given by the flow lines of the  $X_H$, defined to be the unique vector field satisfying $ dH(Y)=d\theta(Y,X_H) $ for all vector fields $Y$ on $M$. Moreover, the action is simply $S=\theta(X_H)$.  Since the dynamics are given by a vector field on the cotangent bundle, only two derivatives can appear in the ; since any classical system can be put in the Hamiltonian formalism, it appears that the equations of motion of any classical system can involve only the first two derivatives (equivalently, $F=ma$ where $F$ is a function of position and velocity).  However, there seems to be no mathematical reason for this limitation; certainly one can write down equations involving $3$ or more derivatives - so what makes them unable to appear in the laws of a classical system?  Phrased more mathematically, instead of starting with $T^*M$ (which can be thought of as the space of first order Taylor expansions to functions on $M$) we can start with the  $J^r(M)$, where $J^0(M)=M$ and $J^1(M)=T^*M$ and in general $J^r(M)$ consists of the $r^{th}$ order Taylor expansions to functions on $M$. For any $r\geq 1$, the jet manifold $J^r(M)$ carries a tautological $1$-form $\theta$ which is defined in a similar way as the tautological $1$-form on $T^*M$; in local coordinates $\bigl(p^{(0)},p^{(1)},\ldots,p^{(r)}\bigr)$ which describe curves $f\colon \mathbb R\to M$ with Taylor expansion $$ f(t)=p^{(0)}+tp^{(1)}+\cdots+t^rp^{(r)}+O\bigl(p^{(r+1)}\bigr), $$ the tautological $1$-form on $J^r(M)$ is given by $$ \theta\bigl(p^{(0)},p^{(1)},\ldots,p^{(r)}\bigr)=p^{(1)}_i dp^{(0)\ i}+\cdots+p^{(r)}_i dp^{(r-1)\ i}. $$ Exactly as before, we get a symplectic manifold $\bigl(J^r(M),-d\theta\bigr)$. Any function $H\colon J^r(M)\to\mathbb R$ may be thought of as a Hamiltonian, giving rise to a Hamiltonian vector field $X_H$ on $J^r(M)$ and thus to dynamics of a physical system.  Question.  Why does classical mechanics stop at $r=1$ and have no need for higher order terms in the Taylor expansion? Alternatively, are there physical systems in which higher order derivatives do arise and thus require some modification (e.g. the one given above) to the Hamiltonian formalism?

What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations?    If someone on the street would flat out ask me that question, then I'd probably mumble something about physicists wanting to be able to use the Lagrangian approach. And to allow a positive rotation and translation invariant energy term, which allows for local propagation, you need something like $-\phi\Delta\phi$.  I assume the answer goes in this direction, but I can't really justify why more complex terms in the Lagrangian are not allowed or why higher orders are a physical problem. Even if these require more initial data, I don't see the a priori problem.  Furthermore you could come up with quantities in the spirit of $F\wedge F$ and $F \wedge *F$ and okay yes... maybe any made up scalar just doesn't describe physics or misses valuable symmetries. On there other hand in the whole renormalization business, they seem to be allowed to use lots and lots of terms in their Lagrangians. And if I understand correctly, supersymmetry theory is basically a method of introducing new Lagrangian densities too.   Do we know the limit for making up these objects? What is the fundamental justification for order two?


I am writing a JSF 2.2 project on Eclipse Neon. I have two arraylists; one is fetched from group of checkboxes that are checked by the user(arrayList1) and the other one is fetched from keywords that are entered into chips component(arrayList2) by user inside .xhtml page. What I need to do is I have to combine those two arraylists.  The problem is when I leave chips empty, arraylist2 returns null while arraylist1 returns empty string when I leave the boxes unchecked as well. So I think the problem is related to else if (lengthlist1 > 0 && arrayList2.size() == 0) part because all the other cases functioning well. If check the checkboxes and leave the chips component empty and then run the code, I get the following error:     Caused by: java.lang.NullPointerException   Again, all the other if - else statements are working fine.  I basically have 4 cases:      private String wordx;     private List<String> arrayList1;     private List<String> arrayList2;      public void arrayList2List() {              arrayList2 = new ArrayList<String>();         }          public void concatenate() throws IOException {                  int lengthlist1 = arrayList1.size();                 int lengthlist2 = arrayList2.size();                  ArrayList<String> concat = null;                  if (lengthlist2 > 0 && lengthlist1 > 0) {                     concat = new ArrayList<>(lengthlist1 + lengthlist2);                      for (int i = 0; i < lengthlist1; i++) {                         concat.add(arrayList1.get(i) + And + wordx);                          for (int l = 0; l < lengthlist2; l++) {                             concat.add(arrayList2.get(l) + And + wordx);                         }                     }                    } else if (lengthlist1 > 0 && arrayList2.size() == 0) { /* I think problem occurs here, when I leave checkboxes list empty */                     concat = new ArrayList<>(lengthlist1);                     for (int k = 0; k < lengthlist1; k++) {                         concat.add(arrayList1.get(k) + And + wordx);                     }                  } else if (lengthlist1 <= 0 && lengthlist2 > 0) {                     concat = new ArrayList<>(lengthlist2);                     for (int m = 0; m < lengthlist2; m++) {                         concat.add(arrayList2.get(m) + And + wordx);                     }                  } else {                     TODO:do something else                 }                 for (int j = 0; j < concat.size(); j++) {                     Search(concat.get(j));                 }              }   Can someone explain the root cause of the error? Where do I go wrong? All help will be appreciated.

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?


I have multiple tables in my thesis with model results. I want to change these tables' names, meaning it wouldn't say Table 1 but Model 1 (also when referencing them). Also, a special table of content for them would be nice.  I get the model output as a .tex-file and include it with \input:  \begin{table}[htbp]     \caption{Example Model}     \label{model:example_model}     \input{../models/example} \end{table}   Is this easily doable? I've searched a bit for this, but to be honest: I don't really know what to look for.  Any hint is appreciated! Thanks in advance!  Edit: I also have other tables in my document, so I assume that changing the whole table-class is not an option.

I am writing my PhD thesis. In my manuscript I have Figures in the text and Photographic plates (a figure of figures) in the annexes. The two elements are different and I would like create a new environment of Plate that follows the same structure of the Figure environment. Where can I find the Figure environment to modify it?  The new environment table should have exactly the same structure than the figure environment but replacing the word figure by the word Planche (in French).


I just recently bought tickets to travel from Mexicali to Guadalajara. However, I am a US Citizen and I live in the US. I am just crossing the border by foot, and catching a flight in Mexico to go to GDL (since they're why cheaper in Mexico) However, do I need some type of Mexican paperwork indicating I am traveling within Mexico? Or can I just use my American Identification to board the flight?

Does a US citizen traveling by plane in Mexico (international flight), for example from Mexicali to Mexico City need to have a passport?


When creating connection(s) between application client and application server via SSH dynamic port forwarding by ssh -D, how is SOCKS protocol used? Is SOCKS used as a protocol for communication   between application client and SSH client,  or between SSH client and SSH server,  or between SSH server and application server?  Once an application client is connected to an application server by SSH dynamic port forwarding, the SSH client and server are often said to “get out of the way”. Does it mean that SSH protocol is not in use now? What protocols are still in use, for example, is SOCKS and/or SSH still? is the communication between the application client and application server still encapsulated inside (so secured by) the SSH protocol?   Thanks.

Dynamic port forwarding using SSH uses SOCKS protocol. How does SSH know where a request wants to go? For example if the request is a HTTP request, SSH doesn't understand HTTP, so where  does it find out where the HTTP request wants to go? Thanks.


I have to defined a function called float_range(start,stop,step). It works the same as a built in function only it can accept float values too.For the content I am not to use the range function at all and I am to assume start, stop and step are integer or float numbers. The problem I am having with my code, is I believe to have created a infinite loop  in one of the while loops and its not passing all the test cases. Some of the examples are float_range(0,1.0,.25) and should count out from 0 to 1 in a list as [0,0.25,.5,.75] or float_range(0,0.25,-1) this would not work because its never true so it would return a empty list. I need help making in finding that infinite loop I created and also passing these test cases.  def float_range(start,stop,step):    range_list = [start]    Value = start    while Value != stop:        if start < stop:          while Value < stop:             Value += step             range_list.append(Value)          return range_list[:-1]       elif start > stop:          while Value > stop:             Value += step             range_list.append(Value)          return range_list[:-1]

Is there a way to step between 0 and 1 by 0.1?   I thought I could do it like the following, but it failed:  for i in range(0, 1, 0.1):     print i   Instead, it says that the step argument cannot be zero, which I did not expect.


I'm reading Øksendal's SDEs book and in Theorem 3.2.5 he proves that the Itô integral  $$ \int_0^t f(s,\omega) dB_s(\omega)$$ has a version such that it is $t$-continous. In order to do this he picks elementary functions $\phi_n$, such that $$ E[\int_0^T (f-\phi_n)^2 dt]\rightarrow 0$$ as $n$ tends to infinity. Then he defines $I_n(t,\omega)=\int_0^t \phi_n(s,\omega)dB_s(\omega)$ and states that $I(\cdot,\omega)$ is continous for all $n$. This is crucial to apply Doob's martingale inequality later and gives the statement without proof, but this doesn't seem trivial to me. My question is, why should be the Itô integral $I_n(t,\omega)$ be continous at all? Aren't there going to be jumps as we increase $t$ and more addends appear in the integral?

Let $B_t$ be a 1-dimensional Brownian motion. I am following  by Bernt Øksendal. On the page 32 (it is displayed in the link I've put) there is a proof of existence of continuous version of the Ito integral. There is stated that for a function $$ \phi_n(t,\omega) = \sum\limits_j e_j(\omega)\cdot 1_{[t_j,t_{j+1})}(t) $$ its integral $$ I_n(t,\omega) = \int\limits_0^t\phi_n(s,\omega)dB_s(\omega) $$ is continuous in $t$.  From what I seen, I think that $$ I_n(t,\omega) = \sum\limits_{t_j\leq t}e_j(\omega)(B_{t_{j+1}} - B_{t_j}) $$ which does have jumps. So I wonder, how can it be continuous in $t$.


I know that this question has been answered back in 2012. But is the answer still valid as of today - 2019?

I am being flown out by a company for an on-site visit. Will I earn miles for this trip, or will the company?


In Trailhead we have the query to get the Contacts for the Account named "SFDC Computing", with an inner query.   SELECT Name, (SELECT LastName FROM Contacts) FROM Account WHERE Name = 'SFDC Computing'   It works fine for my purposes.  "Contacts" is the name of the relationship, per Trailhead. So, I went to Object Manager and examined the Account object's "Fields and Relationships". There is nothing named "Contacts"!   In general, how do I get the name of the relationship, for use in similar SOQL queries?

I have a many-to many relationship between three objects. LGFProducts, PartsinProducts, and Parts. PartsinProducts is the junction object. I want to be able to get data like the names of the parts that are related to the selected LGFProduct.   I understand that parent-child relationship can only traverse one level down while grandchild-grandpa can travel 5 levels at most. What is the parent-child or child-parent in a many-to-many relationship?  I assumed that I should be traversing upwards from Parts to the junction object partsinproduct and then LGFProducts? But my friend who is not a Salesforce expert but has knowledge in CS said that I should do a parent-child query (of LGFProducts to partsinproduct) to child-parent relationship query (PartsinProduct to Parts). Or perhaps both of these options are wrong and another is appropriate.   Also, I am having a little trouble traversing for custom objects. I understand that I need to append the letter r instead of c but get confused. For example, this is my attempt at a three level upward traversal that fails.   SELECT Id, Name, Parts__r.PartsinProducts__r,LGFProducts__r.Name FROM Parts__c   Also if three levels of upward traversal are needed, could one provide an example with custom relationships? As seen above, I am having difficulty successfully querying a three level upward traversal statement for custom objects.  This is my attempt at the parent-child relationship query of LGFProduct to PartsinProducts:  SELECT Name,   (     SELECT Name     FROM PartsinProduct__r   ) FROM LGFProduct__c    I am then given this error:


Can I take your umbrella I haven't brought mine with ... .     1.me      2.mine      3.my      4.myself   It is clear that 2 and 3 are false but I doubt between 1 and 4.I think I have heared the first one but the forth one seems OK.So what is the right answer?

Myself is used as the object of a reflexive verb (“I hurt myself”), as an intensifier (“I myself will go”), and can be used in  (“for my wife and myself it was a happy time”)  What are the similarities and differences between the following?  worsens my confusion.  1. For me it was a happy time. 2. For myself it was a happy time.  I am guessing that in 1, me is an object pronoun, and in 2, myself  is , but this link states:  While English intensive pronouns (e.g. myself, yourself, himself, ourselves, yourselves, themselves) use the same form as reflexive pronouns, an intensive pronoun is different from a reflexive, because the pronoun can be removed without altering the meaning of the sentence.  Yet in 2, 'myself' CAN'T be removed? Obiter dictum: Here's another link on .


For processes with a lot of output or error, trying to redirect standard output and error with a simple  string output = process.StandardOutput.ReadToEnd(); string err = process.StandardError.ReadToEnd(); process.WaitForExit();   will cause the program to hang, and never actually finish.

I have the following code: info = new System.Diagnostics.ProcessStartInfo("TheProgram.exe", String.Join(" ", args)); info.CreateNoWindow = true; info.WindowStyle = System.Diagnostics.ProcessWindowStyle.Hidden; info.RedirectStandardOutput = true; info.UseShellExecute = false; System.Diagnostics.Process p = System.Diagnostics.Process.Start(info); p.WaitForExit(); Console.WriteLine(p.StandardOutput.ReadToEnd()); //need the StandardOutput contents  I know that the output from the process I am starting is around 7MB long. Running it in the Windows console works fine. Unfortunately programmatically this hangs indefinitely at WaitForExit. Note also this code does NOT hang for smaller outputs (like 3KB). Is it possible that the internal StandardOutput in ProcessStartInfo can't buffer 7MB? If so, what should I do instead? If not, what am I doing wrong?


When I update, after some file downloads it shows the below errors.  What should I do now?  W:Failed to fetch cdrom://Ubuntu 14.04.3 LTS _Trusty Tahr_ - Beta amd64 (20150805)/dists/trusty/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs , W:Failed to fetch cdrom://Ubuntu 14.04.3 LTS _Trusty Tahr_ - Beta amd64 (20150805)/dists/trusty/restricted/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs , W:Failed to fetch cdrom://Ubuntu 14.04.3 LTS _Trusty Tahr_ - Beta amd64 (20150805)/dists/trusty/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs , W:Failed to fetch cdrom://Ubuntu 14.04.3 LTS _Trusty Tahr_ - Beta amd64 (20150805)/dists/trusty/restricted/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs , E:Some index files failed to download. They have been ignored, or old ones used instead.

When updating I got this error message:  W:Failed to fetch cdrom://Ubuntu 11.10 _Oneiric Ocelot_ - Release amd64 (20111012)/dists/oneiric/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs W:Failed to fetch http://ppa.launchpad.net/synce/ubuntu/dists/your_ubuntu_version/main/source/Sources  404  Not Found   What to do?


Not sure if this has been asked before, did some digging.  I'm trying to prepare for a few interviews, and I was just curious to see if how Java implements its data structures (arraylist, map), etc is public.

I want to have a look at how Java implements LinkedList. Where should I go to look at the source code?


Is there any case in which volatile is useful in the context of single-threaded programming? I know it's used to make sure the value of the variable is always actually checked in memory so is there any case in which that value may change (in a ST app) in a way that the app/compiler won't notice?

Can anyone provide a good explanation of the volatile keyword in C#? Which problems does it solve and which it doesn't? In which cases will it save me the use of locking?


package temperatureconversion; import java.util.Scanner; public static void main(String[] args) { Scanner keyboard = new Scanner(System.in); System.out.println("Please enter Conversion type: Press C for Celsius to Fahrenheit or press F     For Fahrenheit to Celsius.");   String Vctype = keyboard.next();      if (Vctype == "f" || Vctype == "F"){         System.out.println("Please enter fahrenheit");         double Vfahrenheit = keyboard.nextInt();         Vfahrenheit = (Vfahrenheit)*(9/5)+(32);             System.out.println(Vfahrenheit);     }     if (Vctype == "c" || Vctype == "C"){         System.out.println("Please enter celcius");         double Vcelcius = keyboard.nextInt();         Vcelcius = (Vcelcius - 32)*(5/9);                System.out.println(Vcelcius) ;     }           }    }   Hello guys I was wondering if anyone could help me with the above code. Basically in the output console in netbeans the program just seems to end after I hit C or F, but instead it should ask for a number then allow a number input, then calculate and finally display the calculation. It doesn't seem to be executing the if statements Where am I going wrong?

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?


IMO 1988 question No. 6  I have a confusion in the question.The question is as follows:     $a$ and $b$ are positive integers and $ab+1$ is a factor of $a^2+b^2$. Prove that $\displaystyle\frac{a^2+b^2}{ab+1}$ is a perfect square.   My confusion: According to me, $a$ and $b$ have only one value ie $a=b=1$. What are the other possible values of $a$ and $b$?

Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English.


For this sequence:  $a_1 = 2~~~a_2 =7$  and $a_{n+1} =  \frac{1}{2}\cdot(a_{n} + a_{n-1})$  The questions asks to find the exact formula for the $n$th term of the sequence and hence find the limit as $n \to \infty$   They also gave us this formulae: , I am not particularly sure how to use them though.  Anyways I tried listing out more terms and I found that  $a_3 = \frac{9}{2} ~~~ a_4 = \frac{23}{4}$  And I found out the difference between these terms is $5,\frac{5}{2},\frac{5}{4}$ thus we can write $a_{n+1}=a_{n} + \frac{5}{2^{n-1}}$  I am not sure how to continue though.

The problem is the following: suppose $s_1>s_2>0$ and let $s_{n+1}=\frac{1}{2} (s_n+s_{n-1})$ for $n\geq 2$. Show that ($s_n$) converges.  Now, here is what I figured out:   $s_2<s_4$: Base Case for induction that $s_{2n}$ is an increasing sequence. Assume $s_{2n-2}<s_{2n}$. Induction step: $s_{2n}<s_{2n+2}$ $s_1>s_3$: Base Case for induction that $s_{2n-1}$ is a decreasing sequence. Assume $s_{2n-1}<s_{2n-3}$. Induction step: $s_{2n+1}<s_{2n-1}$.   I have proved those two. However arguing in favor of convergence has me going around in circles. Since $s_1>s_2$ and (as discovered during the formulation of Base Cases) $s_3>s_4$, I figured it might be a good idea ot assume that if every odd member of the original sequence ($s_n$) is greater than the following even member, then the limit would be somewhere in between, the two (odd and even) sequences won't cross. Hence the upper and lower bounds would be $s_1$ and $s_2$ respectively. Here is how I approach this:   Assume $s_{2n-1}>s_{2n}$ Show that $s_{2n+1}>s_{2n+2}$   The proof as I mentioned has me running in circles. Any assistance?


In Microsoft DNS, I'm trying to setup a simple DNS Alias (CNAME) pointing from domain.com to www.domain.com. I also want to forward www.domain.com to a specific IP. In other words, I want to do something like this:  www.example.com. IN A 192.168.3.44 example.com. IN CNAME www.example.com.   When adding the CNAME I get the following Error:  "A new Record cannot be created. An alias (CNAME) record cannot be added to this DNS name. The DNS name conatins records that are incompatible with the CNAME record."  Why doesn't this work and how can I fix it?

I need to create an NS record for a domain that is a CNAME, for the purpose of having two domains pointed at one IP, and not having to maintain the current IP address in two different places.  The DNS provider for this domain is DynDNS, but they block this operation:     CNAME cannot be created with label   that is equal to zone name   I can do this with another domain whose DNS is served by 1and1:  root@srv-ubuntu:~# dig myseconddomain.co.uk  ; <<>> DiG 9.4.2-P1 <<>> myseconddomain.co.uk ;; global options:  printcmd ;; Got answer: ;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 61795 ;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 0  ;; QUESTION SECTION: ;myseconddomain.co.uk.             IN      A  ;; ANSWER SECTION: myseconddomain.co.uk.      71605   IN      CNAME   myfirstdomain.co.uk. myfirstdomain.co.uk.     59      IN      A       www.xxx.yyy.zzz  ;; Query time: 298 msec ;; SERVER: 10.0.0.10#53(10.0.0.10) ;; WHEN: Tue Aug 18 14:17:26 2009 ;; MSG SIZE  rcvd: 78   Is this a breach of the RFCs or does DynDNS have a legitimate reason for blocking this action?  Followup Thanks to the two answers already posted I now know that 1and1 IS breaching RFCs to do this. However it does work and they seem to support it. For a company that hosts so many domains it seems very odd that they get away with doing this on such a massive scale without objection.  More followup  The output of "dig myseconddomain.co.uk ns" as requested.  root@srv-ubuntu:~# dig myseconddomain.co.uk ns  ; <<>> DiG 9.4.2-P1 <<>> myseconddomain.co.uk ns ;; global options:  printcmd ;; Got answer: ;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 18085 ;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 2  ;; QUESTION SECTION: ; myseconddomain.co.uk.             IN      NS  ;; ANSWER SECTION: myseconddomain.co.uk.      4798    IN      NS      ns67.1and1.co.uk. myseconddomain.co.uk.      4798    IN      NS      ns68.1and1.co.uk.  ;; ADDITIONAL SECTION: ns67.1and1.co.uk.       78798   IN      A       195.20.224.201 ns68.1and1.co.uk.       86400   IN      A       212.227.123.89  ;; Query time: 59 msec ;; SERVER: 10.0.0.10#53(10.0.0.10) ;; WHEN: Wed Aug 19 12:54:58 2009 ;; MSG SIZE  rcvd: 111


I was trying to write a "MAXIFS" formula on my excel 2019, but when I opened the file on a computer with excel 2016 it didnt work. And i read that for 2016's version, i should use the "MAX" instead of "MAXIFS" So what should i write if originally the formula was : =MAXIFS(Reference!C:C;Reference!B:B;Sale!B8;Reference!E:E;"<="&Sale!A8;Reference!F:F;">="&Sale!A8)*F8

I am in need of an alternative of MAXIFS/MINIFS function in Excel.   It is needed because I am not a Office 365 subscriber. As you know MAXIFS/MINIFS functions let you calculate under certain criteria, even the criteria that includes another cell/s. I can do a least amount of calculation using MAX/MIN and IF function, but the criteria/condition must be on the same cell/s. So it's my misfortune that can't come up on a solution to this case.   I want to use 2 conditions/criteria, so I couldn't use the ARRAY formula.  Result:


I'm trying to find a proper way to do this instead of simple string concatenation.  I have a (simplified) SQL statement as follows:  SELECT * FROM Zones WHERE id in (@zoneIDs);   I plan to insert an @zoneIDs value like such: 100000,100001,100002  I'm using VB in this particular instance, but it should apply to any .Net language using the MySQL connector. What I'm trying is this:  Private GetZones As String = "SELECT * FROM Zones WHERE id in (@zoneIDs)" Dim Param As MySqlParameter = New MySqlParameter("@zoneIDs", MySqlDbType.String) Param.Value = "100000,100001,100002" Dim adapter As MySqlDataAdapter = New MySqlDataAdapter(GetZones) Dim dt as DataTable = New DataTable() adapter.Fill(dt)   But what's getting filled in dt is just the row for ID 100000, as if none of the others were in the query. My guess is that it's running a command like this:  SELECT * FROM Zones WHERE id in ("100000,100001,100002");   Instead of  SELECT * FROM Zones WHERE id in (100000,100001,100002);   I personally prefer to use Stored Procedures instead of strings like this, but I believe I would hit a similar wall there. What is the proper way to fill an IN clause using parameters like this?

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.


could you help me with the following please:  Show that if $U\subset \mathbb{C}$ is a domain and the function $f:U\rightarrow \mathbb{C}$ is holormorphic and bijective, then $f^{-1}$ is also holomorphic.  I have carefully read the definition of a biholormorphic function and it seems to me that it is the same, so I don't know how it can be proved.  The inverse exists because it is bijective ... but any hint on how to prove that the inverse is holomorphic?  I tried to attack it with the inverse function theorem, but they tell me that the result to be proved does not hold for real functions.

I'm confused about the following proposition  Proposition. Let $U,V$ are open sets in $\mathbf{C}$. If $f:U\to V$ is holomorphic and bijective, then  the inverse  $f^{-1}:V\to U$ is also holomorphic.  The proof of the proposition think that the  continuity of $f^{-1}$ is obvious, but I find it is really difficult to prove  using $\epsilon-\delta$ definition. Can anyone give some hints?


I am working with a shapefile which has several hundred rows and 10 or so columns. Usually, the cells contain data, but at the moment they are just showing nonsense symbols (attached). I have tried using the same shapefile on a colleague's computer, and it worked fine. I have also reinstalled QGIS. What is wrong?

I'm running QGIS 2.1.4 and Windows 7. For each layer, under properties there is a drop down box called 'data source encoding'. Mine is set to 'system'. I am wondering what this means, there seems to be a lot of options one can choose from.


I am trying to define a note environment, currently it is just a wrapper of \marginpar function like this:   \newenvironment{note}{\marginpar}{}   but   \begin{note} Important Notes \end{note}   will only put I in the margin and the rest (mportant Notes) as normal paragraph.   I also tried   \newenvironment{note}{\marginpar\\{}{\\}}   which doesn't work.  What is the right way to do this?

I'm working on an exam document class where the user enters in questions something like this:  \multiplechoice{Question} {Answer #1} {Answer #2} {Answer #3} {Answer #4} {Correct answer} {Explanation}   I'd like to process this information in various ways in one LaTeX run (to create an answer sheet, key, and the test itself), so the questions need to be stored in a macro. The awkwardness comes when one defines:  \newcommand{\sectionA}[1]{\newcommand{\putsectionA}{#1}}   and then asks the user to put 15 questions as an argument to \sectionA. I'd much rather have those questions be the contents of an environment, like so:  \begin{sectionA} lots of questions \end{sectionA}   Mostly because I find it much easier to keep track of environment declarations than curly brackets. Is it possible to have the contents of an environment get packaged up into a macro?  Edit:  The solution would seem to be to us the environ package, but it doesn't seem to be working. Here's what I'm trying:  \documentclass{article} \usepackage{environ} \NewEnviron{foo}{\edef\foot{\BODY}} \begin{document} \begin{foo}   Store This \end{foo} \foot \end{document}   However when running this code \foot remains undefined. It actually seems impossible to define any macro using environ. Even when not using \BODY. For example, replacing the definition above with  \NewEnviron{foo}{\newcommand{\foot}{Print me}}   still fails. I've also tried \Collect@Body from the environ package with similar results. Does \NewEnvrion somehow prohibit defining new commands?


What should we use before a word that started with 'H'?   'A' or 'An'? and why?  Sometime using 'a' seems right, sometimes using 'an' seems right, I am confused

A basic grammar rule is to use an instead of a before a vowel sound. Given that historic is not pronounced with a silent h, I use “a historic”. Is this correct? What about heroic? Should be “It was a heroic act” or “It was an heroic act”?  I remember reading somewhere that the h is sometimes silent, in which case it’s an, and when the h is pronounced, it’s a. But then I also remember reading that it depends on which syllable is stressed. And I also think I read somewhere that it might differ between British and American English.  Personally, I pronounce the h, and believe that a is correct. I find that it sounds incorrect to use an and pronounce heroic without the h.  So how do I know when to use a and when to use an with a word beginning with the letter h? Are both acceptable or is there one that is correct?


$$\lim_{n\rightarrow\infty}\left(\frac{a^{1/n}+b^{1/n}}{2}\right)^n$$  No idea how to do it please help step by step

Let $a$ and $b$ be positive reals. Show that $$\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$$


I have a dataset of project sizes (in $) which is sometimes bimodal, sometimes not (it varies across time and I am using annual data sets). These projects are distributed across two types of project owners, A and B, with about 90% of projects being led by type A people, the rest by type B's. I am running (hand-coded in R) a permutation test based on the ratio of the medians of the project values in each group, to determine whether the medians differ significantly. This involves randomizing the assignment of type (A or B) to the projects, calculating the median project size in each (now randomly assigned) group and then finding the ratio of these two values - this being repeated many times (10,000) to get the sampling distribution for the ratio of the medians in the two groups under the null hypothesis that project type (A, B) is not associated with project size. Naively I expected that the sampling distribution generated would be centered on 1, and indeed most of the time it is, when the distribution of project sizes is unimodal. But in some cases instead I find that actually the ratio tends to become < 1 as the distribution becomes more bimodal. This seems surprising as I am in effect randomly sampling from the distribution. I have searched around and found suggestions that it may be a result of the imbalance in sample sizes, or that it may be something to do with the (lack of) meaning of the median when applied to a bimodal distribution. It could also be that the project sizes, which are power-law distributed, are an issue. But I cannot quite see why the sample size should systematically affect the ratio. It also happens when using the mean, but the effect is less pronounced. Any ideas? (I have no formal statistical training and approaching this as a practitioner.)

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a normal distribution? My understanding is that this is true with the means of a large number of samples, but is it also true with medians?  If not, what is the underlying distribution of sample medians?


Is there a known formula to the sum $$1+\sqrt{2}+\sqrt{3}+\cdots+\sqrt{N}$$ where $N$ is some natural number? Thanks

I was wondering what the estimate for the value $$ S= \sum_{j=1}^N \sqrt{j} $$ is? Is there a way (or a formula) to estimate it well? I am sure it is close to $\int_1^N \sqrt{t} dt$, but I guess I  was interested in estimating it better.  Thanks!


After school, I was doing research on Canadian Blood Service. I went into pages and than it got stuck. I wait for 3 minutes nothing happened so I hold the lock button and try to shut my iPad down but nothing works, I was listening to music at the same time and the music is still playing. I has to do a hard reset by holding home button and lock button. After the reset I found out that every single app has gone missing except for the Stock apps which comes with the phone, and my jailbreaking app suck as Cydia ifile, IAP Free and etc. I reboot many times but nothing happened. The apps are still taking up the storage but I can't see them in usage not search. Does anyone have any idea? I urgently needs help.   Thanks. and here's my iPad's info: iPad 4 White Wi-Fi 32 GB, jailbroken with Evasion 7 IOS 7.0.4 system.

Basically I have my iPhone w/ iOS 7.0.4 jailbroken using the latest evasion software.   I recently ran out of battery, and when I had managed to recharge and get my handset back on, all of my apps (apart from the stock apps that come with the phone) are all gone. No other data is missing, e.g , music, pictures and videos.   When I go to, settings, general, and usage. I can clearly see that my memory is still being taken up by all the apps I "had" on my phone (2.1gb free) yet the apps still aren't there. I'm usually good with tech, especially Apple. But this one has me stumped.


Let $(M,d)$ be a metric space. Let $M \times M$ be the product space, where $d$ is defined (earlier in the book as ) $d((x_1,x_2),(y_1,y_2))=d_1(x_1,y_1)+d_2(x_2,y_2)$ where $d_1$ and $d_2$ are metrics on $M_1$ and $M_2$, respectively.  I must prove that $d$ is a continuous real valued function.  I am very confused about the notation, an I supposed to show that $M \times M$ is the set or $M_1 \times M_2$ is the set in supposed to use? I guess it doesn't really matter but it would really help me.  Can someone help me out on starting the proof?  I know I must choose my delta to be $\varepsilon/2$ since I have two points, but my question is how will some of the notation look like?

Let $X$ be a metric space with metric $d$. Define $d: X \times X \to \mathbb{R}$, show that $d$ is continuous.  I would like to show that the function is continuous the topology way (since it is a course on topology).   Let $(a,b)$ be a basic open set in $\mathbb{R}$, then $d^{-1}(a,b) = \{(x,y): a<d(x,y)<b\}$. Define $A= \bigcup_{x \in X} B_{b} (x)$, where $B_b (x) = \{y \in X| d(x,y)<b$}. Clearly $A$ is open. Now define $C = \{(x,y):d(x,y)>a \}.$ Essentially I hope that $A \cap C$ is open. But I am stuck in showing that $C$ is open.  Any help please? :)


I have the following regex to capture translation strings in a laravel project:  (trans|trans_choice|Lang::get|Lang::choice|Lang::trans|Lang::transChoice|@lang|@choice)\(([\'"]([\/a-zA-Z0-9_-]+([.][^)\'"]+?)+)[\'"])(\s?.*,\s?.*)*?[\)\]];?   The regex will happily capture:  @lang('validation.invalid') @lang('validation.invalid', ['field' => $field])   However, the moment I introduce a line break  @lang('validation.invalid', [ 'field' => $field ])   or a couple in between:  @lang('validation.invalid', [ 'field' => $field,  'message' => $error->getMessage() ])   It no longer targets the string

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


I'm working on derived subgroups because I'm studying for an exam and I want to show that in the case of the dihedral group $D_{2n}=\langle\sigma ,\tau|\sigma^n=\tau^2,\sigma^{\tau}=\sigma^{-1}\rangle$ that the derived series is   $1 \unlhd\langle\sigma\rangle\unlhd D_{2n}$  if n is odd and $1 \unlhd\langle\sigma^2\rangle\unlhd D_{2n}$ if n is even.  I know that the commutator will give $[\sigma,\tau]=\sigma^{-1}\tau^{-1}\sigma\tau=\sigma^{-2}$ which implies that the commutator can always be generated by just sigma , but I am confused as to show the difference between the even and odd cases . any suggestions anyone ?

Let  $G=D_{2n}=⟨x,y|x^2=y^n=e,  $ $yx=xy^{n-1}⟩$  I need to find $G'$ [ the commutator of G]  now I understand that $G'$ is the subgroup generated from $ U=xyx^{-1}y^{-1} , $ $ \ \forall x,y \in G$ So, $U=<y^2>$  whats the strategy  here ?


I deleted a 5gb video using rm video.mp4, but the space hasn't freed.  This was the situation: while encoding a video with FCP X, I ran out of space, I only had 50 MB free. Since in the trash I had some stuff that I wasn't sure that I could delete it yet, I took the terminal and I manually deleted a big video file with rm video.mp4.  The file is gone, but the main problem is that the disk is still full. What I can do to reclaim this space back?  It's normal that manually deleting a file will not free up space?

I had approximately 50Gb of Windows VMs on my MacBook Pro internal SSD (128Gb) (OS X 10.7.3).  I copied them to an external drive, then deleted them from the internal drive, then emptied the Trash.    When I look at disk usage in Activity Monitor it shows the same level of usage as it did prior to deleting 50Gb of files.   Any ideas why the space hasn't been freed up?


I have an alwayson environment (AlwaysOn AG).  Database [UsersDb] in the slave server, His log file is very big . How can I reduce his size(shrink)?

This one seems to be a common question in most forums and all over the web, it is asked here in many formats that typically sound like this:  In SQL Server -  What are some reasons the transaction log grows so large? Why is my log file so big? What are some ways to prevent this problem from occurring? What do I do when I get myself on track with the underlying cause and want to put my transaction log file to a healthy size?


This is my code.  \documentclass{article} \usepackage{amssymb,amsmath,amsthm,enumitem}  \begin{document} How can I decrease vertical space between text above and below \$\$ \ldots \$\$ ? $$x^{2}+y^{2} = 1$$ How can I decrease vertical space between text above and below \$\$ \ldots \$\$ ?  And how can I decrease vertical space between text above and below align command ? \begin{align*} abdefg &= 1\\      &\leq 2. \end{align*} How can I decrease vertical space between text above and below align command ? \end{document}   And it shows as this picture   Everyone know how to fix it? Please help.

How could I go about setting the 'above' and 'below' vspaces around the equation environment?  If the same could be done for the subequations or gather environments, this would be a bonus.


I wanted to book a direct flight from Heathrow to JFK with BA. Over night they put the price up by over £500. Now I can see the exact same flight but you have to go indirect via Newcastle to Heathrow to JFK, it works out way cheaper this way.  Is there anyway I can skip the Newcastle flight if I contact BA before and go direct to Heathrow or if I miss the Newcastle flight will the whole flight be cancelled?

I've a friend that booked a round-trip journey. He booked A-to-B and B-to-A. Somehow he needed to be earlier at location B, so he took a train and did not take the flight from A to B.  When he went to the airport to take the "back home" flight (B-to-A), he was informed that his ticket was canceled because he did not take the A-to-B flight. They canceled the ticket and sold it to someone else.  Is this normal? The company said it was their right to do so, and he could not get the flight back. The company was Iberia.


Prove that if $a>1$ then $(a^n-1,a^m-1)= a^{(m,n)}-1$  where $(a,b) = \gcd(a,b)$  I've seen one proof using the Euclidean algorithm, but I didn't fully understand it because it wasn't very well written. I was thinking something along the lines of have $d= a^{(m,n)} - 1$ and then showing  $d|a^m-1$ and $d|a^n-1$ and then if $c|a^m-1$ and $c|a^n-1$, then $c\le d$.   I don't really know how to show this though...  I can't seem to be able to get $d* \mathbb{K} = a^m-1$.  Any help would be beautiful!


Although I can see many routes to get an education in testing, programming, etc. how can I address the requirement that nearly all jobs seem to require some actual software testing experience as well ?  What should one do to gain experience in software testing ?  Any tips for what should be on your resume for a candidate who is applying for jobs in QA automation ? Apart from the ISTQB Foundation Certification.

I have a BA degree in Biochemistry.  I worked at a research lab for 5 yrs before I quit my job to be a stay at home.  Now I want to change my career and get into the field of QA.  I don't have much knowledge as to what the best way is to get into this field.  I cant afford to take online courses, so I want to self teach it to me.  Any suggestions and help would be greatly appreciated.


I am building an RPM (SLES12) package that installs a service with some software. The package dumps a new file into /etc/rsyslog.d to handle logging.  I would like to have the rpm basically run a "systemctl restart rsyslog" from the install... I guess from %post  Is there any specific way this should get run (like a macro) or should I just literally put that line in the scriptlet?

I want to log my app so that it writes its log into its own log file. I create the log file and save it under /etc/rsyslog.dbut my app doesn't create/write to the designated file. However, once I reload rsyslog, there are log entries the next time my app runs. I package my app into an RPM so I can write post-install scripts if necessary. Is this the proper way to handle this via post-install scripts? /etc/rsyslog.d/serf.conf if $programname == 'serf' then /var/log/serf.log & ~  Sending pkill -HUP rsyslog works but I wasn't sure if that would cause any issues to other programs while they're in the middle of logging.


We all know how important the team when making an idea and a great product.  In my opinion, Stack Overflow is revolutionizing the idea of forums. In other words, Stack Overflow is revolutionizing the web.  I was looking over the , and I'm curious about how the team members found each other and started working on the same product. Stack Overflow team members have different ages and different locations. Maybe one or two were friends before, but what about the rest?  What is the history of, or story behind, Stack Overflow?

I'd like to know how Stack Overflow and other sites started - which was first, who initiated it (OK, that's on the link below) and why, how the different sites evolved, how the rules evolved, etc.  Where can I find such information?  Of course, I know I can look at  for a brief overview but I'm wondering if there is info on this site, particularly more detailed..


This question duplicated with . I asked for answer this question. Because I cannot answer the original question because I don't have 10 reputations.  After hard reset I've encountered with:  BusyBox v1.18.5 (Ubuntu 1:1.18.5-1ubuntu4) built-in shell (ash) Enter 'help' for a list of built-in commands.  (initramfs)

I am running an HP pavilion dv6000 dual boot win7 and Ubuntu 12.04. (well, up until today).  After a reboot, the boot process drops to the BusyBox shell and I end up at the prompt:  BusyBox v1.18.5 (Ubuntu 1:1.18.5-1ubuntu4) built-in shell (ash) Enter 'help' for a list of built-in commands.  (initramfs)   I've been researching others who have had this same problem, but haven't been able to find any of those solutions to work for me.  I tried the method described , and after the final command   mount -t ntfs-3g /dev/sda1 /root -o force   it does nothing and gives me another (initramfs) prompt.  I can boot to a live CD (USB) and get to a terminal, but it doesn't seem to do much good, as I can see the /dev/sda1 in the ls command, but it doesn't recognize it when I try to cd to it.  One more question: using the command fdisk -l how can I tell which mount point (sda1/sda2) is my windows partition and which one is Ubuntu?


I am using Ubuntu 20.04 LTS the nano I have is v4.8 The global version is 4.9.3 Why it is not updated

Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.?


Interview, asking for offer etc. I wonder if Stack Exchange has a sote for this kind of question?   Sample question:     Do company usually do not reveal their benefit package until you sign the accepting offer letter?

Is there a Stack Exchange site for both technical and behavioural interview questions? Where I could ask questions about, for example:   Sample questions and solutions, experiences, or seeking advice for interviews A place where I could ask interview questions and what the best way to answer it (not just a correct way or the most efficient).   What to do in a certain situation such as negotiation, unfair interviews, etc.   Experiences interviewing at so-and-so company.


Would you say:     There is no fire or hot ashes in the fireplace.   or      There are no fire or hot ashes in the fireplace.   And where does that question mark go?

It seems I put a   Bounty assigned by outside party, two lengthy, reference-citing answers, one "-1" (awarded the bounty), one "-2", two others scored "0" and "-2" respectively, the answers suggesting one or the other is correct, 73 comments and no consensus so far - and me, as the asker, lost without a clue what to think of the answers anymore -  this is no longer "Learners' Level" question, so I thought I'd bring it here and hear what the experts have to say.    Original question:  Plurality of verb depending on plurality of list elements  An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that - was my editor overzealous or am I trying to copy rules of my language that don't apply in English?    Someone linked a  for negatives, where the situation is more clear-cut ("There is no..."). Same applies to connection with "or" apparently, per accepted answer there. Still, nothing for "and".  It seems there is a consensus that in that if the verb goes after the list, it will be plural.     an orange, some grapes, two apples and a small pile of cherries were on the plate.   There doesn't seem to be clear consensus for:     On the plate { was | were } an orange, some grapes, two apples and a small pile of cherries   Adding more to the confusion is the abbreviated form: "There's"     One last note. In North America, at least, there is a widespread use of using a singular form like "there is" and "there was", without regard for the subject item or items, and this "there is" is often shortened to "there's":           There's three apples on the table!      Could you please clarify this mess?


public interface Game{    public abstract boolean isValid(int coup); }  public Machin implements Game{     //Do I need to write @Override here ?    public boolean isValid(int coup){      //exemple      if (coup==0){         return false      }      return true    }  }  I don't understand Overriding with abstract method could you help me ? Do I need to put @Override ?

What are the best practices for using Java's @Override annotation and why?     It seems like it would be overkill to mark every single overridden method with the @Override annotation.   Are there certain programming situations that call for using the @Override and others that should never use the @Override?


$X=\{(s,t)\in \mathbb{R}^{2}: 0\neq t\in \Bbb{Z}\}$ and $Y=\{(s,t)\in \mathbb{R}^{2}: 1/t\in \Bbb{Z}\}$ with the subspace topology induced by standard topology of $\Bbb{R}^2$. (i.e. horizontal lines)  Define an equivalence relation on both X and Y by: $(s_1,t_1)\sim(s_2,t_2)$ iff $(s_1,t_1) = (s_2,t_2)$ or $s_1 = s_2 = 0$. i.e identifying all points on y-axis to one point. The question is, is $X/\sim$ homeomorphic to $Y/\sim$ ?  I think they are not homeomorphic, since if the homeomorphism is the 'natural' n$\to$1/n, then consider a sequence $(x_n,\frac{1}{n})$ in Y s.t $(x_n)$ converges to $0$, the image doesn't converge in X. But there may exists other homeomorphisms, so I don't am I right or not, so please give me some hints.

We have two spaces $X=\{(x,1/n):n\neq 0, n\in\mathbb{Z}, x\in\mathbb{R}\}$ and $Y=\{(x,n):n\neq 0, n\in\mathbb{Z}, x\in\mathbb{R}\}$. On both spaces we introduce the equivalent relation $(x,y)\sim (x',y')$ if $x=x'$ and $y=y'$ or $x=x'=0$. That is, all points on the $y$ axis are collapsed to the same point.  We are asked whether $X/\sim$ and $Y/\sim$ are homeomorphic in quotient topologies.  It is easy to show that the original spaces are homeomorphic. However, I don't know how to answer the question about the quotient spaces.   My guess is that they might not be homeomorphic and some problem might occur at the $origin$ but I am not sure.  Any hint would be helpful! Thanks!


I've noticed this discoloration on or near the bottom of my saucepan, which stays even after cleaning. When dry, parts of the pan will appear slightly pinkish or greenish. Furthermore, there is often some white staining.    Is this a cleaning issue (given that I haven't entirely been good with cleaning the pan out promptly)? Or is this perhaps related to something lile my water supply? The saucepan appears to be made of stainless steel.

I know this question has been asked before in some form or another, but I can't seem to find a definitive answer. I've looked on SA, chowhound, martha stewart, about.com, etc., and answers seem to vary. Answers that I've seen vary from using vinegar to washing using special stainless steel soaps (which I'm not very keen on using) to only using soft sponges and hot water.   The one thing I always do is wash my stainless steel with warm soapy water and a soft sponge. If there's burned food stuck on the cookware, I scrape it off with a wood pot scraper (lightly, of course). And I always dry with a soft cloth immediately after washing. Yet I still get stains!  I'd like to get a general consensus on how to prevent those white and rainbow colored stains as well as minimizing corrosion.


Let A be a set.Define the binary operation $\bigtriangleup$ on $P(A)$   by $X \bigtriangleup Y = (X-Y) \cup (Y-X)$ for all $X,Y \in  P(A)$.Prove that $\langle P(A), \bigtriangleup\rangle$ is an abelian group.   In this question I stuck in showing that the binary operator $\bigtriangleup$ is associative.  I wrote what are $X \bigtriangleup (Y \bigtriangleup Z)$ and $(X \bigtriangleup Y) \bigtriangleup Z$, and then by drawing Venn diagrams, I concluded that these two operations gives different results.I checked my calculations, but couldn't find anything.  I can write here my calculations, but the way that I have tried to solve is pretty tedious way to prove such kind of thing, so I am asking that how can I prove that this binary operator is, in fact, associative ?

By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.)


Why is $\mathbb{R}/\mathbb{Z}$ a Hausdorff space, if we assume that $\mathbb{R}$ has the canonical topology, and $\mathbb{Z}$ the induced subspacetopology?  More generally, which requirements for a topologal space $S$ ans it's subspace $U$ allow to conclude that $S/U$ is hausdorff?

$X$ is a Hausdorff space and $\sim$ is an equivalence relation.  If the quotient map is open, then $X/{\sim}$ is a Hausdorff space if and only if $\sim$ is a closed subset of the product space $X \times X$.  Necessity is obvious, but I don't know how to prove the other side. That is, $\sim$ is a closed subset of the product space $X \times X$ $\Rightarrow$ $X/{\sim}$ is a Hausdorff space. Any advices and comments will be appreciated.


Sometimes OpenID providers end their services, like  and  did. How do I add or remove login methods so I don't get locked out of my Stack Exchange account?     For more information, see  in the Help Center.

I no longer use the service that I originally used to register, and would like to change the service I use to log in, or at least add a second account.  Is this possible? How do I change my login provider or associate a backup method to log in?     For more information, see "" in the .


In the book of Mathematical Analysis II, by Zorich at page 128, it is given that     Let $E$ be a Jordan-measurable set of nonzero measure, $f : E →  \mathbb{R}^n$ a continuous nonnegative integrable function on $E$, and   $M = \sup_{x\in E} f (x)$. Prove that      $$\lim_{n\to \infty} [\int_E f^n (x) dx)]^{1/n} = M$$   I have already proved that  $$\lim_{n\to \infty} [\int_E f^n (x) dx)]^{1/n} \leq M$$ since $E$ is Jordan measurable and has nonzero measure, but I'm having trouble proving the reverse of that statement, so any help is appreciated.  Edit:  I'm new to this topic, and I even do not understand the premise of the asked question, so I would appreciate if you could post an answer that is formulated in terms of the statement that I have given in the question.

Could someone help me prove that given a finite measure space $(X, \mathcal{M}, \sigma)$ and a measurable function $f:X\to\mathbb{R}$ in $L^\infty$ and some $L^q$, $\displaystyle\lim_{p\to\infty}\|f\|_p=\|f\|_\infty$?    I don't know where to start.


Can anybody recognize the font or symbol for this . It is used as font for alphabetic letter S, in my text. I did check almost all fonts and symbols but couldn't succeed in finding a good match. I need this symbol in Latex math mode. Or a way, to design this symbol by myself to be use in Latex. thanks

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?


I have searched on the airline websites, but however have not found a concrete answer to my question which is: if I were to take my 55" TV along with me from Germany to India, will the airlines allow this as a checked luggage? If yes, how much would the cost for such a transport be.  Hope someone can throw some light on this.

I'm going to northern Cyprus with Turkish airlines and want to take a 40 inch smart TV that I bought here in the UK with me. Can't find out if this is possible or how much it would cost as it weighs 14kg and as it is fragile how it should be packed if going in the hold. This would be in addition to my 23 kg luggage. Reason is TVs in northern Cyprus are very expensive compared to UK


These wheels are both parented to the leg of a robot u see in the picture below. I want to make the wheels spin while they move with the legs but they rotate around the wrong axis. I already searched for solutions but they all talk about an empty, the thing is, I can't parent them to an empty because they're already parented to the leg.  When I put the transformation of the wheel on local, it uses the same axis as the parent object (I think? correct me if wrong), but this object (the leg) has a different angle so that's why it spins weird. Is there another way to fix the axis? Without parenting to an empty because I can't parent to 2 objects.

So I have these two wheels parented to the leg of a robot. I wanna make them spin a few times but they're spinning around the wrong axis. With other objects I could just press R, Y, Y to make them spin right when they're already at an angle, but for some reason it doesn't work with these. Would be amazing if someone helped me fixing this!


My USB was working 100% fine before I went to college yesterday. I added some new files to it, took it to school, plugged it into my teacher's computer, and nothing shows up. It says it's empty. I tried it with a different computer to see if it was just the teacher's PC. I plugged it in and I got the same thing.  How do I get my files back? Most of my stuff is on there and I would like them back as soon as possible.

I have a flash drive that was used primarily on a Mac, and it was ejected improperly.  Now when I put it back in, the computer (I tried 2 different Macs and 3 PCs) does not even register the flash drive- it does not show up in Finder or in My Computer. Any ideas how to get the lost files back?


Let's use "Coda 2.app" as an example. If to rename it to "Coda.app":   Will it affect the functionality of the app? Is the app still be able to access the sites data saved in Keychain previously? Is there any problem for the in-app auto update?   Thanks.

For example, I have Xcode 4.4.1, and now Xcode 4.5 Golden Master (GM) version is available, but it is also called Xcode (when the .dmg is mounted as an disc image, it shows only one app (or folder), called Xcode)  I think the way is just to double click on the .dmg file, and then drag and drop that app into our Applications folder.  But since the current Xcode and Xcode 4.5GM have the same name, can the new one just be renamed and so we can have both versions on our machine?  I was worried that what if the app writes back data to the /Applications/Xcode folder, then the GM version can write unexpected data for the 4.4.1 version.  And will it work with other software, such as Xcode 3.2, Xcode 3.3, or even different versions of Microsoft Office and Adobe Photoshop?


I created a file in Ubuntu command prompt like this  $ gedit first_file.txt    After editing and saving the file when do ls on command prompt I can see an additional file created   first_file.txt~     My Question   What is this file and why it is created? Will it ok to tell Ubuntu not to created these files and how?

I have observed that in gedit if I edit a file, another file is created in the same directory (the one with the same filename and a tilde '~' suffix). The extra file remains even if I close gedit.  I understand the need for a temp file (eg. in case of a crash), but vim for example deletes the extra file it creates, when I close it.  Is there a way to do the same with gedit? Some configuration perhaps?


Would moon fall to Earth if Earth wasnt rotating ? And if rotating at what height moon would have to be to ignor orbiting and fall ?

Why doesn't the Moon fall onto the Earth? For that matter, why doesn't anything rotating a larger body ever fall onto the larger body?


Is it possible to set off an ecm jammer and kill all the guards and cuff all the civilians so the alarm is never set off in a bank heist?

In the Bank Heist levels for Bain, you're tasked with robbing a bank. This level is also re-used during Hector's Firestarter mission, where you're tasked with burning all of the Mendoza's money which is currently being stored in the vault.  The Firestarter mission specifically states you should stealth it, but it's seems like common sense that if you're hitting a bank that you don't want the police involved.  How can I pull off a Bank Heist without the cops getting involved?


Suppose we have two electric charges $q_1$ and $q_2$ a distance $r$ apart in euclidean three-space. Coulomb's force law states that there's a force  $$\mathbf{F}_{12} = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1q_2}{r^2}\hat{\mathbf{r}}$$  between them. Now, what I'm wondering is how the two charges know about each other? How can one charge know that there's another charge there exerting a force over it? One way I believe could explain this was: "charge $q_i$ generates an electric field $\mathbf{E}_i$ which is felt by charge $q_j$" but this ends up bringing two other questions:   The electric field is introduced more as a mathematical object than a physical object. We introduce the field $\mathbf{E}$ so that the force exerted on a charge $q$ is $q\mathbf{E}$. The field itself can then be considered the force per unit charge with this charge made small enough so that it won't change the original configuration. In that case, what it would really mean to generate a field and percept a field? Even if we explain with the field, the second question naturally is: how the other charge knows that a field is there and how this field interacts with it really?   I didn't study quantum field theory yet, however, I imagine the more fundamental explanation would have to do with photons intermediating the process by which one charge feels the other. Is it really the case? How can we really understand how two charges know each other and by which mechanism they interact?

Is the word "vacuum" equal to "nothing"? Imagine two charges of opposite sign, far from one another in vacuum, and moving with constant velocity - s.t. none radiates energy, none emits photons. At some time though, the course of their movement brings them closer. They begin to accelerate toward one another. How do they feel the presence of one another? During their constant movement no photons are emitted, no "information" spreads in the universe about their presence.


If you look at , it shows that it solves for the gaussian case:  But why does it divide the value of $\parallel \beta \parallel_2^2$ by 2?

I have a question about the elastic net penalty as implemented in glmnet in R compared to the original paper by Zou and Hastie (2005). In glmnet the penalty is listed as   $$ (1-\alpha)/2||\beta||_2^2+α||\beta||_1. $$  but in the paper it is  $$(1-\alpha)||\beta||_1 + \alpha||\beta||_2^2.  $$  Does anyone know where the factor $\frac12$ some from? (Never mind the fact that the $\alpha$'s were swapped between the two parameterisations.) In both cases the penalties are multiplied by $\lambda$, but what are the mathematical/technical arguments for not using a simple convex combination of the lasso and ridge penalties?


I noticed there are many sites where I saw a question being closed by Off Topic instead of, say, Unclear what you are asking. Others which would benefited from This question was closed due to a typographical error were closed by Questions seeking for debugging help ....  I'm not discussing whether those questions should be closed, because they were rightly closed but when I asked about the reasons, I was told that it was due to the limited amount of close options (edit: wait, i'm not talking about the close options inside of Off-Topic reason, but aout the limited number of 1st-level close options) Stack Exchange provided for the sites. But for many questions I read, the close reason was not quite understandable wrt the actual close reason (which I had to ask in the corresponding meta about).  Is there a way to make those close slots variable? Ultimately, only moderators would have access to them as they have today (Edit: or could they ask the staff for more 1st-level close options).  My reason: Closing should be useful for the users at first glance of why. Specially if the user is not well used to the site politics and is a slow-learner about how the site works.  I understand there is the subtext for reasons as off-topic, but this is about communication: it is not about how do you think you send it, but how does the user (in this case the OP and in second place interested users) perceives it.  Edit E.g.: If the user read Closed as Off-Topic at first glance in big bold letters when asking about an on-topic question (but somehow unfitting in other ways), or another main closure title which he perceives inappropriate wrt the involved question (even after shallowly reading the rules) they will feel at first glance the site owners or community does not understand their own rules (which is not the case; instead just a poor way of communicating).  Disclaimer: No. I always understood why MY questions were closed. In this case, I am the... second place interested user, trying to understand how a specific site worked, and what and how was a question permitted in such site.

Custom close reasons are a great boon to Stack Exchange sites, allowing the community to provide more tailored advice to site-specific situations. Their big problem (aside from being limited to three by default) is that they are all lumped under "off-topic". This is often confusing.  I suggest that all close categories but "exact duplicate" should support customized close reasons — not just the "off-topic" category.  For example, the recommendation close reason     Questions asking us to recommend or find a tool, library or favorite off-site resource are off-topic for Stack Overflow as they tend to attract opinionated answers and spam.   This would make more sense as a child of primarily opinion-based.    Similarly, the "why doesn't this work" close reason     Questions seeking debugging help ("why isn't this code working?") must include the desired behavior, a specific problem or error and the shortest code necessary to reproduce it in the question itself. Questions without a clear problem statement are not useful to other readers. See: .   This would make more sense as a child of unclear what you're asking.  Similar examples can be given for pretty much any of the Stack Exchange sites.


Let $A$ be a square matrix such that $a_{i,j}=|j-i|$, show that the determinant is $D_n=(-1)^{n-1}(n-1)2^{n-2}$   I have been struggling with this problem for a while now and I was hoping to get the slightest of nudges towards the solution. I would appreciate it if you phrase your hints in forms of questions so I can work through the idea. Please don't post a complete solution unless I asked, and thank you for your time. I wanted to obtain a recurrence relation between $D_n$ and $D_{n-1}$ but I failed. So far, I attempted to use Gaussian elimination on the first and last row and I obtained $(-1,1,\ldots,1)$ and $(1,1,\ldots,-1)$ for the first and last row respectively but I didn't know how to proceed from then on.

Question states: "Let $D_n$ denote the determinant of the $n$-by-$n$ matrix whose $(i,j)$th element (the element in the $i$th row and $j$th column) is the absolute value of the difference between $i$ and $j$. Show that $D_n = (-1)^{n-1}(n-1)2^{n-2}$."  It seems like that I can get a recurrence relation (especially the question was from a book chapter dealing with recursion). In trying to get a recurrence relation, here is what I have done so far:  (Let $R_k$ denote the $k$th row and let $(i,j)$ denote the element/spot of $i$th row and $j$th spot)  1) replace $R_1$ with $R_1-(R_2+R_{n-1})$ to get $R_1^*$  2) replace $R_1^*$ with $R_1^*+R_{n-2}$  3) If I am not mistaken, I should have $-2$ on $(1,1)$, $2$ on both $(1,n-1)$ and $(1,n)$, and all other element in the first row as $0$.  4) take out $2$ from the first row, and expand the determinant about the first row  5) I should have $D_n=2(-D_{n-1}+(-1)^n B_{n-1})$, where $B_{n-1}$ is the determinant of a not-easily-reducible mayrix whose last column consists of $n-1$ ones followed by one $-1$.  How should I go about from now on? Once I get a recurrence relation, it would be pretty easy to get the explicit formula for $D_n$ using induction.  P.S. This question apparently is a question taken from 1969 Putnam Competition


Any idea on how to solve the following definite integral?     $$\int_0^1\frac{\ln{(x^2+1)}}{x+1}dx$$   I have tried to parameterize the integral like $\ln{(a^2x^2+1)}$ or $\ln{(x^2+a^2)}$, which don't seem to work.

I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?.


As the title asks, does the shiny side of foil really insulate or keep food warm when facing inwards? I've heard that the shiny reflective surface of the foil reflects the infrared energy. Is this true or is it just a marketing gimmick that everyone has come to believe?

Aluminum foil is said to be not absorbing light at all. It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?  If yes, then where does unreflected light go in case of less shiny aluminum foil?  Does less shiny and more shiny actually make a difference? Why?  In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too?


I am getting output for 13195L, 24L, and 23L. But I am not getting output for 600851475143L. The system is going into infinite loop. Please help me identify what is wrong with my code.     package problem3;  public class problem3_version1 {     public static void main(String[] args) {         long dividend = 600851475143L;         // long dividend=13195L;         // long dividend=24L;         // long dividend=23L;         int num_of_divisors = 0;         for (long i = dividend - 1; i >= 2; i--) {             System.out.println("i =" + i);             int count = 2;             for (long j = 2; j < i; j++) {                 if (i % j == 0)                     count++;                 if (count == 3)                     break;             }             if (count == 2) {                 if (dividend % i == 0) {                     num_of_divisors++;                     System.out.println("Highest factor is " + i);                     break;                 }             }         }         if (num_of_divisors == 0)             System.out.println("The number is prime");     } }

What is the best approach to calculating the largest prime factor of a number?  I'm thinking the most efficient would be the following:   Find lowest prime number that divides cleanly Check if result of division is prime If not, find next lowest Go to 2.   I'm basing this assumption on it being easier to calculate the small prime factors. Is this about right? What other approaches should I look into?  Edit: I've now realised that my approach is futile if there are more than 2 prime factors in play, since step 2 fails when the result is a product of two other primes, therefore a recursive algorithm is needed.  Edit again: And now I've realised that this does still work, because the last found prime number has to be the highest one, therefore any further testing of the non-prime result from step 2 would result in a smaller prime.


I just boot up my laptop then run the sudo apt-get update command, but there's an error says:       [username] is not in the sudoers file.  This incident will be reported.    so I search the google for solution and it told me to go to the recovery mode on boot menu.   After I got there,the recovery mode option didn't exist. I searched again for another way, then I found some source says change the kernel option with single on linux line on boot menu. Well, I got problem while deleting the kernel option, which one is it?   If the code is:  Linux  /vmlinuz-3.13.0-44-generic root=/dev/mapper/ubuntu--vg-root ro quiet splash $vt_handoff     which part should I delete?   Anyway, I'm using the ubuntu 14.04; the grub version is 2.2 beta I believe.

I want to boot Ubuntu into recovery mode but there is no grub menu entry allowing me to do so. I pressed e and now I am able to edit boot options. It looks like that:  setparams 'Ubuntu , with Linux 3.6.0-26-generic'  recordfail gfxmode $linux_gfx_mode insmod gzio insmod part_msdos insmod ext2 set root='(hd0,msdos5)' search --no-floppy --fs-uuid --set=root <uuid> linux /boot/vmlinuz-3.5.0-26-generic root=<uuid> ro ipv6.disable=1 quirt splash $vt_handoff initrd /boot/initrd.img-3.5.0-26-generic   The  documentation says:     Boot to the recovery mode even if it is not listed on the menu:         Remove existing kernel options from the linux line and add single      But this sentence doesn't make any sense, maybe the wiki page is broken somehow. How to modify the boot menu to boot directly into recovery mode?  Note: I don't have access to grub config or anything else, only the boot menu edit page is available.


I'm really embarrassed to ask but what is the nilradical of the Lie algebra $\mathfrak{gl}_n(\mathbb{C})$, i.e. the set of ad-nilpotent elements of $\mathfrak{gl}_n(\mathbb{C}) = \mathrm{Mat}_n(\mathbb{C})$$? This must be standard knowledge but I couldn't find a reference.  Clearly, all nilpotent matrices and all diagonal matrices are in the nilradical. What else?

I find it intuitive enough that the radical of $\mathfrak{gl}_n\mathbb F$ is the scalar matrices, but I have trouble finding an easy, but complete proof:  Proof. Let $\mathfrak s$ denote the scalar matrices. Clearly $\mathfrak s\subset\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$. Suppose that $\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$ is generated by more than one element, so that $X\in\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$, but $X\notin\mathfrak s$. We can change basis such that $\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$ is upper-triangular. (The change of basis leaves the scalar matrices invariant.) Then $X$ is upper-triangular.  I want to conclude that there exists a $Y\in\mathfrak{gl}_n\mathbb F$ s.t. $[X,Y]$ is not upper-triangular. How can I see that $Y$ always exists, except by waving hands?


how do I get flight tickets for my schengen visa application without paying? I have spoken to a travel agent and he said he can only 'reserve' it for 24 hours and after that its cancelled. Will that still count as 'confirmed booking'?  I do not want to pay yet in case my application gets rejected.

I have a visa appointment this Friday 19 at the Italian Consulate in Philadelphia and I have a question about the flight reservation requirement: According to the Visa requirements "Confirmed flight reservation for a round trip showing complete itinerary."  Does this mean I have to reserve the tickets, pay and print the itinerary?  In this case if my visa gets denied then I will lose the money I paid or can I just show the planned itinerary (written not booked)? in this case the travel agency would not give me the Travel Insurance coverage until I book and pay for the reservation.   I am a US green card holder and applying from North Carolina.


So I have a website that runs through wamp however if you type a path in the address bar, you get an index of the directory, which I don't want  I have already tried to add a .htaccess file in the directory to stop it indexing (saying IgnoreIndex *) and went into the apache httpd.conf file and changing  Include conf/extra/httpd-autoindex.conf   to:  # Include conf/extra/httpd-autoindex.conf    however none have worked... I have tried restarting my server, restarting services, but nothing... Help?

This is a  about  the use of a *AMPP's stack.    I recently had a talk with some experienced people and they suggested to me not to use a WAMP stack, and instead install apache, mysql and php separately.  I don't understand why they have suggested this, though, so can anyone tell me?  Is there a particular disadvantage of WAMP, or a particular advantage to installing all of them separately?  Since a WAMP stack itself is composed of apache, mysql and php, then what's the difference between using the WAMP stack and installing them all separately?


I've been seeing words with umlauts in prominent publications - for example The New Yorker  re-election like this:     reëlection   What's going on?

There are lots of informal references to the traditional / "New Yorker" style of using diereses to disambiguate runs of vowels, however I have yet to find a definitive guide. See, for example:      My major question is: Is there a definitive reference that one can consult for proper traditional use of the dieresis in English? The accepted answer in last link above outlines some cases (e.g., no dieresis in "coalesce" or "react") but notably does not provide a reference to an authoritative source. My minor questions are:  Is it appropriate to use a dieresis in "prosaïc?"  How does one most correctly differentiate the two words spelled "unionized" ("union-ized" about the formation of a group or "un-ionized" about how many free electrons a material has)? Assume for a moment that you have to write both within the same document.


, the author makes 4 French baguettes. That is probably 2 more baguettes than I can eat before they get stale.  Recipe (transcribed from the video):  Ingredients:   Bread flour, 700 g Instant dried yeast, 0.5 tsp Kosher salt, 1.5 tsp Cool tap water, 520 g   Steps:   Whisk 1st 3 ingredients together. Add water and mix with the handle of a wooden spoon. Cover the bowl with clear wrap and rest for 45 minutes at room temperature. Repeat 4 times:   Turn onto a flat surface, wet your hands, and fold from each side to center, then use a dough scraper to put the dough back into the bowl (2:30 in the video). Cover the bowl with clear wrap and rest for 45 minutes at room temperature.  Sprinkle the work surface with bench flour and turn out the dough. Divide the dough into 4 equal pieces (each about 310 g). Shape the baguettes (6:30). Leaving the baguettes on the work surface, cover them with lightly oiled clear wrap. Let them rest for 15 minutes. Prepare a well floured bakers couche (7:20). Form the baguettes (7:50), dust lightly, and transfer to the couche. Cover with a tea towel and let them rise for 20 minutes, then a further 12 minutes while the oven preheats to 200°C/400°F. Place a pan of boiling water in the bottom of the oven. Transfer each baguette to a lightly oiled baking sheet using a peel or cardboard covered in aluminum foil (10:45). Spray the baguettes lightly with water Score the baguettes with a razor blade or very sharp knife (11:20). Place the baking sheet(s) in the oven and spray a little water over them to moisten the crust. Bake for 8 minutes, then turn the baking sheet(s) 180° for more even baking, releasing the steam from the oven carefully. Transfer the baguettes to a cooling rack.   Note that I have not tried this recipe yet, but plan to very soon.  How late in the process can I freeze the dough? I assume that when I want to eat it later, I can just thaw the dough and continue the process from that point.

I prefer my bread freshly baked (who doesn't?), but my mixer prefers kneading two loaves at a time to just kneading one. I have tried to freeze the second loaf before baking it, but when I thaw it, it does not rise well before baking. I've tried thawing it entirely in the refrigerator and then letting it rise on the counter, but that did not seem to work. Does anyone have a good technique or suggestion for this?


We'd recommend you to book your flight early.     Students are recommended to make an appointment with a counselor.         are correct, while        I recommend her to speak to a lawyer.        is wrong.  Why is the third sentence wrong?

I'd like to ask about the use of the verb "recommend" in the following sentences:  We'd recommend you to book your flight early. The plumber recommended me to buy a new water heater.  The first sentence is taken from the entry for the verb "recommend" in the online Oxford Advanced Learner's Dictionary and the other is from a grammar site. I'm still unsure if the usage "recommend someone" instead of "recommend to someone" is widely acceptable. While the first sentence seems have only one possible interpretation: "recommended to you", the other one, although less likely, could also be interpreted like: "The plumber recommended me, not someone else, to buy a new water heater". My question is whether it is possible to reinterpret the given examples as:  We'd recommend that you book your flight early. The plumber recommended that I buy a new water heater.  meaning that the interpretation is not that "you" or "me" are the objects of "recommend" but the whole proposition following it: "you to book your flight early" and "me to buy a new water heater", same as "that" clauses are in the rephrased examples? Edit: Thanks to all the contributors for the help! The meaning of the rephrases of the examples with "that" clause that I gave do tell essentially the same, but I was looking for the nuance in the interpretation of:  We'd recommend you to book your flight early  by comparing it with "that" clause rephrase:  We recommend that you book your flight early.  The salient reading of the first sentence for me would be : We'd recommend to you..and here is what we recommend.., meaning that there's a prosodic pause between "We'd recommend to you.." and the content of the recommendation which is "to book your flight early", while the second sentence I'd read as "We recommend..and here is what we recommend", which is "that you book your flight early", meaning that now the person who is recommended something is part of the content of the recommendation. In other words, this person doesn't stand prominently as the explicit object of the recommendation as it does in the former sentence. In brief, I was thinking that sentence 1 above may be interpreted as 2 too, not only as "recommend to you". When I use "for" in between the verb "recommend" and the person recommended this is more clearly shown:  I'd recommend for you to book your flight early.  Here again I'd read the sentence as "I'd recommend..and here is what I recommend". The person recommended is part of the whole proposition recommended — "for you to book your flight early", same as with "that-clause" phrasing, and it is not a clear object of the verb "recommend" as it is in "recommend to you" interpretation . By the way,I'd like to know how acceptable "recommend for someone to do something" construction is to you, as I haven't found it noted in Oxford ALD. To clarify my question, I'd like to add that in the original sentences "recommend" takes "to-infinitival" complement, not a bare verb which would be understood as a "that"-clause with "that" elided: "recommend you book your flight early", would stand for "recommend that you book your flight early". Again, my question is if "that-clause" complement, (nevermind if "that" is elided or not) is comparable with "you to book your flight early" or "for you to book your flight early" in the given sentence. Finally, as native speakers you're entitled to question any dictionary or book as it is up to you to decide what works and what not, there's no single ultimate authority for the language people speak, so you can argue even with Oxford guys. "Grammatical" is what is acceptable to the majority of the speakers.


I can't tell where I went wrong, am still a beginner.    Let N be a nilpotent in a commutive ring , let X be any element.   I'll will be showing X + N is a unit .   Assume Y(X+N) =1   Then YX(N^n-1) =  N^n-1   Multiplying both side by  X+N   We get X(N^n-1) =  X(N^n-1)  Thus nilpotent summed with any element gives unit.

If $ua = au$, where $u$ is a unit and $a$ is a nilpotent, show that $u+a$ is a unit.   I've been working on this problem for an hour that I tried to construct an element $x \in R$ such that $x(u+a) = 1 = (u+a)x$. After tried several elements and manipulated $ua = au$, I still couldn't find any clue. Can anybody give me a hint?


Could you help me, please? What is the right option for the following question:  "Why is Google unique?" "Why Google is unique?"  Thank you very much and wish you a good day!

We always change subject and verb positions in whenever we want to ask a question such as "What is your name?". But when it comes to statements like the following, which form is correct?        I don't understand what are you talking about.   I don't understand what you are talking about.      Another example        Do you know what time is it?   Do you know what time it is?      Another example        Do you care how do I feel about this?   Do you care how I feel about this?


How can I add my signature to Preview on a Mac without a built-in camera?  I've got a mid 2012 Mac mini, running macOS 10.11 using a 3rd party mouse and Apple keyboard, connected to 2x 3rd party HDMI displays.   I want to add my signature to the Preview app, so that I can sign documents digitally in Preview without having to print, sign, scan.   In the past I have used a built-in webcam to get my signatures saved into Preview, but I can't do that on this Mac mini.  I have access to another mac with a camera and an iPhone if required.

I have a Mac Mini with no attached camera. I would like to use the feature of Preview that allows you to insert a signature. This relies on taking an image of your signature using an isight/facetime/webcam. I do not have on.  I do have a MacBook pro on which I use the signature function. Is there a way to copy a file from the the MacBook Pro to the Mac Mini to enable this function on the Mini?


Every now and again I have been noticing the following in Haskell documentation: (for example in ):     Subject to fusion   What is fusion and how do I use it?

What is Haskell's Stream Fusion and how do I use it?


I have a CUBOT P7 phone with very little internal memory, so I installed an 8GB external SD card.   However, my apps will not download directly to there, and I have no more space on my internal memory.  How do I modify my phone so that apps download directly to my SD card? with out having to root my phone

If you're running out of memory which happens a lot on low-end android devices like Samsung galaxy Y, Samsung galaxy Y-DUOS etc. and want more free space for your apps, then this post is for you..


Under Settings > Reading, there is a field called Blog pages show at most __  posts. Since all of my queries are based off of the main query, I need to find out what's stored in that field. How would I do that, especially outside of the loop?

I want to retrieve the default value of Post per page (the value that is set in settings->reading.  I've looked around and so far I've only found ways to query it. problem is i dont want to change what was set i just want to retrieve it for pagination purposes. i thought of using $something->post_count.(i might be wrong but as i understand it returns the amount of posts displayed currently) but this could be wrong in some cases.  Also how can i get the total number of posts ?


I used following tags to create equations in my document. But when I tried to add conditional equation within this tag, it didn't work properly. Is there any way to add conditional statement within equation tags?    \begin{equation}     \begin{cases}          xxxxx, & \text{xxx}\\          xxxxx, & \text{xxx}      \end{cases}   \end{equation}

I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex?